Finesse in Quantum Chemistry: Accurate Energetics Relevant for Reaction Mechanisms Citation Carter, Emily Ann (1987) Finesse in Quantum Chemistry: Accurate Energetics Relevant for Reaction Mechanisms. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GVJQ-6Y71. https://resolver.caltech.edu/CaltechETD:etd-11212003-111159 Abstract A general, systematic approach for calculating accurate energetics for chemical processes within the framework of ab initio electronic structure theory is presented. The correlation-consistent configuration interaction (CCCI) method utilizes generalized valence bond wavefunctions as the starting point for the CI, which emphasizes the inclusion of only the dominant correlations dictated by the physics of the problem. The CI expansion truncates quickly, so that processes involving polyatomic molecules, which could not be addressed with conventional CI methodology, may now be treated easily. A variety of applications of the method are presented, including the prediction of bond energies, electronic excitation energies, and energetics of chemical reactions, for both organic and transition metal-containing molecules. In cases where experimental data are available, the agreement is generally excellent (within 1-5 kcal/mol). We have used these quantitative results, along with qualitative aspects of the wavefunctions, to assess the bonding in and reactivity of a series of organic, organometallic, and inorganic molecules. These studies have produced a number of simple concepts useful for predicting the stability and reactivity of ligands attached to transition metals. Finally, key mechanistic pathways in two transition metal-catalyzed reactions have been examined using the CCCI approach: (i) the chain initiation step for the Fischer-Tropsch synthesis of hydrocarbons; and (ii) the Ag-catalyzed olefin epoxidation reaction. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Chemistry Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Awards: Caltech Distinguished Alumni Award, 2019 Thesis Availability: Public (worldwide access) Research Advisor(s): Goddard, William A., III Group: Caltech Distinguished Alumni Award Thesis Committee: Marcus, Rudolph A. (chair) Goddard, William A., III Beauchamp, Jesse L. Bercaw, John E. Defense Date: 20 May 1987 Non-Caltech Author Email: eac (AT) princeton.edu Other Numbering System: Other Numbering System Name Other Numbering System ID Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7576 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7333 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 6832 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7568 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7577 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 6936 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7266 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7336 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7580 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7567 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7409 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7583 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7582 Arthur Amos Noyes Laboratory of Chemical Physics Contribution 7320 Funders: Funding Agency Grant Number NSF UNSPECIFIED Gemini Industries UNSPECIFIED International Precious Metals Institute UNSPECIFIED Standard Oil of Ohio (SOHIO) UNSPECIFIED Record Number: CaltechETD:etd-11212003-111159 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-11212003-111159 DOI: 10.7907/GVJQ-6Y71 Related URLs: URL URL Type Description https://doi.org/10.1063/1.453957 DOI Article adapted from ch. 1A https://doi.org/10.1021/j100278a006 DOI Article adapted for ch. 1B https://doi.org/10.1063/1.452287 DOI Article adapted for ch. 1C https://doi.org/10.1063/1.454099 DOI Article adapted from ch. 1D https://doi.org/10.1021/ja00220a079 DOI Article adapted from ch. 1E https://doi.org/10.1021/j150652a009 DOI Article adapted for ch. 2A https://doi.org/10.1021/ja00269a010 DOI Article adapted for ch. 2B https://doi.org/10.1021/ja00276a011 DOI Article adapted for ch. 2C https://doi.org/10.1021/j100319a005 DOI Article adapted from ch. 2D https://doi.org/10.1021/j100331a026 DOI Article adapted from ch. 2E https://doi.org/10.1021/ja00236a044 DOI Article adapted for ch. 3A https://doi.org/10.1021/om00093a017 DOI Article adapted from ch. 3B https://doi.org/10.1016/0039-6028(89)90071-X DOI Article adapted from ch. 4 https://doi.org/10.1016/0009-2614(86)80064-1 DOI Article adapted for Appendix 1 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. 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Finesse in Quantum Chemistry: Accurate Energetics Relevant for Reaction Mechanisms Thesis by Emily Ann Carter In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1987 (Submitted May 20, 1987) -ii- This thesis is dedicated to my parents, Rebecca and David Carter -iii- We "hall not cea3e from ezploration And the end of all our ezploring Will be to arrive where we 3tarted And know the place for the fir-'t time T. S. Eliot Four QuartetJ -iv- Acknowledgments I am certain that one of the best decisions I have ever made was to come to Caltech and work with Bill Goddard. From day one, he gave me the freedom to work on whatever interested me, realizing that enthusiasm and love for science must come from within. Even so, Bill's supportive attitude and utter enthusiasm for such an enormous variety of scientific problems is infectious. He challenged me with his quickness: it was always a race to see who could understand new results first and see how best to proceed! In all, he has helped me to develop into the kind of researcher and teacher that I had always hoped to be and for that I am tremendously grH.tef11 l. Before I continue, I must say that I am indebted to the National Science Foundation for a predoctoral fellowship, Gemini Industries and the International Precious Metals Institute for a research grant award, and SOHIO for a fellowship in catalysis. I want to thank Jack Beauchamp for the many stimulating discussions we have had over the years regarding gas phase metal ion chemistry - and even positrons! Others who have made life as a graduate student much more enjoyable are Mary Selman and Greg Voth. Without Mary, my world here would be virtually womanless (a curse of the scientific community). Mary and I have taken turns venting frustrations, comro.dcs-in-o.rms against subtle, residual prejudices :still remaining a.ga.inst women in science. Simply put, she is just a great friend. Greg has not only been a terrific friend, but a stimulating verbal sparring partner. I shall miss our many animated discussions following chemical physics seminars! I have enjoyed interacting with a number of fellow group members: Art Voter, for his friendship and wisdom; Mark McAdon, for sharing his insights into metal clusters; Jon Hurley, for his friendship and his ceaselessly sarcastic sense of humor; and Terry Coley, for his friendship and his constant barrage of questions which keep me on my toes! I especially want to thank Mark Brusich, not only for critically pruufreading large parts of this thesis (for which I am immensely grateful), but for being such a good friend and safety valve, helping to ease the stress level which -v- tends tu Luihl H.ruund here. I um:-st a.bu mention Adria McMillan, without whom the Goddard group would most certainly descend into utter chaos. Thanks, Adria, for making order out of ergodicity, and especially for always having a way of brightening every day around Caltech. Finally, I must thank my family. Thanks go first to my aunt and uncle, Murray and Ruth Blumberg, who have provided me with a home away from home, a sense of security, constancy, and love for as long as I have been at Caltech. Next, I thank my parents, who have given me more love and support than any c.hild could possibly expect. My mother is my lifeline, the link to my emotions, the bond that will be there forever. My father is my soul-mate, I am the continuation of him and I am damn proud of it. For him, continuity is everything; I hope he knows that all he has worked for, and what his parents worked for, will continue on in me. Lastly, I want to thank my husband, Henry Weinberg, for his respect, his understanding, his sense of humor (most of the time), and most of all, his love. -vi- Abstract A general, systematic approach for calculating accurate energetics for chemical processes within the framework of ab initio electronic structure theory is presented. The correlation-consistent configuration interaction (CCCI) method utilizes generalized valence bond wavefunctions as the starting point for the CI, which emphasizes the inclusion of only the dominant correlations dictated by the physics of the problem. The CI expansion truncates quickly, so that processes involving polyatomic molecules, which could not be addressed with conventional CI methodology, may now be treated easily. A variety of applications of the method are presented, including the prediction of bond energie:s, electronic e:xcita.tiuu em:rgies, and energetics of chemical reac- tions, for both organic and transition metal-containing molecules. In cases where experimental data are available, the agreement is generally excellent (within 1-5 kcal/mo!). We have used these quantitative results, along with qualitative aspects of the wavefunctions, to assess the bonding in and reactivity of a series of organic, organometallic, and inorganic molecules. These studies have produced a number of simple concepts useful for predicting the stability and reactivity of ligands attached to transition metals. Finally, key mechanistic pathways in two transition metal-catalyzed reactions have been examined using the CCCI approach: (i) the chain initiation step for the Fischer-Tropsch synthesis of hydrocarbonsj and (ii) the Ag-catalyzed olefin epoxidation reaction. -vii- Table of Contents Acknowledgments ........................................................ iv Abstract ................................................................. vi Overview of the Thesis ................................................ 1 Chapter 1. The Correlation-Consistent CI Approach: Theory and Applications to Bond Dissociation and Electronic Excitation in Organic Molecules . . . . . . . . . . . . . . . . . . . .................. 6 A. Correlation-Consistent Configuration Interaction: Accurate Bond Dissociation Energie:1 from Simple Wa.vefuudiums ..................... 7 B. Relation between Singlet-Triplet Gaps and Bond Energies ............ 26 C. Electron Correlation, Basis Sets, and the Methylene Singlet-Triplet Gap .................................................. 31 D. Correlation-Consistent Singlet-Triplet Gaps in Substituted Carbenes ............................................. 36 E. The C=C Double Bond of Tetrafluoroethylene ....................... 75 Chapter 2. Fundamental Studies of Transition Metal-Ligand Bonding ................................................................ 86 A. The Chromium Methylidene Cation: CrCHt ......................... 87 B. Bonding in Transition Metal-Methylene Complexes. 2. (RuCH 2 )+, a Complex Exhibiting Low-Lying Methylidene-like and Carbene-like States ............................................................... 94 C. Bonding in Transition Metal-Methylene Complexes. 3. Comparison of Cr and Ru Carbenes; Prediction of Stable LnM(CXY) Systems ... 107 D. Early versus Late Transition Metal-Oxo Bonds: the Electronic Structure of vo+ and RuO+ ....................................... 117 -viii- E. Relationships between Bond Energies in Coordinatively Unsaturated and Coordinatively Saturated Transition Metal Complexes: A Quantitative Guide for Single, Double, and Triple Bonds ................................................... 149 Chapter 3. Modeling Fischer-Tropsch Chemistry: Kinetic and Thermodynamic Predictions ................................... 167 A. Methylidene Migratory Insertion into an Ru-H Bond ................ 168 B. Modeling Fischer-Tropsch Chemistry: the Thermochemistry and Insertion Kinetics of ClRuH( CH2) .............................. 171 Chapter 4. Chemisorption of Oxygen, Chlorine, Hydrogen, Hydroxide, and Ethylene on Silver Clusters: A Model for the Olefin Epoxidation Reaction ................................ 215 Conclusions of the Thesis ........................................... 269 Appendix 1. Electronic States of Chromium Carbene Ions Characterized By High-Resolution Translational Energy Loss Spectroscopy ............................................... 272 -1- Overview of the Thesis One primary goal of the work presented herein is to construct a general, systematic approach to predicting quantitatively accurate energetics of chemical reactions. To this end, the correlation-consistent configuration interaction (CCCI) method has been developed and applied to a host of organic and inorganic molecules, with bond energies, excitation energies, and heats of reaction among the predicted energetic quantities. A subsequent, perhaps even more important, objective of this thesis is to extract simple concepts from the theoretical results which allow qualitative predictions of thermodynamic stabilities and chemical reactivity. We begin by describing the CCCI technique (Chapter 1.A), which is based on the generalized valence bond (GVB) description of molecules. The orbitals of the GVB wavefunction comprise the basis for the CI expansion. The unique aspects of this new CI approach are: (i) the systematic incorporation of all correlations involving electrons directly affected by the process of interest; and (ii) an unbiased description of the initial and final states, maintained by including consistent amounts of correlation for both endpoints. The CCCI expansion truncates fairly swiftly, allowing the method to be applied to molecules for which traditional CI methods would be impractical. The accuracy uf thi.:; ti.:;chnique is demonstrated for single, double, and triple bond energies in organic molecules, with excellent results for single and double bonds (generally within 1 - 5 kcal/mol of the experimental value) and less accurate results for triple bonds {errors of"" 103). The CCCI approach has also been applied with considerable success to electronic excitation energies. First, Chapter l.B describes an empirical relationship between bond energies ( thermochemistry) and excitation energies (spectroscopy), which is used to estimate singlet-triplet splittings in substituted carbenes from the relative bond weakening in substituted olefins and methanes. The central idea behind this empirical approach is that a ca.1·beue with a siuglet ground state is nonbonding, and it must be promoted to the triplet state in order to form bonds. -2As a result, bonds formed to the carbene are weakened by this promotional energy (the singlet-triplet gap). Chapters 1.C and l.D provide predicted values from CCCI calculations of the singlet-triplet splittings in a variety of carbenes [CXY = CH2, CF 2 , CCh, CHF, CHCl, and CH(SiH3)]. Experimental values and the empirical results of Chapter 1.B are generally in good agreement with the ab initio predictions. Qualitatively, the ground states of CXY may be understood by considering only charge transfer and steric effects, where electron withdrawing substituents with p1t" lone pairs favor singlet ground states, and where electropositive, bulky groups favor triplet ground states. Chapter 1 ends with a calculation of the bond energy in tetrafluoroethylene (Chapter 1.E), as a test of the assumptions built into Chapter 1.B and as a further test of the CCCI method. In the empirical relationship derived between bond energies and excitation energies, we assume that the intrin&ic strengths of C-H and C=C bonds remain constant with substitution at carbon. Since C2 F 4 is expected to perturb the C=C bond (relative to ethylene) more than any other halogenated olefin, it should provide an upper limit to the error of this assumption. We find that the intrinsic C=C bond strengths (the energy required to dissociate to triplet fragments) in C2H 4 and C 2 F 4 are nearly the same, with the intrinsic C=C bond energy in C2F 4 only·~ 4 kca.l/mol la.rgc::r tlum in C 2H4, even though their adiabatic bond strengths differ by more than 100 kcal/mol! Three conflicting experimental values for the adiabatic F 2 C=CF 2 bond energy exist in the literature, ranging from 53.4 to 76.3 kcal/mol. We predict a value of D 298 = 64.5 kcal/mol, in good agreement with the most recent experimental value (derived from the heats of formation of CF 2 and C2F 4) of 69.0±2. 7 kcal/mol. In sum, Chapter 1 introduces the CCCI technique and presents applications for the prediction of bond energies and excitation energies in organic molecules. In addition, Chapter 1 has provided substantial support for the empirical relationship between moleculM bond euergies and the promotional energies in the fragments from which they are composed. -3- Chapter 2 discusses the fundamental aspects of the interaction between transition metal centers and their ligands. Chapters 2.A, 2.B, and 2.C discuss results for two representative early and late transition metal carbene cations, while Chapter 2.D focuses on the differences between early and late metal-oxo bonding. A postscript must be added to the bond energy reported for Cr=CHt (48.6 kcal/mo!) in Chapter 2.A, which was in disagreement with the only experimental value available at the time (65±7 kcal/mol1 ). After the theoretical prediction of 49 kcal/mol was published, the experiment was repeated under different conditions. The revised experimental value is 52±3 kcal/mol, 2 in excellent agreement with the earlier theoretical result. A prediction of the electronic state splittings in CrCHt (Chapters 2.A and 2.C) also prompted an experimental investigation, using translational energy loss spectroscopy to determine the excitation energies. Those results are in good agreement with our early work and are presented, along with new theoretical results, in Appendix 1. The central idea presented in Chapters 2.A - 2.C is that properties of transition metal carbenes may be predicted qualitatively merely by considering the electronic state of the metal center, as induced by the presence or lack of ancillary ligands, and by considering the electronic state of the carbene (Chapter 1 ). In addition to the quantitative results, Chapter 2.A points out the importance of exchange interactions for unsaturated metal centers in the determination of the properties of metal-ligand bonds, Chapter 2.B presents a new way of viewing oxidation states which is based on where the electrons physically reside (as opposed to the traditional, purely ionic convention for electron counting), and Chapter 2.C discusses the relative stabilities of covalent versus donor-acceptor bonding and terminal versus bridge bonding, as a function of the transition metal and of the substituents on the carbene (as in Chapter 1). Chapter 2.D discusses terminal metal-oxo bonding as a function of metal, concluding that the stability and reactivity of metal-oxo systems may be understood just by considering the electronic state o! the metal center. The general result is -4- that early metals can form strong bonds to oxygen which render the oxo ligand inert, while late metals form weaker, biradical-type bonds to oxygen, yielding an extremely reactive oxo species which may act as an oxidant or oxygen atom transfer reagent. In order to relate the work of the previous sections to properties of coordinatively saturated metal complexes, Chapter 2.E concludes by presenting a scheme for converting the experimental or theoretical values for coordinatively unsaturated M-X bond strengths (e.g., those reported in the previous sections) to those appro- priate for coordinatively saturated or low spin unsaturated complexes {which are mmitly unknown). Silllple additive factors, based solely on the atomic properties of the metal itself, are applied to single, double, and triple bonds. The final two chapters are concerned with mechanisms of catalytic reactions. Chapter 3 discusses GVB/CCCI results of modeling the chain initiation step of the Fischer-Tropsch reductive polymerization of CO to hydrocarbons and oxygenates, in which a surface-bound CH 2 is thought to insert into a surface-bound H. We find that the migratory insertion of CH 2 into an adjacent metal-hydrogen bond (Ru-H, 1n this case) is subject to an activation barrier of-~ 11 kcal/ mol and is exothermic by '""' 10 kcal/mo!. These values were obtained by two independent approaches, with excellent agreement between the two methods (deviations of 1-2 kcal/mol). We have also estimated (from a thermodynamic cycle) the exothermicity of the chain propagation step (CH 2 inserting into an metal-alkyl bond) to be 4 kcal/mol, with a higher barrier expected due not only to the lowered exothermicity, but also due to the necessary reorientation of the alkyl group during the insertion. Consistent with these ideas, the primary product from undoped catalysts is generally methane, produced from the less activated chain initiation step. The focus of Chapter 4 is to model the hctcrogcously-ca.talyzed ethylene epox- idation process as it occurs on supported Ag catalysts. We have carried out GVB/CCCI calculations for adsorbates on Ag clusters (primarily Ag 3 ) in order to accurately predict sorely needed adsorbate-surface binding energies as a function -5- of adsite. The binding energies, in conjunction with the qualitative features of the wavefunctions, allow us to present a new interpretation of a series of epoxidation experiments performed on single crystals of Ag, and, most importantly, we present a global picture of various reaction steps, of the nature of the oxygen species active for epoxidation, and of the role of promoters in this catalytic reaction. Thus, we will show in the ensuing chapters that the CCCI approach to calculating energetics is accurate for a wide variety of molecular processes. The predicted energetic quantities, when used in conjunction with qualitative properties of the electronic wavefunction, provide a powerful tool for assessing the feasibility of reaction mechanisms. References (1) P. B. Armentrout, L. F. Halle, and J. L. Beauchamp, J. Am. Chem. Soc. 103, 6501 (1981 ). (2) N. Ari:stov and P. D. Arw.c:11trout, J. Am. Chem. Soc. 108, 1806 (1986) and references therein. -6- Chapter 1 The Correlation-Consistent CI Approach: Theory and Applications to Bond Dissociation and Electronic Excitation in Organic Molecules - 7- Chapter 1._A. Thf'! tP.xt of this section is a Letter coauthored with William A. Goddard III and is to be submitted to Chemical Phyaica Lettera. -8- Correlation-Consistent Configuration Interaction: Accurate Bond Dissociation Energies from Simple Wavefunctions Emily A. Carter and William A. Goddard III* Contribution No. 7576 from the Arthur Amo& Noye& Laboratory of Chemical Phyaics, California Inatitute of Technology, Paaadena, California 91125 Abstract: We have developed a general method employing relatively small but well-defined CI expansions for calculating accurate bond energies [e.g., errors of 1.4 kcal/mol (1.3%) for the C-H bond energy in CH4 and 4.9 kcal/mo! (2.73) for thP. C=C bond energy in ethylene]. The approach includes in a systematic way all correlations involving orbitals that change signi:fico.ntly during bond breakage. The CI expansion truncates rapidly, enabling the application of this technique to polyatomic molecules for which normal correlation approaches would be prohibitively expensive. Thus the bond energy for BH is calculated to within 0.3 kcal/mol of the full CI value, incorporating less than 0.1% of the spin eigenfunctions. For CH4, CH3, CH2, and CH this correlation-consistent CI (CCCI) method leads to accuracies of 1-7 kcal/mol. The double bond energy for C 2 H4 is excellent: n;ak(H 2C=CH 2) = 174.1 versus n:xpt = 179.0±2.3 kcal/mol. However, the method is much less accurate for triple bonds: n;alc(HC:=CH) = 214.3 versus n:xpt = 236.1±0.7 kcal/mol. The advantage of CCCI is illustrated for C2F 4, where a full CI would involve,...., 7 x 10 22 spatial configurations, but only 1,719 are used in CCCI. Here we obtain a C=C bond energy for C 2 F 4 (where experimental values range from 53 to 76 kcal/mol) of De(F2 C=CF2) = 68.3±2.5 (D29s = 64.6 ± 2.5) kcal/mol. -9- I. Int,roduction Accurate bond dissociation energies are essential in assessing chemical reaction mechanisms. Unfortunately, current experimental thermochemical data ( especially for organic radicals and inorganic complexes) often have error bars of 5-10 kcal/mol or more. 1 We propose an approach for obtaining greater accuracy with practical ab initio calculations for systems of experimental mecha.11.i:stic interest. Our goal is to develop methods equally applicable (and accurate) for molecules containing heavy atoms or transition metals as for first row molecules. In order to be useful, it is important to obtain accuracies better than 5-7 kcal/mo!. Thus our efforts are directed at achieving quantitative accuracy within a small CI expansion so that the technique can be applied to a wide variety of large molecules. Our method involves a systematic approach for treating both the molecule and the fragments after bond rupture with consistent levels of electron correlation. Thus we focus on the dominant correlations important in bond breakage. This correlation-conaiatent CI (CCCI) method 2 is also applicable to excitation energies (e.g., singlet-triplet splittings in substituted carbenes 3 ) and is applied below to the doublet-quartet splitting in CH. In the next section, we outline correlation-consistency in the calculation of bond energies. To compare the accuracy of the method to a full CI result, we find that for BH, the CCCI leads to a bond energy within 0.3 kcal/mol of the full CI, 4 although the CCCI has only one-thousandth of the configurations of the full CI. Section III reports CCCI results for the four C-H bond energies of methane, the C=C bond energy in ethylene, and the C:=C bond energy in acetylene. An illustration of the power of this CCCI approach is given for the C=C bond energy for C2F 4 , a molecule for which the experimental data vary over a range of 23 kcal/mol and for which a full CI is currently out of the question ("' 7 x 1022 spatial configurations for full CI, but only 1719 spatial configurations for CCCI). 10- II. Theoretical Method Generalized Valence Bond Wavefunction.a For bond breaking/making processes, the many-electron wavefunction must dissociate smoothly to fragment wavefunctions. This dictates an approach based on the valence bond wavefunction ('1'VB), which unlike the molecular orbital wavefunction ('1'M 0 ), has the correct form for proper dissociation 5 to fragment atomic orbitals for Rbond = oo. The variational counterparts to VB and MO wavefunctions are the self-consistent field generalized valence bond (GVB) and Hartree-Fock (HF) wavefunctions, in which the orbitals are expanded in a basis set and optimized self-consistently. Our starting point, then, for the CCCI calculations is the GVB wavefunction, 5 - 7 since it has the correct functional form for proper dissociation (while HF often dissociates to an ionic limit). For the GVB calculations, only the orbitals comprising the breaking bond are treated as GVB pairs, ~GVB = (ef>a(1)</>b(2) + </>b(1)¢a(2))(o:{j {30:), (1) where <Pa and </>b are the variationally-optimized, overlapping, one-electron G VB orbital:;. All uthcr elcctrumi in the molecule a.re treated at the HF level. Since the number of overlapping terms in the full GVB wavefunction increases as N!, where N is the number of (overlapping) orbitals, 6 it is more effective to do the calculations in terms of orthogonal orbitals. This is accomplished by rewriting each GVB pair in (1) in the natural orbital representation (2) where </>9 and </>u are the (orthogonal) bonding and anti bonding natural orbitals of a GVB pair. For a multipair system, this wavefunction (2') -11- hM a. product of term5 a.5 in (2) and i:s R :special case of the full GVB wavefunction: since the full GVB wavefunction allows all possible spin couplings of the various orbitals, whereas (2') has just a single valence bond or perfect pairing (PP) term. The GVB-PP wavefunction builds in "static correlation" between the electrons in each GVB pair, by allowing them to each occupy their own orbital, on average staying farther apart from one another than if they were restricted to occupy the same spatial orbital (as in Restricted HF theory). Re.stricted CI Calculation& (RGI) Expanding the GVB-PP wavefunction (2') in terms of natural orbitals (2) leads to a total of 2M N-electron configurations where M is the number of GVB pairs. A close approximation to the full GVB wavefunction is obtained with the GVB-Restricted CI (RCI) wavefunction in which each pair is allowed to have all three possible occupations of the two electrons associated with that pair of orbitals, leading to 3M configurations. The RCI lifts the spin-coupling restriction and also builds in interpair correlation (ionic configurations) in which movement of charge in one bond pair induces simultaneous movement of charge in an adjacent bond pair. In general, the RCI wavefunction provides a reasonable description of most molecules by allowing for optiu.U:i.iRtiun of spin-coupling and by including the dominant interpair and intra.pair correlations. In order to obtain very accurate energetics, we must go beyond a valence level CI, including correlations involving excitations to virtual (unoccupied) orbitals. In particular, the CCCI method takes into account two other important sets of correlations crucial for describing the changes in the valence orbitals during bond rupture. First we allow full correlation (within the basis) of the two electrons involved in the breaking bond (u5ing the RCI co11figurations as reference states). Thus we allow all single and double excitations from each (breaking) bond pair to all other orbitals. This is denoted RCI"'SDbond· Since bond dissociation generally leads to geometric and hybridization changes in the resultant fragments, we expect -12that the shapes of the remaining orbitals will also be altered in the bond dissociation event. The second set of configurations included in CCCI is designed to allow for orbital shape changes among the valence orbitals not involved in the breaking bond. Thus to the RCI*SDbond configurations we add, from each RCI configuration, all single excitations from the valence space to all virtuals (RCI*Sva1). 8 BH Tc"t These two sets of configurations supply the dominant correlations important in bond breaking processes. As a rigorous test of how well this CCCI expansion performs relative to a full CI, 4 we considered the BH molecule. The experimental De(B-H) = 82.3 kca.l/mol, 9 while the six-electron full CI within a DZP basis (132,686 spin eigenfunctions) yields 78.9 kcal/mol. 4 The CCCI method applied to the same basis (110 spin eigenfunctions) yields De(B-H)=79.2 kca.l/mol, in excellent agreement with the full CI (and experimental) value. 10 This indicates that CCCI, with only one-thousandth of the configurations, accounts for most of the differential correlation present in the breaking bond. This suggests CCCI as a practical method for larger systems, where full CI calculations would be impractical. Multiple BondJ The simplest extension of the CCCI method to double and triple bonds is to include the configurations corresponding to all single and double excitations out of each bond separately. These RCI*[SDbond l t SDbond :i + · · · + Sva1] calcula.tiom; dissociate to fragments at the HF*Svai level. That is, the correlations included at the equilibrium molecular geometry for the CCCI reduce to HF*S in the limit of Rbond = oo. Note that we do not allow single and double excitations from more than one bond at the same time because that calculation is not dissociation-consistent. It would include some double excitations on fragments, which require triple and quadruple excitations on the molecule in order to be consistent. -13- In all calculations, the carbon atom wn.s described by Dunning's valence double-( contraction 11 of Huzinaga's (9s5p) basis set, 12 augmented by one set of cartesian 3d polarization functions with the 3s combination removed(("= 0.64). 13 The hydrogen atoms were described with Dunning's double-( contraction11 (scaled by 1.2) of Huzinaga's 12 (4s) basis set, with one set of 2p polarization functions ( (P = 1.0) added only to the H atom involved in the breaking bond. Dunning's valence double-( contraction 11 of Huzinaga's (9s5p) basis set 12 for fluorine was also used. Geometrie.'l Experimental geometries were used for CH 4 , CH 3 , the 2 II and 4 ~- states of CH, C2H4, C2F 4, and C2H2. 14 The equilibrium geometries of CH2 (1 A 1 ) and CH2 (3B1 ) were taken from the GVB-POL-CI calculations of Harding and Goddard 15 and the geometries of CF2 (1A 1 ) and CF2 ( 3 B 1 ) were taken from the GVB(l/2) calculations (within the largest basis) of Bauschlicher et al.. 16 III. Results CH Bond" The total energies calculated at levels ranging from HF to HF*S*D (CISD) to RCI*[SDc-H + Sva1J (CCCI) for CHx (X = 0-4) are listed in Table I and the corresponding successive C-H bond energies are shown in Table II. The CCCI method gives excellent results (within 1-3 kcal/mol) for the first two bond energies in methane, with the agreement less good (within 5-7 kcal/mol) for the second two bond energies in CH 4 • The values obtained with the present method are considerably better than the much more extensive studies of conventional CI methodology (e.g., HF*S*D ), due to the error:s of triple and quadruple excitation:s not included at Re for HF*S*D. The exception is the C-H bond energy in CH 2 ( 3 B1), where HF*S*D actually obtains a better bond energy than CCCI. This is due to the bias toward stabilizing high-spin states for HF*S*D. Thus CH 2 ( 3 Bi) is overstabilized -14- and CH (2II) i:s artificially destabilized, leading to a good bond energy through cancellation of errors. Furthermore, the range of error for HF*S*D bond energies in CH 4 is larger than for CCCI (4-10 kcal/mo!), including an order of magnitude more spin eigenfunctions than CCCI. Two multireference CI calculations of the first C-H bond energy in CH 4 have been reported previously: (i) a. CASSCF /MRD-CI1 7 with 63,608 configurations yielded De(H 3 C-H) = 104.3 kcal/mol and (ii) a CASSCF /CCI 18 with 613,941 configurations afforded De(H3C-H) 109.7 kcal/mo!. Our CCCI result, with only 241 (correlation-consistent) configurations, leads to De(HaC-H) = 110.5 kcal/mol. Since the CCCI method requires treatment of correlation equivalently at both endpoints (infinity and Re), two sets of bond energies are listed for CH 2 • The C-H bond in ground state CH 2 ( 3 B 1 ) is formed from the excited state of CH (4 :E-). However, the C-H bond in the 1 Ai excited state of CH 2 is formed from the ground state of CH ( 2 II). The thermodynamic cycle to calculate the adiabatic bond energy [the energy to go from CH 2 ( 3 B 1 ) to CH (2II) + II (2 S)] includes: (i) (first column entry) CH 2 ( 3 B 1 ) tl.EsT CH 2 (1A 1 ) D~H) CH (2II) + H (25) where ~E5¥c(CH2) = 9.0 kcal/mol 3 and (ii) (second column entry) CH 2 ( 3 B 1 ) D~H) CH (4 :E-) + H (2 S) CH err)+ H ( 2 S). The 4 :E- 2 II state-splittings of CH shown in Table III were calculated correlation-consistently using the same CI method which accurately predicts singlettriplet gaps in substituted carbenes. 3 This is accomplished by allowing all single and double excitations to all virtuals from the electron pair involved in the excitation from doublet to quartet. These exdtatio11.:; are taken from RCI reference confl.g- urations where the RCI involves correlation of the C-H bond pair [GVB(l/2)]. This correlation-consistent treatment results in a AEnq = 16.4 kcal/mol, excellent agreement with experiment (AE~4t = 16.7 kcal/mol). 9 -15- Multiple BondJ Table IV compares adiabatic C-C bond energies at various levels for ethylene and acetylene. Both HF and HF*S*D fall considerably short {20-50 kcal/mol) of the final CCCI values, which yield excellent agreement for the C-C double bond but less acceptable agreement for the triple bond. Clearly for triple bonds, simultaneous correlations (up through quadruple or even sextuple excitations to virtuals) must be necessary to approach the experimental value, while for double bonds, such simultaneous excitations appear to be much less important. The possibility of symmetric bent or "banana" bonds in C 2 H2 was explored to see if such a description could account for the correlation error. We find the CCCI bond energies with a bent bond description to be the same to within 0.3 kcal/mo! as with one u and two 7r bonds. 19 D(FlC=CF3 ) Finally, we applied the CCCI method to the bond energy of C 2F 4 • The size of this system precludes full CI treatment ("" 10 23 spatial configurations), but it requires only 1719 spatial configurations for CCCI. The experimental value for D2 98 (F2C=CF2) is extremely uncertain, with values ranging from 53.4±0. 7 to 76.3±3 kcal/mol. 20 - 22 Dissociating the u and 7r bonds of C 2 F 423 smoothly produces excited CF 2 ( 3 B 1 ) fragments. Thus, C=C bond cleavage can be most simply described by a CCCI of C2F 4 dissociating to two CF 2 ( 3 Bi) fragments, followed by a CCCI deexcitation of each CF2 ( 3 B 1 ) to the ground state of CF 2 (1 Ai). The CCCI result for De(F2C=CF2) is 63.4 kcal/mol (Table V). Assuming the same residual correlation error occurs in C2F 4 as in C2H 4 (Acorr = D~xpt - D~CCI = 4.9±2.5 kcal/mol), this leads to (Table V) an estimated adiabatic bond energy of De(F2C=CF2) = 68.3±2.5, a zero temperature value (including zero-point energy) of Do = 63.6±2.5, and a. room temperature value of D = 64.6±2.5 kcal/mol. 24 298 The ubiquitous theoretical approach, HF*S*D, includes an order o{ magnitude more configurations than CCCI, but yields a bond energy low by 30-40 kcal/mol! 16- The CCCI result may be compared with three experimental values of 53.4±0.7, 20 69.0±2.7, 21 and 76.3±3 kcal/mol. 22 The theory rules out the lowest value and agrees rather well with the intermediate value. Using AHJ,198 (C 2 F4) = -157.4±0.7 kcal/mol, 24 b our calculations lead to ..:iH~,:uiis(CF2) = kcal/mol, supporting the experimental value of AH/, 298 (CF2) -46.5 ± 1.6 -44.2±1 li rather than -52. kcal./wol. 20 IV. Conclusions We present the simplest wavefunction emphasizing correlation-con"i"tency while including the dominant electron correlation" dictated by the physics of bond dissociation. This avoids the biases plaguing conventional CI-SD approaches, while retaining a minimum number of configurations. For single and double bonds, the method predicts bond energies in good agreement (errors of 1-7 kcal/mol) with experiment. However, for triple bonds the errors are much larger ("-'22 kcal/mol). An indication of the power of this approach is given for C 2 F 4 where CCCI leads to a.n expected accuracy of 2.5 kcal/mol for 1719 configurations, while HF*SD CI utilizes 18, 772 configurations, engendering an error of 30 kcal/ mol, and full CI would require - 10 23 configurations. Thus the error of CCCI is considerably less than the dispersion in experimental values. Acknowledgments. This work was supported by the National Science Foundation (Grant No. CHE83-18041) and the Shell Companies Foundation. EAC acknowledges a National Science Foundation predoctoral fellowship (1982-1985), a research grant award from the International Precious Metals Institute and Gemini Industries (1985-1986), and a SOHIO fellowship in Catalysis (1987). -17- References (1) For inorganic complexes see, for example: a) J. 1. Beauchamp, A. E. Stevens, and R. R. Corderman, Pure and Appl. Chem. 51, 967 (1979); b) P. B. Armentrout and J. L. Beauchamp, J. Am. Chem. Soc. 103, 784 (1981); c) P. B. Armentrout, L. F. Halle, and J. L. Beauchamp, J. Am. Chem. Soc. 103, 6501 (1981 ); d) M. A. Tolbert and J. L. Beauchamp, J. Phys. Chem. 90, 5015 (1986); e) R. L. Hettich and B. S. Freiser, J. Am. Chem. Soc. 108, 2:>37 (1986). For organic radicals see, for example: f) D. F. McMillen and D. M. Golden, Ann. Rev. Phys. Chem. 33, 493 (1982); g) S. G. Lias and P. Ausloos, Int. J. Mass Spec. Ion Phys. 23, 273 (1977); h) P. Ausloos and S. G. Lias, J. Am. Chem. Soc. 100, 4594 (1978); i) D. Berman, D. S. Bomse, and J. L. Beauchamp, Int. J. Mass Spec. Ion Phys. 39, 263 (1981); j) S. G. Lias, Z. Karpas, and J. F. Liebman, J. Am. Chem. Soc. 107, 6089 (1985). (2) (a) R. A. Bair and W. A. Goddard III (submitted for publication) developed a somewhat more complex dissociation-consistent CI approach also based on GVB wavefunctions. (b) See R. A. Bair, Ph. D. thesis, California Institute of Technology, 1981. (3) a) E. A. Carter and W. A. Goddard III, J. Chem. Phys. 86, 862 (1987); b) ibid., submitted for publication. (4) R. J. Harrison and N. C. Handy, Chem. Phys. Lett. 95, 386 (1983). (5) W. A. Goddard III, Phys. Rev. US7, 81 (1967). (6) R. C. Ladner and W. A. Goddard III, J. Chem. Phys. 51, 1073 (1969). (7) (a) W. J. Hunt, T. H. Dunning, Jr., and W. A. Goddard III, Chem. Phys. Lett. 3, 606 (1969); W. A. Goddard III, T. H. Dunning, Jr., and W. J. Hunt, Chem. Phys. Lett. 4, 231 (1969); W. J. Hunt, W. A. Goddard III, and T. H. Dunning, Jr., Chem. Phys. Lett. 6, 147 (1970); W. J. Hunt, P. J. Hay, and W. A. Goddard III, J. Chem. Phys. 57, 738 (1972); F. W. Bobrowicz and W. A. Goddard III in "Methods of Electronic Structure Theory", H. F. -18- Schaefer, ed., Plenum Publishing Corporation, 1977, pp 79-127; (b) L. G. Yaffe and W. A. Goddard III, Phys. Rev. A 13, 1682 (1976). (8) Because the SCF calculation optimizes the shapes of orbitals and because the Brillouin theorem states that SCF wavefunctions are stable to first-order changes, single excitations (first-order changes) within a CI wavefunction correspond physically to orbital shape changes. (9) K.-P. Huber and G. Herzberg, "Constants of Diatomic Molecules" (Van Nostrand, New York, 1979). (10) The CCCI calculations for BH were carried out with exactly the same basis set and geometry as used in the full CI. 4 We used C2v symmetry with the experimental bond distance of 2.329 bohr. The basis set for BH was the Dunning11 double-( contraction of the Huzinaga12 (9s5p) basis for boron augmented by one set of 3d polarization functions ( (d = 0.5, with the 3s combination included) and the Dunning (4s/2s) basis for hydrogen (scaled by(• = 1.2) augmented by one set of 2p polarization :functions ( (P=l.0). For BH, the total energy for RCI*(SDbond + Sval] (with 110 spin eigenfunctions) is -25.15929 hartrees, while the :full CI (with 132,686 spin eigenfunctions) yields -25.22763 hartrees. 4 The CCCI method dissociates to HF*Sval fragments, yielding a total energy :for B atom of -24.53376 hartrees, while the full CI value for B is -24.60264 hartrees.4 The total energy for H atom is -0.49928 with the (4s/2s) basis. (11) T. H. Dunning, Jr., J. Chem. Phys. 53, 2823 (1970). (12) S. Huzinaga, J. Chem. Phys. 42, 1293 (1965). (13) The carbon d exponent was optimized for CH4 by R. A. Ba.ir and W. A. Goddard III (submitted for publication). 2 (14) a) M. D. Harmony, V. W. Laurie, R. L. Kuczkowski, R. H. Schwendeman, D. A. Ramsay, F. J. Lovas, W. J. Lafferty, and A.G. Maki, J. Phys. Chem. Ref. Data 8, 619 (1979); b) Landolt-Bornstein Tables 7, (Springer, Berlin, -19- . 1976). (15) L. B. Harding and W. A. Goddard III, Chem. Phys. Lett. 55, 217 (1978). (16) C. W. Bauschlicher, Jr., H.F. Schaefer III, and P. S. Bagus, J. Am. Chem. Soc. 99, 7106 (1977). (17) F. B. Brown and D. G. Truhlar, Chem. Phys. Lett. 113, 441 (1985). (18) P. E. M. Siegbahn, Chem. Phys. Lett. 119, 515 (1985). (19) The CCCI total energy [using the symmetric bent bond GVB(3/6)PP wavefunction] for C2H2 is -76.97901 hartrees, with 5138 spatial configurations and 9780 spin eigenfunctions. At the GVB-PP level, bent bonds are higher in energy than u/tr bonds for C2H2 by 0.7 kcal/mol, increasing tu 1.8 kcal/mol for a six-electron full CI within the six orbitals of the triple bond [EavB-CI( 3 ; 6 )(u/tr bonds) = -76.92150 hartrees and EavB-CI( 3 ; 6 )(symmetric bent bonds)= -76.91857 hartrees]. This is in con- trast to GVB-PP results for C 2F2 by R. P. Messmer and P.A. Schultz, Phys. Rev. Lett. 57, 2653 (1986), who found bent bonds ""'2 kcal/mo! lower than u and 7r bonds. (20) This bond energy was obtained indirectly from the heat of formation of C 2 F4 (6.H'}, 298 - -lu7.4 ± 0.7 kcal/mol) 2 n and one experimental value for 6.Hj,298 (CF2) = -52. kcal/mol from S. G. Lias, J. F. Liebman, and R. D. Levin, J. Phys. Chem. Ref. Data 13, 695 (1984). (21) This bond energy was also obtained indirectly from 6.H/, 298 (C2F4) -157.4 kcal/mol and another experimental value for 6.H/, 298 (CF2) -44.2±1 kcal/mol from Ref. li. (22) K. F. Zmbov, 0. M. Uy, and J. L. Margrave, J. Am. Chem. Soc. 90, 5090 (1968). This study using Knudsen cell equilibrium at high temperature ('""' 1200°K) constitutes the only directly determined bond energy for C 2F 4. (23) We explored the possibility of bent bonds being lower in energy than u -20- and 11" bonds for C2F4. We find energies equal (within 0.1 kcal/mol) at the GVB-PP level. For the four-electron full CI within the four orbitals o{ the double bond, the u and 11" bonds are favored by 0.1 kcal/mol over symmetric bent bonds [EovB-CI( 2; 4)(u /11" bonds)= -473.54944 hartrees and EGVB-CI(2/4)(symmetric bent bonds) = -473.54924 hartrees]. (24) Zero point energy and temperature corrections to De were obtained from a) T. Shimanouchi, Tables of Molecular Vibrational Frequencies, Natl. Stand. Ref. Data Ser., Nat. Bur. Stand. 39 (1972) and b) JAN AF Thermochemical Tables, Natl. Stand. Ref. Data Ser., Nat. Bur. Stand. 37 (1971). Table I. Total Energies (hartrees) for CHx, X=0-4.• Cll4 (1 Ai) CHii (2 A~) CH2 ( 3 Bi) CH2 ( 1 Ai) C (3 P) CH calculation• (VDZDF)" (VDZD)" (VDZDP) (VDZD) (VDZDP) (VDZDP) 4E- (VDZD) 2Il (VDZDP) 2Il (VDZD) (VDZD) HF -40.20127 (1/1) -39.56032 (1/1) -38.92254 (1/1) -38.28118 (1/1) -38.27215 (1/1) -38.26997 (1/1) -37.68452 (1/1) -40.21650 (2/2) -40.21650 (3/3) -40.23107 (141/141) II -38.92500 (1/1) -38.93834 (2/2) -38.94041 (3/5) -38.95869 (118/286) -38.88382 (1/1) GVB(l/2)PP -39.56282 (1/1) -39.57750 (2/2) -39.57874 {3/4) -39.59498 (134/245) -38.90032 (2/2) -38.90032 (3/3) -38.91473 (106/106) -38.28918 (2/2) -38.29017 (3/4) -38.30427 (92/164) " " . ccc1c -40.24497 (241/273) -39.569661 (44/86) -39.61:!40 (228/503) -38.934251 (36/76) -38.97640 (203/539) -38.92646 (176/198) -38.292411 (30/54) -38.32192 (136/274) -38.279081 (22/40) -37.699041 (19/33) HF*S*D -40.35755 (1183/1753) -39.68894 (670/1903) -39.69745 {929/2660) -39.02454 (482/1462) -39.03292 (691/2147) - -38.35140 (306/681) -38.37686 (355/850) -38.36823 (144/314) -37.75931 (283/573) RCl(l/2) SDc-H II II .. " " . ti It " a) The total energy for the hydrogen atom within the (unscaled) double-( basis 11sed here is -0.49928 hartree. 1 hartree = 627.5096 kcal/mol = 27.21162 eV = 219,474.8 cm- 1 . b) Calc11lational details are provided in Section II of the text. The couesponding number of spatial configurations/spin eigenfunctions for each wavefunction is given beneath each total energy. c) VDZDP basis: Huzinaga-Dunning (9s5p/3s2p) valence double-( basis plus one set of cartesian 3d functions ((" = 0.64; the 3s-combination was removed) on carbon and the Huzinaga-Dunning scaled (4s/2s) double-( basis for hydrogen, with one set of 2p functions ((P = 1.0) on the hydrogen involved in the C-H bond being broken. d) VDZD basis: the same basis as inc) but with no augmenting 2p functions for hydrogen. [Total energies for calculations using VDZD basis refer to the appropriate limit at R(C-H)= oo, i.e., HF, HF*S ....i, or HF*S*D (Section II).) e) RCI(l/2)*[SDc-H + Svad· /) HF*Sval total energy. I t-..1 ...... I -22- Table II. Adiabatic Bond Energies (De) in kcal/mol for CHx-H (X = 0-3).a CH-Hb C-H 55.4 calculation HF HF*S*D CH3-H 88.9 CH2-H 88.5 106.3 GVB(l/2)PP RCI(l/2) 98.5 98.5 109.0 97.7 98.5 91.2,82.7 91.2,84.0 66.1 66.7 SDc-H CCCI" 107.3 108.7 100.3,95.4 75.6 110.5 112.9 101.9,99.5 77.6 Experimente 111.9±0.3 115.8±1.4 107.4±1.3 84.5±0.2 A!orr ZPE9 1.4±0.3 27.10 2.9±1.4 18.41 5.5,7.9±1.3 10.88±0.22 6.9±0.2 4.09 80.9,74.3 103.8c 74.2 a) Calculational details are provided in Section II of the text. b) values of De(CHH) were co.lcula.ted via two thermutlymu.nic cycles in order to treat CH2 and CH consistently: (i) CH 2 (3 B 1 ) AEsT CH 2 (1 Ai) D(~H) CH (2IT) + H (2 S) (first column entry) a.nd (ii) CH2 (3 B1) D~H) CH ( 4 ~-) + H (:;iS) -~q CH C°1 Il) + H (25) (second column entry). [AEsT(CH 2) = 9.0 and AEnq(CH) = 16.4 kcal/mol, from Ref. 3b and from Table III of this work. c) The value of D(CH-H) for HF*S*D is obtained directly from CH 2 ( 3B 1 ) -+ CH (2IT) + H (2S). d) RCI(l/2)*[SDc-H + Sva1]. e) Experimental De's are derived from AH/,o [taken from Ref. 24b and JANAF supplements in J. Phys. Chew. Ref. Data 4, 1 (1975) and 11, 695 (1982)], with zero point energy corrections from: Ref. 24a for CH 4 ; M. E. Jacox, J. Phys. Chem. Ref. Data 13, 945 (1984) for CH 3; P.R. Bunker, P. Jensen, W. P. Kraemer, and R. Beardsworth, J. Chem. Phys. 85, 3724 (1986) for CH 2 ; and Ref. 9 for CH. f) Acorr = Dexpt(C-H) - Dc•lc(C-H), where Deale is from CCCI. g) ZPE = zero point energy; see footnote e). 23- Table III. Doublet-Quartet splittings ( D..EnQ total energies for CH. a E"E- Ezn) and total energies (hartrees) calculation HF HF*S*D GVB-PP G VB-RCI(PP )b GVB-RCI( opt )c CCCI'l Experiment 4!)- :.!II D..Enq (kcal/mo!) -38.28118 (1/1) -38.35140 (160/364) -38.29150 (2/2) -38.26996 (1/1) -38.36823 (144/314) -38.30799 (4/4) -7.0 -38.29484 (3/6) -38.29599 (3/6) -38.30926 (6/8) -38.30938 (6/8) +9.0 -38.30742 (67 /127) -38.33356 (112/252) +16.4 +10.6 +10.3 +8.4 +16.7e a) VDZD basis. Calculational details are provided in Section II. The corresponding number of spatial configurations/ spin eigenfunctions for each wavefunction is given beneath each total energy. b) GVBRCI using the GVB-PP orbitals. c) Self-consistent GVB-RCI. d) RCI*SDn,(PP). e) Ref. 9. Table IV. Adiabatic: C-C Bond Energies (D .. ) in kc:al/mol for H:aC=CH2 and HC=:CH.• total energies (hartrees) calculation r HF :UF*S*D GVB-PP GVB-RCI RCI*S.,a.1 RCI*[SD.,. + SD.r} CCCI" ExperimentI Llcorr = ~xpt _ eB1)• De(H2C=CH2) H 2C=CH:a CH2 1 HC::::CH CH ( 4E_). - 78.03955 (1/1) -78.29399 (1315/2092) -78.07757 (4/4) -78.09118 (5/6) -78.12864 (239/418) -78.11343 (465/596) -78.14574 (651/944) -38.92241 (1/1) -39.02454 (250/732) -38.92241 (1/1) -76.82438 (1/1) -77.06340 (800/1206) -76.87800 (8/8) -76.92014 (14/20) -76.95463 (536/1306) -76.95428 (l 706/2!l26) -76.97858 (2048/3872) -38.28118 (1/1) -38.35140 (160/364) -38.28118 (1/1) ti -38.93415 (20/40) -38.92241 (1/1) -38.93415 (20/40) D.,(HC=:CH) directc using aEnq"' 122.2 178.5 131.6 153.7 205.2 193.5 146.1 165.3 It 154.6 191.7 -38.29241 (18/36) -38.28118 (1/1) -38.29241 (18/36) 163.4 199.3 168.6 213.1 174.1 214.3 D~CCI I ~ I 179.0±2.5 236.1±0.7 4.9±2.5 21.8±0.7 a) VDZD basis. Calculational details are provided in Section II of the text. The corresponding number of spatial configurations/spin eigenfunctions for each wavefunction are given beneath each total energy. b) Total energies for CH 2 and CH are for the appropriate limit at R(C-C) = (X), i.e., HF, HF*Svat. or HF*SxD. c) Direct D .. (HG:::CH) from D.,(HC=:CH) 2xE(lII CH) - E(HC=:CH). d) D.,(HC=:CH) = 2xE( 4E- CH) - E(HC;::::;CH) - 2xaEnq, where AEoq 16.4 kc:al/mol (see Table III). e) RCI*[SD.,. + SDr + s.. a1] for C 2 H4 and RCI*[SD.,. + SD.r. + SD.,... + Sni] for HC=:CH. /) Expe1imental D.. 's are derived from aHj,o [taken from Ref. 24b and J. Phys. Chem. Ref. Data 4, 1 (1975)] with zero point energy corrections for C2H4 = 30.89 kcal/mol and C2Ih = 16.18 .kcal/mo! from Ref. 24a. = ('.) = Table V. Bond Energies (D.) in kcal/mol fot F 2C=CF2.• tota1 energies (hartrees) D~i•h(F2C=CF2)" D:'1i•h(F2C=CF2) ca.lculation F2C=CF2 ( 1Ai) CF2 ( 3B1)• HF -473.49255 (1/1) -474.07613 (18772/34184) -236.64724 (1/1) -236.92980 (3155/16053) -473.53219 (4/4) -473.54868 (5/6) -473.58045 (941/1724) -473.57245 (849/1098) -236.64724 (1/1) 149.2 34.2 " 159.5 44.5 -236.65739 (63/157) -236.64724 (1/1) 166.7 51.7 174A 59.4 -473.59909 (1719/2728) -236.65739 (63/157) 173.4 63.4 HF*S*D GVB-PP GVB-RCI RCI*S-i RCI*[SD 6 + SD,,.] CCCII IJ:diab + fl.corr' Experimenth direct• using ilEsT" 12U 59.4 9.3 135.9 39.1 20.9 I 63.3±2.5 57.2±0.7,i72.8±2.7/80.1±31 a) VDZD basis. Ca1culational details are provided in Section II of the text. The corresponding number of spatial configurations/spin eigenfunctions for each wavefunction are given beneath each total energy. b) Total energies for CF 2 are for the appropriate limit at R(C-C) = oo, i.e., HF or HF*S....1. c) n:i•h(F:aC=CF 2) = 2xE(3 B1 CF2) - E(C2F.•,). d) Direct D.(F 2 C=CF2) from 2xE( 1 Ai CF2) - E(C2F1) where the HF and HF*S*D total energies of 1 Al CF 2 are -236.69898 and -237.00693 hartrees (2633 spatial configurations/4399 spin eigenfunctions). e) D:4i•h(F 2 C=CF 2 ) = D~iab(F 2 C=CF 2 ) - 2xfi.EsT, where ilEsT = 57.5 kcal/mol (Ref. 31::). /) RCI*[SD 6 + SDT + s...1]. g) fl.corr for C=C is taken from Table IV. h) Experimental D.'s are derived from n;~~t's by correcting for finite temperature (subtract 1.0 kcal/mol) to obtain D~xpt's and then correcting for differential zero point energy (add 4.8 kcal/mol) to obtain n:xpl•s, based on the zero point energies of 13.4 kcal/mo) for C2F1 and 4.3 kcal/mo! for CF 2 (Ref. 24a). i) Ref. 20. j) Ref. 21. k) Ref. 22. ~...) Ul I -26- Chapter 1.B. ThP. tnt of this section is a. Letter coauthored with William A. Goddard III which appeared in the Journal of Phy.!ical Chemi.!try. -27- IL>print..d from Th• Journal or Pby•ical Cbomlatey, 19841, 90, 998 Copyright© 1986 by the American Chemical Society and reprinted by permi1sion of the copyright owner. Relation between Slnglet-Trlplet Gaps and Bond Energies Emily A. Cartert and William A. Goddard Ill* The Arthur Amos Noyes Laboratory of Chemical Physics, 1 California Institute of Technology, Pasadena. California 91I25 (Received: December 6, 1985) We propose that the dominant effect in bond energy trends of CXYH,. SiXYH 2, and substituted olefins is the singlet-triplet energy splitting in CXY or SiXY. New predictions of singlet-triplet gaps in AXY (A = C, Si) molecules, heats of formation of substituted olcfins, and Si-H bond strengths in substituted silanes are obtained. The effects of substituents on bond energies can be quite dramatic. Thus, the C-C bond energy of ethylene (I) is 172 :!: Unpairing the orbitals and separating the fragments leads then to 2 kcal/mo!' whereas the C-C bond energy of tetratluoroethylene (2) is only 76.3 :!: 3 kcal/mol.2 The point of this paper will be to show that these dramatic changes can be understood in terms of changes m the energeti~ at the fragments (CH 2 vs. CF2) within the assumption that the actual character of the C-C double bonds is rather similar. The GVB orbitals of the C-C double bond have the form in (3) involving singly occupied q and ,.. orbitals on each with each CXY fragment in the triplet state. However. depending upon the fragment, the ground state of CXY may be either the triplet (,.,,,.) or the •inglet state (,rl) H .. ~ H_.... ' 1111 O" 1T C spin-paired with a corresponding orbital on the other C.' (1) Chupk.t1, W. A., Li!'=ihil£~ C. J. Ch~m. f'hy:, 1968, 4!t, 1109 (2) Zmbov, K. F.; Uy, 0. M.; Margrave. J. L. J. Am. Chem. Soc. 1968. 90, 5090. (J) Plots of GVB orbitals for ethylene may be found in Hay, P. J.; Hunt. W. J.; Godoard lll, W. A J. Am. Ch,m. Soc 1972, 94, 8293 0022-3654/86/2090-0998$01.50/0 © 1986 American Chemical Society -28The Journal of Physical Chemistry, Vol. 90, No. 6, 1986 Letters I D,.,IC=Cl , ,,.------ I I 6E 5 r(CXY I+ 6E 5 r(::;x· v'; :~~ ~~:: 999 as indicated schematically in Figure 2. We will argue that the sum of these two bond energies should be independent of substituent unless CXY has a r? ground state. Indeed D 12 (H 2C:H,H) = 214.2 :::I:: 1.0 kcal/mol 8 whereas D 12 (F 1C:H,H) 168.0: 19 = 214 46 kcal/mol is weaker by just the 1J2-u11' excitation energy for CF 2! Thus for CXY systems with a u2 ground state we expect ;;~;,~'. D,,(XYC:H,H) "'D 1(XYHC-H) 4- D,(XYC H) D 12(H2C:H,H) - .ll'sT(CXY) (2) Figure I. Figuro l. Consider the simplest carbene, CH 2. It has a triplet u1r ground state (3B 1) with the a1 excited state ('A 1) lying 9 kcal/mo! higher. 4 Notice that while the U'lf' ground state of CH 2 is set up to form covalent bonds, the "" e~clted state cannot, since lt bas no open shell electrons. If we assume that the character of all C-C double bonds is similar at the equilibrium bond distance, a case in which the ground state of CXY is o- 2 would result in a bond energy decreased by just the sum of the u 2 to u'tr excitation energie< (Msr(CXY)j as illustrated in Figure I. Considering the intrinsic C-C bond energy to be D,.,(C=C) 172 :::I:: 2 kcal/mo! (since ethylene dissociates to ground·state fragments), we obtain = D(XYC=CX'Y') = D, 01 (C=C) - [AEsT(CXY) + .iEsT(CX'Y')] (I) for the bond energy in any substituted olefin in which the CXY fragments have a u 2 ground state. Hence for CXY = CX'Y' = CF 2, since Msr - 46.5 kcal/mol, 5 we obtain D(f 2C=CF 2) = 172 :::I:: 2 - 2(46.5) = 79 :::I:: 2 kcal/mo1 6 for the C-C bond energy in tetrafluoroethylene. in good agreement with the measured bond energy of 76.3 :::I:: 3 kcal/mo!. There are of course other factors (e.g. electronegativities. steric bulk. etc.) that can change with substitution; however. we will show that this 2 <T11'-u excitation energy of the CXY products dominates the changes in the C=C bond energy. 7 An analogous effect occurs in the bond energies of saturated hydrocarbons. Thus for CH 4 the sum of the first two C-H bond energies is D 12 (H 2C:H.H) = D 1(H 3C-H) + D 2(H 2C-H) (4) la) Leopold, D. G.; Murray. K. K.; Lineberger. W. C. J Chem. Phy.<. 1984, 8/. 1048. (b) Harding. L. B.; Goddard l!l, W. A Chem. Phys. Leu. 1978, 55, 217 (51 Bauschlicher. C. W., Jr: Schaefer Ill, H. F.; Bagus. P. S. J. Am. Chem. SD< 1977. O<J 7106 (61 The uncertainty in this number is larger than the quoted value since we have no1 included any estimate for the unc.:rtaint) in the theoretical Stnglet-triplet splttting (J) In CXY systems wnh er' ground states it is possible that lhe ground state of the doubly bonded olefin "ill have banana bonds rather than a and for the sum of the first two C-H bond strengths in substituted methanes. What are the physical effects which result in <:arbc11<;> (ur silylenes) with singlet 1J2 ground states') Two electronic factors contribute to the formation of r? CXY: 10 (a) If X and/or Y are electronegative, they will prefer to form ionic bonds. Then the C-X and C-Y bonds will utilize C p orbitals since they have the lowest valence ionization potential, leaving more s character for nonbonding C u orbital. (bl If X and/or Y have pir lone pairs (which can donate electron density into the C p1r orbital), this disfavors pir occupation by one of the C valence electrons Both contributions lead to relative stabilization of the u nonbouding orbital, resulting in a singlet ground state. Thus CXY systems where X and/or Y = F. Cl, OR, NRR', etc. are expected to have singlet ground states. For silylcnc:>, SiXY, the mud1 larger s-p energy difference for second row atoms greatly favors the s2 p2 state of Si and hence the"" state of SiXY. Thus these systems are expected to have singlet ground states for the above substituents (and for X and/or Y = H, alkyl). [For carbon, the small s-p energy splitting renders sp' hybridization more accessible, resulting in a triplet ground state for CRi (R = H, alkyl).) Triplet ground states are also favored by aryl and bulky alkyl substituents (since the u" state favors a large bond angle whereas the a1- state prefers a small bond angle), as well as by electropositive moieties (more favorable electron donation into sp2). In general, then, for CXY (SiXY) with electronegative substitucnts such as F and Cl. the ground state should manifest itself in weaker bonds of CXY to anything. Indeed, we can obtain a quamilative estimate for this bond weakening by assuming that two single u bonds or one double bond should be weaker compared to the CH 2 case by just the energy ro;t to promote the ground-state singlet to the triplet necessary for bond formation. Before examining trends in bond eneriiies and their imnlicatinn< we will test the basic assumption that the C=C and C-H intrinsic bond energies remain approximately constant even though the actual bond energies vary over a range of -100 kcal/mo! (see Table lll) From the two dissociation processes in eq I and 2. we obtain the following relation u" {.:illr0 293(XYC=CX'Y') - .:illr0 m(CXYH,) AHr 0 298 (CX'Y'H1l] = (2D, 1( H 1C:H.H) D 0 m(H2C=CH2) - 4.lHr 0 ios(H)] = [.lHr 0 m(C2H4) - 2[.llir 0 m(CH.)]] (3) where D 11 (H 2C:H,H) and D 0 298 (H 2C=CH 2) are taken to be intrinsic C-H and C-C bond energies. Notice that the right-hand side is independent of X and Y, suggesting that the difference in heats of formation on the left-hand side of (31 ( ..!.(~, :9 8 ) J should be a constant equal to 428.4 - 172.0 - 208.4'- = 48.0 0 (8) Data for (a) .lHr°m(CH 1) 1s from ref;, (b) UH, 0 ,,,(CH,) 15 from Lias, S. G.: Liebman. J. F: Levin, R. D. J. Phys. Chem Ref Data 1984. I 3. ,,.. bond.$. Thus for H~Si......,.Sil-f,, Horowitz and Godd111d (J. Am, Che-m. Soc., O~': (C) 0°,.,(H-tt) is from !\llCMtllcn, V. to be submitted) showed that-1he banana bond description i; 3.5 kcai/mol lower lhan the er and" bond dcsmption for the simple GVB-PP wave function However. with a full GVB-Cl in the double bond, they find a difference of only 0.1 kcal/mol. indicatmg that our assumption of the n description is valid. (R. P. Messmer (priva1e communica1ionl has also shown that c,F, leads to a banana bond description at the GVB-PP level.] Ph~·s t: Golden. D M Aon11. Rec Chem. 1982. .JJ, 493 ·(9) Data for (a) .l}{.0 ,..(CF1 ) is from Berman, D W: Bomsc. D S: Beauchamp. J. L. int. J. Mass. Spectrom. Ion Phys. 1981, 39. ~63. (b) UH,0 198(CF 1H 1 ) is from ref 6b. (10) Goddard IU, W. A.: Harding, L.B. Annu. Rei· Php. Chern 1978. 29, 363. -29JOOO The·Journal of Physical Chemisuy. Vol. 90. No. 6, 1986 Letters TABLE I: Test of the Validity of Eq 3, j.(llH,0 .,..) = Ml,0 .,..(CXY==CX'Y') - MI, 0 .,..(CXYH1) - Ml, 0 .,..(CX'Y'H1) = 48.0 kcal/mol, for the Ideal Umlt" CXY CX'Y' CH2 CF 2 CH, CF 2 CCl2 CCl 2 CH2 CF 2 CH2 CCI, CH2 CHF CH 2 CHCI E-CHI" CHF E·CHCI CHCI CF2 CHF CF1 CFCI ::.H, 0 ,..(CXY=CX'Y') +12• -164.7 ± 5' (-168.0) -2.7 ± 2.0" (+2.4) -82.0' (-78.0) +0.61 ± 0.36' (+7 J) -33.2• (-26.0) +8.6 :I: 0.3' (+10.5) -70.0' (-<>4.0) +1.2 :!: 2.1• (+9.0) -117• (-116.0) -125 :I: 4• (-122.6) ilHr 0 298 (CXYH 2) -18.o> -108.o> ::.H,0 ,.,(CX'Y'H 2 ) ::,.(::,.H,o,.,) -18.0 -108.0 +48.0 +51.3 ± 5 -22.8 ± 0.2' -22.8 ± 0.2 +42 9 ± 2.4 -18.0 -108.0 +44.0 -18 0 -22.8 :I: 0.2 +41.4 :I: 0.56 -18.0 -56 +40.8 -18.0 -19.5 +46. l ± 0.3 -56• -56 +42.0 -19.5 +40.2 :I: 2.1 -108 0 -56 +47.0 -108.0 -02.0 :1:: Y +45.b :I:: -19 s• •All values in kcal/mol. 'Reference Sb. 'Derived from D0 293 (F 2C=CF 2) and AH, 0 29,(CF 2) from ref 2 and 9a. respccuvely. •cox. J. D.; Pilcher. G. Thtrmochemistry of Organic and Organometallic Compounds; Academic Press: New York. 1970. 'Rodgers. A. S.: Chao. J.; Wilhoit, R. C.; s,,. Nntl Rur <;1nnd 19'11. ·'in Zwulin>IU, D J. J. Phys Chem. R<f Data 1!1'14, J, 117. rJAN AF Thcrmochcmic"I T'1ble•, Nal/. Stand. Ref Data 37. TABLE II: Predicted CXY Slqlet-Triplet Gaps from Relllthe A-H ~ ~lbs of_ AXYH1 Molecvles (kcal/moll TABLE Ill: Predicted CXY Singlet-Triplet Gaps from Relative C=<: Bond Strtngths of Substituted Olefins (kcal/mo!) ~ST' Msr• AXYH 2 DdXY A; H. H)' CH, Cf:H 2 t:Cl2H2 CFCIH 2 CFH, CCIH, SiH, Sif,H, SiCl 2H 2 SiFH 1 SiC1H 1 214.2 :!: I 1680 :I: I 1~1.9 :I: z 1748 :!: 3 186.2 :I: 3 194.7 :!: 5 180.8 :I: 3.5" 107.3 :I: 3.5' 138. l :I: 3.6' 14l.1:1:3.5' 153.4 :!: 6' AXY CH2 CF2 CCl2 CFCI CHF CHCI 3SiH 2 SiF 2 SiCI, Si HF SiHCI this work 46.2 :!: 2 32.3 :I:: 3 39.4 :I: 4 28.0 :I: 4 19.5 =6 42.7 :!: 7.] ca led -9.0' 46.5 4 13 ..5.'' 25.9" 9.2' I.6' 16.8' 73.5' 51.5 :I: 6' 37.7• 274 :!: 9.5 'D 12 (XYA: H, H) =the sum of the first two A-H bond energies in AXYH 2 at 298 K. • !}..£sT = E,np1~ - £.,, 11 ~ for AXY listed in the adjacent column. 'Reference 4 (e•pcrimental work). 'Reference 5. 'Reference 12. 'Derived from ref Ila and lib. •Reference 13. •tn these cases the theoretical ~ST was combined with eq 2 for Si and used to predict D11 (XYSi: H. H). 'Derived from ref I la 1::.H, 0 , . . . (SiCl 2H 2 )j and from Farber, M.; Srivastava, R. D. J. Chem. Soc., Farada.v Trans. I 1977. 73. 1672 [::i.H1° 298 (SiC1 2)]. 1Reference I la. • Denved from ref 11 a. kcal/mo!. This equation eliminates heats of formation and excitation energies of CXY, cancelling out substituent effec1s. Examination of Table I reveals that :l(~, 0 298 ) is very nearly constant, lending credence to the assumption that C=C and C-H bonds have the same character and thus the same intrinsic bond energies independent of substitution. The values deviating most from 48.0 kcal/mo! all have significant uncertainties in the olefin heats of formation. Thus by assuming (3) and using :l(:lHr 0 : 0 g} = 48.0 kcal/mo!. we have estimated new values for .::i.Hr 0 298 (XYC=CX'Y') listed in parentheses under the experimental values in Table l. Given that the C=C and C-H intrinsic bond energies are essentially constant, we can utilize ( l) and ( 2) 10 predic1 singlet-triplet energies for two very different bonding scenarios (two a bonds to hydrogens vs. one a and one rr bond to carbon). In Table II we display experimental valu~> for Diz(XYA:H. H) for a variety of substituted methanes and silanes. As the electronega11vity.of the substituent increase:;, the A-H bond energy decreases (going from Cl to F), and as two hydrogens are replaced by For Cl, the bond energ} decrea;,,,; further Equation 2 <tlf!.gNI< olefin D1°298 (C==C) CXY CH 2=CH 2 CF 2=CF 2 li2 ± 2 76.3 :!: 3 112.5 ~ 4 129.8 2 146.3 :!: 3.4 151.2 :!: 4 154 4 6.3 122.0 :I: 6 140.8 :!: 12.I 98.8 :I: 4 88.8 :!: 5 CH, CF2 CCli CF 2 CCI, CHF CHCI CHF CHCI CHF CFC! CCl2--CCI~ CH 2=CF, CH 2=CCl 2 CH,==CHF CH 2=CHCI E-CHF=CHF E-CHCl=CHCI CF 2=CHF CF 2=CFCI = = this work 47.9 :!: 2 5 29.8 .I. J 42.2 ± 4 25.7 :!: 5.4 20.8 :!: 6 17.6 :I: 8.3 25.0 :!: 4 15.6 :!: 7 26.7 :!: 6' 36.7 :!: 7' ca led -9 ()b 46 5' 13.S.C 25.9" 46.5 13.5, 25.9 9.2' 1.6' 9.2 1.6 9.2 • il.EST = E.,,p1c, - E.,..,1., for CXY listed in the adjacent column. •Reference 4 (e.pcrimental work). 'Reference 5. •Reference 12 'Derived by assuming .:l.EsT(CF 2) = 46.5 kcal/mol TABLE IV: Additional Heats of Formation Used in This Study (kcal/moll ~f 2Q8~ 0 CXY CH, CF 2 CCI, CFCI CHf CHCI ::.Hr 298 ( CXY) 92 :!: I' -44.2 ± I' +54.9"' 2' +8.0d +26 :I:: 3' +11 ± s~ 0 SiXY /SiXYH 2 1 SiH 2 SiCl 2 SiHCI SiH, SiC1 2H 2 SiCIH 3 (SiXY/SiX· YH,1 +84.8 :!: y -40.6 :!: 0.61 + 17.0 :!: :Y +8.2 :!: 0 5' -74.5 :!: :Y -32 2 ± y 'Reference I. ~Reference 9a. 'Rademann. K.: Jochims. H ·\I. : Baumgartel, H.J. Phys. Chem. 1985, 89. 3459 ,GMELIS Handbuch der Anorganischen Chemie, Kohlenstoff. Tei! 02. System 1"0. 14: Springer-\ieriag: Berlin. 1974. 'Lias, S. G.; Karpas. Z.; Liebman, J. F. J. Am. Chem. Soc., in press. !Reference I la. 'Farber. M.. Sri· vastava, R. D. J. Chern. Soc.. Faraday Trans. I 1977, !J. 1612 'Reference 11 b that :l£5y(CXY} D 11 (H 2C:H.H) D 12 (XYC:H.H) for the methane series and .:lEST(SlXY) DdH 2Si:H,H) D 12· (XYSi:H.H} for the silane series, where = = Di2\H 2Si:H,H) -:'.l.Hr 0 m(3SiH 2 l - .lHr0 298 (SiH.) + D 0 298 (H-H) 84.8 (±3) 8.2 (± 0.5) + 104.2 = 180.8 (±}.5) kcal/mol 11 = -30The Journal of Physical Chemis1ry, Vol. 90, No 6. 1986 Letters This leads to the predicted singlet-triplet gaps in the next to last column of Table IL As expected, increasingly electronegative X and Y lead to larger singlet-triplet gaps. Analogous predictions arc given in Table III where we show the effects of electronegative substituents on C=C (e:1.perimcntal) bond energies. Equation 1 allows another set of singlet-triplet gaps to be predicted. A wide variety of systems now reveals intcrna!ly consistent predictions for these splittings. For instance, using (I) and (2) lead to AEsr(CF 2) =46.2 :i: 2, 47.9 :I: 2.5, 42.2 :i: 4 kcal/mo! all in good agreement with the theoretical value of 46.5 kcal/mol.' On the other hand. (I) and ( 2) result in AEsr(CCl 2) = 32.3 :i: 3, 29.8 :i: 3, 25.7 :I: 5.4 kcal/mo! whereas the theoretical value is AEsr(CCl2) = J 3.5 kcal/mo!.' Other predictions are A.£ 51 (CHF) = 28.0 ± 4, 20.8 ± 6, 25.0 ± 4, 26.7 :i: 6 kcal/mo! compared to an ab initio value of A.Esr(CHF) = 9.2 kcal/mol.s Also predicted is A.Esr(CHCl) = 19.5 :i: 6, 17.6 :i: 8.3, 15.6 ± 7 kcal/mo! compared to a theoretical value of AEsr(CHCl) "' 1.8 kcal/mol.5 We also predict AEs 1 (CFCl) = 39.4 :i: 4 and 36.7 :i: 7 kcal/mol which has not been previously estimated. We are concerned that there is a difference between our pre· dieted values for the AEsr and some of the previously calculated values. However, these calculations were performed at a very simple level (Hartrce-1"0<,;k for the 111r >late and OVB( l/2)PP for the u2 state) and we suspect that correlation effects may play an important role in obtaining A.Esr. Jn order to test this suspicion, we carried out ab initio GVB-CI calculations for CC1 2, the case for which values for .i£51 (CC1 2) show the greatest discrepancy (-15-20 kcal/mo!) between the previous theoretical calculations and our present estimates. These new GVB·CI calculations lead to a AE51 (CCl 2) = 25.9 kcal/mot in excellent agreement with our empirical estimates (29 :i: 3 kcal/mo!). The dominant cor· relations, which were not included in the previous theoretical work [~Esr(CCl 1 ) = 13.5 kcal/mol],l but which were found to be important in our CI calculations. were ..- donation from Cl p..orbitals to the empty C P"" orbital with simultaneous /1 electron 1001 transfer to the chlorines from the carbon (with excitations to virtual orbitals to allow the orbital shape readjustments needed to properly describe simultaneous electron transfer in the " and ir frameworks). These correlations stabilize the singlet state more than the triplet state of halocarbenes and hence inclusion of these charge-transfer configurations (requiring up to selected sextuple e:1.citations) is essential for an accurate description of the ::.£ 5 T for halocarbcnes. 12 The silane thermochemical data offer further new predictions of AEsr and Si-H bond energies. .i£51 (SiCl 2) "' 42. 7 ± 7. I kcal/mo! is in reasonable agreement with a previous theoretical value of 51.S 6 keal/mol. 11 • EJ<perimental data allow the prediction of the previously unknown A.£51 (SiHCI)"' 27.4 ± 9.5 kcal/mo!, while reliable theoretical calculations' 3 of .iEsT(SiXY) allow the predictions of two previously unreported D 11 (XYSi:H, H) = 143.l ± 3.5 and 107.3 :I: 3.5 kcal/mol for X = H. Y = F. and X = Y I', respecuvely. In conclusion, we suggest that the dominant factor in determining bond energy trends in molecules involving CXY fragments is the singlet-triplet energy splitting. In many cases the ther· mochcmical data 14 are incomplete or controversial so that relations such as (1)-(3) can provide useful estimates of unknown data. The inverse relation of bond strength to singlet-triplet splitting has been shown to be quantitatively accurate and internally consistent for a variety of systems. The fact that many of these valucb fv1 AEsr au:; >ignificaully different from thobc obtained from previous ab initio calculations suggests that more e:1.tensive basis sets and Cl calculations are called for in these systems. 15 * AckflOw/edgment. This work was supported by the Shell Development Comp<lny, Houston, TX nnd the National Soience Foundation (Grant No. CHE83-18041). (11) Valu=i for (a) <l.Hr°,..(1SiH 2) (shonhand forSiH 2• 38 1) is from Ho. P.; Coltrin, M. E.; Binkley, J. S.; Melius. C. F. /.Phys. Chtm. 1!185. 89. 4647; (b) L\11/' ;m(SiH,.) b from JANAf' Thcnm.,.,;hc:mit:al Tat.deb Nud. S1um/, R~J. Data Str., Natl. Bur. Stand. 1978 update in J. Phys. Chtm. Ref Data 1978. 7, 793-940. (12) Caner. E. A.; Goddard Ill. W. A., to be submitted for publication. (13) Colvin, M. E.; Grev. R. S.; Schaefer III, H.F.; Biccrano. J. Chem Phys. lttc. 1983, 99. 399 (14) Additional thermochemu:al data used in this work arc displayed in Table IV. (15) Subsequent to the submission of this Letter. it has b<:en brought to oor attention that recent HF*S*()..CI and GVB( I /2)PP*S*D-Cl calculations by S<:u5eria cl al." on CHF and CHCI yielded revised values for .lEsr of 13.2 and S.4 kcal/mol. rcspcctivelv. These results are still 1n substantial dis· agrocmcnt with our estimates, presumably due to the lack of inclusion of important charge transfer configurations. (16) Scuscria, G. E.; Durdn. M.; Madagan, R. G. A. R., Schaefer Ill. H. F ., lo be submitted for publication. -31- Chapter l.C. The text of this section is an Article coant.horerl with William A. Goddard III which appeared in the Journal of Chemical PhyaicJ. -32- Electron correlation, basis sets, and the methylene singlet-triplet gap Emilv A. Carter and William A. Goddard IWl Arrhur Amos Noyes Laboratory of Chemical Physics."' California Institute of Technology. Pasadena. California 9II 25 (Received I 5 September 1986; accepted 9 October 1986) The effect of basis set and electron correlation on the singlet-triplet splitting (ti.£ 51 ) ofCH 2 is examined using the generalized valence bond ( GVB) approach. For a standard double zeta plus polarization basis, the GVB based calculation (with only 20-25 spin eigenfunctions) approaches the full CI result ( -220 000 spin eigenfunctions) of Bauschlicher and Taylor to within 0.5 kcal/mo! for this basis, but both differ substantially from experiment (errors of 2.4 and 2.9 kcal/mo! for GVB and full Cl, respectively). We have studied the convergence of ti..E si with basis set and find that an extremely extended basis (triple zeta sp, diffuse sp, triple :zeta d, double :zetaf) for GVEI yields AE' u = 9.03 lccal/mol, in excel1ent asreement with the experimental value of9.09 ± 0.20 kcal/mo!. I. INTRODUCTION In principle, the methods of quantum chemistry can provide exact answers to quantitative questions of physical and chemical interest such as molecular geometries, vibrational frequencies. excitation energies, bond energies, and even activation energies for chemical reactions. However, even for such small molecules as methylene, calculations must always be restricted in the basis set and level of electron correlation. Hence, it is essential to understand the level of error engendered by restrictions in basis or level of correlation. Because the relative energies of the lowest singlet and triplet states ( ti..E ST = E,. 081,,-E •riple• ) of substituted methylenes have been shown to be critical in determining the chemistry of such systems,' and because the singlet-triplet g:ap of methylene is now well established experimentally to be t:.£ 51 = 9.09 ± 0.20 kcal/mol, 2 we have selected CH 2 for a study of the dependence of ti..E sT on basis set and level of correlation. There are two paradigms for including electron correlation in wave functions. One ts to start with the Hartree-Fock (HF) wave function and then to include some level of excitation from occupied to virtual orbitals (commonly single and double excitations denoted HF•S•D). The problem with this approach is that a bias in the HF level of description may well remain upon any fixed level of excitation. Thus, for CH 1 using a standard basis set (valence double zeta plus pvh.ui.laliun, VDZp), the t..E ST 26.11'.cal/mvl fo1 Ilr and 15.3 kcal/mo! for HF*S*D (see Table I). The limit of this approach is to carry out a full CI for the given basis set. Unfortunately such full Cl calculations may quickly become Impractical \ - 220 000 spin eigenfunctions for DZp and - 114 000 OOOspin eigenfunctions for the TZ3p2/n basis discussed below) . The alternative approach, which has proved practical tor moderate-sized systems, is to solve self-consistently ror the orbitals of the correlated wave function. In general, such wave functions are referred to as MCSCF (multiconfigurational self-consistent field); however, to obtain energy differ" Author to whom correspondence should be addressed. ••Contribution No. 6832. 662 J. Chem. Phys. 86 (2). 15 January 1987 ences, 11 is important to have a scheme that specifies which level of~CSCF is consistent for the two states. This is provided by the generalized valence bond ( GVB) approach 14 in which there is one valence orbital for each valence electron. Thus, the GVB wave function for both the singlet and triplet states of CH 2 involve six optimized orbitals (in addition to the doubly occupied C ls-like orbital). This wave function is often denoted GVB(3/6) to indicate that three pairs of electrons are described with six orbitals. Advantages of the GVB approach are that (i) the correlated wave function can be interpreted in terms of one-electron orbitals, and (ii) accurate excitation energies and bond energies can be obtained using rather simple wave functions. Recently 5 there has been discussion of whether such restricted wave functions may provide energy differences more accurate than is consistent with the basis set being used. In order to understand the magnitude of any such basis set bias. we carried out systematic studies of the convergence of GVB-like wave functions as a function of basis set. II. GVB CALCULATIONS The full GVB wave function for 1CH 2 or 1CH 2 would involve six overlapping orbitals optimized simultaneously with the combination of all permissible spin eigenfunctions 1 (five for 1CH 2 , nine for .iCH 2 ). Although practical for CH 2 , the N! overlapping terms makes such calculations impractical for large systems, but we have found the following approach to serve quite adequately. Starting with the dominant spin eigenfunction (the valence bond or perfect-pamng spin function), the orbitals are optimized, allowing the two orbitals describing each electron pair to overlap but requir- ing the orbitals of different pairs to be orthogonal. These GVB orbitals are calculated in terms of the two natural orbitals for each patr to yield the GVB-PP wave function. In terms of these natural orbicals, the GVB-PP wave fum:tion of 'CH 2 has 23 8 closed-shell determmants. An advantage of !he GVB-PP wave function is that all two-electron interactions can be expressed in terms of Coulomb and exchange terms so that It is not necessary to transform the twoelectron integrals from the atomic orbital basis to the molecular orbital representation.' F<Jr the VDZp basis, GVB-PP 0021-9606/871020662·04$02.10 o:s. 1986 Amencan Institute of Phys.cs -33E. A. Carter and W. A. Goddard, Ill Methylene singlet-triplet gap 863 TABLE I. The singlet-tnplct energy gap (/l/;' 5T) for CH, for vanous levels of calculauon within a VDZp basis." 'B, 'A, Calculation Hf ( 1/1) <Ill> Hr·~·u 39.010 70 J9.04l 07 GVB-PP (415/577) 38.938 i7 38.939 40 (8/8) (479/1485) - 38.953 29 38.953 90 (4/4) j8.941 'l .18. 9,9 2! - 38.942 12 38.959 73 (9/25) 38.960 35 - 38.960 82 (9/25) -3904462 ( 5078/22 230) GVB-RCI (PP)' ( 18/20) 38 941 89 - 38.942 50 (18/20) GVB-RCl(opt >" U.30 9 11 9.10 11.13 1105 11.59 1149 39 025 4q (7759/16 674) 39.027 18 39 046 26 ( -44 000/- 220 000) GVIJ....RC!(opt)•s•o· Full Cl DZp VOZp 12.00 l t.97' 9.09 ± 0.20" Experiment •The corresponding number below each total energy. Basis sets wave given for the full CJ results i are described in Sec. m. • l h = l hamee = 627.5096 kcal/mo!= 27.211 617 eV = 219 474.65 cm· 1• ' (PP) orbitals from the GVB perfect-pairing wave function were used for the CJ basis. •orbitals were optimized for the GVB-RCI. 'All single and double excitat1ons of the siJ\ valence electrons were allowed from the self-consistent G VB-RC! wave function. 'Reference 5. Reference 2. 1 figuration interaction (RC!} in which the two electrons of each pair are allowed to occupy the two natural orbitals of the pair in all three ways. For 'CH 2 , this leads to 33 = 27 configurations (nine of which are not allowed by symmetry). The GVB-RCI wave function can still be interpreted in yields tJ..E ST = 9. I I kcal/mo!, but as the basis is increased, /:J..EsT becomes 7.01 kcal/mo! (see Table IIJ. The major discrepancy between GVB-PP and the full GVB wave function is the lack ofother spin couplings. These spin couplings are included by carrying out a restricted conTABLE JI. 6.£ ST (kcal/moll as a function of basis set.• OVB-RCI Basis set HF D7p VDZp l6.!1 (0.052 90) VDZlp!TZ2p PP" Opt' 9 IO I L05 ( - 0.00063) ( - 0.003 35) 11.13 ( - 0.002 74) GVIJ....PP 9 II (0.00000) 8. 15 ( - 0003 19) VDZ2pn!TZ2p 7.84 ( -0.004 50) 8.01 0.008 29) TZ2p 9 98 11.49 ( -0.003 73) 11.59 ( -0.003 12) 10.42 ( - 0.006 6)) ( - 0.007 07) 9.63 10.06 ( -0.00783) 10.07 0.01185) ( - 0.007 38l 9.69 0.011 36) TZlp//TZ2p 7.81 TZ3p2/n!TZ2p 24.87 (0.045 141 0008 83) 7.01 ( - 0.01046) ( - 0.013 52) 1 24 2.09 2.45 Change with basis ~.84 9.4\ 0.011 93) 8.60 Full Cl ( -0.012 41) 9.03 ( - 0.014 02) 2.46 (9.09)' (2.88)' - N•umt>ersin parentheses are the energies m hartrees of the singlet stale relattve to the GVB-PP wavefunction within the VOZp basis (total energy 38.938 77 h). •s.e Table l, footnote c. 'See Table I, footnoted. "Reference 5. 'Assuming that the fu:l CI with the most extensive basis leads to the expenmental value. J. Chem. Phys .. Vol. 66, No 2, 15 January 1967 -34864 E. A. Carter and W A. Goddard. Ill Methylene singlet-triplet gap terms of the GVB orbital picture. and the GVB-RCI wave function is generally a good approximation to the full GVB wave function. Using the orbitals from the GVB-PP wave function. the GVB-RCI leads to ilE sT = 11.13 and 11.05 kcal/mol for VDZp and DZp bases, converging to 8.60 kcal/mo! for the extended TZ3p2fn basis. Rather than using the GVB-PP orbitals, we may solve self-consistently for the orbitals of the GVB-RCI wave function,•<bl obtaining thereby an even better approximat10n to the full GVB wave function. Calculating the orbitals for the GVB-RCI selfconsistently, leads to 11.59 and 11.49 kcal/mo] for VDZp and DZp bases, in good agreement with the full CI rc5ult ( DZp) of 11. 97 kcal/mol. i For the largest basis set used, this self-consistent GVB-RCI yields 9.03 kcal/mo!, in excellent agreement with experiment. tained by scaling the previous 4/ exponent of 0.96 by 2.5. yielding;/ 1.52 and 0.607. The 3s and 4p combinations of the d and/ functions were removed. For hydrogen, the same Huzinaga triple zeta basis as above was used with two sets of p-polanzation funct10ns scaled by 3.0 from ;P = 0.91, yielding ;P = 1.58 and 0.525. B. Geometries The equilibrium geometries for 1A 1 and :1B 1 CH 2 were taken from the GVB-POL-CI calculations of Harding and Goddard 11 whofoundB, = 133.2'andR, = l.084Aforthe 'B 1 stateandB, IOl.8°andR, l.113Aforthe'A 1 state. For calculations involving the DZp basis set, the geometries were taken from Ref. 5. IV.RESULTS 111. CALCULATIONAL DETAILS We used the following basis sets: VDZp: The Dunning valence double zeta contractions 6 of the ( 9s5p) and the ( 4s) H uzinaga Gaussian primitive bases 7 for carbon and hydrogen (exponents scaled by 1.2) an: u5c:d with one set of 3d polarization functions <ri 0.64) on carbon and one set of 2p polarization functions (~P = 1.0) on hydrogen. Thes combination of the carbon 3d functions are excluded from all basis sets and all calculations, except for calculations using the DZp basis set for direct comparison to the full CI result.' DZp: This basis set is given explicitly in Ref. 5. It differs from the VDZp basis by having a DZ core on carbon, different 3d polanzation functions tor each state, and the s combination of the d functions was included in the calculations. 8 VDZ2p/TZ2p: For carbon, the same (9s5p/3s2p) basis was used as above, with two sets of 3d functions centered at 0.64 but scaled by 2.3 (f' = 0.971 and 0.422). For hydrogen, the H uzinaga' unscaled ( fu) basis was contracted to triple zeta, with two sets of 2p functions centered at 0. 91 (optimized 9 for H bonded to Cl but scaled by 2.3 W l.38and0.60). VDZ2pn!TZ2p: To the VDZ2p/TZ2p basis was added one set of diffuse s (t' = 0.045) and p c::-p = 0.034) func- The ilE sT using the VDZp and DZp bases for various wave functions are shown in Table I together with experimental (corrected for relativistic effects and zero-point mo· tion) 2 and full Cl 5 values. (The full CI calculation involved all excitations of the six valence electrons in CH 2 , with the C ls frozen at the HF level.) The self-consistent GVB-RCI (with 20 tu 2.5 spin eigeufum:liuus) lt:a<.h lu ti.E sT = 11. 5 kcal/mo!, only 0.5 kcal/mo! below the value ilE sr 12.0 kcal/mo! obtained from the complete CI for this basis (with - 220 000 spin eigenfunctions). Allowing all single and double excitations from the self-consistent GVB-1<.Cl wave function (with one-tenth the number of spin eigenfunctions of the full CI wave function) yields ilE sr 12.0 kcal/mo!, in complete agreement with the full CI. While a study of basis set convergence at the RCI*SD level is impractical. the small error engendered for ilE sT ( 0. 5 kcal/mo!) with the simpler GVB wave functions suggests that they may prove adequate for studying the convergence of ilE sT with basis set. This convergence with basis set is shown in Table II, where we see that for an extremely large basis, the self-con· sistent GVB-RCI converges to 11£ sT = 9.03 kcal/mo!. in excellent agreement with the experimental result. For smaller bases, the values for ilE ST decrease smoothly as the basis is extended, with the differential effects being quite tions optimized for negative ions of carbon. 9 This is denoted siinilar for all three calculational levels. Solving self-consis- as "n'' for negative ion. TZ2p: The Huzinaga (lls7p) basis 10 for carbon was contracted to ( 6s3p) triple zeta for both core and valence. The carbon 3d and hydrogen 2p polarization functions are the same as in VDZ2p/TZ2p. TZ2pf /TZ2p: One set of carbon 4/ functions [t1 = 0. 96, chosen to maximize overlap with the carbon d-function cri = 0.64) J, with the three 4p combinations removed, was added to the carbon TZ2p basis. TZ3p2fn!TZ2p: The Huzinaga (I 1s7p) basis for carbon was contracted triple zeta for both core and valence as berore, but d1ttuse sand p runcuons were added by scalmg out (by 2.5) from the most diffuse exponents of the ( 1ls7p) set. yielding;·· = 0.0388 and ;r = 0.0282. Three sets of carbon 3d-polarization functions were added, centered at 0.640 and scaled by 2.5 (leading to exponents (;" 1.60, 0.64(), and 0.256). Two sets of carbon 4f functions were included. ob- tently for the orbitals of the GVB-RCI wave function con· tributes -0.43 kcal/mo! energy lowering to the excitation energies. This occurs because the RCI wave function in· eludes spin-couplings important for the triplet state which are omitted in the perfect singlet pairing wave function. resulting in orbital shape changes for the self-consistent G VBRCI. For the uncorrelated HF wave function. the total change in ilE sT between the VDZp basis and the full basis set is - 1.24 kcal/mo!, while it is 2.09 kcal/mo! for GVB-PP and - 2.46 kcal/mo! for GVB-RCI. Similar studies of convergence for full CI as a function of basis set completeness are not available. Indeed, such a full CI test on our extended basis (TZ3p2fn!TZ2p) may well be beyond the scope of current computers, since it would require - 23 million spatial configurations, - 114 million spin eigenfunctions, or -455 million determinants! However. if we assume that the full Cl would agree with experiment for the full basis A. Basis sets J Chem Phys .. Vol 96. No. 2, '5 -anuary 1987 -35E. A. Carter and W. A. Goddard, Ii' Methy!ene singlet-tnplet gap set we have used, the drop in the excitation energy would have to be 2.88 kcal/mo!. This is reasonable since the corresponding quantities for lower level wave functions are 1.24 (HF), 2.09 (GVB-PP), and 2.46 (GVB-RCI) kcal/mo!. 'E. A. Carter and W. A. Goddard Ill, J. Phys. Chem. 90. 998 ( 1986), J Am. Chem. Soc. 108, 4746 ( 1986) 'T0 = 9.023 ::': 0.014kcal/mol is taken from P.R. Bunker. P. lenser.. W P Kraemer. and R. Beardsworth, J. Chem. Phys. 85, 3724 ( 1986). and 1s corrected for relativistic effects and zero point mmion by 0.07 :±: 0.20 kcal/mo! I I. Shav1tt, Tetrahedron 41, 1531 ( 1985)) to amve at a nonrelat1vistic T, 9.09 ;t 0.20 kcal/mo! 'R. C. Ladner and W. A. Goddard Ill. J. Chem. Phvs. 51. 1073 ( 19691 '(a) W. J Hunt. T. H. Dunning, Jr .. and W. A Goddard Ill. Chem. Phy,. Lett. 3. 606 ( 1969): W. A. Goddard Ill. T. H. Dunnmg. Jr., and W. J. Hunt, ibid. 4, 231 I 1969); W. J. Hum. W. A. Goddard Ill. and T. H. Dunning, Jr .. ibid. 6. 147 ( 1970): W. J. Hunt. P. J. Hay, and W. A. Goddard Ill. J. Chem Phys 57, 738 ( 1972): F. W. Bobrowie1 and W A Goddard Ill. in Merhods of Electronic S1ruc1ure Theory. edited by H. F Schaefer (Plenum. New York. 1977 ). pp 79-127: (b) L. G. Yaffe and W. A. Goddard Ill. Phvs. Rev. A 13. 1682 ( 1976) 'C. W. Bauschlicher:Jr. and P.R. Taylor. J. Chem. Phys. 85. 5936 ( 1986 l "T. H. Dunn1n11. Jr.. J. Chem. Phys ~3 /~)1 ( !970J 'S. Huzinaga. J. Chem. Phys. 42, 1293 ( 1965). 'Excludmg the s combination of the 3d funct1or.s m the DZP bas1; leads to an increase m ilE sr (at all levels reported 1n Table I) of no more than 0.02 kcal/mo! and a destabilization of the total energies by no more 1han o~ '~ h~rtrl"M. (n 18 kcal/mol). 9 R A. Bair and W. A. Goddard Ill (submined). "'S. Huzinaga and Y. Sakai, J. Chem Phys. 50, 1371 ( 1969) '' L. 8. Harding and W. A. Goddard Ill, Chem. Phys. Len. 55. 217 ( 1978). = V. CONCLUSION We have shown that the simple GVB description of the two lowest states of CH 2 (1A 1 and 3B 1 ) leads to singlettnplet gaps within 0.5 kcal/mo] of the full Cl result for a DZp basis set (still off from experimPnt hy? 4 kc:>l/mol). However, with GVB it is practical to use extremely extended bases, leading to results within 0.1 kcal/mo! of the experimental value. ACKNOWLEDGMENTS This work was supported by the National Science Foundation (Grant No. CHF.R:1-IR041) FAC acknowledges a National Science Foundation predoctoral fellowship ( 19821985). 865 J. Chem. Phys .. Vol. 86. No. 2, ~ 5 .ianuary 1987 -36- Chapter 1.D. The text of this section is an Article coauthored with Willium A. Goddard III and is to be submitted to the Journal of Chemical Phy3ic3. -37- Correlation-Consistent Singlet-Triplet Gaps in Substituted Carbenes Emily A. Carter and William A. Goddard III* Contribution No. 7568 from the Arthur Amo" Noye" Laboratory of Chemical Phy .. ics, California Jn .. titute of Technology, Pa.rndena, California 91125 Abstract: Ab initio GVB-CI (generalized valence bond with configuration interaction) and MCSCF (multiconfiguration self-consistent field) wavefunctions are used to calculate electronic state splittings for the lowest singlet and triplet states of substituted carbenes. The calculations ewphasize correlation con,.iatency between the two electronic states, resulting in short CI expansions. The singlet-triplet gaps (~EsT) for CH2, CH(Sili3), CF2, CC!i, CHF, and CHCl are reported. in good agreement with available experimental data. They are -.38- I. Introduction The diverse reactivity among substituted carbenes, CXY, is well-known. 1 In particular, stereoselective versus nonstereoselective reactions can be understood in terms of singlet versus triplet character in the carbenes, respectively. The triplet state ( cr 1 7r 1 ) of CXY has one valence electron in each of two non bonding orbitals on carbon, one er and one 7r as in (1 ), while the singlet state ( 0" 2 ) can be considered to have both of these nonbonding electrons in the O" orbital. However, GVB calculations indicate that the cr2 state actually involves one electron in a u + 7r orbital with the other electron in a u - 7r orbital. (1) Ci1T The "biradical" character of the triplet state results in nonstereospecific reactivity (involving nonconcerted, sequential steps of bond formation), while the closed shell character of the singlet state allows concerted, one-step, stereospecific chemical rca.etions. 1 Thu:;, in oLdt:L tu predict the reactivity expected for a given set of substituents at carbon in CXY, it is necessary to predict the singlet-triplet splittings of ex y. (.lualitative predictions of whether particular substituents will give rise to singlet or triplet ground states can be based on the following considerations. Factors favoring singlet or u 2 ground states are: (i) Electron-withdrawing substituents will produce ionic bonds ( c+ x-). The strongest ionic bonds will be formed to carbon orbitals with the lowest ionization potential, namely, to the carbon p-orhital:;. This incLt:ti.::se of p-character in the C-X bond induces a decrease of p-character (and hence an increase of a-character) in the nonbonding valence u orbital. This stabilizes the O" orbital relative to the 7r orbital (which has no a-character) and hence favors -39the u 2 or singlet state of CXY. Thus, for strongly electron-withdrawing X or Y, the ground state of CXY is u 2 • (ii) Substituents with p7r lone pairs can stabilize them by donation into the carbon p11" orbitn.l. Since the p7r orbital on carbon is nea:dy empty in th~ u 2 state, this energy lowering is larger for the singlet state than for the triplet state, resulting in a u 2 ground state. The above requirements are fulfilled for halogen, alkoxy, or amido substituents, since all are relatively electronegative with respect to carbon and all have p7r orbitals which can donate into an empty carbon p7r orbital. Therefore, we expect a bias toward singlet ground states for X,Y = F, Cl, OR, NRR', etc. Factors favoring stabilization of triplet ground states are: (iii) For electropositive substituents (with respect to carbon), the bond to carbon will have the opposite polarity to that discussed in (i). These substituents will favor a carbon hybridization with greater a-character (higher electron affinity), with more carbon a-character in the C-X bonds and concomitantly more p-character in the carbon nonbonding u orbital. This will make the relative energies of the nonbonding valence u and 71" orbitals more similar (due to similar amounts of p-chara.cter present), favoring the triplet state of CXY. (iv) Sterically bulky substituents favor a large X-C-Y bond angle. Since two bonds to pure p-orbitals favor angles of 90-105° angle, while two bonds to sp 2 like ("lobe") orbitals prefer bond angles of 115-135° ,2 the effect of increasing the X-C-Y bond angle is to increase the amount of s-character in the C-X bonds. As in (iii), this results in more p-character in the carbon nonbonding valence u orbital, producing energetica.lly similar nonboncling valence orbitals on carbon ( u and 7r), favoring the triplet state. Thus, triplet ground states of CXY are expected for substituents which are -40electropositive (with respect to carbon) and/or are bulky. Thus the following groups favor triplet ground states: X,Y = hydrogen, alkyl, aryl, SiR3, etc. Less conventional substituents in CXY which also fulfill (iii) and (iv) are X or Y = A1R 2 or BR 2 • Synthesis and subsequent reactions of the latter carbenes should yield unusual reaction chemistry due to the presence of a Lewis acid site next to the nucleophilic triplet carbene. While these qualitative arguments help in predicting which state of CXY (u 2 or u 1 7r 1 ) is lowest, it is often important to have quantitative information on the magnitude of the singlet-triplet splittings, A.EsT, for various CXY. Ezperimental Valuea for A.EsT(CXY) = E•inglet - Etriplet The controversies between experiment and theory regarding the singlettriplet gap in the parent carbene, methylene, have recently been reviewed. 3 - 5 The first direct measurement of the methylene singlet-triplet gap was obtained from laser magnetic resonance spectra due to rotational transitions within the v = 0 level of the 1 A1 excited electronic state and to transitions from those singlet levels to vibrationally excited levels of the 3 B 1 ground electronic state. 6 With a nonrigid bender Hamiltonian analysis of the 3 B 1 bending potential, in combination with ab initio calculations of the spin-orbit coupling responsible for the perturbations causing the transitions, a AEsT(CH 2 ) of To = 9.05±0.06 kcal/mo! was obtained. The most recent direct measurements 1 yield a value of To = 9.023±0.014 kcal/mol, from vibronic analysis of the photoelectron spectra of CH; .8 Electron detachment from the ground electronic state of CH2 ( 2 B 1 ) results in the formation of either 1 A1 or 3 B 1 CH:;i, depending on whether an electron is removed from the nonbonding carbon 71" (lbl) orbital or the nonbonding carbon u (3a1) orbital, respectively. While 2 B 1 CH; and 1 A1 CH1 have similar equilibrium geometries, the 3 B 1 state of CH 2 has a bond angle,..., 30° larger than the other two [O(H-C-H)~ 103° for 2 B 1 and 1 A 1 versus 134° for 3 B 1 }. 3 •8 The photoelectron spectrum is indicative -41- of these differing geometries, revealing a single (0-0) peak for the 1 Ai +- 2 B1 transition and a bending vibrational progression for the 3 B 1 +- 2 B 1 transition. From proper identification of the (0-0) peaks for both singlet and triplet, To is obtained. Recently, Shavitt 3 has estimated the correction for the conversion of an experimental determination of T 0 ( CH 2) to a non-relativistic theoretical calculation of Te(CH 2) (~EsT) to be 0.07±0.20 kcal/mol. Thus, currently the best experimental value (with which to compare theoretical results) for ~EsT(CH2) is 9.09±0.21 kcal/mol. While CH2 has been studied in depth, both experimentally and theoretically, AEsT's for substituted carbenes have, for the most part, eluded experimental determination. Only two other AEsT(CXY) have been measured: (i) A value of -56.6 kcal/mo! for AEsT(CF 2) has been deduced from emission spectra observed during the reaction of ( 3 P) oxygen atoms with tetrafluoroethylene. 9 The products of this reaction are known to be CF 2 and CF 20, with the initial spin-allowed product being the 3 B1 excited state of CF 2, which is then observed to phosphoresce down to the ground state, 1 Ai CF 2. The vibronic transitions are well-resolved, with the expected bend- ing progression observed, due to the greatly different bond angles predicted for the singlet and triplet states of CF 2 •10 (ii) An approximate value 0£ ~EsT(CHF) has been assigned from photodetachment studies from the negative ion CHF- ( 2 A"). As for CH 2 , both the 1 A' ground state and the 3 A" excited state of CHF are formed, with varying degrees of vibrational excitation. Although the spectrum is not as well resolved as in the photoelectron studies of CH 2, a tentative value of,..._, -15 kcal/mol has been assigned to To(CHF).11 Previou& Theoretical Value& for ~EsT(CXY) The first reliable ab initio study of substituted carbene singlet-triplet split- -42- tings was carried out by Hauscblicher et al. 10 Although the calculations were performed at a relatively low level [Hartree-Fock (HF) for the triplet and GVB(l/2) for the singlet], the important feature of these calculations is that the two states are treated in a balanced manner. 12 In particular, since the triplet nonbonding electrons on carbon occupy two orbitals, the singlet nonbonding electrons in this calculation are also allowed to occupy two orbitals [hence the GVB(l/2) calculation]. This leads to a relatively unbia.sed calculation of the electronic energy splitting, since the same number of orbitals arc included in the description of both states. However, this level still has biases, with a higher degree of residual electron correlation error in the singlet than in the triplet. Using this level of theory, Bauschlicher et al. 10 optimized the geometries of the lowest singlet and triplet states of CH2, CF 2, CCh, CHF, CHCl, and CHBr, using double-( plus polarization bases, and obtained the following AEsT's (negative values indicate a singlet ground state): 12.8 (CH 2 ), -46.5 (CF 2 ), -13.5 (CC1 2 ), -9.2 (CHF), -1.6 (CHCl), and 1.1 kcal/mol (CHBr). Other fluorine-substituted carbenes have been examined by Dixon,13 at the same calculational level. With a valence double-( basis augmented by polarization functions on the central carbon and on the atoms directly attached to the central carbon, he found the following AEsT's: 14.0 (CH2), -46.0 (CF 2 ), -8.1 (CHF), 13.0 (CHCF 3 ), -9.1 (CFCF3 ), and 17.8 kcal/mol [C(CF 3 )2]. Luke et al. 14 used MP4 (Moller-Plesset perturbation theory through fourth order), starting from RHF (singlets) and UHF (triplets) first order wavefunctions, in order to calculate a variety of carbon and silicon based small molecules. Pertinent to our work (vide infra) are AEsT = 16.8 (CH 2 ), -12.7 (CHF), and 25.7 [CH(SiH3)] kcal/mo!. Schaefer and co-workers, 111 using a CI-SD approach, and Kohler et al., 16 using the CEPA (correlated electron pair approximation) method, have also obtained theoretical values for AEsT[CH(SiH 3 )] of 27.2 and 20.3 kcal/mol, respectively. Finally, Scuseria. et al. 11 used CI-SD calculations to obtain values of-12.9 (CHF), -3.7 (CHCl), and -43- -3.1 (CHBr) kcal/mol, respectively. All of the methods used above tend to overe.,timate AEsT(CXY) for ground state triplets and to undere.,timate AEsT(CXY) for ground state singlets. This is due to the fact that the above techniques do not include balanced levels of electron correlation for both singlet and triplet states: the triplet is always correlated to a greater extent than the singlet, leading to an artificially destabilized singlet. The objective of this paper is to obtain more accurate AEsT 's, but from simpler wavefunctions. Section II discusses several levels of correlation~consistent CI calculations designed to obtain unbiased excitation energies; Section III reports new results using the methods described in Section II to obtain AEsT for CH 2 , CH(SiH3), CF2, CCh, CHF, and CHCl; Section IV discusses these predictions by comparison with experiment, previous theory, and thermochemical estimates, 18 with Section V offering concluding remarks. II. Theoretical Method Baaia Set.s The same carbon and hydrogen basis sets were used for all of the carbenes studied. The Dunning 111 valence double-( (VDZ) contractions of the carbon (9s5p) and the hydrogen (4s) gaussian primitive bases of Huzinaga20 were used (hydrogen exponents sea.led by 1.2), augmented by one set of 3d polarization functions (3s- combination removed) on carbon ('d = 0.64) 21 and by one set of 2p polarization functions on hydrogen ((P=l.O). Dunning's VDZ contraction10 of Huzinaga's (9s5p) primitive basis 20 for fiuorine was employed. The shape and hamiltonian consistent effective core potentials of Rappe et al. 22 were used for Cl and Si. The valence electrons of Cl and Si were treated explicitly, within the double-( basis sets of Rappe et al. 22 for Cl and Si, with one set of 3d polarization functions added to the Si basis (3s-combination removed; (d=0.3247). -44Geometriea The equilibrium geometries of 1 A 1 and 3B 1 CH 2 were taken from the Harding and Goddard GVB-POL-CI calculations, 23 with Be = 101.8° and Re = 1.113A for the 1 A 1 state and Be = 133.2° and Re=l.084A for the 3B 1 state. The optimum geometries for the 1 A 1 and 3B 1 states of CF 2 and CCh were ° taken from the HF /GVB(l/2)PP calculations of Bauschlicher et al. 1 For 1 A 1 CF 2, Be = 104.7° and Re = 1.291A. For 3 B1 CF2, Be = 118.2° and Re = l.303A. For 1 Ai CCh, Be= 109.4° and Re l.756A. For 3B1 CCl2, Be= 125.5° and Re= 1.730A. The equilibrium geometries used for the singlet and triplet states of CHF and CH Cl were taken from the HF /GVB(l/2)PP geometry optimizations by Scuseria et al. 17 For 1 A' CHF, 9e = 103.3", Re(C-F) = l.294A, and Re(C-H) = 1.104A. 1.304A, and Re(C-H) = 1.073A. For 1 A' CHCl, Be = 102.1°, Re(C-Cl) = 1.725A, and Re(C-H) = 1.092A. For 3A" CH Cl, Oe For 3 A" CHF, Be 121.1°, Re(C-F) = 124.4°, Re(C-Cl) = 1.699A, and Re(C-H) = 1.07oA. The geometries for the 1 A' and 3 A" states of CH( SiH 3 ) were optimized in the present work, with the following constraints imposed: (i) overall c. symmetry was assumed; (ii) The Si-H bond lengths were fixed at 1.487A and the H-Si-H angles were fixed at 108.3° (with local C3v symmetry imposed), which correspond to optimum values from GVB calculations 24 on Si 2 H6; and (iii) the SiH 3 group was assumed to be staggered with respect to the HC bond (as found from MIND0/3 calculations). 25 Using those parameters, the H-C-Si angle and the C-Si and C-H bond lengths were optimized at the GVB(2/4)PP level for the triplet and the GVB(3/6)PP level for the singlet (see below for a description of the calculation). The optimum values obtained are shown in Table I. MC-SCF and CI Calculation" In order to predict accurate excitation euergie5, it i5 essential that both electronic states involved in the excitation process be treated equivalently. This -45- includes both the number of orbitals optimized in the SCF and the degree of electron correlation included in the wavefunction. Several research groups 12 •26 realized early on the importance of utilizing two configurations ( 0" 2 and 11' 2 ) in order to describe the 1 A 1 state with the same de- grees of freedom enjoyed by the single configuration description of the 3 B 1 state 1 ( <T 1 7t' ). This two-configuration wavefunction description of the lone pair on car- bon is the simplest form of the generalized valence bond (GVB) method, 27 which usually describes each of the M valence electron pairs with two natural orbitals leading to a 2M configuration self-consistent field (MC-SCF) wavefunction. This MC-SCF wavefunction is designated GVB{M/2M)-PP, where M electron pairs are described by 2M natural orbitals and PP refers to the perfect singlet-pairing restriction (each electron pair optimized in the SCF is constrained to be singletcoupled). Since a triplet state involves one pair of electrons with two orbitals as in a GVB(l/2) singlet, we will denote the HF triplet wavefunction also as GVB(l/2). The GVB(M/2M) wavefunction satisfies our requirement that the same number of orbitals are optimized in the SCF for both states. In particular, for CH 2 , the six valence electrons are allowed to occupy six orbitals in both states. While the GVB(M/2M)-PP wavefunction provides a reasonable first-order description of most molecules, lifting the restriction of singlet-pairing within GVB pairs is necessary in order to allow the other spin-couplings of a full GVB wavefun~­ tion. By allowing the two electrons in each GVB pair to occupy the two natural orbitals of the pair in all three ways, all other pos5ible spin-coupling5 between the valence electrons are included. This wavefunction is referred to as GVB-RCI(PP) to indicate that the H.Cl (restricted configuration interaction) is performed within the orbitals optimized at the PP level. If the orbitals of the GVB-RCI wavefunction are calculated self-consistently, it is denoted GVB-RCI( opt). The GVB-RCI wavefunction (lJtRCI) maintains the GVB orbital picture of one electron per orbital, while obtaining optimized spin-coupling for each electronic state. In addition to -46- optimized spin-coupling, the RCI also incorporates ionic configurations and interpair correlation (i.e., dynamic correlated movement of charge within adjacent bond pairs). The effectiveness of the RCI was illustrated in a recent paper 28 on the singlet-triplet splitting in CH2, where GVB-RCI(opt) using a DZP basis (20-25 spin eigenfunctions) calculates LlEsT to within 0.5 kcal/mol of the six electron full CI result 29 ( """220,000 spin eigenfunctions). Furthermore, for a.n e:x:tended ba- sis, the GVB-RCI(opt) yields LlEsT within 0.06 kcal/mol of the best experimental value. 3 •7 •8 Thus the GVB-RCI includes the dominant correlations important for an accurate and balanced description of electronic excitation processes, while eschewing irrelevant terms. For substituted carbenes, the RCI with six active electrons describes the dominant u charge transfer in the C-X and C-Y bonds and the optimal spin coupling for both the singlet and triplet states. However, for the carbenes with halogen substituents, 71"-donation from the halogen p lone pairs into the carbon p7r orbital is extremely important in the stabilization of the singlet state. Thus, for the halogensubstituted carbenes, we carry out the following calculations: RCI*IICI(PP): starting from the GVB(M/2M)PP wavefunctions (where M = 2 for the triplets and M = 3 for the singlets), we allow a full Cl within the -rr orbitals for each of the RCI configurations described above. This allows synergistic 11"-donation to the carbon and er charge transfer from carbon to the halogens. \Ve have also optimized this wavefunction self-consistently [denoted RCI*II Cl( opt)], to evaluate possible orbital shape changes induced by the charge transfer in this CI. Since the RCI and RCI*IlCI wavefunctions build the same correlations into both the singlet and triplet states of CXY, they o.rc both correlation-consistent. (For CXY without lone pairs on X or Y, the RCI and the RCI*IlCI wavefunctions are equivalent.) The above wavefunctions only utilize valence space excitations. Since the process of interest involves an electronic excitation between the u and 71" orbitals, it is -47- essential to allow full correlation (full freedom within the basis) of the two electrons involved in the <r and 7r orbitals. Therefore, to the RCI [for CH 2 and CH(SiH3 )] or to the RCI*IICI (for CHF, CHCl, CF2, and CCh) configurations, we include (from each RCI configuration) all single and double excitations of the two carbon electrons in the nonbonding <rand 7r orbitals to all virtual orbitals [designated as RCI*[IlCI + SD,,.,..](PP)]. We refer to this level of CI as the correlation-consistent CI (CCCI), since it allows the same correlation and spin-coupling degrees of freedom for both singlet and triplet states, resulting in a balanced de5cription of each. The CCCI (RCI*[IICI + SDn(PP)]) is performed using the GVB-PP wa.vefunction as the first order description, since the 7r orbitals after the RCI*IICI( opt) calculation are not unique (thus single and double excitations from the carbon nonbonding electrons are not uniquely defined), which might lead to an imbalanced description of the two states. Our overall approach is to include the dominant excitations dictated by the physical interactions in the process of interest. Namely, for an electronic excilH.Liuu involving one pair of electrons, it is essential to allow the best possible description of those two electrons (i.e. a full CI within the basis). Secondly, substituents at carbon which form partially ionic bonds [either donating to carbon (e.g., CHSiH 3 ) or withdrawing charge from carbon (e.g., CHF) in the u system] require an RCI description to allow for such <r charge transfer. Thirdly, substituents at carbon with p7r lone pairs can donate charge to the carbon p7r orbital, requiring the full CI in the 11" valence space. Finally, the MC-SCF solves for the optimum orbital shapes of the RCI*IICI wavefunction, with optimal spin-coupling included. We have left out many second order excitations which would be included in a typical CI scheme. However, these other excitations may not treat the singlet and triplet states of CXY equivalently. Since the RHF level has much less electron correlation error in the triplet state than in the singlet state [two singly-occupied orthogonal orbitals (triplet) versus one doubly-occupied orbital (singlet)], a single -48- and double excitations CI (CI~SD) can fully correlate each of the C-X and C-Y bond pairs in the triplet, but not in the singlet (e.g., double excitations in the O" pair would go with an uncorrelated C-X bond, while double excitations in the C-X bond would go with an uncorrelated O" pair). For example, starting from the HF wavefunction for CH 2 ( 3 B 1 ) and the GVB(l/2) wavefunction for CH 2 (1 A 1 ) (using a valence double zeta basis set 19 plus one set of 3d functions on carbon 21 and a triple zeta basis set 19 plus one set of unscaled 2p functions on each H) and allowing full correlation of the two non bonding carbon electrons (single and double excitations to all virtual:s), the triplet is stabilized by only 6.8 millihartrees while the GVB(l/2) er pair is lowered by 15.2 millihartrees. Using the HF description of' the singlet, the u pair is stabilized by 36.2 millihartrees. Therefore, the triplet nonbonding electrons have less correlation error than either description of the singlet nonbonding electrons, and thus single and double excitations from all valence orbitals will overcorrelate the triplet relative to the singlet. In addition, CI-SD also suffers from a spin-coupling bias. Consider a. double excitation from two closed shell orbitals (e.g., one single excitation from each C-X and C-Y bond pair). The triplet configuration has six open shell electrons which have nine possible spin-couplings while the singlet configuration has only four open shell electrons with only two possible spin-couplings. Therefore the triplet CISD wavefunction, with a maximum of six open shells can mix in up to nine spin eigenfunctions per spatial configuration, but the singlet CI-SD wavefunction, with a four open shell maximum, is restricted to two spin eigenfunctions per spatial configuration, resulting in greater flexibility for the triplet. Both of the problems listed above (unbalanced correlation and spin-coupling) for CI-SD result in a bias in favor of the triplet state, leading to singlet-triplet splittings too high for ground state triplets and too low for ground state singlets. In contrast, the CCCI has the .mme mazimum number of open Jhella for each Jtate {-'fa} and allows the same correlations for each state, treating the spin-coupling (as -49- well a.,s the correlation) in an unb.ial:)e<l 1m1m1er. III. Results The singlet-triplet splittings in methylene are summarized in Table II. The CCCI result [RCI*SD.,,,,..(PP)] yields liEsT = 9.0 kcal/mol, in excellent agreement with experiment (.6.EsT 9.1 kcal/mol). We should note that there is appar- ently a cancellation of errors between basi:::; ::;et <leficiencies and inclusion of higher correlation, resulting in an extra accurate value for CCCI within a DZP type basis. B. CHSiH3 Since Si is more electropositive than H, we expect larger amounts of c.arbnn 2s character in an SiC bond, leaving more 2p character in the carbon nonbonding t7' orbital. This renders the two nonbonding orbitals on carbon close in energy, favoring the triplet state and leading to a larger singlet-triplet splitting for CHSiH 3 than for CH2. Indeed, as shown in Table III, D.EsT for CHSiH 3 is 18.4 kcal/mol, about twice that for CH 2 • As consistent with the discussion in Section II, other methods 14 - 16 appear to overestimate the singlet-triplet gap. As further support for our qualitative analysis of the bonding, the GVB one electron orbitals are shown in Figs. 1 and 2 for the ground (3 A") and excited (1 A') statPi:. nf CHSiH 3 , respectively. A dramatic difference is visible in all valence orbitnls for each state. For the triplet state, the carbon orbitals involved in the C-Si and C-H bonds have dominantly .s-character, while for the singlet, these orbitals have dominantly p-character. Concomitantly, the nonbonding carbon <:T orbital changes from mostly p in the triplet to mostly s in the singlet. A quantitative indication of the .s and p contributions may be evaluated using the Mulliken approximation (shown in Table IV). 30 Although Mulliken populations at best provide a qualitative inr1ic.Rtion of charge transfer, relative trends are expected to be reliable. For the triplet state, the hybridizations at carbon in the -50- C-Si and C-II boml::s urc:: 00.8% 2::;/39.2% 2p and 45.4% 2s/54.6% 2p, respectively (mores-character in the C-Si bond, as expected), while the lone pair hybridization is 11.23 2s/88.83 2p. The carbon pulls off 0.37 electron from the Si, illustrating the polar nature of the carbon-silicon bond. In the singlet state, the hybridizations at carbon in the C-Si and C-H bonds are dramatically different, with 20.93 2s/79.13 2p and 17.13 2s/82.93 2p character, respectively, while the (J' nonbonding orbital is 61.43 2s/36.63 2p. The singlet favors s-character in the nonbonding O' lone pair and concomitantly more p-character in the bonrl~- The singlet-triplet splittings for CF 2 are shown in Table V. In this case, the electon-withdrawing fluorines force more p-character into the C-F bonds and more s-character in the nonbonding er orbital, favoring a singlet ground state. As seen in Table V, the singlet is stabilized greatly with respect to the triplet even at tht> HF level, and increasing the level of electron correlation yields AEsT = -57.5 kcal/mol, in excellent agreement with the experimental value of -56.0 kcttl./mul. The only previous theory involved a GVB(l/2) calculation, 10 yielding -46.5 kcal/mo!. Notice that jAEsTI increases greatly upon the inclusion of 71'-donation to the carbon p7rorbital, since this stabilizes the singlet much more than the triplet. The single and double excitations from the O' and 7r nonbonding carbon orbitals serve to increase IAEsTI even further. The self-consistent RCI*IICI(opt) calculation (for all the carbenes) yields results close to the RCI*[IICI + SDn] calculation, even though it is a much smaller (valence level) CI, providing an independent estimate of the true D.EsT( CXY). The orbitals for the 3 B 1 excited state of CF 2 are shown in Fig. 3 (we do not show the i Ai orbitals since they are very similar). Comparing the bond pairs in Figs. 1 and 3 shows that the fluorines do indeed bond preferentially to the carbon p-orbitals (even more so in the 1 Ai state of CF 2 ) to form the best ionic bonds, while SiH 3 and H form bonds with much more s-character. The carbon a -51- radical orbital in 3 B 1 CF 2, displayed in Fig. 3b, has a large s-component while the same radical orbital in 3 A" CHSiH 3 is nearly all p in character. Therefore, electronegativity differences do indeed dictate the character of the C-X and Cy bonds, thus controlling the amount of s-character in the nonbonding carbon u orbital and hence the relative energies of the non bonding u and 7r orbitals (which determines whether the ground state of CXY is a triplet or singlet). Analysis of the Mulliken populations for both the 1 A 1 and 3 B 1 states quantify the hybridization and charge transfer in the CF2 bonds (Table IV). The 1 A 1 ground state has 19.03 2s/81.03 2p character in the C-F bonds and 69.83 2s/30.23 2p in the carbon u nonbonding orbital. The 3 B 1 excited state has 45.33 2s/54.73 2p character in the C-F bonds and 52.73 2s/47.33 2p in the carbon u nonbonding orbital. These results are consistent with the expectation that the singlet state will have mainly p-character in the bonds and dominantly s-character in the u nonbonding orbital. D. CCl2 Since Cl is less electronegative than F, we expect that AEsT will be less negative for CCh than for CF 2 • This is borne out in Table VI, where the singlet-triplet gaps for CCh are listed as a function of increasing electron correlation. Hartrt>PFock theory actually finds the triplet lower than the singlet by 0.1 kcal/mol, but GVB-PP already yields a. singlet ground stn.te. Similar to the other ROI prediction::> of AEsT(CXY), the RCI results using PP orbitals stabilize the triplet slightly more than the singlet, since the optimum spin-coupling introduced by the RCI is more important for the triplet. Inclusion of the p11" donation from the Cl's increases IAEsT I substantially, with the optimized orbitals in the RCI*II CI( opt) calculation increasing the gap still further. Inclusion of single and double excitations from the carbon nonbonding electrons yields our best value for 6.EsT(CCh) = -25.9 kcal/mol. The only previous theoretical result for AEsT(CCb) is from GVB(l/2) calculations 10 which yielded -13.5 kcal/mol, falling in between the HF and GVB(M/2M)PP val- -52- ues (M = 2 for triplet and N 7r 3 for singlet), as expected. Clearly, inclusion of donation and full correlation of the carbon lone pair (non bonding electrons) is crucial for predicting the singlet-triplet splitting correctly. Mulliken population analyses (Table IV) of the GVB(M/2M)PP wavefunctions for 1 A1 and 3 B 1 CCl2 are consistent with the fact that Cl is not as electronwithdrawing as F, so that somewhat less p-character is found in the C-Cl bonds (relative to the C-F bonds). The amount of p-character in the C-Cl bonds is still much larger in the singlet than in the triplet, as expected from arguments outlined in the introduction (19.5% s/80.53 p for 1 A 1 and 53.5% s/46.53 p for 3 B 1 ). The carbon lone pair u orbital is primarily .s-like for the singlet (72.83 s/27.23 p) and primarily p-like for the triplet (39.03 s/61.03 p ), as expected. The total amount of charge transfer is the same overall (0.1 electron transferred to carbon in each state), but the partitioning is different: in the singlet, 0.20 electron is pullP.rl off carbon in each u bond, countered by 0.50 electron donated to carbon in the 7r system, while in the triplet, only 0.06 electron is removed from carbon by each rr bond, cumpensated by the 7r charge transfer of 0.23 electron. Since 71"-donation is larger than u charge transfer, it is as important as the (]' charge transfer in determining the separation of singlet versus triplet states. E. CHF The singlet-triplet splittings for CHF are displayed in Table VII. Hartree Fock theory again predicts (incorrectly) the ground state to be 3 A", while GVBPP correctly predicts the groun<l btate tu be 1 A'. CCCI yields AEsT(CHF) = -17.7 kcal/mo!, in good agreement with a tentative experimental value of,....., -15 kcal/mol. 11 Previous theoretical values include -9.2 kcal/mol 10 from GVB(l/2) [less negative than the GVB(M/2M)PP value reported here, as expected], -12.7 kcal/mol1 4 from MP4 calculations (these start with the RHF wavefunction for the singlet, building in a bias toward a smaller 6.EsT ), and -12.9 kcal/mol 17 from CISD calculations which utilized a GVB(l/2) reference state for the singlet and an -53- HF reference state for the triplet. Even though the CI-SD was carried out with a triple-( plus double polarization (TZ2P) basis set and included as many as 119,604 configurations 17 (CCCI has 1192 configurations), this method still undereJtimate" ~EsT(CHF) by 5 kcal/mol. The singlet-triplet splitting is not as large for CHF as for CCh or CF 2 , presumably because only one electronegative/pi-donating substituent is attached to carbon. The Mulliken populations (Table IV) substantiate this; while the fluorine pulls off 0.36-0.40 electron from carbon in the C-F bond, the 7T'-donation brings the net charge at carbon back to +0.04 for 1 A' and +0.01 for 3 A". The hybridizations of the C-F and C-H bonds follow the trend, with more carbon p-character for the singlet than for the triplet ( C-F: 79. 73 p for 1 A' and 63.53 p for 3 A"; C-H: 85.53 p for 1 A' and 40.23 p for 3 A"). The nonbonding u orbital at carbon has concomitantly more s-character for the singlet (67.43 s), whr.reas the triplet has more p-character (65.23 p ). F. CHCl The singlet-triplet gaps for 1 A' and 3 A" CH Cl are shown in Table VIII. Hartree-Fock theory again predicts a triplet ground state, while GVB-PP finds a ground state singlet, consistent with higher levels of electron correlation. AEsT(CHCl) is smaller than for all the other substituted carbenes examined in thii:i work, consistent with the smaller electronegativities of H and Cl. The la.rge5t correlation-consistent CI calculation yields -9.3 kcal/mol for ~EsT(CHCl), which may be compared with previous theoretical values of -1.6 [GVB(l/2)]1° and -3. 7 kcal/mol [GVB(l/2)*SD with a TZ2P basis]. 17 Again, even though the CI-SD calculation involved up to 74,546 configurations and used a TZ2P basis, 17 the correlationconsistent CI method yields a more accurate value for AEsT (based on the results for CHF), with only 1192 configurations. Much less charge transfer is found for CHCI than for the other halogen substituted carbenes (Table IV). Chlorine pulls off 0.10 and 0.22 electron from -54- ..rbon in the C-Cl bond of CHCI in the 3 A" and 1 A' states, respectively, but this is completely countered in 71" system (leaving the Cl with +0.02 and +0.03 total charge in the 1 A' and 3 A" states, respectively). As found for all of the halogen-substituted carbenes, 1 A' CHCl has mostly p-character in the C-H and C-Cl bonds (C-H: 82.6% p and C-Cl: 78.53 p) and mostly s-character in the nonbonding <J' orbital (67.83 s), while 3 A" CHCl has less p-character in the C-H and C-Cl bonds (C-H: 44.43 p and C-Cl: 51.43 p) and more p-character in the nonbonding u orbital (70.33 p ). IV. Discussion Our results for the singlet-triplet splittings in six carbenes are summarized in Table IX for the three highest calculational levels, along with comparisons to a full CI value 29 for AEsT(CH2), experimental data for AEsT (CH2, 3 •7 •8 CF , 9 and 2 CHF 11 ), and thermochemical estimates for ~EsT (CF 2 , CC1 2 , CHF, and CHCl). 1 1! The agreement between CCCI and experiment is excellent, where experimental ~EsT's are available (CH 2 , CF2, and CHF). As reported previously, 28 the RCI(opt) method with only 20-25 spin eigenfunctions yields a AEsT for CH 2 which is within 0.5 kcal/mol of the full CI result for a DZP basis. Using the correlation error incurred by all three calculational levels relative to this full CI result, we can estimate the full CI results for the other carbenes studied here (ignoring differential correlation errors for substituted co.rbencs ). These full CI estimates are shown in parentheses. The CCCI wavefunction yields a .6.EsT(CH 2 ) value close to experiment, and assuming the residual correlation error present in CCCI for CH 2 is the same in other systems, we have estimated "experimental" values for AEsT of the substituted carbenes (shown in parentheses). The agreement is good where experimental data are available. We ho.ve shown in previom1 work 184 that the dowimwt coutribution to the bond weakening in substituted olefins and methanes (relative to the parent com- -55- pounds C 2 H 4 and CH 4 ) is the promotional cost to excite CXY from a ground state singlet (nonbonding) to the excited state triplet (bonding). This relationship was used to derive thermochemical estimates for ~EsT(CXY) by evaluating C=C and C-H bond weakening in various substituted olefins and methanes. 18 a The estimates for ~EsT shown in Table IX are different than those derived in Ref. 18a, since more than one value for the heats of formation of CXY are used in the present work (Table X). The large uncertainties associated with our thermochemical estimates of l::i..EsT are a direct result of the uncertainties associated with the experimental heats of formation and bond energies (Table X). For instance, the estimated AEsT for CF 2 in Ref. 18a was based solely on a value for the C=C bond energy in C2F 4 (76.3±3 kcal/mol), measured by Margrave and co-workers 31 from the heat of the reaction C 2F 4 ~ 2 CF 2. The thermal decomposition of C2F4 to form CF 2 was followed at temperatures between 1127 and 1220°K in a Knudsen cell to obtain the equilibrium constant as a function of temperature from the appearance potential (AP) intensities of C 2 Ft and CFit. Errors in the equilibrium constant may be due to the assumptions needed to convert tlu: AP inten5ities to partial pressures or to the lack of a true thermal equilibrium (C2F 4 was formed by pyrolysis of Teflon and an equilibrium was assumed since CFt was observed in the mass spectrometer). Indeed, a third law analysis of shock-tube experiments yields AHj, 298 = 67.5 kcal/molfor the C 2 F4 ~ 2 CF 2 equilibrium. 31 •32 The discrepancies between these two direct measurements of the C=C bond energy in C2F4 (67.5 versus 76.3 kcal/mol) suggests that a more reliable estimate of this bond energy might be obtained from independent measurements of the heats of formation of C 2 F4 and CF 2 • Unfortunately, while three independent measurements for ~H/, (CiF4) agree to within 0.7 kcal/mol (-157.4 ± 0.7 kcal/mol), 33 the 2118 heat of formation of CF 2 is much less certain. The two most recent values are -52. 34 and -44.2 ± 135 kcal/mol, leading to D~~~t(F 2 C=CF 2 } = 53.4±0.7 and 69.0±2. 7 kcal/mol, considerably different from Margrave's determination. If these -56- two estimates are used for the C=C bond energy, then the thermochemical estimate for AEsT(CF 2) becomes -55.4±3.9 kcal/mol, in much better agreement with both theory and experiment. Table X displays new predictions for C=C honrl energies m substituted olefi.ns, based on the premise 18 a that when CXY has a singlet ground state, the C=C bond in the corresponding olefins will be weakened rd1:1.tive to the C=C bond in ethylene by AEsT(CXY). We obtain the new predictions by subtracting our best ab initio values for AEsT (the CCCI calculations in Table IX) from 172.2±2.1 kcal/mo! (the C=C bond energy in ethylene): 33 Dj, 298 (XYC = CX'Y') = Dj, 298 (H2C = CH2) - AEsT(CXY) - AEsT(CX'Y') = 172.2 ± 2.1 - AEsT(CXY) - AEsT(CX'Y'), (2) where .6.EsT (CH~.I) is set to zero in Eq. (2) (ground state triplets incur no promo- tional. costs). 1811 These new estimates for Dj, 298 (XYC=CX'Y') compare favorably in most cases with the experimental. bond dissociation energies al.so shown in Table X. While the discrepancies are due in part to uncertainties in the experimental heats of formation of CXY, Eq. (2) assumes the intrinsic C=C bond strength for all olefins to be constant (that of C 2 H4 ). 18 a Recent calculations on the intrinsic C=C bond strength (to dissociate to triplet fragments) of C2 F 4 reveal that D~9t8 (F2C=CF2) is greater than D~9t8 (H2C=CH2) by 6.9 kca.l./mol. 36 Since C2F4 should perturb Dk9t8 (C=C) more than any other halogenated olefin, AD~n9t8 = 6.9 kca.l./mol should be an upper bound on the error of our predicted C=C bond energies. V. Conclusions Ab initio GVB-CI calculations have been carried out to determine the singlettriplet splittings for a variety of substituted carbenes. Emphasizing correlationconaiatency and including the dominant charge transfer processes in the choice of the Cl expansion leads to accurate values for AEsT( CXY) using quite small CI -57- calculations. Explanations have been offered as to why other methods tend to overeatimate D..EsT for ground state triplets and undere.Jtimate D..EsT for ground state singlets. The new values for fl.EsT obtained in the present work are used to predict new C=C bond energies in substituted olefins. Acknowledgments. This work was supported by the National Science Fuundation (Grant No. CHE83-18041) and the Shell Companies Foundation. EAC acknowledges a National Science Foundation predoctoral fellowship (1982-1985), a research grant award from the International Precious Metals Institute and Gemini Industries (1985-1986), and a SOHIO fellowship in Catalysis (1987). -58References (1) a) W. Kirmse, "Carbene Chemistry" (Academic, New York, 1971); b) P. P. Gaspar and G. S. Hammond, in "Carbenes", R. A. Moss and M. Jones, Eds. (Wiley, New York, 1975), Vol. 2; c) R. A. Moss and M. Jones, in "Reactive Intermediates", M. Jones and R. A. Moss, Eds. (Wiley, New York, 1981), Vol. 2; d) ibid. (Wiley, New York, 1985), Vol. 3; e) E. R. Davidson, in "Diradicals", W. T. Borden, Ed. (Wiley, New York, 1982). (2) W. A. Goddard III and L. B. Harding, Ann. Rev. Phys. Chem. 29, 363 (1978). (3) I. Shavitt, Tetrahedron 41, 1531 (1985). (4) W. A. Goddard III, Science 227, 917 (1985). (5) H. F. Schaefer III, Science 231, 1100 (1986). (6) A. R. W. McKellar, P.R. Bunker, T. J. Sears, K. M. Evenson, R. J. Saykally, S. R. La.nghoff, J. Chem. Phys. 79, 5251 (1983). (7) a) D. G. Leopold, K. K. Murray, and W. C. Lineberger, J. Chem. Phys. 81, 1048 (1984); b) D. G. Leopold, K. K. Murray, A. E. S. Miller, W. C. Lineberger, J. Chem. Phys. 83, 4849 (1985). (8) a) P.R. Bunker and T. J. Sears, J. Chem. Phys. 83, 4866 (1985); b) P. R. Bunker, P. Jensen, W. P. Kraemer, and R. RP.arch:worth, J. Chem. Phys. 85, 3724 (1986). (9) a.) S. Koda, Chem. Phys. Lett. 55, 353 (1978); b) idem, Chem. Phys. 66, 383 (1982). (10) C. W. Bauschlicher, Jr., H.F. Schaefer III, and P. S. Bagus, J. Am. Chem. Soc. 99, 7106 (1977). (11) D. G. Leopold, K. K. Murray, and W. C. Lineberger, private communication. (12) Earlier work which focused on the necessity of a balanced description of -59- correlation to provide unbiased excitation energies may be found in P. J. Hay, W. J. Hunt, and W. A. Goddard III, Chem. Phys. Lett. 13, 30 (1972). (13) D. A. Dixon, J. Phys. Chem. 90, 54 (1986). (14) B. T. Luke, J. A. Pople, M.-B. Krogh-Je5per5en, Y. Apeloig, M. Ka.rni, J. Chandrasekhar, and P. v. R. Schleyer, J. Am. Chem. Soc. 108, 270 (1986). (15) J. D. Goddard, Y. Yoshioka, H. F. Schaefer III, J. Am. Chem. Soc. 102, 7644 (1980). (16) H.J. Kohler and H. Lischka, J. Am. Chem. Soc. 104, 5884 (1982). (17) G. E. Scuseria, M. Dur6.u, R. G. A. R. Mo.da.ga..n., a..ud H.F. Schaefer III, J. Am. Chem. Soc. 108, 3248 (1986). (18) (a) E. A. Carter and W. A. Goddard III, J. Phys. Chem. 90, 998 (1986); (b) These values have been revised here to reflect the latest experimental values for .6.H~ 12118 (Table X). (19) T. H. Dunning, Jr., J. Chem. Phys. 53, 2823 (1970). (20) S. Huzinaga, J. Chem. Phys. 42, 1293 (1965). (21) Optimized for CH 4 by R. A. Ba.ir and W. A. Goddard III, submitted for publication. (22) A. K. Rappe, T. A. Smedley, and W. A. Goddard III, J. Phys. Chem. 85, 1662 (1981). Note that the second p exponent for the Cl basis listed in Ta.ble I of this reference should read 0.641, not 0.691, and the s orbital energy for Cl in Table IV of this reference should read -1.0675, not -0.1068. (23) L. B. Harding and W. A. Goddard III, Chem. Phys. Lett. 55, 217 (1978). (24) D. S. Horowitz and W. A. Goddard III, to be published. (25) R. Noyori, M. Yamakawa, and W. Ando, Dull. Chem. Sue. J1:1.p. :St, 811 (1978). (26) C. F. Bender, H.F. Schaefer III, D.R. Franceschetti, and L. C. Allen, J. -60- Am. Chem. Soc. 94, 6888 (1972). (27) (a) W. J. Hunt, T. H. Dunning, Jr., and W. A. Goddard III, Chem. Phys. Lett. 3, 606 (1969); W. A. Goddard III, T. H. Dunningi Jr.i and W. J. Hunt, Chem. Phys. Lett. 4, 231 (1969); W. J. Hunt, W. A. Goddn.rd III, n.nd T. H. Dunning, Jr., Chem. Phys. Lett. 6, 147 (1970); W. J. Hunt, P. J. Hay, and W. A. Goddard III, J. Chem. Phys. 57, 738 (1972); F. W. Bobrowicz and W. A. Goddard III in "Methods of Electronic Structure Theory", H. F. Schaefer, ed., Plenum Publishing Corporation, 1977, pp 79-127; (b) L. G. Yaffe and W. A. Goddard III, Phys. Rev. A 13, 1682 (1976). (28) E. A. Carter and W. A. Goddard III, J. Chem. Phys. 86, 862 (1987). (29) C. W. Bauschlicher, Jr. and P.R. Taylor, J. Chem. Phys. 85, 5936 (1986). (30) Mulliken populations were obtained by summing over the electron populations of each carbon s and p basis function within each natural orbital for each GVB pair. (31) K. F. Zmbov, 0. M. Uy, and J. L. Margrave, J. Am. Chem. Soc. 90, 5090 (1968). (32) A. P. Modica and J. E. LaGra.:.ff, J. Chem. Phys. 43, 3383 (1965). (33) "JAN AF Thermochemical Tables", Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. 37 (1971) and supplements to JANAF in: J. Phys. Chem. Ref. Data 3, 311 (1974); ibid. 4, 1 (1975); ibid. 7, 797 (1978); and ibid. 11, 695 (1982). (34) S. G. Lias, J. F. Liebman, and R. D. Levin, J. Phys. Chem. Ref. Data. 13, 695 (1984). (35) D. W. Berman, D.S. Bomse, and J. L. Beauchamp, Int. J. Mass. Spectrom. Ion Phys. 39, 263 {1981 ). (36) E. A. Carter and W. A. Goddard III, J. Am. Chem. Soc., submitted for publication. -61- Table I. Optimum geometries for the 1 A' and 3 A 11 stat.es of CH(SiH 3 ). geometrical parameters iA' a A" 0e(H-C-Si)a 106.1° 140.4° Re(C-Si)"' L951A 1.867A Re(C-H)a i.123A i.o91A R(Si-H)b 1.487 A 0(H-Si-H)b 108.3° e D(H-C-Si-H)c 60.0° a) Optimization carried out at the GVB(3/6)-PP level. b) Ref. 24. c) Ref. 25. -62- Table II. Singlet-triplet splittings (6.EsT) and total energies for the 1 A 1 and 3 B 1 states of CH2. total energies(h)b 1 3 B1 6.EsT(kcal/mol)c -38.88587 -38.92749 26.1 (1/1) (1/1) -38.93877 (8/8) -38.94151 (18/20) -38.94189 {18/20) -38.95329 (4/4) -38.95925 (9/25) -38.96035 (9/25) Full Cld -39.02718 -39.04620 12.0 ccc1e ( "'44,ooo / "'220,000) -38.96706 -38.98135 (1174/1989) (774/2070) 9.0 calculation 4 HF GVB-PP GVB-RCl(PP) GVB-RCI( opt) Previous Theory Experimenth Ai 9.1 11.1 11.6 13.5( CI-SD)/16.8(MP4)9 9.1±0.2 a) Calculational details are provided in Section II. The corresponding number of spatial configurations/ spin eigenfunctions for each wavefunction is given beneath each total energy. b) 1 h = 1 hartree = 627.5096 kcal/mol = 27.211617 eV = 219,474.75 cm- 1 . c) 6.EsT = Eainglet - Etriplet• d) Ref. 29. e) RCl*SDn(PP). !) R.R. Lucchese and H. F. Schaefer III, J. Am. Chem. Soc. 99, 6765 (1977). g) B. T. Luke, J. A. Pople, M.-B. Krogh-Jespersen, Y. Apeloig, J. Chandrasekhar, and P. v. R. Schleyer, J. Am. Chem. Soc. 108, 260 (1986). h) Ref. 3, 7, and 8. -63- Table III. Singlet-triplet splittings (AEsT) and total energies for the 1 A' and 3 A" states of CH(SiHa). calculation HF GVB-PP GVB-RCI(PP) GVB-RCI(opt) CCCI• Previous Theory total energies(h) iA' aA" -328.96121 (1/1) -329.01135 (8/8) -329.01551 (18/20) -329.01614 (18/20) -329.04260 (4180/7447) AEsT (kcal/ mol) -329.01652 (1/1) -329.04047 (4/4) -329.04698 (9/25) -329.04857 (9/25) -329.07199 (3318/9030) 34.7 18.3 19.7 20.4 18.4 20.3(CEPA),ll25.7(MP4),e21.2(CT-Sn)" a) RCI*SD.,.,,.(PP). b) Ref. 16. c) Ref. 14. d) Ref. 15. -64- Table IV. Bond populations, total charges, and carbon hybridization for CXY." Bond CXY State Bond on Carbon11 c x Hybridization C Uc C-X Bond % 2s % 3 2s 3 2p CH2 C-H 1.16 6.30 0.85 51.0 49.0 19.0 81.0 CH2 CHSiH3 3B1 1A1 C-H 1.06 6.21 0.89 17.5 82.5 62.1 37.9 3A" 6.40 45.4 60.8 17.1 20.9 54.6 39.2 82.9 79.1 88.8 lA' 0.86 13.45 4 0.90 13.53 4 11.2 CHSiH3 C-H C-Si C-H C-Si 61.4 38.6 CF2 CF2 CCl2 CCI, 3 B1 9.14 9.10 16.94 45.3 19.0 53.5 54.7 81.0 46.5 52.7 69.8 39.0 47.3 30.2 61.0 6.10 5.99 CHF CH!'' C-X Popnlation 'Total Cha:rge!I A1 aB1 C-Cl 1.13 1.37 1.02 1.23 0.67 0.59 0.94 1 A1 3A" C-Cl 0.80 C-H C-F 1.18 0.64 1A1 C-H LUO C-F 0.60 1.18 0.90 1.06 1 C-F C-F CH Cl 3A" C-H C-Cl CH Cl lA' C-H C-Cl 6.29 5.72 5.80 6.11 5.96 6.20 6.16 16.95 19.5 80.5 72.8 27.2 0.86 9.15 59.8 36.5 40.2 63.5 34.8 65.2 67.4 32.6 0.92 14.5 55.5 9.12 20.3 79.7 0.83 16.97 0.86 16.98 55.6 48.6 44.4 51.4 29.7 70.3 17.4 82.6 67.8 32.2 a) Based on Mulliken populations (Ref. 30). b) Perfect covalent bonding would lead to a carbon bond population of 1.00. c) Carbon u nonbonding orbital. d) Ea.ch H on SiH 3 pulls 0.10 electron off of Si. -65- Table V. Singlet-triplet splittings ( -6.EsT) and total energies for the 1 Ai and 3 B1 states of CF2. total energies(h) calculation HF GVB-PP GVB-RCI(PP) RCI*IlCI(PP) RCI*IlCI( opt) CCCI 0 Previous Theory Experiment 1 3 B1 AEsT(kcal/mol) -236.69898 (1/1) -236.75904 -236.64724 (1/1) -236.68387 -32.5 (8/8) (4/4) -236.75979 (18/20) -236.77747 (63/91) -236.68597 (9/25) -236.69470 (27 /75) -46.3 -236.79045 -236.69510 -59.8 (63/91) -236.80127 (1219/2060) (27 /75) -236.70966 (792/2120) -57.5 Ai -47.2 -51.9 -46.5[GVB(l/2)]b -56.6c a) RCI*[IICI + SDn](PP). b) Ref. 10. c) Ref. 9. -66- Table VI. Singlet-triplet splittings (~EsT) and total energies for the 1A 1 and 3 B 1 statt~s of CCl2. total energies(h) 1 3 B1 ~EsT(kcal/mol) -956.67142 -956.67156 0.1 (1/1) (1/1) -956.72841 (8/8) -956.73338 (18/20) -956.74827 (63/91) -956.70211 (4/4) -956.70863 (9/25) -956.71457 (27/75) RCI*IICI( opt) -956.75250 -956.71550 -23.2 ccc1a (63/91) -956.77628 (1219/2060) (27/75) -956.73495 (792/2120) -25.9 calculation HF GVB-PP GVB-RCI(PP) RCI*IICI(PP) Ai Previous Theory a) RCI*[IICI + SDa-11'](PP). b) Ref. 10. -16.5 -15.5 -21.1 -13.5[GVB(l/2)]b -67- Table VII. Singlet-triplet splittings (~EsT) and total energies for the 1 A' and 3 A" states of CHF. calculation HF GVB-PP GVB-RCI(PP) RCI*IICI(PP) RCI*IICI(opt) CCCI" Previous Theory Experiment total energies(h) a A" iA' -137.78206 (1/1) -137.83874 (8/8) -137.84018 (18/20) -137.85094 (36/47) -137.86149 (36/47) -137.87560 (1192/2016) -137.78916 (1/1) -137.82013 (4/4) -137.82333 (9/25) -137.82858 (18/50) -137.82931 (18/50) -137.84740 (783/2095) ~EsT(kcal/ mol) 4.5 -11.7 -10.6 -14.0 -20.2 -17.7 -9.2[GVB(l /2)], b-12. 7(MP4), c:-12.9( CI-SD ) 4 ""-15 4 a) RCI*(IICI + SDn](PP). b) Ref. 10. c) Ref. 14. d) Ref. 17. e) Ref. 11. -68- Table VIII. Singlet-triplet splittings ( ~EsT) and total energies for the 1 A' and 3 A 11 sb.tes of CHCI. calculation HF GVB-PP GVB-RCI(PP) RCI*IICI(PP) RCI*IICI( opt) CCCI" Previous Theory total energies(h) aA" 1AI -497.78302 (1/1) -497.83563 (8/8) -497.83910 (18/20) -497.84773 (36/47) -497.85006 (36/47) -497.87415 (1192/2016) A.EsT(kcal/mol) -497.80255 (1/1) -497.82949 (4/4) -497.83502 (9/25) -497.83843 (18/50) -497.83943 (18/50) -497.85933 (783/2095) 12.3 -3.9 -2.6 -5.8 -6.7 -9.3 -1.6(GVB(l/2)],"-3. 7( CI-SD)c a) RCI*(IICI + SD.,"lr)(PP). b) Ref. 10. c) Ref. 17. Table IX.. Singlet-triplet split.tings (AEsT ::::: Eaingltt of CI (keal/mol)."' Etriptet) in CXY for thret correlation-consistent levels Theory• CXY RCI*llCI(PP) RCI*II CI( opt) Experiment• Full CI cccie Thermochemical Estimate' CH2 CHSiHa CF, 11.l 11.6 12.0' 9.0 19.7 -51.9 20.4 -59.8 (21.0±0.4) (-55.2±4.2} 18.4 -57.5 -56.6,'(-~7.4±0.2) -50.0±10.8 CCl2 -21.l -23.2 (-21.6±1.4) -25.9 (-25.8±0.2) -31.0±10.7 CHF -14.0 -20.2 (-16.5±3.4) -17.7 ~ -1&,h(-17.6±0.2) -22.4±6.6 CHCI -5.8 -6.7 (-5.6±0.7) -9.3 (-9.2±0.2} -16.7±8.2 9.09±0.21' (18.5±0.2) a) Details of the basis sets and MCSCF /Cl calculations a.Je given in Section II. b) Values in parentheses represent our best estimates for A.EsT for both a full Cl within a DZP basis and experimental values, based on comparisons of the present CI calculat.ions with full Cl and experiment.al values for CH,. c) RCI*[IICI + SD,,11 ](PP). d) Based on the theoretical relationship between D(C==C) and '1EsT(CXY) (Ref. 18). Values revised according to new thermochemical data (see Section IV). e) Ref. 29. f) Refs. 3, 7, and 8. g) Ref. 9. h) Ref. 11. I Q\ l.O I Table X. Piedicted bond energies for XYC=CX'Y' from Dj, 298 (XYC=CX'Y') = Dj, 298 (H2C=CHi) - LlEsT(CXY) LlEsT(C'Y') (kcal/mol).•·• CXY CX'Y' D~~~d ( C=C)" o;~t(C=C) 41 LlHj, 298 (XYC=CX'Y') LlHj, 298 (CXY) ilHj, 298 {CX'Y') CH2 CF2 114.7±2.1 122±1, 129.8±2 -82.0 92±1• -52., -44.2 ± 1 e CF2 CF2 57.2±2.1 53.4±0. 7,69.0±2. 7 -157.4 ± 0.71 -52., -44.2 ± 1 -52.,-44.2 ± 1 CF 2 CF2 57.2±2.1 64.5±2.5,•76.3±3" -157.4± 0.7 -46.5± 1.6• -46.5± 1.6 CH2 CCh 146.3±2.1 146.3±3.4,136.4±1.4 0.61±0.36; 92±1 54.9±2/45. CCh CCh CHF 120.4±2.1 112.5±6, 92.7±2.0 -2.7 ± 2.0i 54.9±2,45. 54.9±2,45. 154.5±2.1 151.2±4 -33.2 92±1 26±3• CHF 136.8±2.1 122.0±6 -70.0 26±3 26±3 CHF 97.0±2.1 91.0±3,98.8±4 -117. -52.,-44.2±1 26±3 71±5. CH2 CHF CF2 CH:a CH Cl CCh CH Cl CHCI CH Cl 162.9±2.1 154.4±6.3 1 8.6±0.3 92±1 153.6±2.1 140.9±12.1 1.1±2.1' 71±5 71±5 137.0±2.1 127.9±8.6,118±6.6 -2.0±1.6' 54.9±2, 45. 71±5 a) E.rperimental heats of formation and bond energies are from Ref. 34 unless otherwise noted. b) Dj, 298 (H 2C=CHa) = 172.2±2.1 kcal/mol (Ref. 33). c) Using the Te= LlEsT values from column 5 of Table IX. These should he conected to To using differential zero point energies of 0.1±0.1 kcal/mol for CHX and CCI 2 and 0.2±0.1 kcal/mol for CF 2 , however these corrections have been omitted since they are small. d) Obtained from the heats of formation listed here unless otherwise noted. e) Ref. 35. /)Ref. 33. g) Ab initio theoretical value (E. A. Ca.rter and W. A. Goddard III, submitted for publication). h) Ref. 31. i) J. D. Cox and G. Pilcher, "Thermochemistry of Organic and Organometallic Compounds" (Academic, New York, 1970). j) K. Rademann, H.-W. Jochims, and H. Baumgartel, J. Phy-s. Chem. 89, 3459 (1985). k) S. G. Lias, Z. Karpas, and J. F. Liebman, J. Am. Chem. Soc. 101, 6089 (1985). I 'l 0 I -71- Figure Captions Fig. 1. The GVD(2/4)-PP one-electron orbitals for 3 A" CHSiH3; a) the C-Si bond pair; b) the C nonbonding <J' orbital (singly-occupied); and c) the C-H bond pair. Contours are from -0.5 to +o.5 a.u., with increments every 0.05 a.u. Fig. 2. The GVB(3/6)-PP one-electron orbitals for 1 A' CHSiH 3 : a) the C-Si bond pair; b) the C nonbonding <J' natural orbital (nearly doubly-occupied); and c) the C-H bond pair. Fig. 3. The GVB(2/4)-PP one-electron orbitals for 3 B 1 CF 2 : a) a C-F bond pair; b) the C nonboncling u orbital (singly-occupied); and c) a C-F bond pair. -72- ,.._' ONE + + a) • ' \PAIR\ - ONE 0 + + C-Si BOND PAIR ONE + + b) C a- RADICAL ONE + + c) + ' ' \ /,..I • ONE + jPAIRj • C-H BOND PAIR Figure 1. -73- a) • \ \":I I - - ' ONE .~ [PAIR! ,- ' .;.: ONE + + + C-Si BOND PAIR TWO b) O" LONE + c) ,- ' - ' + ONE + --I PAIR + - I IPAIRI "" . ~ -- • ONE ~ C-H BOND PAIR Figure 2. • -74- , ONE -' I II' ... ' ' d a) ' \ -- ' cG: , I'::-::"'.,' \ ! ' ONE ' IPAIRI ' -- ' ' -' I +- ~ C-F BOND PAIR ONE b) C a- RADICAL ONE ONE ·+ c) + 1:; IPAIRI ,,.. • () ·:~·i)~ ,', ' -- e ,, ' ~\~~ '--11;/I I I ~\ ...:~'¥-.~/I I \:::'~' , , C-F BOND PAIR Figure 3. I / -75- Chapter 1.E. The text of this section is a Communication coauthored with William A. Goddard III which has been submitted to the Journal of the American Chemical Society. -76- The C=C Double Dond of Tetra:fluoroethylene Emily A. Carter and William A. Goddard III* Contribution No. 7577 from the Arthur Amo.! Noye.! Laboratory of Chemical Phy.!ic.!, California In.!titute of Technology, Pa.rndena, California 91125. Abstract: Current experimental values for the C=C bond dissociation energy of tetraftuoroethylene (C 2 F.t) range from 53.4 to 76.3 kcal/mol. Since traditional theoretical approaches for calculating accurate bond energies would be impractical for a system as large as C2F 4 (a full CI for a double zeta. plus polarization basis would be . . . . 10 23 spatial configurations), we have applied the recently developed correlation-consistent configuration interaction (CCCI) method to C 2F,4 [requiring only 1719 configurations but obtaining De(H2C=CH2) to an accuracy of 4.9 kcal/mol]. We find: (i) D29s(F2C=CF2) = 64.5±2.5 kcal/mol; (ii) the CCCI value for D2 98 (F2C=CF2) implies a new value for the heat of formation of CF 2 : Ll.Hl, 298 (CF2) = -46.5±1.6 kcal/mol [recent experimental values for Ll.Hl, 298 (CF 2 ) range from -52. to -44.2±1 kcal/mol]; (iii) the intrinsic C=C bond strengths to dissociate to triplet fragments are nearly constant (within 4 kcal/mol) in C 2 H4 and C2F4, even though their adiabatic bvm.l :stn::ugth:s differ by over 100 kcal/mol; and (iv) u and 7r bonds are favored over bent bonds in C2F 4 • -77- Tetrafluoroethylene is an unusual olefin, with one of the weakest carbon-carbon double bonds known [D(C=C) ,. . ., 60 kcal/mo!]. Unfortunately, the experimental C=C bond energy for C 2F 4 remains quite uncertain, with values ranging from 53 to 76 kcal/mol. 1 - 3 In addition, the nature of the double bond in C 2F 4 has also been disputed: the importance of bent or "banana" bonds versus the conventional u and 7r bonds has not been addressed quantitatively, although a recent paper has suggested that bent bonds may be preferred in C 2F 2.4 In order to settle these issues, we carried out ab initio generalized valence bond with configuration interaction (GVBCI) calculations, utilizing a new approach in the CI expansion which systematical}y includes all correlations likely to change appreciably in the bond cleavage process. This correlation-conJiJtent CI (CCCI), so named to indicate that no biases are built into the wavefunctions of either reactant or product, truncates much more rapidly than traditional singles and doubles CI approaches, yet gives much more accurate results. 5 Table I provides a systematic study of the C 2F 4 bond strength as a function of electron correlation. 6 Hartree-Fock (variational M 0) theory predicts a direct bond energy of 59.4 kcal/mol, using ~EHF = 2 x EHF(1A 1 CF 2) - EHF(C 2F 4 ). This is close to our best estimate of 68.3 kcal/mo!, but only as an artifact of the incapability of HF theory to properly describe the singlet states of carbenes [e.g., ~EsT(CF2) = 32.5 kcal/mo! for HF, whereas the CCCI value is 57.5 kcal/mol 7 and the experimental value is 56.6 kcal/mol 8 ], leading to an artificially destabilized dissociation limit. Including singles and doubles CI (HF*S*D) leads to a bond 20 kcal/mol weaker than HF because it leads to a good description of singlet CF 2 but cannot remove all problems in the HF description of C 2F 4 , even though as many as 34,184 spin eigenfunctions are included in the CI calculation. The problem with HF*S*D i~ that the triple and quadruple excitations required to properly describe the fragments are not accounted for in the molecule, resulting iu a low bond energy. The GVB-CCCI method yields much more accurate bond energies (despite -78- using only one-tenth of the configurations), due to its correlation-consistent nature and emphasis on including the dominant correlations important for describing bond rupture. Indeed, with increasing amounts of correlation starting :from GVB-PP through RCI*[SDa- +SD"'+ Sva1], the bond energy smoothly converges to a value of 63.4 kcal/mol. Briefly, the GVB-CCCI method begins with the generalized valence bond wavefunction which allows the electrons in the breaking bond to each occupy their own orbital (rather than doubly-occupied as in restricted HF theory). Two sets of correlations are included in the CCCI: (i) full correlation of the electrons in the breaking bond (i.e., all single and double excitations to all unoccupied orbitals) and (ii) all single excitations :from all valence orbitals to allow for orbital shape changes which accompany bond scission as the :fragments relax. 5 CCCI calculations on ethylene5 lead to a residual correlation error of 4.9±2.5 kcal/mol in describing the double bond energy (Table I). Assuming the same error for C2F4 yields a final prediction of De(F2C=CF 2) = 68.3±2.5 kcal/mol. Using experimental values for the zero-point energies of C2F 4 (13.4 kcal/mol) and CF2 (4.3 kcal/mol), 9 along with the temperature correction (1.0 kcal/mol) to the bond energy of C2F 4 , 10 we calculate D 208 (C 2 F 4 ) = 64.5±2.5 kcal/mol. Of the three experimental values for D 298 (C 2F 4) listed in Table I, we can rule out the lowe11t value of 53.4±0. 7 kcal/mol, since the CCCI method provides a lower bound on the bond energy (electron correlation error is larger in the molecule than in the fragments). Our theoretical prediction agrees most closely to the intermediate value of 69:0±2.7 kcal/mol. 2 From our prediction of D 298 (C 2F 4) plus the experimental 6.Hr 129a(C2F4) = -157.4±0.7 kcal/mol, we derive 6.Hi 298 (CF 2 ) ' -46.5±1.6 kcal/mol, in good agreement with the most recent experimental value. This suggests that the 1977 value 1 of -52. kcal/mo! for the heat of formation of CF 2 is in error and that the 1981 value 2 of -44.2±1 kcal/mo! is correct. Recently, we reported a simple relationship between bond energies [D( C=C)] in substituted olefins or methanes and singlet-triplet excitation energies (6.EsT) in substituted carbenes. 11 We showed that trends in C=C bond strengths in halo- 79gena~ed olefins could be explained by considering only whether the CXY fragments comprising the olefin have singlet or triplet ground states. Diabatically breaking the er and 7r bonds in an olefin results in triplet fragments, but if the ground state of CXY is a singlet, the adiabatic bond energy is weaker by the electronic relaxation energy, !1.EsT. Assuming that the diabatic C=C bond energy (to dissociate to triplet fragments) is independent of substitution, we used experimental adiabatic olefin bond energies to estimate the !!_inglet-triplet splittings of substituted carbcnca. 11 In turn, we u:sed CCCI calcula.tiona of tl.EsT tu uLtu.i.11 m::w e:;timates of the adiabatic bond energies, D29a(C=C). 7 Since ethylene dissociates to triplet fragments adiabatically, these estimates were based on the assumption that the intrinaic olefin C=C bond strength is D 298 (H2 C=CH 2) = 172.2±2.1 kcal/mol. 10 As a quantitative test of this premise, we have calculated the intrinsic bond energies in ethylene and tetrafluoroethylene (Table I). The CCCI calculations yield intrinsic bond energies (to CX 2 ( 3 B 1 ) fragments] of De = 178.4 kcal/mo! for C2F 4 and De = 174.1 kcal/mol for C 2 H4. 5 Thus the assumption that the diabatic bond energy is independent of substitution is correct to 4.3 kcal/mol (23). When zero point energy and heat capacity corrections arc included 9•10 •12 to arrive at D 29 a for each olefin, the intrinsic bond energy for C 2F 4 is larger than for C 2 H4 by 6.9 kcal/mol. Thus the error in using the relationship between D(C=C) and !1.EsT as presented in ref 11 is 6.9 kcal/mol. Considering that the observed adiabatic bond strengths differ by more than 100 kcal/mo!, the change in the intrinsic bond strengths is very small. Recently there has been some concern whether the CC double bond in C2F 4 is better described as a sigma bond plus a pi bond or as two "banana" or bent bonds. 4 To address this issue, we calculated the relative energies of three C=C bonding configurations: (i) er and 7r C-C bonds; (ii) skewed u and 'lT' bonds wit.h no symmetry restrictions; and (iii) symmetric bent bonds. The one-electron GVB orbitals for (i)-(iii) are shown in fig 1. At the self-consistent GVB-PP level, all three descriptions are within 0.1 kcal/mol in energy, with the unsymmetrical wavefunction -80- (ii) lowest. When the four electrons involved in the C=C bond are allowed any occupation of the four bonding orbitals (GVB-CI), the three descriptions remain very close in energy (within 0.3 kcal/mol), but the u and 7r bond wavefunction prevails as the lowest energy structure. 1_3 Thus we believe that the double bond is best thought of in terms of the u and 7r bond description. In conclusion, we report an accurate ab initio theoretical prediction of the bond energy of C 2 F 4 [D 298 (C=C) CF2 (~Hj, 298 64.5±2.5 kcal/mol] and of the heat of formation of = -46.S ± 1.6 kcal/mol), using the newly-developed CCCI methods. The predicted bond energy helps distinguish between the large discrepancies in existing experimental values for D29 8 ( C2 F 4 ), ruling out one estimate ( 53.4 kcal/ mol) and strongly supporting the 69.0 kcal/mol value. Furthermore, intrinaic C=C bond energies are found to be nearly constant (within 7 kcal/mol), even though the observed bond strengths differ by up to "' 100 kcal/mol, supporting the previously proposed approach for estimating ~EsT( CXY) based on C=C bond weakening.11 Finally, we find thR.t the traditional picture of multiple bonds (er and 71" bonds) is correct for C 2 F 4. Acknowledgments. This wurk was supported by the National Science Foun- dation (Grant No. CHE83-18041) and the Shell Companies Foundation. EAC acknowledges a National Science Foundation predoctoral fellowship (1982-1985), a research grant award from the International Precious Metals Institute and Gemini Industries (1985-1986), and a SOHIO fellowship in Catalysis (1987). We also thank M. H. McAdon for help with the convergence of the skewed u and 7r bond wavefunction. -81- References (1) An indirect determination of D(F 2C=CF2) from the heat of formation of C2F 4 (LlH~, 298 = -157.4±0.7 kcal/mol) and a 1977 experimental value for LlH.f, 298 (CF2) = -52. kcal/mol (Lias, S. G.; Liebman, J. F.; Levin, R. D. J. Phy3. Chem. Ref. Data 1984, 19, 695) yields D 298 = 53.4±0.7 kcal/mol. (2) Using another (more recent) determination of LlH/, 298 (CF2) = -44.2±1 kcal/mol (Berman, D.; Bomse, D. S.; Beauchamp, J. L. Int. J. Ma33 Spec. Ion PhyJ. 1981, 99, 263) yields D2 98 = 69.0±2.7 kcal/mol. (3) This value constitutes the only directly determined bond energy (D2 98 = 76.3±3 kcal/mol) for C2F 4 in a Knudsen cell equilibrium study at high temperature (""' 1200°K) by Zmbov, K. F.; Uy, 0. M.; Margrave, J. L. J . ..4.m. Chem. Soc. 1968, 90, 5090. (4) Messmer, R. P.; Schultz, P.A. Phy3, Rev. Lett. 19~6, 57, 2653. (5) Carter, E. A.; Goddard III, W. A. Chem. Phy3. Lett., submitted for publication. (6) The Dunning valence double-( contraction (Dunning, Jr., T. H.J. Chem. PhyJ. 1970, 59, 2823) of the Huzinaga (9s5p) gaussian bases for carbon and fluorine (Huzinaga, S. J. Chem. Phy•. 1065, .j!l, 1293) were used, with one set of carte sian 3d polarization functions added to the carbon basis [(d= 0.64; optimized fur CH4 by R. A. Bair and W. A. Goddard III (submitted for publication)], with the 3s combination omitted. The experimental geometry of C2F 4 was taken from the "Landolt-Bornstein Tables"; Springer: Berlin, 1976; Vol. 7. (7) Carter, E. A.; Goddard III, W. A. J. Chem. PhyJ., submitted for publication. (8) a) Koda., S. Chem. PhyJ. Lett. 1978, 55, 353; b) idem, Chem. PhyJ. 1982, 66, 383. (9) a) Shimanouchi, T. Tables of Molecular Vibrational Frequencies, Natl. Stand. Ref. Data Ser., Nat. Bur. Stand. 1972, 1; b) Jacox, M. E. J. Phy3. Chem. Ref. Data 1984, 13, 945. -82(10) a) JANAF Thermochemical Tables, Natl. Stand. Ref. Data Ser., Nat. Bur. Stand. 1971, 37; b) JANAF Thermochemical Tables, 1982 Supplement, J. Phy3. Chem. Ref. Data 1982, 11, 695. (11) Carter, E. A.; Goddard III, W. A. J. Phy3. Chem. 1986, 90, 998. (12) Zero point energies for CF 2 were taken from ref 9b (4.3 kcal/mol) for the 1 A 1 state, while the zero point motion of the 3 B 1 state was estimated ( 4.1±0.1 kcal/mo!) from the frequency shifts in C2D49 a going to CD 2 (Bunker, P. R.; Jensen, P.; Kraemer, W. P.; Beardsworth, R. J. Chem. Phya. 1086, 85, 3724) and the frequencies in C2F4. This leads to T 0 (CF 2 ) = 57.3±0.1 kcal/mol (6.EsT = Te(CF2) = 57.5 kcal/mol]. (13) The calculations on FC::::CF (ref 4), which find bent bonds ""'2 kcal/mol lower than 177r bonds, did not go beyond the GVB-PP description. Table I. C::=C Bond Energies (De) in kcal/mol for F 2 C=CF2.• total energies (hartrees) D~iab(F2C=CF2Y calculation FzC=CF 2 ( 1 Ai) CF2 ( 3 Bi)~ HF -473.49255 (1/1) -474.07613 (18772/34184) -236.64724 (1/1) -236.92980 (3155/16053) 124.3 GVB-PP -473.53219 (4/4) -236.64724 (1/1) GVB-RCI -473.54868 (5/6) -473.58045 (941/1724) -473.57245 (849/1098) HF*S*D RCI*S,....1 RCI*[SD.,. + SD,,.) CCCI• D:diab + A~orr Dz9s 1 Experiment (D29s) -473.59909 (1719 /2728) .. -236.65739 (63/157) -236.€4724 (1/1) -236.65739 {63/157) De(H2C=CH2)" D!fab(F2C=CF2) directe using AEsTJ 122.2 59.4 9.3 135.9 153.7 39.1 20.9 149.2 146.1 34.2 159.5 15!.6 44.5 1667 163.4 51.7 174.4 16!U 59.4 I co Vl I 178.4 17U 63.4 68.3±2.5 64.5±2.5 53.4±0. 7/ 69.0±2. 7' "76.3±31 a) VDZD basis on C and VDZ basis on F. See ref 5 for details of the calculations. The corresponding number of spatial configurations/spin eigenfunctions for each wavefunction are given beneath each total energy. h) Total energies for CF 2 are for the appropriate limit at R(C-C) = oo, i.e., HF or HF*S,....1. c) D~iab(F 2 C=CF 2 ) = 2xE( 3 B 1 CF 2 ) - E(C 2F 4). d) Included for comparison to D~iab(F 2 C=CF 2 ) to indicate convergence [D:xpt (H 2 C:::CH 2 ) = 179.0±2.5 kcal/mol]; ref 5. f) Direct De(F 2C=CF 2) from 2xE( 1 A 1 CF2) - E(C2F4) where the HF and HF*S*D total energies of 1 A 1 CF 2 are -236.69898 and -237.00693 hartrees (263:J spatial configurations/4399 spin eigenfunctions). J) D:'1iab(F2C=CF 2 ) = D~iab[F 2 C::=CF 2 ) - 2xAEsT, where AEsT = 57.5 kcal/mol (ref 7). g) RCI*[SD.,. +SD,,. + SvaJ). h) Acorr = 4.9 kcal/mol is the corre'.ation error inherent to the CCCI method for double bonds (obta'.ned from n:xpt - D;a1c:::::: 179.0±2.fi - 174.1 == 4.9±2.5 kcal/mol for C 2H 4); see ref 5. i) The predicted D, is converte:i to D 29 ~ by using the temperature and zero point energy corrections fo1 C 2 F 4 from refs 9 and 10. j) ref 1. k) ref 2. l) ref 3. -84- Figu,re Caption Fig. 1. The GVB(2/4)PP one-electron orbitals of the C=C bond in C 2 F 4 are shown for (i) (symmetry-constrained) er and 7r bonds, EPP(2/ 4 ) EcvB-CI(:i/ 4 ) = -473.53219 hartrees, -473.54944 hartrees; (ii) skewed <rand 71' bonds (no symmetry c.on- straints), Epp(2/ 4 ) = -473.53242 hartrees, Eovs-c1( 2 ; 4 ) = -473.54899 hartrees; and (iii) symmetric bent or "ba.na.na" bonds, EPP(2/4) EovB-CI( 2 ; 4 ) -473.53226 hartrees, = -473.54924 hartrees. Contours are plotted from -0.5 to +0.5 a.u., with increments every 0.05 a.u. -85- ~O:AIRI ~ ~ ~E SYMMETRIC r;;AND 7T B~ (i l F,'cv '"~ v o<3--E:>o C'~..-·· \ J ,,,~~"""''' . ----- .. ~~F ~ , '''::',.'; .... ,,,.. ... \ I - \ \ ~...1-; I I ' ...,' ........... ~, -. -. ""..- I .... ... ----, ,, ONE ONE • : • · IPAIRI • ; • : ONE •• -- SKEWED r;;AND7T~ \ F (iil '°'c ~ c.;"" F F1~~F ', I .. _,, .. .._•,.. I I ONE ONE ~ ~NE .~ \ - I ..... I ., I (iii) ONE Figure 1. ONE -86- Chapter 2 Fundamental Studies of Transition Metal-Ligand Bonding 87- Chapter 2.A. The text of this section is an Article coauthored with William A. Goddard III which appeared in the Journal of Phy&ical Chemi&try. -88- Reprinted from The Journal of Physical Chemistry, 1984, 88, 1485. Copyright© 1984 by the American Chemical Society and reprinted by permission of the copyright owner. The Chromium Methylldene Cation: CrCH 2+ Emily A. Cartert and William A. Goddard III* Arthur Amos Noyes Laboratory of Chemical Physics, I California Institute of Technology. Pasadena, California 91125 (Received: October 26, 1983) We have examined the electronic structure and bonding characteristics of the experimentally observed cation CrCH 2+. We find a 48 1 ground state with a covalent double bond between 6S Cr+ and 38 1 CH 2• These results are in contrast to previous theoretical studies which found a lowest state with 68 1 symmetry and a single Cr-C bond. We calculate a direct bond energy of 44 kcal/mol and estimate the fully correlated limit to be 49 kcal/mot, which may be compared with the experimental value of 65 :I: 7 kcal/mo! and the previous theoretical results of 18.3 and 22.3 kcal/mo!. The differences in results between the two theoretical studies on CrCHt are discussed. lotroducdoo Although the bonding and thermodynamic properties of organic molecules are reasonably well understood, little reliable thermochemical information is available for organo-transition·metal complexes. Metah:arbon bond streniths arc of particular interest because of the possible role of metal-alkyl, metahlkylidene. and metal-alkylidyne intermediates in the mechanisms of both homogeneous and heterogeneous reactions, e.g., the elucidation of the mechanisms of reductive polymerization of CO by H 2 (Fischer Tropsch synth<:11ia of hydrocarbons), olefin metathesis polymerization of olefins, and many other industrially important catalytic processes. In the past few years, advances in both theoretical and ex· perimental characterization of metal-carbon species have been attained. GVB calculations of bond energies for several transition-metal alkylidene complexes led to bond strengths of 48-86 kcal/mol. 1•2 Experimental bond dissociation energies for gasphase, first-row transition-metal-methylene positive ions, ranging in value from 65 :I: 7 to 96 :I: 5 kcal/mo!, have been determined by Buuchamp and co-worken.l Schaefer and c0-workers have by early transition-metal alkylidene complexes, Ziegler-N atta (I) Rap¢, A. K.; Goddard Ill, W. A. J. Am. Chtm. Soc. 1982, 104, 448. 'National Science Foundation Predoctoral Fellow, 1982-85. !Contribution No. 69l6. 0022-3654/84/2088-1485$01.50/0 (2) Caner, E. A.; Goddard III, W. A. Organometallics, submitted for publication. © 1984 American Chemical Society -89- J4S6 The Jounu:il of Physical Chemistry, Vol. 88, No. 8, 1984 Carter and Goddard Vibrational Frequencies (cm-') for •a 1316 1336 Figure J. Equilibrium geometrics for 'B 1 CrCH,+ and 6 8 1 CrCHt. GVB •s, ONE a Frt:4ut:m.:it::s an: L'.a.lL:ulatcll from Llit: harmuuil.: furL:t: l.:onslall l~ obtained from spline fits to (RCl*S>va1ence calculations. character, as indicated in Figure I. Thus the ground state has a Cr-C double bond with orbitals as shown in Figure 2. Each bond pair is quite covalent, involving one electron in an orbital localized on Cr and one electron in an orbital localized on C. Analyzing the orbital character in the Cr u bond 5 indicates that although the available a orbital in the ground state of Cr+ [(3d)l] j~ rl,,-, the r'r "llrhit"l nf tht' rr-r" hnnrl i< 479?. 4<p "nrl 'ii% 3d. The reason for the large amount of s character in the ir bond is analyzed below. As would be expected from these descriptions, we find Ci.. symmetry (stable with respect to both in-plane and out-of-plane distortions) in the equilibrium geometry for the 11rounu ~t.a\c. ol Cr-C <>BONO _,,..----....., ONE ·-~,! ' ', '•·',': I bl Cr-C "'BOND Flpre l. GVB orbitat. for 4 B, CrCH,+ at ilo oqvilibrium geometry: (a) GVB orbitals for the Cr-C a bond; (b) GVB orbitals for the Cr-C .. bond. Long dashes indicate zero amplitude; the spacing between contours is 0.05 au. The same convention is used in all plots. carried out Hartree-Fock and configuration interaction calculations on two of the metal-methylene cations observed by Beauchamp, CrCHt and MnCHt.• However, the calculations lead to a bond energy of 18.3 kcal/mo! for CrCHt, whereas Beauchamp's result is 65 :t: 7 kcal/mo! for CrCH 2+. (Similarly, for MnCH 2+,theory and experiment yield 36.0 and 94 :t: 7 kcal/mo!, respectively.) The current study was undertaken partly to resolve this large disagreement in bond energies and partly to elucidate the nature of metal-carbon double bonds. Results and Discussion Orbitals, Geometry, and Vibrational Frequencies for the Ground State (4B 1). Starting with the ground state of Cr+, (3d)l or 68, with its five singly occupied orbitals and the ground state (38 1) of CH 2 with its two singly occupied orbitals (11,,..), we might The geometry for this state is given in Figure I where we see that the HCH bond angle is identical with that in ethylene ( 117 .6°). The calculated Cr=C bond length ( 1.91 A) cannot be directly compared with experiment since no chromium-alkylidene complexes have been structurally characterized. The Cr-C bond length may be compared with theoretical values for MnCH 2+ [R(Mn-C) = 2.01 A.] and FeCH 2+ [R(Fe=C) 1.96 AJ. 6 The Mn-C bond is substantially longer than the Cr-C bond be<:ause Mn(I) bonds to CH, in its (4s)'(3d)l ground state, using the larger 4s orbital to make the u bond and a 3d orbital to make the,.. bond, whereas the u bond in CrCH2 + is only 47% sp and hence is much smaller than in MnCH/. For the same reason, a Cr°==CH 2 (s 1d5 Cr) would have a much longer bond (the u bond would Involve firirnarily the 4s orbital on Cr) than our Cr'=CH 2, whereas a Cr 1-<::H 2 (d 4 Cr2+) complex should have a much shorter bond (since the u bond would involve a pure Cr 3d orbital). The vibrational frequencies for both the 48 1 ground state and the 68 1 excited state are listed in Table I. To our knowledge, no experimental metal-carbon double bond vibrational frequencies have been reported; however, these values (542 and 495 cm· 1) can be compared with calculations on ClRuH(CH 2), where the Ru-C stretching frequencies were calculated to be 746 and 798 cm· 1 for the two states cxamined. 2 Given the much stronger bond strength in the Ru complex (91 kcal) compared with the Cr system (49 kcal), coupled with similar M-C distances, leads to the prediction of a higher vibrational frequency in the Ru system, as observed. The C-H stretching frequencies (3339 and 3.336 cm- 1) are a bit high when compared with the C-H stretch in CH 2=CH2 (3056 cm·1). However, Schaefer has noted that theoretical X-H vibrational frequencies are generally high by 10%. 7 The H-C-H scissors mode (1316 and 1336 cm- 1) is similar to the value for the same mode in ethylene (1393 cm-1), as expected for an H-C-H bend of an sp 2·hybridized center. The Sextet Excited State (6B1). As discussed below, the sextet ground state of Cr+ results from the large number of (negative) exchange interactions engendered by this high spin state (the basis of Hund's rule). Spin pai~ing of the CH, and Cr+ orbitals bas expect to find a double bond by simply spin pairing the Cr dr orbital with the CH 2 u orbital and the Cr d,, orbital with the CH 2 ,.. orbital. Indeed, we find the ground state to have exactly this (3) Armentrout, P. B.; Halle, L. f.; Beauchamp, J. L. J. Am. Chem. Soc. 1981, 103, 6501. (4) Vincent. M.A.: Yoshioka. Y.: Schaefer Ill. H. f. J. Phvs. Cktm. 1982. 86, 3905. the effect of decreasing this exchange stabilization, and thus for sufficiently small overlap, bond pairing will not be able to overcome the spin stabilization. Thus we find a low-lying excited state consisting of a u bond (CH 2 u with Cr ct,.,) but no ir bond. In thlS case the CH 2 ,.. orbital is coupled high spin With the remaining four Cr d orbitals to yield an S = 5/2 or sextet state (68 1). The geometry for the 6B 1 state is shown in Figure J. The Cr-C bond length has increased from 1.91 to 2.07 A, as expected from the (5) Analyses of orbital character in the GVB orbitals arc carried out by summing over Mulliken populations for the first and second NO's of each GVB pair. (6) Brusich, M. J.; Goddard Ill, W. A., to be submitted for publication. (7) Schaefer Ill, H. f. "The Electronic Structure of Atoms and Molecules": Addi&0n-Wesley: Reading, MA, 1972. -90The Journal of Physical Chemistry, Vol. 88, No. 8, 1984 The Chromium Methylidene Cation 4 B, CrcH; : LOSS OF GVB EXCHANGE UPON 1487 BONDING er"'" (s'a... J •s, I rf:.;.' \1(« \.Y-1')~ Cr·C"' BONO; pure Cr 4soCr·C .. BONO: pure Cr 3d" ONE \ ~ \+ ·.:.' ..• c ~ .; 4$0' ( Cr·C<TBOND: pure Cr 3d<r Cr· C" BOND : pure Cr 3d" 9:'h:: r2 4SO' 1/2 3d<r z ol Cr-C er BONO 3dY1 r 2 112 I ONF ONF + + 3d8... ,. + ·-~-'---bl Cr-C TRIPLET rr PAIR f1s11R 3. OVB urbital> fur •5 1 CrCHt at ii• equilibrium geometry: (a) GVB orbitals for the cr-c 11 bond; (b) GVB orbitals for the Cr-C,.. bond. TABLE II: d-d arid s-d Exchange Integrals" for Cl" (kcal/mot) 3dw, 3d8., 3d8,•.,a •s (d'l 'D (s 1 d•) 5.0 16.5 18.4 a Averaged over the various d orbitals. repulsion induced by triplet coupling of tbe 1f electron pair. The C-H bond length and the H-C-H angle are approximately the same for both states, indicating that the hybridization of the carbon orbitals has not changed. We find C,. symmetry for the equilibrium geometry of the 68 1 state, again stable with respect to in-plane and out-of-plane distortions. The cr-c bonding orbitals for the sextet state are shown in Figure 3. Again, the cr-c u bond is quite covalent, with one electron in a Cr d orbital and one electron in a C sp hybrid orbital. The triplet-coupled 1f orbitals of the sextet state look similar to the 1f pair in the quartet state, except that the triplet 1f orbitals must get orthogonal to one another, as evidenced from the node around Cr built into the carbon P1f orbital. Exchange Coupltngs. Before proceeding, 1t 1s appropriate to be a bit more explicit about the role of exchange interactions in Cr+ and CrCH 2+. Cr+ bas a high-spin, (3d)s, 6S ground state and a high-spin, (4s) 1(3d) 4, 60 first excited state which lies 1.52 eV (35. I kcal/mo! hil!her in energy. 8 The 6S state is lower than the 60 state because the magnitude of the exchange terms is larger for the high-spin ds case. The 6S state bas ten d-d exchange terms (K.,.i) between the five d electrons, whereas the 60 bas six K.,.i and four K..i terms between the four d electrons and the s electron. £ ..(d5) = -lOK.,.i £ ..(s 1d 4) • -i>Kdd - 4K..i The d-d exchange terms are larger than the s-d exchange terms ( <itt Table II), leo.ding to a lo.rger overall exchange energy con- tribution in the 6S state. Using the average d-d and d-s exchange terms from Table II, we can now predict the nature of the bonding in CrCH 2+, Indeed, analyzing the differential loss of exchange terms (sec Figure 4) expected upon bonding CH 2 to Cr+ in either the (3d) 5 ground state or the (4s) 1(3d) 4 excited state allows a prediction of the fraction (8) Moono, C. E. Natl. Stand. R.ef Dala S«:., Natl. Bur. Stand. 1971, No. + + + Kdd -6 -4.5 +1.5 -10 -6.5 +3.5 K•o -4 -2 +2 0 0 0 K7t+::: Number of exchange terms (Kddand Ksdl for Cr+ before bonding to CH 2 K~,· = Number of exchange terms ( Kdd ond K,d J for er+ nftPr state 35, Vol. 2, p 10. 3d .., 3d8., hnnrtinq tn Cl-lz .O.Kcr+ lJ Differential loss of uchonge for Cr+ upon bonding to CH . 2 Figure 4. Diagram depicting the origin of the differential loss of exchange upon bonding CH 2 to a 4sa/3d1f combination or to a 3du/3d .. combination on Cr. TABLE III: Excitation Energies for AE'· (48 1 ). no. r.onfig/ calcula lions GVB-PP GVB-RCI (GVB-RCl*S lvalence RCI,,*D 0 +RCI 0 •D,, +(RC!• S lva1ence no. SEF 0 ('8 1 ), no. ('B,- r.nnftg/ •R,), e..round no. SEF kcal state -53.7 -1 J.3 +12.5 +18.0 1415/8928 482/2146 +19.0 •B, a The geometries used were the optimum values calculated at the (GVB-RCl*Slva1ence level. 0 no. config =number of spatial configurations. SEF = spin eigenfunctions. of 4s and 3d character in the Cr-C u bond. Pairing the orbitals of Cr+ and CH 2 into a simple, doubly bonded 48 1 state for CrCH 2+ leads to a loss of favorable (negative) exchange terms due to spin pairing in the bond. 9 If both the Cr-C bonds are to Cr d orbitals, 3.5Kdd are lost upon bonding (57 .8 kcal/mo!). If the u bond involves the Cr 4s orbital instead of a 3d orbital, l .5Kdd and 2K.i are lost (27.6 kcal/mo!). Thus it is intrinsically (30.2 kcal/mo!) more favorable to bond methylene to one Cr s orbital and one Cr d orbital than to two Cr d orbitals. However, the excitation energy to the (4s) 1(3d) 4 state of Cr+ is 33.9 kcal/mol. 10 Thus one expects an almost 50 / 50 mix of s and d (instead of pure d) in the 11 orbital, ao ob><;;rvc:d. 6B - 4B State Splitting: The Importance of Correlation. The 1 1 energy difference between the sextet state and the quartet state (9) Th.is simple analysis is true only for perfect singlet pairing in each bond If we include other spin-coupling terms (e.g., in an RC! wave function), we gain back some of the exchange energy we lose by singlet pairing each bond pair, complicating the hybridization analysis. (10) Our calculations on Cr+ lead to 33.9 kcal/mol as the state split1ing for Cr+(d 1)-Cr+(s 1d'). The experimental re.ult is 35.1 kcal/mo!, averaged over total angular momentum st.ates. See ref 8 -91- 1488 The Journal of Physical Chemistry, Vol. 88, No. 8, 1984 as a function of the level of electron correlation is given in Table III. Note that Hartrce-Fock prefers the 6 B1 state by 54 kcal, whereas the basic GVB description (GVB-RCI, including the spin-coupling configurations) leads to a 'B 1 ground state by 12.5 kcal. The highest level calculated leads to a 'B 1 ground state by J9.0 kcal. Why is there such a dramatic effect of electron correlation upon the stability of these spin states? In Brooks and Schaefer's previous work on MnCH 2, 11 Hund's rules were assumed valid for these systems, which would then suggest a sextet ground state for CrCH 2+. However, Hund's rules only apply in cases of mutually orthogonal orbitals, where the exchange terms necessarily favor a high-spin ground state. For orbitals that overlap, one-electron terms generally dominate exchange terms, so that low-spin ground states are expected. Thus the 'B 1 state is the expected ground state for CrCH 2+. Why does Hartree-Fock theory not lead to the correct ground state? The reason is that Hartree--Fock cannot describe the doubly bonded state properly. This state involves a ... bond with low overlap (Ser-<:• 0.33), whereas in Hartrc:e-Fock the two orbitals in the bond pair must have unit overlap. To resolve this conflict, the optimum Hartrc:e-Fock orbitals become very ionic (... electrons on the metal; u electrons on the CH 2) so as to be consistent with the doubly occupied orbitals. This charge separation is highly = o"".HJ+ ~ QCr00c'' 6- [ + v ~+ @'H - unfavorable, forcing the Hanrce-Fock. 'B 1 state very high in energy. On the other band, for the 68 1 state, triplet pairing of the Cr 1f, and C ..., electrons forces these "' electrons to be in separate, mutually orthogonal orbitals. To whatever the CH 2 "'. ond Cr ..... otnmi<' nrbital• overlap, th4're will be an antibonding interaction. However, for +cr--CH 2 this overlap is small so that Hartrc:e-Fock predicts a high-spin ground state, with a single Cr-C u bond. In the GVB wave function, we allow the two orbitals of each pair to have their optimum overlap, removing the restriction that causes Hartrce-Fock to yield an ionic description of the "' bond for the 'B 1 state. For a purely covalent bond, the GVB wave function would have the form it= Ir+ rl, eitccpt that the GVB wave function allow I and r to have whatever shape minimizes the energy of the wave function. 1/IHF = If>,</>. 1/1.,,.m, = q,,q,, + ¢r'P1 ij!<GVB - <P.<J>;, "I" <J>o<Pa Generally the optimum wave function is about -90% covalent and -10% ionic. In the GVB wave function for a double bond, there arc two possible spin couplings (VB structures) that should be optimized along with the orbitals. However, for computational convenience, we generally optimize the orbitals only for one structure (perfect pairing), leading to the GVB-PP wave function. These spin coupling terms are then included by a CI in which the two electrons in each pair arc allowed to have all three possible occupations of the two orbitals for that pair. This wave function, the GVB-RCI, has nine spatial configurations for a double bond. In addition to the GVB spin coupling, this wave function allows for interpair correlation and atomic high-spin coupling. The interpair correlation allow• for c.orrelattd movement of electron• in one pair to one side of a bond, while electrons in another pair move to the other side of a bond, for an overall covalent structure: ( l l) Brooks. B. R.; Schaefer Ill. H. F. Mo/. Phys. 197'1, J<f, 193. Carter and Goddard TABLE IV: Cr-C Bond Energies (kcal/mo!) of CrCH, • •s, calculation HF GVB(2/4)-PP GVB-RCI RCl,,•D 0 + RCla*D,, (RCl*S)v.1 • ., •• RCJ,,*D0 + RCJ 0 *D,, + (RCl*S>valence •e. state state total ~nergy. bond hartree energy 'B, B1 state state tot.al energy. hartree bond 6 en erg.~ -I 080.829 94 -60.9 -I 080.91549 -I 080.91549 -7.2 -I 080.933 53 -I 080.956 I 8 +] 8.3 - I 080.936 22 -I 080.983 98 +35.8 - 7.2 +4 I +5.8 -l 081.00043 -I 081.00868 +38.8 -1 080.97167 +?OR +44.0 -I 080.978 39 +25.0 The RCI wave function allows the Cr d electrons in hon<i peir< to gain back some of the exchange energy they have lost in bonding by including the atomic high-spin coupling. These spin-coupling effects are expected to be more important for the 'B 1 state than for the 68 1 state, since more exchange terms are lost by bond pairing two Cr orbitals to CH 2 to form a double bond instead of a single bond. The 68 1 state gains little back from atomic high-spin coupling since it already has five electrons high-spin coupled. Thus the major element that brings about the inversion of ground states is including optimal spin coupling in the GVB wave function. Allowing Cr to have both favorable exchange interactions as well as favorable bonding interactions results in the doubly bonded 48 1 ground state for CrCH 2+. Bond Energies. Calculating the Cr-<: bond strength dissociation oon<i•ll!'ntlyll (vide infra) lead• to a direct b<>nd energy of 44.0 kcal/mol for 'B 1 CrCH/, dissociating into ground-state fragments, 6S Cr+ and 3B1 CH 2• An indication of the importance of electron correlation in transition-metal systems is exhibited in Table IV. As the level electron correlation accounted for in"rCi:lliCI,..., t.11.>Cl> the bond energy, as expected when a more accurate description of the bound molecule is obtained. All bond energies for CrCH 2+ are calculated in a ~dissociation-consistent" manner. This means that we calculate a wave function at R.(Cr--C) which smoothly dissociates to the proper covalent limits at R(Cr--C) = 00 , retaining the same description of electron correlation in the wave function for R = 00 that existed for R.. Thus our bond energies are said to be "dissociation-consistent". Such dissociation consistent wave function• ohould be cJ1pc<;tc<l to yield bond energies that are too small, although the bond energies will increase as the level of electron correlation is increased. In order to ei;timate the role of reduced correlation energy at our best level of calculation, we will compare the results of the same calcutauonal level on a known bond energy of CH 2, namely, in H 2C=CH 2• The results for various levels of dissociationconsistent calculations on ethylene (using the same bases as for CrCH 2+) arc shown in Table V. Using the same basis set for carbon and hydrogen as was used for the CrCH 2+ calculations (vide infra) and the same level of dissociation-consis,\ent CJ leads to a direct bond energy for CH 2=CH 1 of D. = 175.4 kcal/mol as compared with the experimental value of 180.0 kcal/mol. This 4.6 lccal/mol of residual correlation energy for CH 2=CH, is e~pected to be a lower bound on the residual error in our calculation of the CrCHt bond energy (since Cr may have additional correlation errors from the other Cr d orbitals). Thus. our best (probably,conscrvative) estimate for the bond energy for CrCH: + is D, = 4j.6 kcal/mol. . Comparisons with Previous Theoretical Studies Vincent et 6 al.' carried out Hanree-Fock calculations on the B1 state, leadmg to an optimum geometry with Rc,-c = 2.064 A and OH-c-H = l 13.5°, whereas using correlated wave functions we find Rcr·<= 1.91 A and llH-<:-H = 117.6° for the 'B, state and Rcr-<. = 2.07 A and OH-C·H = I 18.3° for the 6B1 state. The smaller OH c-H in the Hartrcc-Fock geometry is indicative of a larger amount of (12) Bair, R A.; Goddard Ill, W. A. J. Phys. Chern .. submitted for publication. See Bair. R. A. Ph.D. Thesis, California lnst1tute of Technology. June 1981. -921489 The Journal of Physical Chemistry, Vol. 88. No. 8, 1984 The Chromium Methylidene Cation for Ethylene (kcal/mo!) no. VDZd 0 calculation HF GVf!(2/4l-PP G\iB·RCli4 l (GVB-RCI *Slvalence D11 *RCI 0 + D0 ' RClrr + (RCI *Slvalence ex pt -78.011 30 -78.051 39 -78.066 J -78.096 61 -78.10180 s -78.040 81d - 78.079 57" -78.092 -78.130 16d -78.14801. I /I 4/4 soa 5/6 167/292 367/544 VDZd VOZ VDZd 1/I 4/4 5/6 263/460 75911096 115.7 140.8 150.3 160.2 163.4 J 22.8d 141.0• J 55.3d 164.2d l 754• 180.0' a Given for CH,=CH, only I> VDZ =valence double~ bases for C and H. Reference 18. c VDZd = VDZ + one set of Cd polarization functions d Reference 6 •This work. Reference 19. f "JAN AF Thermochemical Tables". Natl. Stand. Ref. Data Sec., Natl. Bur. Stand. 1970. No. 37. TABLE VI: Davidson's Correction for 'B, and 6 8 1 CrCH/ state limit of CJ" no. config/SEF total energy, hartree 'B, 'B, 'B, doubles quadruples unlimited doubles quadruplesb 502/2197 1373/8829 1415/8928 320/1699 482/2146 -1 080.984 89 -1 081.00861 -1 081.008 68 -1 080.977 70 -1080.97839 'B, 'B, quadruples contnbn, kcal/mo! Davidson's cor, kcal/mo! 12. l 14.9 2.2 0.4 • The "unlimited" CI is our dissociation-consistent D,,•RCl 0 + D0 •RC!Tr + (RCI *Slvalence· Titis CI is then limited to doubles or quadrub "Quadruples" is the same as the unlimited CI in this orbital space. ples. 'A 1 character in the CH 2 pan of the: wave: function (tr""~ 104°) as opposed to 3B1 character (8"1" = 133°). At the optimum Hartree-Fock geometry, Vincent et al. carried out a singles and doubles CI (SD-Cl) calculation leading to a bond enerRY of 18.3 kcal/mol. Including Davidson's correction 13 for quadruple excitations yielded a bond energy of 22.3 kcal/mo!. Since Davidson's all"l"eCtion is only an estimate, we decided to test the calculation of the quadruples correction by carrying out our best level of calculation restricted first to doubles and then to ~' 's, I ~Vi~{· "{!~~.... i' quadruples to directly calculate the conelation energy gain...:! by including excitations up to quadruples. The results are shown in Table VI. Davidson's correction was also calculated from the formula. ti.E.Q = (I - C02)ti.E. 0 (where C0 refers to the Cl coef· ficient for the dominant configuration in the singles and doubles CI calculation, tlEo is the difference In total energies of the SCf' wave function-in this case a GVB-PP wave function-and the singles and doubles Cl wave function, and ti.E.Q is the estimated difference in the total energies of the SD-CI wave function and the wave function that includes up throuRh Quadruple excitations). By knowing C0 and ti.Er» we have calculated ti.E.Q for comparison with the ab initio ~Davidson's correction". The results show that Davidson's formula underestimates the amount of correlation for low-spin states and O\lercstimates the correlation error for high-spin state<1. Thus, the Vinunt et al. ostimato of tho bond energy in 6 B 1 CrCH/ may be slightly high, due to an overestimate of Davidson's correction. Perhaps a more accurate estimate of their bond energy would be 18.3 (SD-CI result)+ 0.4 18.7 kcal/mo!. Vincent et al. also carried out Hartree-Fock calculations on the 4 H 1 state; however, the •0 1 state is not bound in this description. The major problem here is that the Hartree-Fock description of the 4B 1 state is extremely high in energy (54 lc.cal above 6B1) with quite distorted orbitals (sec Figure 5). The Hartree-Fock q MO is localized primarily on the CH 2 ligand. while the Hartree-Fock r MO is localized primarily on Cr, with a small amount of delocalization onto the CH 2 ligand. Thus the Hartree-Fock description is not a covalent description where each bond has one electron localized near each nucleus. Even with HFSD-CI. the 4 8 1 state is not bound. Thus double excitations are not sufficient both to change the shape of the orbitals and to include correlation effects. Starting with a Hartree-Fock wave function, we should include at least triple excitations and preferably quadruple excitations in order to get a description comparable to GVB. The strength of the GVB approach is that the correlation effects are = ( 13) (a) Davidson, E. R. In "The World of Quantum Chemistry"; Daudel, R.; Pullman. B.: Eds.: Reidel: Dordrecht, Holland, 1974: p 17. (b) Langhoft, S. R.: Davidson, E. R. Int. J. Quant. Chtm. 197<1, 8. 61. \ TW() I J rwn r~~-;> b) Cr-C ..,.,MO al Cr-C er MO Hartree-Fock orbitals for 4 8 1 CrCHt at its equilibrium geometry: (a) the Cr-<:: a bond: (b) the Cr-<:: r bond. Fiaur~ 5. included self-consistently so that the orbital shapes are optimum for various electron correlation terms. This allows a small CI to obtain a high-Quality result. Comparison with ExperimenJ. Experimental bond energies for metal-carbon doubly bonded species have only recently become available through the ion beam studies by Beauchamp and coworkers. 3 The bond energies were determined from measuring the reaction cross section for the reaction of CH,==CH, with first-row transition-metal ions. M+ + CH 2=CH 2 - MCH/ + CH 2 Although these values are for isolated gas-phase ions, they have provided the only clue into a thermochemical description of solution organometallic chemistry. Beauchamp and co-workers have determined M=CHt bond strengths for Cr'" through Ni+ that range from 65 to 96 kcal/mo!, with D(Cr=C) = 65:: 7 kcal/mo!. The weak point of the ion beam technique is lack of structural information. It is not possible to decide between two isomeric structures. Our results suggest a weaker bond energy ( 49 kcal) for cr+==CH 2; however, it is conceivable that another isomer could have a stronger bond. As mentioned previously, there are no examples of structurally characterized chromium-alkylidene complexes with which to compare. Fischer has characterized chromium singlet carbene complexes with typical Cr-C bond lengths of 2.~ 2.15 A, 14 ,,..... OR (0C) 5 Cr <-0 C ......._ ~R' (14) Fischer, E. 0. Purt Appl. Chtm. 1972, JO. 353. -93t-490 Carter and Goddard The Journal of Physical Chemistry. Vol. 88, No. 8. 1984 somewhat longer than the results presented above. However, since Fischer carbcnes have a single dative bond from a doubly occupied 17 orbital on the carbcnc ligand, they are expected to nave longer bonds than those found for doubly bonded Cr-C systems. Most known metal-alkylidcne complexes are found among third-row tranSition metals. Two examples of third-row, terminal al.kylidcnc 5-C,H,) with complexes are Schrock's Cp,Ta(CH,)CH, (Cp a Ta-CH 2 bond length of 2.03 A1l and W(O)(CHCMe3)(PEtJ)Cl2 with a W-CH 2 bond length of 1.88 A.1 6 Both systems are cxperu.d to have M-CH 2 double bonds with primarily d character in the 11 bond. As a result. the W-C bond is shorter than our Cr-=C bond! . Summary. We find that the ground state of CrCH 2+ consists of a covalent Cr-C double bond, where the Cr-C u bond has nearly equal parts 4s and 3d character. The hybridization and nature of the ground state has been explained in terms of differential changes in exchange terms, Kdd and Ktd· The •5 1-'8 1 energy difference as a function of correlation has been discussed. In addition, we find a direct bond energy of 44 kcal and an estimated bond energy of 48.6 kcal/mol, in fair agreement with experiment, 65 :*: 7 kcal. =,., CalcW.tional Details Basis Sets. We explicitly considered all electrons for Cr, C, and H. We used a valence double basis for Cr (10s8p5d/ ~o.4p2d)• 7 and the Dunning-Hurinaga valence double I bases for carbon (9s5p/3s2p) and for hydrogen (4s/2s).1 8 One set of d polarization functions was added to the carbon basis, optimized for CrCHt () • 0.69). 19 Wave Functions. The geometry optimizations for both the 68 1 r and 'D 1 •t.atC3 of CrCI12+ were .,..rri<X! out by utilizing" (GVB- RCI'S)..- wave function (generalized valence bond restricted configuration interaction times singles from all valence orbitals). (a) For the 48 1 state, the GVB(2/4) wave function corresponds to correlating the Cr-C u and cr-c ... bond, each with a second natural orbital, leading to four natural orbitals in all. The C-H pairs were left uncorrcla ted but solved for self-consisten ti y. The RCI allows all configurations arising from different occupations of each pair of natural orbitals for each GVB bond pair (3 2 = 9 spatial configurations and 34 spin eigenfunctions">. allowing for interpair correlation and GF coupling. Then we allow all single excitations from all valence orbitals of the nine spatial configurations of the RCI wave function to all virtual orbitals (this includes single excitations from the CH pairs and the singly occupied Cr d orbitals), for a total of 507 spatial configurations and 3912 spin eigenfunctions. The single excitations allow for orbital readjustment upon stretching or bending the molecule. (b) For the 68 1 state, the GVB(l/2) wave function corresponds to correlating the cr-c u bond pair with a second natural orbital, while the Cr-C" system 1s descnbcd by two h1gh-spm-couplcd orbitals. This is comparable to the GVB(2/4) wave function for the '8 1 state. Both have four valence orbitals, with two Cr-C u natural orbitals and two Cr-C " natural orbitals. The RCI (15) Guggcnberger, L. J.: Schrock, R.R. J. Am. Chtm. Soc. 1975, 97, 6578. (16) Wcngrovius, J. H.; Schrock, R.R.; Churchill, M. R.; Misscrt, J. R.; Youngs, W. J. J. Am. Clitm. Soc. 1980. 101. 4515. (17) Rapp!, A. K.; Goddard Ill, W. A., unpublished l'tllullJI. See, for example, R.appt, A. K.; Smedley. T. A.; Goddard III, W. A. J. Phys. Clu!m. 1981, 85, 2607. (18) Hurinaga, S. J. Chem. Pliy$. 1'65, 42, 1293. Dunning, Jr., T. H. Ibid. 1970, 53. 2823. ( 19) The Cd function H • 0.69) wu optimized by using a fixed geometry (R(Cr-C) • 2.10 A, ~K-C-H • 120', R(C-Hl • 1.078 A) at the RCI•S level. allows all single and double excitations within the GVB "pair and within the two singly occupied Cr-C 11' natural orbitals (the valence bona orbitalS that compose tile 11' bon<l In the ground state, 'B 1), resulting in five spatial configurations and ten spin eigenfunctions. For the GVB-RCI•S wave function, we start with each of the five spatial configurations of the RCI wave function and allow all single excitations from all valence orbitals to all virtual orbitals, for a total of 327 spatial configurations and 150 I spin eigenfunctions. To calculate the Cr-C bond energy in CrCHt. we used several different dissodation-consistent CI" wave functions at the equilibrium geometrics of CrCH 2+ and of 3B1 CH 2 [8H-C-H = 133°, R(C-H) 1.078 AJ. 20 In addition to calculating the Cr-C bond energy at the HF level, 21 the GVB-PP (generalized valence bond with perfect pairing restriction) level, the GVB-RCI level (vide supra), and the (GVB-RCI•S)vtJeooo level (vide supra), we also <:arricd out two further dissociation-comisu:m Cf's on the 'B 1 ground state and one further dissociation-consistent CI on the 68 1 excited state. (a) RCI.•D. + RCI.•D,: This CI (for '8 1 CrCH 2+ only) consists of all single and double excitations from the three RC! configurations of the Cr-C "bond pair, simultaneous with an RCI in the Cr-C ... bond pair plus the opposite-all singles and doubles from the Cr-C " bond RCI configurations, simultaneous with an RCI in the Cr-Cu bond pair. Note the e:tcitations are from = the Cr-C bond pair< to all virtuals, induding ~xdtations to Cr singly occupied d orbitals and to the other GVB pair. This leads to a total of 1025 spatial configurations and 5810 spin eigenfunctions for the 4B 1 state {note that this includes the generic "GVB·CI" configurations). This wave function dissociates correctly lo HF fn:1gme11ls, "S er• aml 'B 1 CH 1. (b) RCI. •o, + RCI.'D. + (RCI'S),.i.""": This CI wave function includes all tbe configurations for the wave function described directly above, but, in addition, includes the RCl'S configurations (same as described for the geometry optimization) not present in the previous wave function, leading to 141 S spatial configurations and 8928 spin eigenfunctions for the 'B 1 state and 482 spatial configurations and 2146 spin eigenfunctions for the 6 B state. This wave function correctly dissociates to Hf•S (all 1 •ingl~ M1'itatinn• frnm th~ HF wav~ functinn) fragment< The C-C bond energy of ethylene was calculated at the HF, GVB(2/4)·PP, GVB-RCl(4), (GVB-RCl'S)-.... and RC!, •o, + RCI, *D. + (RCI*S)-.., levels, as described above, using VDZ bases for C and H. 11 The effect of C d functions on the C-C bond energy was examined by using the d function optimized for CrCHt. 19 The i5 1 CH 2 fragment was calculated at the equilibrium geometry (IJ = 133°, R(C-H) • 1.078 A) 20 at the HF and HF*S levels. The 68 1-'8 1 state splittings were calculated by using all of the above methods. The 0 D-°S state splittings for Cr"' were calculated at the Hartree-Fock level, using an averaged-field Hamiltonian to represent the four d electrons in 60 er+. The exchange integrals for 6D Cr+ and 6S Cr"' were taken from Hanrce-Fock calculations. Acknowledgment. This work was supported in part by grants from the National Science Foundation (No. D~R82-15650) and the Shell Development Company. Repstry No. CrCH 2+. 88968-5S-5. (20) Shih, S.-K.; Peycrimboff. S. D.; Bucnkcr, R. J.; Perie, M. Chtm. Pltys. utt. 1978, 55, 206. (21) Although Hartree-Fock does not disaociatc correctly. we include this calculation for complelcness. 94- Chapter 2.B. The text of this section is an Article coauthored with William A. Goddard III which appeared in the Journal of the American Chemical Society. -95Kepnntea rrom u1e Journal or the Amertcan Chemical society, Ill&&, HJtJ, ZJ&O. Copyright© 1986 by the American Chemical Society and reprinted by permiuion of the copyr:ilht owner. Bonding in Transition-Metal-Methylene Complexes. 2. (RuCH 2 )+, a Complex Exhibiting Low-Lying Methylidene-like and Carbene-like States 1 Emily A. Cartert and William A. Goddard 111• Contribution No. 7266 from the Arthur Amos Noyes La5oratory of Chemical Physics. California Institute of Technology. Pasadena. California 91125. Received August J5, 1985 Abltnlct The electronic structure for a representative late-transition-metal-methylene complex, Ru-CHt. has been studied by ab initio methods (generalized valence bond/configuration interaction). The electronic-state spectrum reveals five states close in energy (spread of 12.9 lccal/mol) that partition into two groups in terms of energy separation and mode of metal-carbon bonding. The ground state has 2A 2 symmetry and contains covalent M-C (f and r bonds ("metal-methylidene"): a 1 A 1 state of tho oamo bond obar•oto1 i• only 1.2 li.oal/mol higher. A <.l""t•r of tbr.,.; dogonerato c;~oitcd •U.t1:;• (• A 2, •0 1• aml •a 1) 12. 9 kcal/mo! above the ground state exhibits completely different bonding character, namely, (f·donor/r-acceptor M-C bonds are formed ("metal-carbene"). We conclude that for highly unsaturated, latc-transition·metal systems, metal-carbene bonding m.ay be competitive with mctal-ali:ylidene bonding, leading to donor/a~tor bonds comparable in strength to that of covalent double bonds! I. i.troducdoa Metal complexes containing CH2 Iigands have been postulated states of the system are formed by combining the various low-lying metal atomic configurations with JO and 11 to form various a.> intcrmo:Ui.. L"11 fur numi:;ruu. cul.>llytii.; rgi.;Lion• (e.g., fi:M.;b1:r- bonding >late>. Tropsch reductive polymerization of CO and olefin metathesis) and have been isolated in a number of cases including2a.b Metal-methylene complexes involving 10 have covalent metal-carbon double bonds and are termed metal methylidenes to emphasize the double-bond character. Examples include the so-called Schrock complexes 1. Metal-methylene complexes involving 11 require empty der ors orbitals on the metal (that can accommodate the CH 2 er pair) and prefer a doubly occupied dr orbital on the metal that can overlap the empty r orbital of cr 2 CH 2. This leads to a metal-carbon bond best described in terms Me....._c.,.,OMe oc., 11 ,.•. co '"w~ ""'1' and oc c co 0 1 2 In the simple oxidation-state formalism, the CH 2 is thought of as (CH 2) 2", with the metal oxidized by two units; however, the chemistry of these systems tends to fall into one of two distinct classes. one of which is nucleophilic and the other electrophilic. A series of generalized valence bond (GYB) studies on high· oxidation-state metal complexes such as 3 Cl 2Ti=CH 2 (3), Cl 4• Cr=CH 2 (4), and Cl,Mo=CH 2 (5) showed that these systems all have the form 6 with a covaltnr metal-carbon double bond ~Mg,,.H ()~ of donor-acceptor or Lewis acid-Lewis base concepts (as in "Fischer"-type carbcnes such as 2, or, in general. as 12). We ll will refer to such systems as metal carbencs. Supporting evidence for «1~h rliff,.ren('.e< in the metal-<.'arbon bonrl "hara<:'ter i< the drastic contrast in chemical reactivity of 6 with 12. Metal methylidenes such as H are precatalysts for metathesis 6 and po· lymerization reactions with olefins. 7 whereas metal carbenes such as 2 generally exhibit stoichiometric reactivity with olefins, leading to tbe formation of cycloprupanes. • '"H 6 involving a r bond composed of one electron in a metal dr orbital spin-paired with one electron in a C pr orbital, and a er bond consisting of one electron in a metal der orbital spin-paired with one electron in a C sp2 (f orbital. Similar studics 1" on (Cr=CH 2 (7). (Mn=CH 2)+ (8), and (feo=•CH 2)+ (9) lead also to a double bond with a similar covalent M dr-<: pr bond but a er bond having varying amounts of d(f and ser character on the metal. Such studies suggest the following valence bond view of metal-methylene bonds. The metal is considered to be in the atomic configuration (s 1d,.. 1, d", etc.) appropriate for its charge and environment (no formal charge transfer to the CH 2}, and the CH 2 is considered to be neutral and in one of its two most stable forms, the triplet err gruund sLate 10 or the singh:t er"' ciu.:itcd otate (9 kcal/mol higherl) 11. The ground state and low-lying excited r (I) Paper I in tbill sc:ris: Caner, E. A.; Goodard, W A.. Ill. J. Phys Chtm. 1934, 88, 1485. (2) (a) Schrock. R.R. J. Am. Clitm. S0t::. 1'75, 97. 6577. Guggenbergcr. L. J.; Schrock. R.R. /bid. 1975, 97, 6578. (b) fochcr, E. 0. Adv. OrganoftU!I CMm. 1976, U. I. For an extensive review of both Fischer· and S<:hrock-lype carbenes. DOtz, K. H.: F..cber, H; Hofmann. P.: Kreiss!, f. R.: Schubert. Li.: Weiss, K. Transition Metal Car~ne Complexrs; Verlag Chemie: Dcorficld Beach, FL, 1984. (3) (a) Rap¢, A. K.; Goddard, W. A., Ill. In POltntia/ EMrgy Sur/acts aod Dynamics Calcularion.s; Truhlar, D. G., Ed.; Plenum: ~ew York. 1981: pp 661~84. (b) J. Am. Chem. Soc. 1!181. 104, 297. (c) Ibid. 1982. 104, 448 (d) Ibid. 1980, 102, 5114. (4) MnCH!' and FeCH 2• work.: Brusich. M. J.; Goddard. W. A. Ill. lo be published. For another recent Jlllper on Cr<:H,• ooncurring with our earlier resulu (ref I), sce Alvarad<rSwaillgood, A. E.; Allison, J.: Harrison. J. F. J. Phys. Chtm. 1985, 89, 2517. (S) i..e(ipold, D. G.; Murray, K. K.; Lin<:berger, W. C. J. Chun. Phys. 1934, 81, 1048. (6) (al Lee. I. B.; Ott. K. C.; Grubboi. R.H. J. Am. CMm. Soc. 1982, 104. 7491. (b) Wcngrovius, I. A.; Scbroclr.. R. R.; CburcbiU, M. R.: Misscr1. I R: Ynnn&:1.. W I lhi.d ltMIO, In,, 4.c;1.; (c) Gilet, M '. Mnrtreu:r. A · Foll!s.t l1 'National Science Foundation Pri:doctoral fellow. 1982-1985. 0002-7863/86/1508-2180SOl.50/0 J.·C.; Petit, f. Ibid. 19113, 105, 3876. (d) Kress, J.: Osborn, J. A. Ibid. 1983. /Qj, 6346. (e) Katt, T. J.; Han, C.·C. Orranometallics 1982, I, 1093. (f) Howard, T. R.; Lee. J.B.; Grubbs, R.H. J. Am. Chtm. Soc. 1980, 102. 6876 (7) (a) Turner, H. W.; Schrock. R.R. J. Am. CMm. S0t::. 1982. 104, 2331 (b) Levisalles, J.; Rose-Munch, F.; Rudlcr, H.; Daran, J.·C.: Dromzec. Y.: Jeannin. Y. J. Chtm. Soc .. Chem. Commun. 1'1'111. 152. © 1986 American Chemical Society -96J. Am. Chem. Soc .. Val ln8. No. 9, 1986 Bonding in Transition-Metal-Methylene Complexes This gestalt view of bonding in terms of combining complete many-electron states is a characteristic distinguishing the valence bond viewpoint from the molecular orbital viewpoint in which one-electron orbitals are constructed (from the &ame o.tomic orbitals). but where distinctions between atomic configurations such as a2 vs. n methylene or s1d' vs. d 5 er+ become blurred. Although this valence bond view of bonding has been implicit in several papers, no examples of the metal-1:11rbene bonding (as in 12) have been examined with GVB techniques. ln this paper we report all-electron ab initio GVB calculations on a system (RuCH 2)'• ( 13) that exhibits both methylidene- and carbenc>-like states having comparable bond strengths. Indeed, the lowest carbene-likc state Ru=<' H 13 ('A 2) is only 12.9 kcal/mo! above the lowest methylidene-like state (2A 2). The results for the 2A 2 ground state of 13 (methylidene) are e:11.amined in section II, while the wave function for the 'A 2 excited state of 13 (carbene) is described in section III. A summary of our conclusions is presented in section IV, while further details of the calculations arc outlined in section V. II. Tbe GrOUDd State of RuCH 1+: Metliylldene Bonding A. Low-Lying Co•aJent States. Using the coordinate system y i .. /H Ru=C °"H -z we will denote the five valence d orbitals of Ru as ti.,.== d,• (a,) d'I', "" d,, (b,) dlt, "' d,,. (b2) d6,, = d..,, (a2) d~,,._,., = d,,._,.i (a1) In Cl< symmetry, do and du have the same symmetry (shown in parentheses); however, the du and d~ character perseveres. To pn:dict low-lying states of the metal-methylene complex, we utilize the valence bond picture in which the ground-state molecular or atomic fragments are brought together to form two-electron bond pairs in the resulting complex. Starting with the high-spin d7 configuration associated with tho 'F ground state of Ru+ and the ground state of CH 2 (10), we see that singly occupied du and dr orbitals arc required on Ru•. This leaves three orbitals (do, d3, and dlt) for the remaining five valence electrons on Ru•. Thus, double-bonded RuCH/ leads to three low-lying states with the following occupations of the nonbonding Ru d orbitals. 28 2 2 1 2 2 (do) (do) (dlt) (20.0 kcal/mol above A 2) 2A; (do) 2(do) 2(dlt) 2 (1.2 kcal/mol above 2A ) 2 2A (I) 1 2 2 2 (d<l) (d3) (d-t) (ground state) Using simple ligand-field considerations, one might argue that the 28 2 state would be the lowest, since the di' orbital, which (8) (a) FiJChcr. E. O.; Wtz.. K. H. CMm. &r. 1970, 103, 1273. (b) Oil!z. K. H.: Fischer. E. 0. Ibid. 1971. I 356. (c) Sle'Yens. A. E.; Beauchamp, J. L. I. Am. CMm. Soc. 1979. IOI. 6'449. (d) Brandt, S.; Helquist, P. J. /bid. 1979, 101, 6473. (e) Brookhart, M.; Humphrey, M. B.; Katzer, H. J.; Nelson. G. O. Ibid. 1980. 102, 7803. <0 Brookhart, M.; Tucker, J. R.; Husk:. G. R. /bid. 1'91, IQ.J, ~!~. IJl) UUCy. C P.; Voilendol'f, N. W.; Haller, K. !. Ibid. 19114. 106, 3754. (h) Casey. C. P.; Sh111tennan, A. J. Orf'lll01'l"talllcs 1915, .f, 736. (i) Brookhart. M.; Studabaker, W. B.; Husk:, G. R. Ibid. 1915• .f, 943. Ul Cucy, C. P.; Mila, W. H.; Tukada, H.J. Am. Ch~m. Soc. 1985, 107, 2924. (k) Stevens. A. E.; Beauchamp, J. L. Ibid. 1'18. JOO, 2584. 21 g I overlaps the CH bonds. is singly occupied (less clectron~lectron repulsion in the molecular plane than for the other two states). However, this state is 20.0 kcal/mo! above the ground state. In order to coiuilltcntly predict •ud1 ordering uf states in 1he bOund complex, it is useful to examine the energies for the corresponding atomic configurations of Ru+. As shown in Table I. the three configurations in ( l) lead to the following atomic energies: 2B (du) 1 (dr) 1 (do) 2 (d~) 2 (di') 1 (20.1 kcal/mo! above 2A ) 2 2 2A 1 1 2 2 1 (du) (dr)'(d6)'(do) (dt') (degenerate with A 2) 2A 1 1 2 1 2 2 (du) (dr) (d6) (db) (dlt) (2) Although all three o.onfiguro.tion.s o.rc d 7 Ru+, they have diffc1cnt electron repulsion energies (even when the orbital shapes are identical), and we see by examination of (2) that it is this atom· ic--el11c1ron repulsion energy that determines the relative energies in (I). For example, 2B2 has four electrons in the xy plane (6 252), whereas 'A 1 and 'A 2 have the doubly occupied orbitals in different planes (a 2lt2 or o2it2), leading to lower electron repulsion. Thus, in predicting the ground configuration of RuCH/ we need only consider two factors: (i) which states of Ru+ can form two covalent bonds, and (ii) of the states satisfying (i), which occupation of the nonbonding d orbitals has the lowest atomic energy (lowest electron repulsion). B. Bonding in the Ground State, RuCH 2+ ( 2A2 ). The generalized valence bond (GVB) one-electron orbitals for the Ru-C u and 'I' bonds are shown in Figure I where we see that both bonds arc quite covalent. The Ru--C u bond pair has an overlap of 0.68, with 1.04 electrons ascribed to Ru+ and 0.96 electron associated with CH 2•9 The Ru--C r bond pair has an overlap of 048, with 1.16 electrons localized on Ru+ and the other 0.84 electron on CH 2• The bonding orbitals on Ru are almost entirely 4<l in character (the Ru u bonding orbital is 87.8% 4<l and 12.2% Ssp, while the Ru r bonding orbital is 99.1% 4<l and 0.9% Sp). Thus th" RuC'f-1,+ r.omple" is best de•cribed as d' Ru+, forming u covalent double bond with triplet methylene. The covalent nature of tbe Ru=CH 2 bond is further supported by comparison with the bonds in ethylene. The G VB orbitals for the u and r bonds of CH 2=CH 2 are shown in Figure I, where it is evident that the carbon u and 'I' character in both RuCH/ and CHt=CH 2 are very similar. The C--C u overlap in ethylene is 0.88, while the C--C r bond overlap is 0.65. The overlaps are lower in RuCH 2+due to the longer bond lengths [R(Ru=C) = 1.88 A vs. R(O=C) = 1.34 A; 10 see Fiiz:ure 21 and some mismatch in orbital extent for Ru 4d vs. C 2sp. However, the trends in overlap (u vs. r) compare well: S,-s. = 0.23 for CHi=CH 1 and S.-s. = 0.20 for RuCH 2• (2A 2). One further indication of covalent bonding becomes evident as we pull the molecule o.part, breaking the double bond. For covalent bonds, the overlap in each bond decreases monotomcally as the bond length is increased from its equilibrium position, and this is indeed observed for RuCH/ (2A 2) (see Figure 3). The opposite behavior of the: bond pair overlap observed for the low· lying 'A 2 excited state of RuCHt will be discussed in section Ill. C. Oxidatioa-State Fonm.lisms. The result of a c01:alenr double bond between a metal atom and CH 2 is in direct contradiction with the literal interpretation of the popular oxidation-state formalism, which denotes the methylidene ligand as CH/· when bound to transition metals. The oxidation formalism implies ionic bonding-, our theoretical results show clearly that bond~ between transition metals and CH 2 are often coualenr. not ionic. From these and other GVB calculations. the following alternativc;s formalism ha• <0vohed; (I) Consider every ligand as neutral and start with the appropriate charge state of the metal (Ti 0 for 3. Cr0 for 4, Mo0 for (9) The electron 1'0Pulations and hvbrid character are determined by aummins the Mulliken populations from both natural orbitals (weighted b; tlfXllJltllion) of each GVB bond pair. (10) Hannony, M. O.; Laurie, V. W.; Kuczkowski. R l.; Sch"endeman. R. H.; Ramsay, 0. A.; Lovas, F. J.; Laffeny, W. J.; Maki. A. G. J. Phys CMm. Rt/. Data 1979, 8, 676. -972182 J. Am. Chem. Soc .. Vol. 108. No. 9. 1986 Table I. Single Configuration SCF and CI Energies for d7 Ru+ Ru+ hole Ru+ full config relevant RuCHt configb symmetry" 11 r ii' 6 ii' l 'B, "ii' •A2 Cf 'B, Cf 2A , 'Bf 1 " " " .. •s, 2 A2 .. 3 3 3 3 3 ii' ii' ii' Ru+ SCF total energy, hartrccs Ru+ H(i,i)' total energy, hartrccs M(SCF)! kcal/mo! M(CI),' kcal/mo! -4437.14079 -4437.13959 -4437.15049 -443715049 -4437.172 29 -4437.17229 -4437.172 29 -4437.17229 -4437.17229 -4437.18319 -4437.18319 +26.8 +27.4 +20.5 +20.5 +6.8 +6.8 +6.8 +6.8 +6.8 0.0 0.0 6 6 2 l 2 2 I 2 l -4437.15145 -4437.172 83 -4437.17282 -4437.172 82 -4437.17282 -4437.17282 6 l l -4437.18354 . . 3 ii' Carter and Goddard +20.I +6.7 +6.7 +6.7 +6.7 +6 7 0.0 •The Ci. symmetries listed for RuCH 2+ doublet states correspond to 38 1 CH 2 bound to the configuration of Ru+ listed in the next column. The quartet states of RuCHt correspond to 1A1 CH 2 bound to the configuration of Ru+ listed in the next column. •The doubly occupied orbitals have been omitted for clarity in discussions. Our convention for d-orbital symmetries has 11 = 4<1,,, r = 4-0.,. ii' • 4<1,,. 6 = 4-0,,. 3 = 4<1,i.y>. where the Ru-C axis is :t and the RuCH,+ plane is yz. Thus, r and 6 are "pi-like" (antisymmetric) with respect to the molecular plane. 'Usine field-averaged orbitals from the SCF wave function('/, electrons per d orbital to obtain equivalently shaped d orbitals), we constructed all 10 states corresponding to the d7 configuration of Ru+. A IO-configuration CJ leads to seven states corresponding to 'F (each with total energy -4437.183 19 hartrees) and three states corresponding to •p (higher by 34.2 kcal/mo!). When real orbitals are used, only two of these 10 configurations (rit6) and (rt"o) have pure 4 f symmetry and none has pure •p symmetry. The diagonal energies for these configurations arc given by H(i, i). For some configurations we solved for the SCF wave function (rather than using field-averaged orbitals); this leads to energies lower by 0. Hl.6 kcal. The energy differences in H(i, i) arc a measure of the increased electron repulsion energy (exchange energies) in these states. 'SCF excitation energy (in kcal/mo!) from the rt"6 ground state of Ru+. •CJ excitation energy (in kcal/mo!) from the ril'~ ground state of Ru+. fRuCH 1+ (48 1) excited state with a single u·donor bond. ONE ONE (il 111.1 (,,I) C Co- DONO C er OONO ONE ONE (iv) C-C 1T BOND (11) Ru·C 11' BONO Flaure 1. GVB orbitals for the mcthylidenc complex RuCH,+ (2A2) [(i) and (ii)] and for CH 2=-CH 2 [(iii) and (iv)]. (i) Ru--C 11 bond; (ii) Ru-C r bond; (iii) C--C u bond; (iv) C-C r bond. Contours reflect regions of constant amplitude ranging from --0.5 to +0.5 a.u., with increments of 0.05 a.u. 2A2 •A2 Flaure 2. Optimum geometries at the GVB(2/4)-RCI level for (a) ground-state RuCH 2+ ('A 2 ) and (b) excited-state RuCH,• ('A 2). 5, and Ru+ for 13), and consider first the ground atomic configuration for the metal (s2d 2 for Ti, s1dl for Cr and Mo, and d 7 for Ru+). (2) Ligands such as cyclopcntadienyl (Cp) or Cl prefer larger amounts of ionic character in the bond and consequently prefer to bond to s·like metal orbitals rather than d orbitals (lower ionization potential {IP) for s than d and hence easier charge transfer). t•or a qualitative analysis it is just as well to consider these ligands as reduced (e.g., cp- or and the metal oxidized. For two such electronegative ligands to both obtain partial ionic bonds requires an s2 metal configuration. In the G VB description, an sl pair is described by (< + p•) and (< fl') hyhri<I nrhita I•, and each plays the role of bonding to one electronegative ligand (thus preferring a 180° bond angle). If there are more than two such electronegative ligands, the ionic bonds mu.st involve metal d electrons (since s3 is not allowed and s2p is generally quite high) en and consequently the bonds become less ionic. (3) Bonds to alkyl, aryl, and hydride ligands prefer covalent bonding, particularly if the metal has enough electronegative ligands to utilize the s electrons on the metal. (4) More subtle effects can be involved for groups with active p-like lone pairs such as oxo or alkox.ide groups, but we will eschew them here. Although more cumbersome than the usual mddation-state formalism, we find that this VB formalism provides a simple means of correctly predicting the character of numerous quite different stAtcs of organometallic complexes. Some example• follow: (I) For RuCH 2+ we label the Ru atom as Ru(l) and consider the ground d 7 configuration, since the bonds are covalent and there is a +I charge on the metal. (2) Since neutral Ru atom has an s1d 1 ground state and Cl is very electronegative, we expect R.uCI to have a very ionic bond, 11 and hence the Ru in RuCl is labeled as Ru(I). Further, ligands added to Ru 1Cl should form covalent bonds, since all remaining unpaired Ru electrons are ind orbitals, as in Ru 1-CHt. (3) GVB calculations on C!Ru(H)(CH,) 12 show the metal to have the same electronic character as in Ru 1-CH 2+; namely, the (I I) Carter, E. A.; Goddard, W. A.. III, unpublished. (12) Carter, E. A.; Goddard, W. A., Ill. manuscript in preparation. -98Bonding in Tran.ritinn· Mnal-Ml'thylen£ ComplexP.< J Am. Chem. Soc .. Vol. JOB. No. 0, 1086 1.e- ""'·•.... ,_;;; ;; 1.9- ,." . a: ,_a: Table II. Vibrational frequencies (cm·') for tbe 2 A 2 and 'A 1 States of . -!!-. 442 ,IT 1A 4A 1.6- a: .. .... ~ 'I - \ .J er lo.I > 0 "' J \ 1.2- z I v'•z,<7 0 1.8I 1.85 "' --'-. ...__ 2Az' 7r 0 665 464 2 1 3245 3256 1461 1437 •Based on w, from cubic spline fits to results from GVB(2/4)-RCI calculations. iii <l. 2183 I 2.11:1 J.85 R(Ru-Cl,A Fipre 3. Ru-C "and r bond overlaps for the 4 A 2 (donor-acceptor or carbene-like bond) and 2A 2 (covalent or methylidene-like bond) states of RuCH 2+ as a function of distance. Overlap decreases with distance for covalent bonds but is approximately constant for donor-acceptor bonds. bonds to H and CH 2 are quite covalent and the CH 2 bonds in both Ru(I) systems arc nearly identical in character. 14 depicts the d~-.; /" ' '(.'.;'H '~ 14 electronic character at Ru(I) as three covalent bonds drawn as lines, one dative bond from c1- as an arrow, and two doubly occupied d orbitals by two pairs of dots. (4) (Cl)(NO)(PPh 3h0s(CH 2) 13 is written as figuration at the metal, and the overall degree of saturation of the metal complex. This new VB oxidation-state formalism provides logical explanations and predictions for bond character trends in the forthcoming sections. D. ~ The optimum calculated geometry for RuCH 2+ ('A 2) is shown in Figure 2a. The Ru-C bond length of 1.88 A may be compared with experimental values for metal-mctbylidene bond lengths such as R(Os1-CH 2) = 1.92 A in 15 13 and R(Re11-CH2) 1.898 A in 16. 14 The Ru 1-C bond length is expected to be shorter than the Os 1-C bond length since the d-orbital extent for Ru( I) is smaller than that for Os(l) ( 4d for Ru vs. 5d for Os). For d 5 Re(IJ), the greater orbital extent due to a higher n quantum number is nearly canceled by the higher effective nuclear charge, which causes a greater contraction of the orbitals for Re(ll) than for Ru(I). Consistent with our expectations, covalent d bonds involving d orbitals of similar size result in very similar bond lengths. The other geometrical parameters of RuCH 2+ arc not unusual. The C-H bond lengths (J.08 A) arc typical for sp 2 C-H bonds. The HCH bond angle of 121.6° is characteristic of a triplet methylene forming two covalent bonds to another moiety (a metal or another CH 2). For instance, CrCHt ( 4 8 1) bas ll(HCH) 117 6° and CH,-CH, hu 8(HCH) = It 7 .6° .1.10 On th" oth"'r hand, 6(HCH) = 133° for free CH 2 (38 1), 15 indicating that electron pair-pair repulsions decrease 6(HCH) upon cootple:ution. E. Vibratt-1 Fneq11e11eies.. The vibrational frequencies for RuCH 2+ ( 2A 2) arc shown in Table 11. The Ru-CH 2 stretching fn:qucm,;y i> 66.5 <.w·•, which may be compared with thcorcaicaI values for CrCHi' ('B 1) of "er-< 542 cm- 1 and the values obtained for two rotamers of CIRu 1H(CH 2) of "R•-C = 746 and 798 cm· 1• 1•12 The M=C frequencies correlate well with bond strength in order of Cr+ < Ru+ < C!RuH. The D.(M 1=CH,) are 44.0, 68.0 (vide infra), and 85.5 kcal/mo! for M =er+, Ru+, and CIRuH, respectively. A recent matrix isolation study 16 on FcCH 2 provides the first experimental M-CH 2 stretching frequency, 623.6 cm- 1, in good agreement with our value for RuCHt. The C-H •ymm.,tric stretch at 3245 cm·I and tbe HCH scissors mode at 1461 cm· 1 are in reasonable agreement with those expected for sp2 C-H bonds. (The corresponding values in CH 2= CH 2 are 3056 and 1393 cm· 1, respectively. 17 ) F. Tile R.....C Boad Strngth in RuCH 2+ (2A 2). Few metalligand bond strengths for saturated organometallic complexes arc known, either experimentally or theoretically. The majority of those that have been measured arc for gas-phase. highly unsaturated bare metal cations with just one ligand. 18 In this section we will consider the relationship expected between the bond energies in such unsaturated species as compared with saturated organometallic complexes. All calculations carried out on RuCH,+ are such that the wave function for RuCHt at its equilibrium geometry (given in Figure 2a) dissociates smoothly to the appropriate covalent fragments, retaining the same level of electron correlation in the fragments as that included for the complex. In addition, we allow the fragments to relax to their equilibrium geometrics, thus obtaining = = = 15 indicating that the metal is thought of as a d 1 Os(I) (after making an ionic bond to Cl to form with three covalent d bonds (two to CH 2 and one to the T orbital of NO), leaving two double en """'upie>J <I urbitiilo. In 11.J<liliun tu !he; live <I urbii.ab uf O:;(I), the four arrows indicate the ligands overlapping the four empty Os 6s and 6p orbitals to yield a total of 18 electrons associated with the metal (four in doubly occupied d orbitals, six in three covalent metal-ligand bonds. and eight in the pairs indicated with arrows). (5) (Cp•)(NO)(PPh 3)Re(CH 2)+ 14 is written as ~ l• ON)~~=w,j "'•p 16 to show that the Cp• (Cp• .. C 5 Mei) has formed an ionic bond and thus the metal should be thought of as d 5 Rc(II). In this case there arc five ligand-to-metal donor bonds, requiring an empty 5d orbital in addition to the four empty 6s and 6p orbitals, so that the d 5 configuration of Re(ll) has one doubly occupied d orbital plus three singly occupied d orbitals (which arc used in the three covalent bonds). Examples l-5 illustrate how to designate and predict the character of metal-ligand bonds, the nonbonding electron con(13) Hill. A. F.; Roper, W.R.; Waters, J.M., Wright, A.H. J. Am. Cltem. Soc. 1913, 105, 5939. (14) Pat1on, A. T.; Strause, C. E.; Kuoblcr, C. B.; Gladysz. J. A. J. Am. Chtm. Soc. 1913, 105, 5804. (15) Shill, S.-K.; Peycrimhoff. S. D.; Bucnkcr, R. J.; Perie, M. Chtm. Pliy1. Lm. 1971, 55, 206. (16) Chang. S.-C.: Kafafi, Z. H.; Hauge, R.H.; Billups, W. E.; Margr-avc. J. L. J. Am. CMm. Soc. 1985, 107, 1447. (17) Shimanouchi, T. Tobit• of Moltcwlar Vibrational Frtqutncies; U. S. GOYCrnmcnt Printing Office: Washington. DC, 1972, NSRDS-NBS-92. (18) Sec, for example. (a) Armentrout, P. B.; Beauchamp, J. L. J. Am. CMm. Soc. Ull. /OJ. 784. (b) Armentrout, P. 8.; Halle. L F.; Beauchamp, J. l. Ibid. 1911, /OJ. 6501. (c) Mandich, M. L.; Halle. l. F.; Beauchamp, J. L. Ibid. 191M, 106. 4403. -992184 J. Am. Chl'm. Soc .. Vol. 108. No. 9, 1986 Carter and Goddard Tallle ID. Bond DiSIQCiation Energies (kcal/mo!) for the Methylidene State of RuCH 2+ ('A 2) calculational level" HF -11.5 GVB(2/4)-PP 27.6 RCl(2/4) 45.4 RCl. ·o. + RCI. •o. 59.5 (RCl(2/4)"S)...iJwt 63.3 •o. •o. RCI. + RC!, + (RCl(2/4)':SJ..i.MI -4476.088 67 (1/1) -4476.15100 (4/4) -4476.179 23 (9/17) -4476.194 88 (989/2627) -4476.202 74 (321 /1233) -4476.22028 (507 /2091) -4476.227 77 (1379/4377) 55.2 (RCl(2/4) 0 S)nl.Jl• fragment total energies, hartrces RuCH,•('A 2) total energy, hartrces• D.(Ru-C) 68.0 Ru+ CH,('B,) -4437.183 54 -38.923 41 (1 / l) -38 923 41 ( l / 1) -38.923 41 (I/ l) -4437.183 54 ( l / l) -4437.183 54 <l Ill ( l / l) -4437.183 54 -38.923 41 ( l /l) -l8.923 41 (I/ l) -4437.18449 (21/48) -4437.18449 (21/48) -4437.18449 (21/48) (I/ I) -38.93499 (22/44) -38.93499 (22/44) •Each of these calculations is explained in detail in section V. •The number of spatial configurations/number of spin eigenfunctions are given in parentheses. the adiabatic, dissociation-consistent 19 bond energy. The Ru=C bond energies for RuCHt (2A 2) as a function of electron correlation arc shown in Table III. At the highest level, we find a direct, adiabatic Ru=C bond energy of D. 68.0 kcal/mo!, for RuCHt (2A 2) dissociating into ground-state = fragmcnu Ru+ (~F) (-.-lto and -.-ii'~ in Table I) and CIIi ('D 1). Note that although the metal is in a promoted state at R. (6.7 kcal/mol above 4 F; see Table I), the metal relaxes to 4 F Ru+ as the bond breaks. 20 This direct bond energy is expected to be a lower limit since electron-correlation effects increase when more electrons arc in the same regions of space. Analogous calculations for the double bond of CH 2=CH 2 (using the same basis sets and level of Cl as in RuCH 2+) lead to a calculated bond energy of 174.4 kcal/mo!, 1 which is 5.6 kcal/mo! smaller than the expcrim.,nrol volu" nf n.(C:H 2=-f'H 2) = ll!O 0 21 which arise (from the Pauli principle) only for orbitals with the same spin. For d 7 Ru+, the quartet state (S = 3/ 2) with five a spins and two fl spins leads to 11 exchange interactions, each of which contributes an average of negative 15 kcal/mol to the energy. 23 In contrast, the atomic doublet state (S = 1/ 2) with four u •pins and llm:ic; {J •µin• lead• lv vnly nine Cll<.:hange interactions and an energy about 30 kcal/mol higher. However, formation of a covalent bond (perfect pairing) between a ligand and a singly occupied d orbital necessarily requires that the bond pair be coupled into a singlet (low-spin) with the result that the metal d orbital is half the time a and half the time fl. This results in a decrease in atomic exchange stabilization that goes hand in hand with covalent bonding to singly occupied d orbitals. The magnitude of this effect increases with the number of other singly W~ "'~!"""' th~ occupied high-spin-paired d orbitals and hence it depends on how residual correlation error in Ru=CHt to be at least as high as in CHi=CH 2 (due to the presence of the other valence d electrons on Ru); hence, we estimate the exact bond energy for RuCH 2"' (2A 2) to be D.e>act(Ru+-CH 2) = 73.6 kcal/mo! saturated the bonding to the metal is. In forming a covalent double bond to CH 2 in (singlet) ClRu(CHi)H, the two metal orbitals that were originally high-spin (aa, leading to a -14i exchange tenn) in the (triplet) ClRuH fragment must now each become a half the time and fl half the time, with the result that they have the same spin only half the time (i.e., aa + afJ +{la + flfJ leads to a - 1JiK64 average exchange term). The result is that the atomic exchange energy becomes less negative by 1J,K.., 7.5 kcal/mo!. Thus G. Correlation between Satunted and U1111tunted M=CH 1 8oad Energies. Since gas-phase RuCHt has not yet been ob- served, a direct comparison cannot be made with exoeriment. However, we have carried out equivalent calculations on the larger Rul=CH 2 complex. CIRu 1H(CH 2), 14, which in the 1A' state should model coordinativcly saturated, 18-electron rutbeniumalkylidene complexes such as CpRu 1(L)(R)(CH 2) (where L = CO or PR, and R ~alkyl, aryl, or H), which ha• been poatulatcd as an intermediate in the isomerization of a dimethylruthenium complex to an olefin hydride complex. 22 For 14, at the same level of electron correlation and the same basis sets as used in the present study, we find a direct, adiabatic Ru=C bond energy of D.(Ru=C) = 85.5 kcal/mo! (vs. 68.0 for RuCHt). 12 Why is the bond stronger in the more highly saturated system even though the metal-carbon bond bas not changed character? The answer involves the change in spin coupling necessarily associated with covalent-bond formation. For atoms, the ground state has the singly occupied orbitals coupled to form the highest spin state (Hund's rule). This results from the exchange energy terms = D,[(Cl)(H)Ru=CH 2] "'Dini(Ru=CH 2) - 7.5 kcal/mo! where Di01 (Ru=CH 2) is the intrinsic (excbangeless) metalmethylene bond strength {for any RuCH 2 system). If there is a third unpaired d orbital on the metal (as in Ru•), the spm of the free atom is aaa. leading to -3.K.i.t among tha;e three electrons, but after bonding to two of the d orbitals, the spins on the metal are aaa + afla + {3aa + fJfJa, leading to an average of (I /4)(3 + I+ I + I)= 3/2Kdd. Thus, in RuCH/, the M=CH 2 bond loses 3/2Kdd = 22.5 kcal/mo!. Thus D,(Ru+=CH 2 ) = D,.,(Ru=CH 2) - 22.5 kcal/mo! and we expect D.((Cl)(H)Ru=CH 2] - D,(Ru+=CH 2) = 15 kcal/mo! (3) Indeed, from the calculated bond energies (85.5 and 68.0), we obtain 17.5 kcal/mo! for the quantity in (3). Thus 1he differences in lx.md smmgihs for surnru1ed vs. unsa1ura1ed me1af complexes (19) Bair. R. A.; Goddard. W. A.. Ill. submitted for publication in J. Phys. Chem. (20) At R., RuCH,• (2A,} bas the Ru• configuration <1 1.>T1nt'.J 2,.i_.,.kl',,. which, under C'f symmetry, relaxes a.s the bond lmab by nuxing d,i and d r'-r' to form •· ,z..,n .,t-2 ,}2i.,.L,1-,i6...,'. Thi> latter configuration has •f symmetry with respect to the x axil. (21) JANAF TMrmochemica/ Tables; U.S. Government Printing Office: Wuhington. DC, 1970, NSRDS-NS.S-37. (22) Kletzin, H.; Werner, H.; Scrha.dli. O.; Ziegler. M. L. A11,pw. Chem .. /111. Ed. E11gl. 1983, 22. 46 are dominall'd by /.Jte differenria/ loss of exchange coupling on the metal. Hence. we obtain D1.,(Ru=CH 2) = llR 0 + 22.5 = 90.5 kcal/mo! ( 4) YiKdd "' 83.0 kcal/mo! (5) D,..(Ru=CH 2) ' _ ,., - (23) X.. •average exchange energy between two d orbitals. K..,(Ru•) • 15 kcal/mo! and X.. • 7.5 kcal/mo! from our ab initio Hartrce-Fock <:al· culations on Ru•. -100Bonding in Transition-Metal-Methylene Complexes J. Am. Chem. Soc .. Vol. 108, No. 9, 1986 (where D,., is the bond energy expected for a saturated Ru-CH 2 complex) from our direct GVB calculations. Including the es· timated correction of 5.6 kcal/mo!, (4) and (5) become Din1....,.(Ru-CH 2 ) = 96.1 kcal/mo! (6) D,.«'.."(Ru-CH 2) = 88.6 kcal/mo! (7) We expect Din,(Ru-CH 2) to remain fairly constant, regardless of the nature or existence of ancillary ligands, for a given electronic state of the metal atom. This is borne out in the cases above, RuCH/ and CJRuH(CH 2), for which Dint = 90.5 and 93.0 kcal/mo!, respectively. To see how to use these quantities for predicting bond energies, consider the 18-electron complex, Cp(dppe)Ru-CH/ (the Fe analogue is known 24 ): Ru(ll) is d6 , but this complex requires 2185 the larger Ru(I) complex, CIRuH(CH 2 ), and in other electronically analogous systems. Second, the simplicity (and generality) of the expression for the intrinsic bond strength is provocative; it suggests that we may be able to estimate the bond energies of saturated organometallic (or any other) complexes from bond energies known for unsaturated complexes containing the same ligand. Calculation of Dint = D.(unsaturated) + AKd<l yields D.(saturated) = D,.(unsaturated) + AK<l<l - Y2Kd<l assuming covalent bonds to d orbitals are formed in the saturated complex. (This does require that the metal atoms have the same electronic state in both <:ompl<:><<:a.) H. Summary, We see that each property of the 2A 2 state of RuCH 2+ taken separately or together, implicates one possible description of the bonding between Ru+ and CH 2• Thus, we may best think of this complex as consisting of high-spin d7 Ru+ forming two covalent bonds to 'B 1 CH 2. m. A Low-Lying Excited State of RuCH1+: Carbeae Bonding five empty acceptor orbitals (the 5s, three 5p, and one 4d) on the metal (as indicated by the arrows). The requirement of ad hole plus two singly occupied d's that can bond to CH 2 forces the other four electrons to occupy the two remaining d orbitals, leading to A. Co•aleat YS. Donor-Acceptor Bonding. As discussed in section 11.G, the intraatomic exchange stabi.li7.ation of a free metal ion necessarily weakens metal-ligand bonds, since this stabi.li7.ation is at least partially quenched upon complexation. In section II, we examined the lowest spin state of RuCH/, formed from the int<:rmediat<: triplet spin st4tc of R11(1l}. Th11$, in bonding ground-stat<: fragments, and found a 2A 2 ground stnte. However, CH 2 to the fragment Cp(dppe)Ru+, the two unpaired electrons in the intermediate spin state I~ 1/ 2Kdd, and we predict a bond energy of D('*"'[Cp(dppc;)R11-CH 2+] - Din 1(R11-CHz) 7.5 - 96.1 - 7.5 = 88.6 kcal/mo! In contrast, removal of the chelating phosphine should lower the bond energy, since CpRu-CH 2+, does not require ad bole for donation from the Cp- ligand, leading to a high-spin d6 Ru(ll). In this case, the fragment CpRu+ has four unpaired spins with -6Kdd between them, while CpRuCH 2+ with two unpaired elec· trons has only -3 1fiKdd involving these four electrons (after forming the bond). Therefore, we expect D:''"''(CpRu+-CH 2) ,. 96.J -(%)(15) =58.6 kcal/mo! Thus, dramatic differences in bond energies are expected bewtccn unsaturated vs. saturated complexes, even as the nature of the bond bt1ing brok1m ,.,,.,a;,,, "'"'•ttmt This leads to the exchange moderated ligand effect: Added ligands serve to quench many of the intraatomic exchange terms (due either to covalent bond formation or to coordinated Lewis bases forcing the metal into a lower spin state). The differen· tial-exchange energy lost in the more saturated complex will be less than that lost in a highly unsaturated system, leading to a larger observed Ru-CH 2 bond energy. As another example, consider the saturated system (Cl)· (NO)Ru 1(PPh 3)i-CH 2• Although RuCH/ bas an estimated Ru-C bond energy of 73.6 kcal/mol, here we expect to have an Ru-C bond energy of 96.1 - 1/ 2Kdd 88.6 kcal/mol, the same as predicted for our model compound CIRuH(CH 2) and for Cp(dppe)Ru-CH 2+. Thus, saturated metal complexes are ex· = pected to have substa,.tially larg"r bond """'gi"" titan those of their unsaturated counterparts. This result suggests two further extensions. First, the fact that the intrinsic bond strengths of these two ruthenium(l}-alkylidene systems are essentially identical implies that the character of the bonding is also the same for bOth systems. Tbus, by understanding the simple case of RuCH/, we can understand the bonding in (24) Brook.hart, M.; Tucker, J. R.; flood, T. C.; Jensen, J. J. Am. Chem. Soc. 1980. 102, 1203. higher spin states may be important if they lead to less exchange energy quenching in the complex. Thus we investigated the possible existence of low-lying quartet states of RuCH 2+. There are three ways in which quartet states may be formed for RuCHi"'. First, we can form a quartet state directly from the ground 2A 2 state by triplet-coupling the weakest bond, namely, the T bond. This leads to a singly bonded 'A2 state of Ru+-CH 2, which suffers less exchange loss than the doublet ground state (only I K.., 1S lrC'~l/mnl), hut it i• d"'tahili7M by forcing the overlapping Ru dr orbital and the C pr orbital to be orthogonal. The 4A 2 state formed in this manner lies above the 2A 2 ground state by 50.9 kcal/mo!. A second way to form a quartet state of RuCH 2+ is to promote d 7 Ru+ to s 1d6 before bonding to triplet CH 2• This costs 28.4 kcal/mol, 23 but in return we can form two covalent bonds to CH 2, thus avoiding the r repulsions which caused the above quartet to fail. Promoting Ru+ to the s 1d6 excited state leads to five equivalent states (the 60 state). When the same labeling scheme as in section II.A (the corresponding RuCH 2+ symmetries are shown in parentheses) is used, these become = (5s) 1 (dcr) 2 ~) 1 (d't) I (dli) I (do) I ('Bi) (5s) 1(dcr) 1(dr) 2( d't) 1(dli) 1(do) 1 ( 6A 1) (5s) 1 ~) 1 .(!!!) 1 (dr) 2 (dtl) 1 (do) 1 ('A 2) (5s) 1 ~) 1 ,{!!!") 1 (d't) 1 (dtl) 2 (do) 1 1 1 1 1 1 (5s) ~) .(!!!") (dt") (dli) (do) 2 (48 2) (4B 1) Bringing up the CH 2 in the yz plane, we can form a double bond involving 4da and 4dr orbitals for the last three (' A2, 4 8 2, and 48 ), and we can form a double bond involving Ss and 4d'lt for 1 the last three and the first (also 48 1). Thus we expect three nearly degenerate, doubly bonded quartet states (symmetries 4A 2, 48 2, and 4Bi) to arise from binding Ru+ (s 1d6) to CH 2 (38 1). The a bond 1s allowed to be either s- or d·like on the metal. In addition to the promotional energy (d7 - s 1d6 ), we must also consider the loss of intraatomic exchange interactions for s 1d6 Ru+ in order to fully assess the energetics of complexation. Assuming pure da and pure dT orbitals are utiliz.ed on the metal. formimr; (25) Our calculations at the HF level lead to Ep('F - 60) • 28.4 kcal/ mol, while the experimental £1 • 25.1 kcal/mol averaged over angular momentum states (~p • promotional energy). Moore, C. E. Atomic Enugy UIJl}/s; NSRDS-NBS·35, 1971, Vol. 3, p 25. -1012186 J. Am. Chem. Soc .• Vol. JUIJ, No. 9, 198Ci Carter and Goddard and Ru+• of Related State state total energy, hartrecs energy, kcal/mol •s, •s 2 'Ai -«76.16398 -4476.16413 -4476.16419 -4476.14738 -4476.177 31 -4476.17923 +9.6 +9.5 +9.4 +20.0 + 1.2 0.0 19 2 2A, lA 2 hole config H(I, i), hartrecs energy, kcal/mo! " ,, " • • u ,.. • ,, a ,.. ,.. i -4437.17229 -4437.17229 -4437.17229 -4437.13959 -4437.172 29 -4437.17229 o.o +o.o +o.o +20.6 +o.o 0.0 o •These RuCH/ results are based on calculations at the GVB(2/4)-RCI level. All quartet states were calculated by using the optimum geometry for 'Ai RuCH 2•, while all doublct·rnitc calculation• utilized tbc optimum geometry ror 'A 2 RuCH 2+. Ru• rcoults arc taken rrom the Cl described in Table I, footnote c. More accurate 'A 2- 2A 2 energy splittings arc reported in Table V. a double bond leads to a differential Joss of exchange energy of M = I Kw. + 2.5K.i.t. The average s-d exchange interaction in Ru+ Is Kw. "" 1.5 kcal/mo! and the average: Kdd "" 15 kcal/mo!, leading to a loss of 45.0 kcal/mol upon forming a double bond. Adding this loss to the promotional energy of 28.4 kcal/mo! results in a weakening of the double bond by 73.4 kcal/mo!! This suggests that such a state would be high above the ground state. Repeating the analysis for a double bond comprised of a 5su orbital and a 4drx, orbital on Ru+, we find that formation of a double bond to triplet CH 2 leads to a differential exchange energy loss of M = 2Ktd + 1.5 Kdd = 37.5 kcal/mo!. Adding the promotional energy yields an inherent weakening of the Ru-C double bond of 65.9 kcal/mot. Thus, if this quartet state is formed at all, we would expect a weak Ru"'=CH 2 bond in which the u bond involves primarily the Ss orbital on Ru"'. Summarizing, the formation of covalent bonds to s1d6 Ru"' leads to highly excited states for Ru=CH/. However, all is not lost: there is yet another possibly favorable manner to form a quartet state. We now consider binding singlet CH 2 to d 7Ru+. The questions which must be answered for this new case include what &Ort of bonding ia po33iblc, what the coata 11re con<:<:rning pro- motional and exchange energies, and how these quartet states are related (by symmetry) to our previous constructs. The bond of singlet CH 2 (11, with its doubly occupied sp orbital ( u) in the molecular plane and empty pw, orbital perpendicular to the molecular plane) and Ru+ involves a 11-donor bond from CH 2 to Ru+ and a possible dr-pr "back-bond" from Ru"' to CH 2• The situation here is slightly more complicated than the usual concept of u-donor/r-acceptor bonding in which the u lone pair of the ligand is thought to donate into an empty dcr orbital on the metal, while the metal dw lone pair delocalizes or "back-bonds" into the empty CH 2 pr orbital. The complication is that d 7 Ru"' wishes to be high-spin; the cost in energy to force Ru+ to have an empty du orbital is 2Kdd = 30 kcal/mo!. Thus, it is less favorable to force d7 Ku ... into its low-spm conflgurallon than to promote d 7 Ru+ to s1d6 Ru+. However, promoting Ru"' does not alleviate the problem, since now the singly occupied 5s orbital is in the u space, inhibiting u donation. In addition, high-spin s1d6 Ru+ (6 D) (with all d orbitals occupied) is favored over interme· diate-spin s 1d6 Ru+ (with a du hole) by IKtd + 3Kdd = 52.5 kcal/mo!. Thus, forcing Ru+ to have an empty u orbital is unfavorable by at least 30 kcal/mo!. (Furthermore, the RuCH/ states formed from such Ru+ configurations with singlet CH 2 lead to doublet states, whereas we seek quartet states.) The question now is whether singlet CH 2 can form a good bond to a state with an occupied du orbital. Perhaps by mixing in the 1 s d6 excited state, Ru+ can form a singly occupied 5s-4d,: hybrid u orbital which is localized away from the Ru-C bonding area. leaving negligible electron density in the molecular sigma system and thus allowing u donation from CH 2 (1A 1) into the "vacant" u space of Ru+, as shown below. If so, we expect the favorable state to have a doubly occupied dr xz orbital (to allow d11'-p11' back-bonding) and a singly occupied du,1 orbital (to allow s-1:1 hybridzation out the back of the complex so as not to interfere with the u-donor bond). This leads to three plausible (high-spin) Ru+ configurations (degenerate for the free ion), (sdu) 1(d11' )2(d't) 2( do) 1( d3) 1 ('A 2) (sdo-) 1(dw) 2(d't) 1( do) 2( d3) 1 ('B 2) (sdu) 1(dr) 2(d't) 1(do) 1 (d~) 2 ('B 1) (where the symmetries are for RuCH/). These (degenerate) quartet states predicted for Ru+ (d7) forming a 11-donor/r-acceptor bond to singlet CH 2 have the same symmetries as for Ru+ (s 1d 6 ), forming two covalent bonds to CH 2 3 (8 1)! Hence, by calculating the 'A 2, 'B 2, and 'B 1 wave functions for RuCH 2+, we will determine which mode of bonding (donor-acceptor vs. covalent) is preferred. Of course we can in fact predict a priori which bonding mode is preferred by comparing the promotional and exchange costs for both systems. For covalent bonding we found a total destabilization of 65.9 kcal/mo! for forming u and r bonds utilizing the Ru+ 5s and 4dx, orbitals. For donor-acceptor bonding, the miAing of isome s'd' chara<..'ter into ground-state d 7 Ru ... will ~l no more than the s 1d6-1:1 7 promotional energy of 28.4 kcal/mo!, and the promotion of CH 2 from triplet to singlet costs 9 kcal/ mo!, 5 for a total promotional energy of :S38 kcal/mo!. Since no covalent bonds have been formed with Ru"', we retain all intraatomic exchange stabilization on Ru+. Thus, donor-acceptor bonding is predicted to be more favorable than covalent bonding by 66 - 38 ;:: 28 kcal/mo! for the quartet states. This simplistic analysis does not address the probable differences in intrinsic bond stengths of covalent vs. donor-a=c:ptor bonds, as well as the cost of or· thogonalizing the singly occupied sdu orbital away from the donor u bond. However, with such a large bias toward donor-acceptor bonding due to the retention of exchange terms on Ru+, we expect that donor--acceptor bonding will be the preferred mode of bonding for the quartet state. The question of where this donor-acceptor state lies relative to the ground state will depend on the two factors neglected in the above analysis: (i) the intrinsic strength of a u-donor / 11'-acceptor bond relative to the intrinsic strength of a covalent double bond and (ii) the magnitude of the repulsive interaction in the three-electron u system. B. The Quartet State Spectrum for RuCH 2"'. From the results in Table IV, we find that the quartet states ('A 2, 4 8 1, and 'B2) of RuCH 2+ are indeed degenerate, as predicted. In addition, we sec that they are not far above the 2A 2 ground state of RuCH2 ·•-. The 'A 2-2 A 2 state splitting as a function of electron correlation is given in Table V, where we sec that further inclusion of electron correlation yields a 'A 2-2A2 state splitting of 12.9 kcal/mot. This sm.a.11 stat" •plitting is su88<"'tive of at least two oonclusions. First. RuCH 2+ ('A 2) makes use of the least destabilizing mode of bonding available, namely, donor-acceptor bonding, in which little promotional energy and no exchange energy are lost on Ru+ and only 9 kcal/mo! promotional energy is lost by exciting CH 2 from 38 to 'A . Thus we propose that the bonding in RuCH2' ('A2J 1 1 consists of a 11-donor-w-acceptor bond between CH 2 ( 1A,) and 7 Ru+ (d ), a description consistent with its molecular properties (vidc infra). The second major conclusion to be drawn from the 'A 2 - 2A 2 state splitting of 12.9 kcal/mo! is that donor /acceptor bond en- -102Bonding in Transition-Metal-Metliylene Complexes Table V. 'A 2- 2A 2 Excitation Enc:rgies (kcal/mo!) for RuCH/• no. of config/SEF" J. Am. Chem. Soc., Vol. I QIJ, No. Y, I Y86 Roper and co-workers structures of 27 218 7 have synthesized and obtained X-ray ea.lculationo.l level -20.l HF 1/1 1/1 4.9 GVB-PP 4/4 8/8 15.0 GYB-RCI 27/76 9/34 2875/11486 8.9 RC!, •o. + RCI. •o. 1065/5886 442/2570 816/4150 13.0 (GYB-RCf•S),.1.R• 14.2 (GYB-RCl"S),.,1,11 637 /4962 1365/8156 12.9 RCI,•D, + RCJ,•D. 1579/10042 3895/18102 + (RCl"S),.11.11 •Optimum geometries at the GVB(2/4)-RCI level were used for 2A 2 and 'A 2 RuCH,+. For excitation energy calculations, the GVB(3/6) level is used for 2A,. while the GVB(2/4) level is used for 'A,. to maintain an "orbitally balanced" description (sec section V). •No. of config.JSEF is the no. of spatial configurations/number of spin eigenfunctions. Flpre 4. Qualitative potential curves for 'A 2 and 2A 2 RuCH,+. Our theoretical values are D, ('A 2) • 68.0 kcaJ/mol, D, ('A 2) "' 65.9 kcal/mo!, and AE('A 2-2A 2) • 12.9 kcal/mot. Our best estimate for 2 ) • 73.l kcal/mo!. o,-·· ('A. ergies can be comparable in strength to covalent bond energies. That is, D,(Ru==CHt, 4 A 2) can be predicted from the cycle illustrated in Figure 4 to be D,(Ru==CH/. 'A 2) = D.(Ru==CH2+. 2A2) + t:.E(flo'fi - 'F. Ru+) + t:.£( 1A,-3B1o CH2) - t:.E('Ar-2 A,) This calculation is explicitly for the diabatic bond strength of CH 2 comple~e•, liow.,vcr, thb wuuld be the adiabatic bond str~ngth for metal--carbene systems in which the free carbene has a singlet ground state (e.g., CF 2, C(OR)R, etc.) and thus is the relevant quantity to use for comparison with currently observed metal carbenes The abuve equation leads to a predicted D.(Ru==CH, +. 'A 2) of 6s.o + 6.9 + 7.3 - 12.9 = 69.3 kcal/mol, 26 which is of the same magnitude as the covalent Ru-CH 2 bond strength. Calculated bond energies for RuCH2+ (4Az) dissociating to d7 Ru+ and CH 2 (IA 1) arc discussed in detail in section 111.D. C. Prop.wt1es of tM Low-Lyiag Exdt.e.J State, RuCH2., ('A2)• It is important to emphasize that it suffices to examine any one of the three degenerate quartet states of RuCH 2+,since they all exhibit the same properties, with the only physical difference between them being the configuration of electrons in nonbonding d orbitals. We choose to examine the 'A 2 state simply because it is of the same spatial symmetry as the ground 2A 2 state, which allows a more direct comparison of the two spin states. The optimum geometry for the RuCHt ('A 2) excited state (at the GVB{2/4)-RCI level) is shown in Figure 2b. The Ru-C ~d length of 1.93 A is O.OS A longer than the Ru-C bond length m the covalently bonded 2A 2 ground state, suggestive of a change in the bonding scheme for the 4A 2 state. Supporting eviden~ that this bond lengthening is due to a change from a covalent (tnplet) alkylidene structure to a donoNi.~ (singlet). carbene structure is given by examination of the following expenmental example. (26) At the highest level of calculation UICd herein, we find A£(.,.~ - 'F. Ru+)• 6.9 kcal/mol and AE( 1A 1-'B" CH,)• 7.3 kcal/mo!. where X = H or F. We would expect the CH 2 case to have an Os==C covalent double bond and thus to have nucleophilic, alkylidene character. However, the triplet state of CF2 is about 46 kcal/mo! above the singlet, 28 and hence we would expect electrophilic, carbene character in the latter. The Os=CH2 bond length is 1.92 A, 27• whereas the Os==CF1 bond length 1s 1.967 >.,2-ro a bond lengthening of0.047 A upon going from an alkylidene to a carbene bonding structure. This is in excellent agreement with the bond lengthening of 0.05 A we find for Ru, lending credence to the assignment of RuCH 2+ ('A 2) as a singlet carbene bound to Ru+. Further indication of the singlet nature of the CH 2 ligand in RuCH/ ('A 2) is seen in the decrease in HCH bond angle from 121.7° to 113.0°, going from 2A 2 to 'A 2 RuCHz+. (The HCH bond angle in CH 2 ( 1A 1) is 103°, whereas in CH 2 (3Bi) the angle is 133°.28) The C-H bond lengths in RuCH/ ('A 2) remain the same as in the ground state, R(C-H) = 1.08 A. The GVB orbitals for the Ru-C fl and ... bonds as well as for the nonbonc:ling singly occupied u orbital (5s/4dz') are shown in Figure Sa. Notice the difference in character of the .fl and -.. bonds of Figure Sa from the covalent u and-.. bonds of Figure la. The fl bond for RuCH 2+ ('A 2) resembles an ~in/out" correlated u pair of CH, (1A,) 0 .27 electrons are locali7.ed on CH,. while the ot?er 0.73 electron is donated to Ru+), as can be seen by comparing Figure Sa with Figure Sb, which depicts the two fl donor electrons of free CH 2 ( 1A 1). By comparing Figures 5a and la we see also that the.,. bond for RuCH/ (4A2) has much more character on Ru+ (I.SS clectrollli) than Jue;:; the RuCH 2+ ('Az) 'K bond (J.lti electrons). This is consistent with the description of the RuCH 2+ ('A 2) 11' bond as an "in/out~ correlated Ru+ dT·orbital backbonding into the empty CH 2 p... orbital. By comparing the -.. bon.d of Figure Sa with the "in/out~ correlated two-electron d-.. pair in free Ru+ depicted in Figure Sc, we see that the ... bond of RuCH 2+ ('A 2) is indeed ad-.. pai; on Ru"' deloca~zi~g on.to ~H 2 • Thus, the fl- and -..-bonding orbitals of RuCH 2 ( A 2) indicate fl-donor ;-..-acceptor bonding as in 12. Howe~er, recall that hish·•pin d 7 Ru+ does not have an empty d.,. orl:ntal ready for o donating by CH 2 ( 1A 1). The discussion in section III.A proposes that if the singly occupied 4dfl orbital can mix in 5s character to rchybridize away from the Ru-C bond, Ru"' may simulate an empty du orbital by having no electron. density in the 0: region between Ru and c. The bottom plot of Figure 5a shows this singly occupied Ru+ orbital, which indeed rehybridizes out the back of the molecule to minimize repulsions with the Ru-C bonds. The Mulliken population of this singly occupied valence orbital show the predicted mixing of the 6 exciter! state into the d 7 ground state in order to effect this rehybridization (28% Ss, 72% 4d). This donor-acceptor bonding mode is further indicated by the Mulliken populations of each bond pair. For the u bond, there is considerable charge tranfer (0.73 electron) from the CH2 u orbital to Ru+, indicating a strong donor-acceptor interaction. This is complemented in the -.. system with a "-.. back-bond" which transfers 0.43 electron back to the CH 2 P...x orbital. Because Ru"' is paiitively charged, the back-donation from Ru"' is not as effective as it is e~pected to be in a saturated, neutral Ru==CH 2 complex, resulting in a slight overall charge transfer to the metal. The fl and -.. bond overlaps in RuCH 2+ ( 4A 2) provide further verification of our bonding description. In marked contrast to •'rl (27) (a) Hill, A. F.; Roper, W.R.; Waters, J. M.; Wright, A.. H.J. Am. Cltem. Soc. 1983, 105, 5939. (b) Roper, W.R. "Group VIII Trans1llon Metal Complexes of CH,. CF,. and Other Simple Carbenes". Presented at a Seminar at the California Institute of Technology, July 23, 1984. (28) Bauschlicher, C. W., Jr.; Schaefer, H. F., III; Bagus, P. S. J. Am. Chem. Soc. 1977, 99. 7106. 103- 2188 J. Am. Chem. Soc., Vol. 108, No. 9, 1986 Carter and Goddard ONE ONE @..~.·· : : w- .:' z z o) Ii) CH2 <:r DONOR BOND • . .. bl FREE CH2 <:r LONE PAIR ~,i·., ~' : - .,.: ONE ONE . z (iii Ru rr BACKBOND cl FREE Ru+ d7r LONE PAIR {£] z (iii) Ru 4d<:r RADICAL ORBITAL Flpre S. GYB orbitals for (a) the carbene complex RuCH 2 ~ (4A 2): (i) Ru-C /1 bond, (ii) Ru-C,.. bond, and (iii) Ru sci,> singly occupied; (b) CH 2 ( 1A 1) sp11 pair; (c) Ru+ (d7) d,..., pair. the covalently bonded state of RuCH 2+ (2A 2), which has u and r bond overlaps of 0.68 and 0.48, respectively, the RuCH 2+ ( 4A2) 11 and r overlaps are significantly larger, 0.83 for the 11 bond and 0.69 for the r bond. This fact by itself is suggestive of bonds more localiz.ed over only one center, since an Min/out" correlated /1 lone pair on CH 2 ( 1A1) has an overlap of 0.85 and a 4d lone pair on range from 37 to 46 kcal/mol29). Previous theoretical calculations for transition-metal carbenes have been limited to low-level calculations (HF) using experimental geometries with an MBS (minimum basis set) description of (C0) 4Cr-CH(OH) and (C0) 4Fe-CH(OH).)I) HF calculations are expected to describe covalent bonds poorly, but may provide acceptable descriptions Ru+ ba.s ;rn uverlap uf 0.93. Thw;, the "u bundft ha• almuot the uf dunur-.......,ptur bund5 in whi,;h the duubly """upicd dunur same overlap as the u orbital in free CH 2 (1A 1), highly suggestive of a localiz.ed 11 pair on CH 2 along with a localiz.ed r pair on Ru+ in RuCH2 + (4 Az). Even stronger evidence for this donor-acceptor model is provided from the behavior of the overlaps as we stretch the Ru-C bonds, shown in Figure 3. As discussed in section 11.B, the overlaps in covalent bonds arc expected to decrease monotonically to zero at infinite separation. The overlaps of the Ru-C bond pairs for orbitals have high overlap. Nakatsuji et al. )I) found bond energies for the above two hydroxycarbenes of 44.4 kcal/mol for the Cr system and 36.8 kcal/mol for the Fe complex at the HF level. The present bond-energy calculations as a function of electron correlation are given in Table VI. We have chosen here to calculate the (nonadiabatic) bond energy for RuCH 2+ ("A 2) dissociating to the uf/8 state of Ru+ (see Table I) and CH 2 ( 1A1). Since Ru+ and CH 2 adopt these electronic states in the complex, the •A, st.. te exhibit the opposite behavior. Here the overlaps dissociation with geometrical relaxation (i.e., to the equilibrium increase as the bond is stretched, with the maximum values reached at the infinite limit [corresponding to the overlaps of the lone pairs in the fragments Ru+ and CH 2 ( 1A 1)]. This behavior is completely consistent with our formulation of two lone pairs which clelocaJJ.ze at X. to form donor-aaieptor bonds and rclocaJJ.ze as the bond is broken. The vibrational frequencies of the 4A2state arc shown in Table II, where we see that the C-H symmetric stretching and scissors bending frequencies are nearly identical with those for the ground state. The only true indicator of a bonding change comes from the much smaller Ru-CH 2 stretching frequency (464 cm- 1 for the 4A2 state vs. 665 cm-1 for the 2A2 ground state). This suggests a looser, if not a weaker, bond (as discussed in the next section), geometry of singlet CHi) but no electronic relaxation (e.g., from 11<18 to ~F Ru+) will yield an intrinsic (promotionless) donor-acceptor bond energy. For comparison with experimental metalcarhene bond energies, this (promotionless) bond energy is the unportant one, SIDCC the metaH:arhene bond energy m a saturated metal complex is very likely to involve no electronic relaxation of fragments. For instance, the bond energy in a Fischer carbene complex, e.g., (CO)~W-C(OMe)Mc, involves the reaction a$ mi11ht be c!lpcct<:d intuitively from the nature of a donor-ac- ceptor interaction (not a strong function of distance). To summari;zc, all of the properties of the low-lying 4A2excited state of RuCH 2+ are in sharp contrast to those of the ground-state structure, with the orbitals, geometry, Mulliken populations, d'll'""f'1t back-bonding interactions, orbital-<lVerlap behavior, and vibrational frequencies completely supporting the description of the bonding in RuCH 2+ ( 4A2) as a 11-donor/r-acceptor situation. D. Bond Energies for RuCH 2+ ( 4A2). Donor-acceptor bond strengths for tro.nsition-metal systems have presently been limited experimentally to M-CO bond dissociation enthalpies (which (CO)sW-C(OMe)Me - (CO)sW + :C(OMe)Me. Since both W(CO)s (low-spin d6) and C(OMe)Me are expected to be singlets, no electronic relaxation is expected to occur (i.e., W(CO)s is not likely to relax to a triplet or change its low-spin d6 orbital occupation). Thus, the bond energy measured for W-C(OMe)Me will involve no promotional energies in the fragments and will therefore be an intrinsic donor-acceptor bond energy. To make a comparison with bond energies for saturated systems, we report electronically nonadiabatic bond energies that (due to the lack of electronic relaxation) correspond to intrinsic (29) Lt.Wis, K. E.; Golden, O. M.; Smith, G. P. J. Am. Chem. Soc. 1984. 106, 3905. (30) N.a.Uu.uji, H., U1hiu, J .• Harn, S-. Yuuc;uwa., T. J. Am. Chem. So.:.. 1983, 105, 426. -104J. Am. Chem. Soc., Vol. 108, No. 9, 1986 Bonding in Transition· Metal-Methylene Complexes 2189 Table VI. Bond Dissociation Energies (kcal/mo!) for the Carbenc State of RuCHt ('A 2) calculational level D,(Ru==C)• HF 41.3 GVB(2/4)-PP 42.5 RCl(2/4) 52.9 RCI, •o, + RC!, •o. 61.7 (RCl(2/4)•S),,1,1t. 64.0 (RCl(2/4) 0 S)..uJ.u 70.3' •o. •o. RCI. + RCI. + (RCl(2/4) 0 S),.uuu fragment total energies, hartres RuCH2+<'A2) total energy. hartrees• 65.8 Ru• -4437.173 31 (l/ l) -4437.17741 (2/2) -4437.177 63 (3/6) -4437.17909 --4476.120 76 (I I l) -4476.147 40 (4/4) -4476.164 19 (9/34) -4476.19480 (1065/5886) -4476.20096 (442/2570) -4476.216 96 (637 /4962) -4476.226 38 (15711/10042) (51/123) 4437.19659 (57 /168) -4437.19659 (57/168) -4437 .198 08 (101/269) 1 CH 2( A 1) -38.881 64 (l/l) -38.90231 (2/2) -38.902 31 (2/2) -38.91742 (53/53) 38.902 3 I (2/2) -38.908 31 (37 /40) -38.92342 (79/Q2) •Bond energy (D,) dissociating to the u~ state of Ru+ (see Table I) and the 1A 1 state of CH 2 (using the optimal GVB(l/2) description for CH 2 (11/f" correlated"' pair)]. •The number of spatial configurations/number of spin eigenfunctions are given in parentheses. 'We believe this value is an overestimate; see discussion in section IILD. donor-acceptor bond energies.11 •32 Examination of Table VI reveals that the O"-donor/..--acceptor bond strength (65.8 kcal/mol) in RuCH 2+ (4A2) is predicted to be nearly as strong as the covalent D,(Ru=CH 2, 2A2) of 68.0 Thus, two Ru-CO" bonds are more stable than one 86 kcal/mo! Ru=C terminal double bond, which implies D(Ru-C) :!: 43 kcal/moL k\;lil/mul. Huwcm:a, the; covalc;nl D, pn::di,;tc;d for a :saturat.::d IV. Summary Ru=CH 2 complex {68.0 + 15 83.0 kcal/mo!) is larger than the donor-acceptor saturated complex D., because the donoracceptor bond cl)ergy as defined does not depend on the degree of saturation (since the metal and CH, fragments do not electronically reorganize or change spin couplings). The progression of bond energies as a function of electron correlation in Table VI indicates a convergence to D.(Ru+=CH 2, 4A ) = 65.8 kcal/mo! as our best value for the donor-acceptor 2 Ab initio electronic structure calculations on RuCH 1+ reveal the following conclusions: i) RuCH 2+ has a 2A2 ground state with two covalent Ru-C bonds, resulting in a bond energy of 68.0 kcal/mo! for the unsaturated metai-<.:H 2 complex. ii) From the present calculations and others on more saturated complexes, a means of estimating covalent·bond energies for fully saturated metal complexes from bond energies known for un- intrinsic bond energy of Ru+ bonding to any oarbcne (CF 2, CR- saturated <'.omplexes is put forth, with th,. re<i11 It (OR), CCl 2, etc.). We consider the value of 70.3 kcal/mo! for RCI*S ••1,r, 11 to be an overestimate of the true bond energy due to an artifact of this particular calculation for donor-acceptor bonding configurations. This level leads to an imbalanced inclusion of electron correlation in which the complex is correlated to a greater degree than the fragments. This is consistent with the large 1A1...JB 1 splitting for CH 2 at this level (16.7 kcal/mo! rather than 13.2 kcal/mo! as found for other levels), leading to a bond In particular, this yields an estimate for an Ru=CH 2 bond energy in a coordinatively saturated complex of 83.0 kcal/mo!, which agrees well with a model saturated Ru==CH 2 complex (with a calculated bond energy of 85.S kcal/mo!). iii) A low-lying (12.9 kcal/mo! up) triply degenerate excited state exists (4 A1, 4Bi. 4 ~ with an Ru-C double bond of completely = energy which is too high. For covalent bonds, however, this calculational level leads to a fairly balanced description at R. and R = "" as borne out in the convergence of covalent bond energies for both Cr=CHt (•8 1) 1 and Ru=CH 2+ (2A 2). In summary, we predict donor-acceptor bonds of typical {singlet) carbenes such as :<.:1' 2, :<.:<.:1 2, :<.:R(UR), etc., to Ru to have bond strengths of -65 kcal/mo!, while covalent Ru=C alkylidene bond strengths in saturated complexes are expected to be -85 kcal/moL In addition, since Ru=CF 2 and other ruthenium-carbene complexes have been synthesized by Roper and co-workers,ll while terminal Ru-CR 2 alkylidene systems are as yet unknown (although postulated by Knox, 14 Werner, 22 and Shapley 3l), this suggests a lower bound on an Ru-C single (covalent) bond energy of 2:43 kcal/mo!. We conclude this simply by observing that many µ-CR 2-Ru complexes exist, with two Ru-CO" bonds in preference to terminal Ru=CR2 complexes.:w-36 ( 31 l No exchanac encraY is loot UPOn boodina in the&e complexes. Thus the intrinsic bond energy for a donor-aoceptor bond is "promotionleu" illstcad of "exchangeless". (32) To calculate an adiabatic bond energy for RuCHt ('A 2) merely involves D,( 1A1) - AE('A 1-1A 1) (see Figure 4). (33) (a) Clark, G. R.; Hoeldns, S. V.; Jones. T. C.; Roper, W.R. J. Cltmi. S<>c .. Chem. C<>mm~"· 1!183, 7/9. (b) CIAr~. G. R.; H<>ol<ins, S. V,; Roper, W. R. J. Organomet. Chem. 1982, 134, C9. (c) Hoelrins, S. V.; Pauptit, R. A.; Roper, W. R.; Waters, J. M. Ibid. 198-4, 269, C5S. (d) Roper, W. R.; Wright, A. H. Ibid. 19112, 233, C59. (34) Dyke, A. F.; Knox, S. A. R.; Mead, K. A.; Woodward, P. J. Chtm. Soc .. Chem. Commun. 19111, 861; and paper immediately following. (35) Holmgren, J. S.; Shapley, J. R. Orga110m11tallics 19115, 4, 793. (36) Lin, Y. C.; Wreford, S. S. J. Am. Chem. Soc. 1983, 105, 1619. D .. tura!l>d =Dintrittt.ic Y2Kdd "' Do...,tunted + M1.,.1 Y2Kdd diffcn:;nt ~lru,;;tu.11:; from the ground state; namely, the cxc;itcd state exhibits metal-carbene O"-donor / r·acccptor bonding. This donor /acceptor bond is worth 65.8 kcal/mol for both unsaturated and saturated complexes. iv) A lower bound of 43 kcal/mo! is obtained for ihe covalent Ru-C single bond strength in a saturated complex. V. Calculadoaal Details A. Basis Sets. All atoms were described with all-electron valence double-! (VDZ) basis sets. In addition, one set of dpolarization functions (Id= 0.69) was added to the C basis set. t A Four's level VDZ basis set was used for Ru with the (16s13p7d/6s5p3d) contraction, shown in Table VII. 37 The Ru and Ru+ state splittings obtained with this basis set contraction at the HF level are given in Table VIII. The standard Huzinaga-Dunning VDZ bases were used for C (9s5p(3s2p) and H (4s/2s). 38 B. Geometry Opdmizadoos. All geometrical parameters of the •A, and 2A, states of RuCH,+ were optimized at the GVBRCl(2/4) level (generalized valence bond-restricted configuration interaction). The GVB-RCl(2/4) description allows a full Cl within each pair of natural orbitals (NO's, two natural orbitals (37) Rappe. A. K.; Goddard. W. A., III, to be published. This basis set was optimized for the d• configuration of the metal as laid out in Rappe. A. K.; Smedley, T. A.; Goddard, W. A., III J. Phys. Chem. 1981, 85, 2607. The 4d VDZ basis optimized in this manner is an adequate description of tne valence space. (38) (a) Huzinaga. S. J. C/i,,m. Phys. 1965, "2. 1293; (b) Dunning. T. H .. Jr. Ibid. 1970, 53, 2823. -1052190 J. Am. Chtm. Soc .. Vol. 108. No. 9, 1986 TaWe VII. The Ru Basi> Set (ref. 37): Cartesian Gaussian Functioru with Exponents (a 1) and Contraction Coefficients (C,) function c, type a, 24880.0 0.020012 7 3752.0 0.138 963 2 0.483 648 9 848.1 231.5 331.7 60.94 24.01 35.38 9.385 3.929 5.203 1.285 0.4912 0.7682 0.097 77 0.03488 1212.0 284.7 88.76 30.9 20.06 11.68 4.489 0.495 2994 -0.1331553 0.4216589 0.672 7022 -0.305 4903 0.405 974 8 0.772575 7 -0.404813 7 0.690 5008 0.5490496 -0.531 7929 1.155993 9 1.0000000 0.028 609 8 0.187 631 2 0.522 389 5 0.427965 0 0.0639444 0.5004604 0.512 7291 p 9JJ9/ -0.04093 I I p 1.534 0.5207 0.8698 0.1292 0.631 7161 0.462 236 4 -0.202 323 5 1.056 815 3 p p p p p p p p p p 0.04051 p d d d d d d d 136 9 39.33 13.58 4.817 3.873 1.281 0.3139 l.0000000 0.044 6661 0.2414630 0.527 2307 0.4114895 0.195 821 5 0.8701024 l.000 0000 Table \llil. Hartree-Fock State Splittinl!S for Ru and Ru•• excitation energies (eV) total energy, hart recs -4437.30190 -4437 .350 33 -4437.397 94 -4437.138 66 -4437.183 54 this work ex.pt" NHF' 2.61 1.69 l.09 0.87 l.30 1.42 0.00 0.00 0.00 7.06 7.10 8.46 Ru•('F) 5.83 7.37 5.92 •Results arc for the Ru basis set contraction shown in Table VIL state Ru(1F) Ru( 50) Ru<'Fl Ru•( 6 D) • Numeriea! Ha.rtru-Foek rosult& from rof 39. 'E"'perimcnt.a.I do.ta from ref 25. averaged over angular momentum states. per M-C bond) describing the Ru-C u and ,,. bonds, resulting in nine spatial configurations. For 2A 2 RuCH 2+ these nine configurations have: 17 """°"iatc;d $pin oigcnfuni;;tivn• (SEF'>), while for the 'A 2 state the nine oonfigurations have 34 a.sS()ciated SEF's. The physical interpretation of the RCI wave function involves inclusion of interpair correlation and high-spin coupling on the metal atom. C. Boad Energies. I. RuCH/ (2A 2): CotaJmt Boock. Bond energies for RuCH/ were calculated at the Hartrcc-Fock (HF), generalized valence bond with perfect-pairing restriction [GVBJ(2/4)-PP, GVB-RCl{2/4), RCI. •o. + RCI. •o .. RCl(2/4)*S •• ,,R •• RC'1(2/4)*S, •.r.11 • and ((RCI,*D.-+- RCl,*D.)-+RCl(2/4)*S ..1,1u11) lcvels. The bond energies given in Table III are for the adiabatic dissociation pathway Ru-CHt ( 2A 2) ..... Ru+ (4F) + CH 2 <3B1) Calculations at large R(Ru-C) distances (e.g., 5.00 A) indicate that the u 111' 1 1 configuration of Ru+ at R. smoothly converts into 'F Ru+ at large R, giving rise to a truly adiabatic potential energy o {l9) Martln, R. L.; Hay, I'. J. J. CMm. l'hyl. 1!1111, I~. 4).l~. Car1er and Goddard pathway. We now define the higher order Cl's listed above: I) RCl,*D. + RCl.*D,: From the nine RC! configurations for RuCHt <'Ai). we allow all single and double excitations to all virtuais from one Ru-C bond pair at a time, while maintaining the RCI description in the other bond pair. In particular, while the Ru-C r bond is described at the RCI level, we simultaneously allow all single and double excitations from the Ru-C /1 bond pair and then vice versa, hence the name RCI. *D. + RCI. This Cl dissociates properly to HF fragments. (Note that all single and double excitations from both bond pairs simultaneously do not dissociate to a cleanly described limit.) 2) RCl(2/4)*S.•1.Ru: From the nine RC! configurations we allow all single excitations from the valence Ru orbitals and the Ru-C bonds to all virtuais. This Cl is also dissociation-consistent, dissociating to HPS......,. for Ru+ and HF for CH 2• 3) RCl(2/4)*S..1.ru11 : From the nine RC! configurations we allow all single excitations from all valence orbitals (including CH pairs) to all virtuals. We allow this Cl to dissociate to HP5,..i fragments, although this is overcorrclating the dissociated limit and thus will give too small a bond energy. Test calculations indicate this leads to at most a 0.2 kcal/ mol underestimate of the bond energy. 4) ((RCl,*D, + RCl .. D,) + (RCl(2/4)*S.,.. 1.ruu)]: This CI is merely the superposition of the previous two Cl's listed above, dissociating to HF"S.,.1 fragments, with the same slight overo.;orrclation problem resulting in -0.2 kcal/mol too low a bond energy. 2. RuCH 2+ ('A2): Donor/ Ac:ceptor Boads. The bond energies for the• A 2 state were calculated at the same levels as the ground state; thus the Cl's arc identical at R. for both states. However. this state dissociates to CH 2 ( 1A 1) and 110~ Ru+ (since the electronic configuration of Ru+ at R. docs not change upon stretching this type of bond). We allow the CH 2 u pair to use a r-correlating orbital as a second natural orbital, since this is the optimum GVB(l/2) description of singlet CH 2. Note that at R., 'If back-bonding from Ru+ forces the dominant correlating orbital to be u• for the CH 2 <T pair. Thus the dominant correlation changes from R. to R = '"" and we allow the optimal correlation for both limits. We now discuss the Cl's in terms of their dissoetation limits, since these limits arc different from the covalent case. I) RC!, *D. + RCI. *D,: This CI dissociates to a GVB( I/ 2)-corrclated Ru• d... pair and a GVB(l/2)-correlated CH 2 u pair, from each of which all single and double excitations to all virtuals are allowed. This overcorrclates the infinite limit (since simultaneous double excitations on both fragments result in overall quadruples), leading to a lower bound on the bond energy. However, test calculations at R = "' show these quadruple ex1.;il.ation~ do not contribute to the bond energy. Thus the bond energy is effectively dissociation-consistent. 2) RCl(2/4)*5..i.Ru: This wave function dissociates properly to RCI(l/2)*S ••1 on Ru+ and RCl(l/2) on CH 2 ( 1A 1). 3) RCH2/4)•S...uui1: This wave function dissociates to RCI(l /2)*S...i Ru+ and RCl(l/2)*Sval CH 2, which provides a lower bound on the bond energy, but in practice, test calculations suggest this overcorrelation is negligible (<0.02 kcal/mo!). 4) ((RCl,*D, + RCI,•D,) + (RCI(2/4)*S,.1,ruli)]: The SU· perposition of the two Cl's above dissociates to [(RCl(l/2)*D~) + (RCl(l/2)*5,..i)) Ru• and ((RCI(l/2)*D,) + (RCl(l/WS..aJl] CH 2• Again this wave function involves higher order excitations at R = "' that arc not included at R., resulting in a net overcorrelation of 0.3 kcal/mol from test calculations. 5) "Test Calculations": We superimpose the two fragment wave functions without allowing any electronic interaction between them, to simulate the infinitely far apart fragments. Then we perform the same Cl's for this superimposed fragment wave function as were calculated at ·R.. This provides a check on potential ovcrcorrclation problems. The largest difference between the ~test" bond energies and the bond energies calculated from the (sometimes overcorrelated) fragments was 0.3 kcal/mo!. D. State SpUtings. The 'A 2 state at the GVB(2/4)-PP level has a valence space consiStlng of two C-H doubly occupied orbitaiS •o.. -1062191 (treated as HF MO's), two Ru-C bond pairs each with a second NO for a total of four Ru-C bonding orbitals, one doubly occupied nonbumling dit.vz orbilal, and three singly occupied dO', dll, d~ orbitals, for a total of 10 orbitals in the valence space. At the GVB(2/4)-PP level for RuCH 2+ (2A 2), there is the same orbital space for CH 2 and for the Ru-C bonds, but there are two doubly occupied nonbonding d orbitals (dit,, and do.,_,)) plus one singly occupied dtl,, orbital, for a total of nine valence orbitals. To treat the states of RuCH 2+ with the same degree of flexibility, we must have the same number of valence orbitals in the SCF calculations. Therefore, for RuCHt (2A 2) we correlate the do.,_; with a second natural orbital (leading to a GV li(3 /6)-PP description) in order to compare with the GVB(2/4)-PP description of RuCH/ (4A 2). Acknowledgment. This work was supported by the Shell Development Company, Houston, TX, and the National Science foundation (Grant No. DMR82·1'6)U). Registry No. Ru===CH,+. 101031-94-1. -107- Chapter 2.C. The text of this section is an Article coauthored with William A. Goddard III which appeared in the Journal of the American Chemical Society. -108- Reprinted from the Journal of the American Chemical Society, 1986, 108, 4746. Copyright© 1986 by the American Chemical Society and reprinted by permission of the copyright owner. Bonding in Transition-Metal Methylene Complexes. 3. Comparison of Cr and Ru Carbenes; Prediction of Stable L,.M(CXY) Systems 1 Emily A. Cartert and William A. Goddard III* Contribution No. 7 336 from the Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91125. Received December 9, 1985 Abslnlct: The electronic structure of the lowest carbene state of a representative early-transition-metal complex. CrCH, + ( 6A 1 symmetry), has been examined by using ab initio techniques. Its properties reveal a complex with a single u-donor bond from singlet CH 2 to high-spin (d 5) er+ and no ll'·back-bond, resulting in a low bond energy (38.7 kcal/mo!) and a large carbene-alkylidene state splitting (18.8 kcal/mo!). These results are contrasted with Ru carbene (possessing both u· and ir-donor bonds) properties [D.(Ru=C) = 65.8 kcal/mo! and M(carbene-alkylidene) = 12.9 kcal/mot]. This comparison enables, for the first time, a separation of u-donor bond strength• from ...donor bond strengths. Finally, using only valence electron properties, we are able to predict stabilities of L.M(CXY) complexes (e.g., how substituents at carbon affect the preference for bridging vs. terminal CXY), discussing trends for the entire transition series. I. Introduction Terminal metal carbene and alkylidene complexes arc ubiquitous throughout the transition elements. 2 The nomenclatural distinction between "carbene" and "alkylidene" represents a fundamental difference in rcactivity. 3 Metal carbene complexes usually behave as electrophiles, with typical reactions including Lewis base adduct formation via attack at the carbon center• ~B 0 ,_..R' Ln M-~"'·R' L.M=C'-OR + B: - and olefin metathesis. 9 d (I) R R _.,.R" /C"LnM OR R', ,_..R" R',,,C=C'-R" and stoichiometric cyclopropanation of olefins 5 [ l ,1 R' R' RO R' 'i /, + '-c/ C""·R" - R'c=c,,-R" R/ 'R" (6) (2) These two greatly different modes of reactivity reflect a dra- On the other band, metal alkylidene complexes are nucleophilic, undergoing Wittig-type alkylations, 6•7 Lewis acid adduct formation,8 ( 1) (a) Paper I of this series: Caner, E. A.; Goddard, W. A., Ill J. Phys. Chem. 1984, 88, 1485. (b) Paper 2: Caner, E. A.; Goddard. W. A., l1l J. Am. Chem. Soc. 1986, 108, 2180. (c) Earlier work on high-valent alkylidene complexes includes: Rappe, A. K.; Goddard W. A., Ill J. Am. Chem. Soc. 1982. 104, 291; 1982, 104, 448; 1980, !02, 5114. .1-r-· (2) For a comprehensive review. see: D-Ot2, K. H.; Fischel', H.; Hofmann, 0 + II c /\ R X [(Y~Ta =o ]• .,. " • x, c-c R' 0 CH 2 RCOR' R-C-OR II II ,x (3) 'H , (4) tNational SQi111mO(ll Foundation Predoctoral Fellow, 1982 1985. 0002- 7863/86/1508-4746$01.50/0 P.; Kreiss!, F. R.; Schubert, U.; Weiss, K. Transirion Metal Carbene Com· plexes; Verlag Chemic: Deerfield Beach, FL, 1984. (3) Collman, J.P.; Hegedus, L. S. Principles and Applicarioll.! of Organotransition Metal Chemistry; University Science Books: Mill Valley, Ca, 1980; Chapter 3. (4) (o) Wung, W.-K., T•UI, W., Ol•<ly><, J. A. J. ,-(m. Chem Sue 1979, JOI, 5440. (b) Yu, Y. S.; Angclici, R. J. Organomttallics 1983. 2, 1018. (c) Kuo, G.·H.: Helquist, P.; Kerber, R. C. Ibid. 19114, 3, 806 (5) (a) Fischer, E. 0.; DOU'., K. H. Chem. Ber. 1970, 103, 1273. (b) Dotz. K. H.; Fischer, E. 0. lbid. 1972, 105, 1356. (c) Stevens. A E.; Beauchamp, J. L. J. Am. Chem. Soc. 1979, IOI, 6449. (d) Brandt, S.: Helquist. P. J. Ibid. 1!17!1, 101, 6473. (e) Brookhart, M.; Humphrey, M. B.; Kratzer, H. J.; Nelson, G. O. /bid. 1980, 102, 7803. (f) Brookhan, M.; Tucker, J. R.; Husk, G. R. Jbid. 1981, 103, 979. (g) Casey, C. P.; Vollcndorf, N. W.; Haller, K J. /bid. 1984, 106, 3154. (h) Casey, C. P.; Shusterman, A. J Organomera/lics 1985, 4, 736. (i) Brookhart, M.; Studabakcr, W. B.; Husk, G. R. Ibid. 1!185. 4. 943. (j) Casey. C. P.: Miles. W. H.: Tukada. H. I Am. Chem Soc. 1985 107, 2924. (k) Stevens, A. E.; Beauchamp, J. L. Ibid. 1978, /00, 2584 (6) S<:hroclc, R. R. J. Am. Chem. Soc. 1976, 98, 5399. (7) (a) Tebbe, F. N.; Parshall, G. W.; Reddy, G. S. J. Am. Chem. Soc. 1978, JOO, 3611. (b) Pine, S. H.; Zahler, R.; Evans, D. A.; Grubbs, R H. Ibid. 1980, 101, 3270. (8) Schro<>k, R. R. J. Am. Chem. Soc. 1?75, 97, 6577 © 1986 American Chemical Society -109Bonding in Transition- Metal Methylene Complexes matic difference in the metal-carbon bonding. Conventional design prescriptions call for "low-valcnt" metal fragments [e.g., W(CO)i] for carbencs and "high-valent" metal moieties (e.g., Cp2TaR) for alkylidenes in order to maximize stability of the resultant complex. In addition, the presence of a heteroatom on the CXY ligand is known to stabilize carbenes, while alkyl or hydrogen groups are thought to stabilize alkylidene ligands. The combination of a "low-valent" metal fragment with a C(OR)R' (or C(NR 2)R'. etc.] carbene ligand translates into the now-familiar 11-donor bond from the carbene and donor r-back-bond from the "low-valent" metal. As we have shown previously, 1 "high-valent" metals interacting with an alkyl-only-substituted CXY ligand J. Am. Chem. Soc .. Vol. 108. No. 16. 1986 4747 (11?r) state of the CXY ligand (two unpaired electrons) A triplet ground state of CXY will be favored when X and Y are not heteroatoms but rather are alkyl (or hydrogen) substituents. Hence, the statement that •high-valent" metal fragments and alkylcarbenes are necessary for stable metal-alkylidene formation translates physically to high-spin metal atoms (in which the selectrons are utilized in ionic bonds), forming covalent metalcarbon double bonds to ground-state triplet CRR' ligands. rl!'.imlts in an olefinic-type, c-m1afPnt douhle hnnd These contrasting bonding structures (donor/acceptor for carbene and covalent for alkylidene) are given physical justification via the valence bond view of metah:arbene (alkylidene) bonds. I. Metal Carbenes. The "low-valent" metal fragment is generally surrounded by closed-shell ligands (such as CO or PR 3). In this environment, the metal atom is forced into a low-spin, d" electronic state to minimize Pauli repulsions (orthogonality) with ligand lone pairs. A low-spin, d" metal atom has doubly occupied d-orbitals set up for ir-back-bonding to a carbene (or other ancillary ligands with low-lying acceptor orbitals). The carbene fragment will be a 11-donor as desired, if the singlet state of the CXY ligand is the ground state. The purpose of the electronegative heteroatom linkage (e.g., X OR, NR 2, F, Cl) is to •LabiliL.<: the: oinglc;t (u') •late; uf CXY. The lwu lowc•l •tall:> uf CXY are triplet (.rr) and singlet (.r2). = In this paper we compare and contrast properties of simple metal carbenes, (M=CH 2)+, involving an early, first-row transition metal (Cr) and a late, second-row transition metal (Ru). In particular, their relative stabilities and M-C bond strengths are examined, with the emphasis on how early transition metals are expected to differ from late transition metals in these unsaturated systems. Section II discusses new results of ab initio calculations on the lowest carbene state of CrCH 2+ ( 6A 1), while section III briefly reviews previous work on the lowest carbene state of RuCH 2+ ( 4A2). The comparison of Cr and Ru carbenes allows, for the first time, donor/ acceptor bond strengths to be separated into 11-donor and r-donor single bond strengths (section IV). Fiually, u•ill!! iuformaliun glc:anc;u frum our presem and previous work on both carbenes and alkylidenes, we predict stabilities of L.M(CXY) complexes, discussing trends for the entire transition series (section Y). Section VI contains a summary, while section VII supplies calculational details. II. Carbene Bonding for CrCH 2+: The 6A1 State 2 If either X or Y is electron-withdrawing, then the C-X and C-Y bonds will involve mostly p-character on carbon (lower ionization potential (IP) than s]. In addition, the p?r lone pairs on X (or Y) will donate electron density into the C pir-orbital. Both of these effects work to destabilize the carbon p?r and to stabilize the carbon .r-orbital, resulting in a .r2 (singlet) ground state. Thus the requirement of "low-valent" metals and ~heterocarbenes" for the formation of stable metal-carbenes physically means that doubly occupied metal d-orbitals and a ground-state singlet carbene will result in .r-donor / ?r·acceptor metal-carbene bonds. 2. Metal Alkylidenes. The Mhigh-valent" metal fragment generally has a ligand set consisting of one or more ionic ligands (Cp, Cl, O(t-Bu), etc.) and alkyl ligands (odd-electron fragments). The ionic ligands prefer to bond to s-electrons (lower IP than d-electrons) on the metal, while the alkyl ligands require singly occupied metal d-orbitals to bond to. As described previously, 1b the ionic ligands effectively oxidize the metal (e.g., Cp2Ta 11 CH 3, where "II" indicates Ta is oxidized by two units in essentially transferring the metal s-electrons to the Cp ligands), leaving a d" metal ion. Without closed-shell ligands to force a low-spin metal configuration, the metal adopts the lowest energy configuration available, namely, the highe•t spin state allowed within the five d-orbitals. This metal atom (ion) is now set up to covalently bond to any ligand with unpaired electrons, be it alkyls or the triplet (9) (a) Lee. I. B.: Ott, K. C.; Grubbs, R.H. J. Am. Ch<!m. Six. 1982. 104, 7491. (b) Wengrovius. I. A.; Schrock, R. R.; Churchill, M. R.; Misscrt, l. R.; Youngs, W. I. Ibid. 1980, 102, 4515. (c) Gilet, M.; Mortreux, A.; Folcst, J.-C.; Petit, F. Ibid. 1983, 105, 3876. (d) Kress. J.; Osborn, J A. !bid. 1983, 105, 6346. (e) Katz, T. J.; Han, C.-C. Organometa//ic-s 1982. 1, 1093. (I) Howard, T. R.; Lee, J. B.; Grubbs, R. H.J. Am. Chem. Soc. 1980. 102, 6876. The lowest (two) states of CrCH 2+are formed by combining the ground state of CH 2 (38 1; see l) with the ground state of er+ (65). This combination of spins (S = l with S = '/ 2) leads to three possible values of total spin: S = 3Ii (with a double bond). S = 5/ 2 (with a single bond), and S = 7/ 2 (with no bond). Thus the ground state of CrCH 2+ is 4 8 1 with covalent .rand ir bonds [leading to a total bond energy of D.(Cr=C, 4B1) = 44.0 kcal/mol (49.6 kcal/mo! at the fully correlated limit)], leaving three unpaired d-electrons on the Cr center. The first excited state is 6 8 1 with a covalent 11 bond, leaving four unpaired d-electrons on Cr and the unpaired C p?r·electron all coupled high spin to yield S - 'Ii [kallin!! tu a tutal 1.>onu cncr!!Y uf D,(Cr-C,6B 1 ) = 25.0 kcal/mol (30.6 kcal/mo! at the fully correlated limit)]. The other combination of ground-state Cr+ and CH 2 where S = 7/ 2 has no bond, leading to a repulsive potential curve. 'a A simple-minded interpretation of the above results would suggest a 11 bond worth 30.6 kcal/mol and a .. bond of 19 kcal/mo!, both seemingly quite weak. Jn fact, the interatomic spin pairing essential to covalent bond formation necessarily leads to a reduction in the intraatomic high-spin coupling favored for each atom (Hund's rule), so that the observed bond is much weaker than it would be if no extra unpaired orbitals were available. Indeed, the spin pairing for the double bond of 4B 1 leads to a loss of 57.8 kcal/mo! in exchange energy. Thus. the intrinsic strength of the double bond is 107.4 kcal/mol even though the observed bond strength is only 49.6 kcal/mol On the other hand, for the 68 1 excited state, with only one covalent bond, the loss of intraatomic exchange is only 33 kcal/mol, so that the intrinsic strength of the <r bond is calculated to be 63.6 kcal/mol This enormous loss of intraatomic exchange energy engendered by covalent bond formation to ground state CH 2 (methylidene bonding) leads to the possibility that states involving the singlet excited state (2) of CH 2 might be low-lying. In this case, the bonding is dominated by overlap of the <1 pair of CH 2 with Cr+ + ~,,.H <:::>er ~c" " H -1104748 J. Am. Chem. soc .. Vol. 108. No. 16, 1986 Carter and Goddard Table I. CrCH,+ State Splittings• and Bond Dissociation Energies (kcal/mo!) for the Carbene State of CrCH 2+ ( 6A 1) calculational level D,(Cr-C) 6A CrCH • total energy. hamee• 1 2 HF GVB(l/2)PP GVB-RCl(2) RCl(2J•D, RCl(2J•S," RCI(2)"D, + RCI(2)•S,. 1 35.8 29.9 30.3 33.4 36.7 38.7 -1080.94226 (I/I) -1080.953 62 (2/2) ·-1080.95427 (3/8) -1080.97403 (184/759) -1080.97048 (211/1184) -1080.98848 (366/1799) A£( 6A 1- 6B 1)' _ _ __::AE=(...:'A..:..:_,-_'::.B'-'1 )' -16.8 -70.5 -12.6 -23.9 -11.3 +1.2 +0.8 •a, +18.8 = = •The 6 8 1 and CrCH,+ total energies are reported in ref la. 'Total energy in hartrees where I hartree 27.2116 eV 627.5096 kcal/mo!. The values in parentheses are (number of spatial configurations)/(number of spin eigenfunctions). 'The values shown are at the correlationally consistent calculational levels for 'A" 68 1, and 48 1, as discussed in section VII. with no loss of intraatomic exchange energy. 10 This requires the promotion of CH 2 from 38 1 to 1A 1, at an energy cost of 9 kcal/mol, 11 followed by complexation via a tr-donor bond to ground-state, high-spin d 5 Cr+ to form the 6A 1 (carbene) state. In contrast to the 48 1 and 68 1 states, no exchange terms are lost on er+' since all five high-spin paired electrons on er+ remain high spin. Since the C p..--orbital is empty, this donor-acceptor state could be stabilized by d..--p..--back-bonding. However, we find that with only one electron in the Cr d..--orbital, this backbonding provides negligible stabilization. The 6A 1(carbene)-4 Bi(methylidene) state splitting as a function of electron correlation is given in Table I. The three GVB calculational levels used here to obtain 6.£( 6A 1-'B 1) are correlationally and orbitally wm;istcnt. That is, at each level, the same number of orbitals and the same types of excitations are included for both the 6A 1 and the '8 1 states. [Other levels of calculation examined in evaluating the Cr-C bond energies (see Table I) do not treat these two states comparably and are not used in considering the state splitting.] From Table I, we see that the state splitting is sensitive to the level of electron correlation. Notice the complete about-face of 6.£( 6A 1- 4B1) upon relaxation of the perfect pairing restriction, as in the GVB RCI wo.vefunction. At the best level of .::alculation, we find that the carbene state (6A 1) lies 18.8 kcal/mo! above the methylidene ( 4 8 1) ground state. Thus. 6A 1 is only 0.8 kcal/mol above the 68 1 state at the same level of theory. 12 Supporting evidence for the presence of two excited states of CrCHz"' ly1ng about 18-19 kcal/mo! above the ground state comes from recent experiments by Beauchamp and co-worker:s 13 in which translational energy loss spectroscopy was used to search for excited states of CrCH 2+ formed from Cr+ colliding with CH 4 -.. 0 E ~ , c;-e:.-c."'1-1 ~ ."' '"" M<L<>?.." 00 c;cHi t'e11 ti~ c1 ti c w c:c.., ,..,, ~~" r;rM" 1•"'11 c1'F6~ Figure I. Electronic state correlation diagram for the three lowest states of CrCH,+: 6A1. 6 81. and 4 8 1 . The two R 1 "'tMt':<i. rli1:;.1:0l'i~:it(" to 6<;. er+ and 38 1 CH 2, while the 6A 1 state dissociates to 65 Cr• and 1A, CH,. + • ' <.,,l>')H in a mol.,c.nl~r heam The •peetnim indieate• a wide weak peak consistent with at least one spin-forbidden transition at an energy of -24 kcal/mo! less than the elastic peak. Given an energy resolution of 0.2 eV ( -5 kcal/mo!), our theoretical values for the sextet-quartet energy gaps are within the ellperimental error. The relative energies of the three low-lying states of CrCH 2+as well as their respective limits at infinite R(Cr-C) are displayed in Figure I. The optimum geometry of the single-bonded donor /acceptor 6A, state [see Firmre 2a: RCCr-c) = 2.32 A. 8(HCH) 108.9°) differs considerably from the covalently single-bonded 68 1 state 6 6 [R(Cr-C, 8 1) = 2.07 A, li(HCH, 8 1) 118.3°], with a Cr--C bond length longer by 0.3 A and a much smaller HCH bond angle, 14 15 close to that in free singlet CH 2 (102°). • • The long Cr--C bond = = (10) An exception to this statement exists if enough ligand donor bonds force the orbital into a lower spin state in order to allow more effective o-·donation. In this case, the spin coupling is indeed affected, and some exchange energy is lost. For CrCH,+, however, we need not force the metal into a lower spin state. (11) Leopold, 0. F.; Murray, K. K.; Lineberger, W. C. J. Chem. Phys. 1984, 81, 1048. (12) There is no corrclationally consistent calculational analogue for 6A 1 CrCH 2• at the RCJ•S.,1 + [RC!, •o. + RC!, •o.] caiculational level (see ref la) which yielded A.E('B,-'B,) • 19.0 kcal/mo!. Therefore we compare excitation energies at the highest corrt/ation·consistent level. RCl•Svalcnoe· (13) Hanratty, M.A.: Carter. E. A.; Beauchamp, J. L.; Goddard Ill, W. A.: Illies, A. J.; Bowers, M. T. Chem. Phys. Lett. 1986, 123, 239. ( 14) The C-H bond length is insensitive to mode of bonding and was kept fixed at 1.078 A. 8(H-C-H) for 'A, CH 2: Harding, L.B.: Goddard, W. A., III Chem. Phys. Lett. 1978, 55, 217. /H Ru~C)113.o• a b Figure 2. Optimum geometries for the carbene states of (a) CrCH/ ('Ai) and (b) KuCtt 2• ('A 2). length and the small HCH angle are expected for a tr-donor bond with negligible d11'-p11'-back-bonding from the singly occnpied Cr d11' -orbital, a description that is also indicated by Mulliken populations and orbital plots. The orbitals for the carbene state, CrCH/ (6A 1), are shown in Figure 3a where we see a Cr-Ctr bond consisting of an "in/out" correlated CH 2 tr pair (l.75 electrons on CH 2 with a high bond orbital overlap of 0.83) delocalizing toward the Cr cation (0.25 electrons transferred to er+), similar in character to the u-donor bond for the carbene state of RuCH 2+ (4A 2), as shown in Figure 3b.i. In contrast to the carbene state of RuCH/, however, we find no d11'-p11'·back-bonding for the carbene state of CrCH/. Thus, Mulliken populations indicate only 0.01 electrons donated from the Cr 3d..-,, singly occupied orbital to the CH 2 2px orbital, and even at the much shorter Cr-C bond length of 2.07 A, the d11' delocalization is only 0.05 electrons for CrCH/ (6 A 1). In contrast, for the carbene state of RuCH/, there are 0.43 electrons transferred from the Ru d..- doubly occupied orbital into the C 0 ( 15) (a) Bauschlicher, C. W., Jr.; Schaefer, H. F .. Ill; Bagus, P. S. J. Am. Chem. Soc. 1977. 99, 7106. (b) Carter, E. A.; Goddard, W. A .. III J. Phys Chem. 1986, 90, 998. (c) Koda, S. Ibid. 1979, 83, 2065 -111Bonding in Transition-Meta/ Methylene Complexes J. Am. Chem. Soc., Vol. 108. No. 16, 1986 ONE ONE al . ·~· 4749 b) y z z (' l CHz O" DONOR BONO (,) CH 2 O" DONOR BOND • ONE ' x .. z (i,) Cr 3d7rxz + . z RADICAL ORBITAL (id Ru 1T BACK BONO IE [£] z z (tu) Cr 3dcr PADIC/\L ORSITAL (,;,) A1.1 4d~ f"{AOICAL Of10JTAL GVB one-electron orbitals for the carbene states of (a) CrCHi' (6 A 1) Flpre 3. [(i) CH 2 a-donor bond; (ii) Cr 3dr singly occupied orbital; (iii) Cr 3da singly occupied orbital] and (b) RuCHt ('A 2) [(i) CH 2 a donor bond; (ii) Ru 4dr-back-bond; (iii) Ru 4da singly occupied orbital]. Contours represent regions of constant amplitude ranging from -0.5 to +0.5 au, with increments of 0.05 au. P1f empty orbital. The difference here is that electron repulsion in the doubly occupied orbital drives one of the electrons toward delocalization, as displayed in Figure 3b.ii. The lack of a 11"· back-bond leads to the long bond length of 2.32 A for c~rbene and a low Cr-C carbene stretching frequency of 295 cm· 1 (in comparison with 464 cm- 1 calculated for the doubly bonded Ru==C carbene stretching frequency). Another difference between the bonding in the carbene states of CrCHt and RuCHt is in the behavior of the singly occupied metal du-orbital. illustrated in Figure 3, parts a.iii and b.iii. For CrCH/ ( 6A 1), there is minimal s-d mixing into the singly occupied Cr u orbital (94.1 % 3d/5.9% 4s) because the small size of the 3d orbital and the long Cr-C bond length leads to little overlap between Cr 3d and the u pair of CH 2. However, for RuCH/, the M-C bond length is much shorter (due to the 11"-back-bond) and the Ru+ 4d-orbital is larger (than Cr 3d), leading to a high overlap with the u pair of CH 2• As a result, the singly occupied Ru du-orbital·must s-d hybridize in order to minimize repulsive interactions (the singly occupied Ru u orbital has hybridization 72% 4d/28% Ss). Summarizing, the various properties (orbital character, long bond length, small vibrational frequency, and small HCH bond angle) in the carbene state CrCH/ (6 A 1} reveals a bond involving a donor u bond from singlet CH 2 to high-spin, di er+. The carbene-methylidene state splitting (6A 1- 48 1) is larger for CrCH 2+ than for RuCH 2+ ( 4A 2- 2A 2) due to the presence of a strong two-electron 1' back-bond for RuCH 2+ (4A 2) and no 11"-back-bond for CrCH,+ (6A,) The basic properties of the carbene state of RuCH 2+ necessary for comparison with the Cr carbene system include the following: (i) The carbene-alkylidene energy gap [6.£(4A 2- 2 A 2}) is 12.9 kcal/mo! at our highest level of theory. (ii) The optimum geometry at the GVB-RCI(2/4) level is shown in Figure 2b. The carbene nature of the Ru-C bond is supported by the small H-C-H bond angle of 113° and the longer bond length of 1.93 A compared to that of the ground alkylidene state (1.88 A). (iii) The GVB orbitals are shown in Figure 3b where we see that the CH 2 forms au-donor bond to Ru+ involving an in/out correlated, sp2 hybrid, while the Ru+ forms a 7'-back-bond to the empty C pir orbital. The charge transfers involved in these bonds work in concert (electroneutrality principle). Thus, the' Mulliken populations indicate 0. 73 electrons donated to Ru+ in the u system and 0.43 electrons donated to CH 2 in the ,,. system. (iv) The Ru==C carbene bond energy is 65.8 kcal/mol in RuCH/ (4A 2), probably a representative bond energy for coordinatively saturated, low-valent metal heterocarbenes. The Ru=C alkylidene bond energy in RuCH/ (2A 2) is 68.0 kcal/mol, leading to an estimated 1b Ru==CH 2 alkylidene bond energy of 83.0 kcal/mo! for a saturated complex. (An independent, direct calculation on a model saturated system yielded 84. 7 kcal/mo! for the Ru==C bond strength.) IV. Partitioning the Double Bond into u- and 11"-Donor Contributions Ground-state high-spin d 7 Ru+ forms three degenerate carbene states upon interaction with CH 2 ('A 1). These three states (4A 2• 4 8,, 4 8,) arise from de2enerate valence electron confi2urations 1b on Ru+ and differ in the CH 2 complex only in the occupation of the nonbonding cl-orbitals. They have equivalent bonding descriptions, namely, that of a Ru-C a-donor/ ?r-acceptor double bond. We chose to examine the 4A 2 state in the most detail simply 11"-Back·bondlng ls commonly involved in discussions or organometallic metal-ligand bonds having ligands with low-lying 11"-acceptor orbitals (e.g., CO or CXY, where X and/or Y are electron-withdrawing groups), but little quantative evidence is available reurding the strength of and the extent of char~e transfer in such a 'Jl"·bond. The only experimental verification of this effect is obtained indirectly by assigning changes in bond lengths and vibrational frequencies in M-CO or M==CXY systems as due to changes in the eJttent of back-bonding. The calculation because it hns the same spatinl symmetry ns the ground (2A 2 ) outlined below provides a dirc:ct, quantitative a.>ae33ment regarding alkylidene-type state. such bonds. Ill. Carbene State of RuCH 1+: A Re~iew -1124750 J. Am. Chem. Soc .. Vol. 108, No. 16. 1986 Carier and Goddard From two independent analyses, we find that the 'll'·back·bond in the carbenc state of Ru Cl 11+ ('1'1 2 ) is worth appro,.im11tcly 30 kcal/mo!. Our approach was to eliminate the C 2p, and 3d..., basis functions from the SCF calculation, thereby prohibiting 11'back-bondmg since no delocalization into the C 'll' system is poosible. This results in an energy destabilization of 27.4 kcal/mol. Since the rest of the bonding remains the same as m the full basis set description, this destabilization may be attributed solely to the strength of the 11'-back-bond. A more reliable estimate for the ... bond strength is obtained by examining the 'B 1 carbene state of Ru<'H,+ which rliffer. frnm RuCH,• ('A,) nnly in having r~ersed d'll',,- and do,>-orbital occupations ((d11',,,) 1(d6,,.) 2 for 4 8 1 and (d ....,) 2(dcl".)1 for 4A 2 j.l 6 Since the 4 8 1 state has a negligible one-electron 'll'-back-bond (vide infra) and the 'A 2 state has a significant two-electron x-back-bond, the 48\-'A 2 splitting is a choice of metal and ligand environment. The purpose of thi!l section is to discuss how to """ ouch valence bond ideas to control metal-ligand bond character, thus opening up the possibility for distinctive changes in chemical reactivity of organotransition-metal systems. Our premise is that control of the electronic configuration of the metal center-not merely oxidation state-is the key to controlling both the bond type and bond strength for a given metal-ligand system. For the sake of brevity we will illustrate such effects only for M-CXY systems, but the arguments expressed may be applied to any other met· al-ligand sy~tem with nverall covalent character First, we discuss how intraatomic exchange stabilization and promotional energies affect metal-;>rbital hybridization, bond character (covalent vs. donor /acceptor), and bond strengths in metal-carbon bonds. Second, we describe how ligand type affects Th~ energy •pliuiug Wd5 the nature of tin; mctal-,;arbon bond. Third, we cuncludc: with calculated to be 31.5 kcal/mo!. in close agreement with the other x bond strength estimate of 27.4 kcal/mo!. Thus, we conclude that the strength of the ir·back-bond for RuCH 2 + ('A 2) is -30 kcal/mol. For neutral, less electrophilic metal centers. we expect T·back-bond strengths to be higher than 30 kcal/mo\, since delocalization into the carbene ,.. system should be more facile. Both the RuCH/ ( 4 8 1) excited state with its singly occupied dir-orbital and the CrCHt ( 6A 1) excited state (high-spin d5 Cr+) can only provide one-electron dir--P'Jf·back-bonding to CH 2 1). The extent of charge transfer is negligible in both cases. with 0.10 electrons transferred by Ru+ and 0.0 I electrons transferred by er+. (We expect slightly more electron transfer for Ru+ since 4d-orbitals are larger than 3d-orbitals and can thus delocalize more effectively.) Thus. for both first- and second-row transition-metal ions, the one-electron dir--pir-back-bond is negligible in comparison with a two-electron d ...-p,,.·back-bond. The bond energy of the CrCH 2+ ( 6A 1) is interesting because it provides quantitative determination of the strength of a single u-donor bond, unlike the case of RuCH/ ('A 2). in which there is both a u- and a r-donor bond. making it difficult to determine the energy partitioning in the Ru-C double bond. Table I contains an analysis of the Cr-C bond energy for CrCH/ ( 6 A 1) as a function of electron correlation. [The Cr-C bond energy is for the symmetry-allowed process a general prescription of how to bias the outcome in favor of alkylidene, carbene. or intermediate bonding in M-CXY complexes. A. Mellll Exchange and Promotional Effects on M-CTY Bonds. Due to the greater number and larger magnitude of favorable exchange interactions between valence electrons in a transition metal as compared with a main-group or nonmetal atom. 11 the loss of exchange energy upon forming covalent bonds with ligands {via spin pairing in the bonds) plays a much more significant role in determining bond properties for transition metals than for other atoms. If this exchange loss destabilization is large enough. promotion of the metal atom to an excited state may be favorable if it results in less exchange loss. These two effects are evidenced by changes in hybridization of metal bonding orbitals, bond character, and bond strength. Since these effects are most dra· matic in bare metal systems, we will discuss only bare M-CXY svstems. · 1. Hybridization. Metal orbital hybridization in M-CXY bonds can be predicted qualitatively by comparing the relative metal destabilization upon bonding the ligand to an s- vs. a d-orbital. Valences - p and d - p excitations for transition metals are sufficiently high in energy that valence p-orbitals make little contribution to bonding. Thus the hybridization changes are greatest in the M-C er bond. with little d-p mixing in the 7T bond (>90% d). Therefore we will describe only hybridization effects in the a bond. For a ground-state metal atom or ion with an occupied valence s orbital (s 1d"" 1 or s2d""2 state), the CXY covalent a bond will have a large amount of s character in the metal-bonding orbital. This is due to spin pairing of the metal s-electron with the ligand electron in the bond. resulting in the loss of only s-d exch:rnge terms (K,,J. each typically -5 kcal/mo! ( tc>-15 kcal/mo! •m:aller than d-d exchange terms). In e<1ses where the metal has a choice betweens and d, the s-orbital is preferred since it loses less exchange energy upon forming the metal-ligand bond. For example. binding Mn"' (s 1d 5 ground slate) to CHi <3B 1) leads to a a bond which has 117%. s character." This is due to the reluctance of Mn+ to destroy the stabilization of the half.filled d·shell (i.e .. a large loss in exchange energy) If the metal has a d" ground state, then to form a bond to a metal s-orbital will require the d _..., s promotionai energ\' in addition to various s-d + d-d exchange losses (£p<i-s + .i.K,,;+Qd\. 1• To decide whether bonding to an s orbital will occur, we must compare this sum with the d-d exchange loss incurred upon bonding to the d" ground state (.l.Kddl· These relative energies will determine the dominant hybridii;ation. In other words. for 4 + ..i.K..i+dd > ..iK<JtJ, we expect >50'if d-character in the M-C a bond and vice versa. As the difference between these two values grows. so does the dominant orbital contribution to the metal er-orbital. mca•urc uf lhc Ru-C ,.. wm.J Mrcnglh. eA ( 6 A 1) CrCH 2+ - (6S) Cr++ ( 1A 1) CH2 yielding an intrinsic u·donor bond strength.] At our highest calculauonal level, we tmd a bond energy ot .i~. t kcal/mol. Hence, we estimate the strength of a C to Cr er-donor bond with no r·back-bond to be worth -39 kcal/mol. Since the total bond energy for the carbene state of RuCH 2 + (4A,\ i<; D, = 65.8 kcal/mo!. then WC estimate the <T·dOnor bond energy to be D: D, De' 65.8 3 l.5 = 34.3 kcal/mo!. This value is quite close w the value (39 kcal/mo!) obtained for Crcarbene. For systems with a singly occupied nonbonding derorbital, we would expect the values for u-donor bond strengths = tu ..J.:<reuu going from firs\ ww to >c<A>nd 1 ow due to the highc1 metal 4d/carbene er overlap for the more diffuse 4d electrons. Our value of 30 kcal/mo! for the two-electron x-back-bond of a second-row transition metal is probably a lower limit on the strength of such a bond in a neutral complex. However. the strength of such a two-electron 11'-back·bood for low-spin d" first-row metals is probably less than 30 kcal/mol (due to the small radial extent of the 3d-orbitals). V, Transition-Metal-Ligand Bonding Trends: Control of Reactifity ln the above sections. we found that. with proper choices of metal and ligands. one can obtain complexes in which the ground and excited states ex:hibit vastly different bonding character. Given the opportunity of added ligan<i< to pnturb thr elt>ctronic <tarr splittings at the metal center, we have the potential for designing complexes either with covalently bonded alkylidene ligands or with a-donot/'ll'·back·bonding carbene ligands depending upon the ( 16) The corresponding Ru• occupations arc degenerate, leading to no added promotional effects. Sec Table l in ref I b. E/ (I 7) Typical values: K"" - I 5-20 kcal/mol and K,. 5-8 kcal/mo! for transition metals; K.,, - 10 kcal/mo! for non-transition metals (18) Brusich, M. J.; Goddard, W. A .. 111. unpublished results ( 19) £,'""designates the d' - s 1d.. 1 promotional energy. ~..... refers to a loss of both s.-d and d-d exchange terms when tormmg both <J and -r bonds -113Bonding in Transition-Mera/ Methylene Complexes As an illustration of this competition, consider that the <1 bond in CrCH 2+ is 53% d/47% sp on the metal, arising from Et.,+ ~ - Mdd = 13. 7 kcal/mot.•• The difference in destabilization energy suggests that metal d-character should dominate. However, the large difference in the size of the 3d and 4s orbitals favors s-bonding, leading to rather balanced d vs. s character. The case of covalently bonded RuCH,+ ( 2A,) provides an example at the opposite extreme. Forming two covalent bonds to d' Ru+ costs l.5Kdd = 22.5 kcal/mo!, while forming ones bond and one d bond to s 1d6 Ru+ costs £Pit-<+ 2Ktd + l.5Kdd 65.9 kcal/mol.'b Thus a du bond is favored over an s<1 bond by 43.4 kcal/mo!. This is borne out convincingly in the actual Ru-C <1-bond hybridization of 88% 4d/12% Ss character on the metal. Thus we see that knowledge of the ground-state configuration of the metal, coupled with values for promotional and exchange energies. allows qualitative prediction of the hybridization in metal-ligand covalent a bonds for all ranges of cases: mostly s character (MnCH 2+), a 50/50 mixture of sand d (CrCH 2+), and mostly d character (RuCH/). 2. Boad Character. The same analysis also yields predictions about donor /aoccptor vs. covalent bond character. Donor /acceptor bonds will be favored when the exchange and promotional destabilizations for forming covalent bonds are prohibitively large and when two-electron ir-back·bonds arc achievable. Covalent bonds will be favored when little promotional or exchange energy = J. Am. Chem. Soc., Vol. 108, No. 16. 1986 4751 exchange loss coupled with no ir·back·bonding possibilities leads to the formation of a covalent, nucleophilic metahtlkylidene bond. CompetlUve carbcne and alkylldene bonding shOuld O<X:ur when ,...back-bonding is possible and there is an intermediate loss of exchange in forming covalent bonds. We expect this behavior in second- and third-row group 8-10 metals, since 11'-back·bonding L~ passible and the exchange loss is not as large (the avera)!e K";s for second· and third-row group 8-10 metals are -5 kcal/mo! smaller than for their first-row congeners 22 ). RuCH/ is one example of this. in which the d~ back-bonding is great enough (30 kcal/mo!) and exchange loss is large enough (66 kcal/mo!) to allow competitive carbene/alkylidene states. Binding CH 2 (3B,) to the ground-state d 7 Ru+ leads directly to a stable alkylidene. Due to the lack of exchange loss and the strength of the donor /acceptor bond, a CH 2 ( 1A 1) bound to d1 Ru+ results in a carbene of nearly the same stability as the alkylidene. Experimental examples from group 8-1 U second- and tturd-row metals span the range of behavior from nucleophilic to electrophilic. Roper and co-workers 23 have shown that the complexes Cl(NO)(PPh3)2M-CH1 (M =Ru, Os) are nucleophilic. reacting with acids not bases, while Thom and Tulip2' isolated the pyridine adduct of the electrophilic Br(PMe 3}i(CHi)Jr+=CH 2. 3. Bond Strengths. Although conventional wisdom correlates bond strengths with orbital overlaps, other factors contribute significantly to bond energy trends. M-CXY bond strengths are is 11.lliL upuu bvndiul!l u1 when 11 ,.--b111;1\.-buud i• nuL pu"il.1lc: (1c:- wc:all.cned by bvth c;;\dlirngc lu_. 1111d pv>•ible p1uumliuu uf 1hc ducing the prospective donor bond order from two to one). A competition between covalent and donor/acceptor bonding will be expected when the exchange loss is intermediate and ir-backbonds are possible. We expect group 8-10 metals to be go<Xi candidates for carbenc bonding, since two-electron ir-back-bonds may be formed without requiring intermediate or low-spin metal centers. We expect those metals that can have a a hole (allowing formation of a <1-donor bond from the ligand) to be even more likely to e,.;hibit carbene bonding. In addition, carbcne bonding is also favored for those systems where covalent bonding costs too much in exchange loss. For example, the loss of exchange and promotional energies for forming two covalent bonds in FeCH/ is -40 kcal/mot, bonding to either the s'd 0 ground state of te"' (°UJ or to the low-lying (£p•""'<i"' 6.7 kcal/mol) 20 d 7 eltcited state of Fe+ ( 4 F). 21 Since 60 and 4F Fe+ have both singly and doubly occupied d-orbitals, 11'-back-bonding from Fe+ and a-donation from CH 2 can both be achieved as in RuCH 2+ ( 4A 2). Since the loss of exchange and/or promotion is greater for Fe+ than for Ru+ [AKdd (Ru ..,d 1) = I.5Kdd = (l.5)(15) 22.5 kcal/molj, we expect carbene bonding to be favored for Fe+. This is nicely illustrated by the experiments of Brandt and Helquist who isolated the dimethyl sulfide adduct of metal and/or the ligand. In general, due to small e:1.change loss. early transition-metal alkylidenes are expected to have strong bonds, with the bond strengths increasing down a column due to the decreasing size of the exchange terms. 22 The bond strengths in metah:arbenes depend on the effectiveness of u-donor / Jtback-bonding, since the metal need not incur exchange loss. Promotional effects may sometimes be required for effective a-donor/ 7r·acceptor bonding. Hence the bond strengths in unsaturated late-transition-metal carbene systems are e:1.pected to be stronger than for early-transition-metal carbene systems due to more effective 11'-back-bonding. In addition, we expect these bond strengths to increase down a column since the increasing size of the d-orbitals may allow more effective delocalization for the 'II'· back-bond. I he intermediate cases suggest metal--<::arbene bond strengths can be as strong as the corresponding metal-alkylidene bond strengths (for the unsaturated systems). The trends for saturated metal complexes are even simpler to analyze. For a given set of ligands. the valence electron configuration at the metal is expected to be consranl for metals in the same column. Thus, there is no need to consider promotional energy (since the constant ligand set induces the same ground-state valence electron configuration for each metal) and the same the FcCH 2"' ~u111plcJ1. [(Cp(CO)ifc;CH2SMc2J"'. This cvmplc,., W-4mber of cx..:;;hangc tcrm..s i:s J1J;St as we go down d wlumn. Sin,;.e or perhaps the free L,FeCHt species, was found to directly cyclopropanate olefins, as expected for the reaction chemistry of an electrophilic carbene. Id Gas· phase work of Stevens and Beauchamp 5• also implies cyclopropanation chemistry by CpFe(COhCH/. Covalently bonded metal alkylidenes are most favorable for early transition metals, since two-electron 'Ir-back-bonding is not po&sible (no doubly occupied valence d-orbit.als in the ground state) and only a minor loss of exchange and promotional energy is incurred (due to the small number of valence electrons) A classic example of this is the first-isolated M-CH 2 complex, Cpr (CH 3 )Ta-CH 2• which exhibits nucleophilic alkylidene character. 8 This can be understo<Xl by an exchange energy analysis modified by the presence of other ligands. Ta has an s'ct' ground state in which the s electrons and one d electron are involved in bonding to the Cp and CHi ligands. leaving two high-spin d-electrons to bond 10 CH 2. Binding CH 2 10 the 16-electron Cp 2(CH 3 )Ta fragment results in only 0.5Kdd loss (-7 kcal/mo!). The small (20) Moore, C. £.Nall S1arrd. Ref Data Ser. (US. Natl. Bur. Sta/Id.) 1971. 3. (35) (21) Since K..,(fe•) 20.7 kcal/mol and K.,(Fe•) • 5.0 kcal/mal. ~K­ (fc-CH,+. s'd'fe•)"' 1.5 K"" + 2K.," 41 kcal/mol. .lK..,(FeCH,+. d'fc•) + E,'...,,{Fe')"' I.SK.,+!::,~ 3L05 + 6.7 = 37 7~ kcal/mo!. = .lEP = 0 and 6.Kdd = (constant)Kdd• then the only variable in determining the bond energies is the magnitude of the intraatomic exchange integral. which decreases as we go down a column. 22 This decreases the destabilization due to exchange loss and hence increases the bond energy as we go down a column. Conventional wisdom attributes this trend solely to the increasing size of the d orbitals inducing larger overlap and hence stronger bonds 8. Effect of Ligand Type on t~ M-cxY Bond. Metah:arbon bond character is determined not only by electronic interactions on the metal but also by the nature of the CXY ligand. The substituents on the carbon ligand can greatly influence the stability of alkylidene vs. carbene bonding. We have shown that alkylidenes involve triplet CXY fragments forming col'a/enr bonds, whereas carbenes involve singlet CXY fragments forming donor ( accepwr bonds to a metal center. Therefore, if X and Y are chosen to stabilize the triplet. alkylidene bonding will be favored, while if (22) Froese Fischer. C. The Hartrte-Fock Merhod for Awms-A .'lummcal Approach; Wiley·lnterscicnco: "lew York, 1977 (23) (a) Hill. A. F.; Roper. W. R; Waters. J. M.; Wrighl. A. HJ. Am Chem. Soc. 1983. 105. 5939 (b) Roper. W.R. Group Vll/ Transition Mera/ Complexes of CH,. CF,. and Other Simple Carbtnes; Seminar at !he Cali· fornia Institute of Technology, 23 July 198• (24) Thorn. D. l.; Tulip. T. H. J. Am. Chem Soc. 19111. 103. 59S4. -1144752 J. Am. Chem. Soc., Vol /08, No. 16, 1986 Carter and Goddard X and Y are chosen to stabilize the singlet, carbene bonding will be favored (ignoring the metal's electronic interaction already discussw iu •~1.:1iu11 V.A). In general. electronegative substituents (e.g., F, Cl, OR) on the carbon ligand stabilize the singlet carbene statc, 15 whereas electron-donating substituents favor the triplet alkylidene state of CXYY For instance, while CH 2 has a /rip/et ground state (with 1A lying -9 kcal/mo! higher 1:). CF has a singlet ground state 2 1 with the triplet state lying -57 l::cal/mol higher. 15< Thus, replacing CH 2 with CF2 will lead to a bias of -66 kcal/mol toward formation of a metal-carbene! If carbene bonding is desired, a contract as we go across a row. Thus reactions which would form M=CR2 comple~es in early transition metals lead instead to dinuclear brtdgtng CR 1 comple~es in !ate transition metals.' 0 C. Design Prescription of Carbenes and Alkylidenes. From ~tions V.A and V.B, we see that the electronic state of a meta\ and its ligands greatly influences its bond character and reactivity Usinll the ideas presented thus far. we can now predict. based <nlely on the electronic structure of the metal complex, what elements are necessary to form stable carbenes and alkylidenes. To ensure the formation of a rnetah!lkylidene with nucieophilic character, we require the CXY ligand to be a triplet so that it CXY ligand (X,Y ~ F, Ci, OR. H; R ~alkyl) in conjunction with can form two covalent bond. to a metal ato111. Thi> >Ul!;Ji;~" CXY a metal from groups 8-10 increases the driving force for formation of a ternrinal u-donor / 11'"-acccptor bond. Examples of such bonding in group 8-10 systems included CH 2 comple.ites of Fe 26 and lr 24 and CF 2, CCl 2, C(F)(Cl). and C(F)(O-r-Bu) complexes of Fe, Ru, and Us. all of which e:uubit the e.itpectcd electrophilic, singlet carbene character (e.g., facile reactions with nucleophiles). 27 The only exception is found in CF 2 comple.ites of Ru(O) and Os(O) where the w--back-bonding is so effective as to inhibit the electrophilicity of these carbenes, rendering them slight!} nucleophilic. 2s It is well-known that group 6 metals readily form the so-called Fischer carbenes in which a Iow-valent metal, usually surrounded by five carbonyl ligands, is bonded to an alko.itycarbene ligand in a donor/ acceptor fashion. 2 These systems are metal carbenes partly because the alkoxycarbene has a singlet ground state and partly because the closed-shell ancillary ligands (e.g., PR 3, CO) force the metal into a low-spin d" configuration primed for forming donor/acceptor oonds (with doubly occupied dll'"-orbitals). A dramatic e.itample of how the chemistry (and. we believe, the bond character) changes going from an unsaturated to a saturated metal comple.it (with closed-shell ligands) is found in the work of Stevens and Beauchamp5< who demonstrated that MnCH/ undergoes metathesis reactions, while (CO)sMnCH 2 + yields only cyclopropanation products. The unsaturated systems 1d 5 Mn+. being unable to form a w-·back-bond, is forced to form a covalent alkylidene bond which, as such, undergoes metathesis. Attaching the CO's forces Mn+ into a low-spin d6 state which can now form ll'"·back-bonds, leading to a donor/acceptor carbene bond that can undergo cyclopropana tion. In order to prepare stable alkylidenes, we require CXY to have a triplet ground state or a low-lying triplet e.itcited state. This ligands where X and Y are u-donating or electropositive. Then the C-X and C-Y bonds will use more Cs character to lower the energy of the carbene, destabilizing the C u non bonding orbital Second. use of substituents X and Y without p,,. lone pairs will favor occupation of the C 11'" nonbonding orbital. Third, use of bulky X and/or Y will force sp 2 hybridization on the C to obtain larger X-<:-Y bond angles to relieve steric (Pauli) repulsion. The increased s character in the C-X/C-Y bonds results in increased p character in the nonbonding carbon u-orbital. These three factors leading to the destabilization of the carbon u-orbital and the stabilization of the carbon w--orbital favor u,,. (triplet) alkylidene (I) over u2 (singlet) carbene (2). Indeed, the metal alkylidenes which have been synthesized to date contain hydrogen, alkyl. or aryl substituents on the carbon. which are u·donating (Hand R), do not possess p11' lone pairs (H. R. and Ar). and may be bulky (Rand Ar). As a further synthetic e.ittension. we suggest that X and/or Y = SiR 3, AIR 2, and BR 2 should be effective in stabilizing triplet CXY (and hence metal alkylidenes), since all three are electropositive. are u-donating, lack pw- lone pairs, and are bulky. While a tungsten C(H)(SiMe 3 J alkylidene system has been synthesized. 31 CX(AIR 1) and CX(BR 2 ) alkylidenes are unknown. However, M-<:(X)(AlR 2 ) and M-C. (X)(BR 2) should e.ithibit unusual reactivity due to the presence of a Lewis acid adjacent to a nucleophilic carbon center. In particular, such systems may show enhanced reactively as olcfm polymerization or metathesis catalysts, since those reactions often require Lewis acid cocatalvsts. The formation of a tcmporan olefin adduct at the Lewis acid site may promote reacuon at the M=C bond. To form a stable alkylidene, the metal center must incur litt;e e.itchange loss upon bonding to the CXY ligand. This requirement requirement is fulfilled by methylene and mono or diulkyl or uryl is SAtisfied best by early transition metals, where the >mall nu111Lx::1 carbenes. Examples are prevalent among the early transition metals, as evidenced by their nuclcophilic chemistry. For instance, Ta neopentylidene comple.ites are catalysts for ethylene polymerization,29 Ti alkylidene complexes are postulated intermediates in olefm metathesis.' and other early trans1t1on metals participate in the reactions shown in (3 )-(5).<>- 8 This predominance of alkylidenes in the early metals is due to small e.itchangc losses. strong M-<: 11'" bonds (large d-orbitals for early metals). and the lack of doubly occupied d orbital• (rli•favorine rlnnnr/occeptnr bond fonnation). The late transition metals generally prefer not to form terminal alkylidene bonds in a mononuclear complex. Late transition metals form weak covalent w- bonds since d-orbitals of valence d electrons results in small exchange losses. It i> abo important that these metals can form stable, coordinat1vel} unsaturated comple~es (e.g .. 14- and 16-electron complexes) in which the metal has unpaired electrons set up for bonding to mplct CXY." Thus stable terminal alkylidenes are e.~pected (Jnd found) for early-transition-metal mono- and dialk)I or aryl aikylidenes, with the most stable alkylidenes found among the third· row elements (due to a smaller Kdc and a stronger r. bond 1 (25) (a) Ab initio theoretical calculations on CLiH and CLi, (extreme electron-donating substituents) yield triplet ground states. Su: Harrison. J. F.; Liedtke. R. C.; Liebman, J. F. J. Am. Chem. Soc. 1979, IOI. 7162. (b) GVB-CI calculations yield a triplet ground state for CH(SiH 1): Carter. E. A.; Goddard Ill. W. A., unpublished results. (26) Brookhart. M.; Tucker. J. R; Flood. T. C.; Jensen. J. J. Am. Chem. Soc. 1980. JOI. 1203. (27) (a) Clark. G. R.; Hoskins, S. V.; Roper. W.R. J. Organnmet. Chtm. 1982. 234. C9. (b) Mansuy. D.; Lange, M.; Chottard, J.C.; Bartoli. J. F.; Chevrier. B.; Weiss. R. Angtw Ch<m .. Int. Ed. Engl. 1978, /7, 781 (c) Roper. W R.: Wrigh1 A H 1 n,sn""'"" r~,.., 10!!2. 1H. ('~Q (d) Clark. G. R.; Marsden. K.: Roper, W.R.: Wnght. L. J. J. Am. Chtm. Soc 1980. 102, 1206. (c) Hoskins. S. V.; Pauptil. R A.; Roper. W.R.; Waters. J. M. J. Organomei. Chtm. 1984, 269, 05. \28) Clari:.. G. R.; Has.l:.in.. S. V ·.Jones, i. C:. Roper. W.R. J. Chtm. Soc .. Chem Commun 1983. 719. (l9) Turner. H. W:, Schrock. R.R.: Fellmann. J. D.: Holmes. S. J. J. Am. Chem Soc 1983. 105. 4942. Terminal alkylidene complexes involving late transition metal" will generally be less stable due to weaker covalent ,,. bonds. and thus late transition metals will prefer to make two (I bonds to CXY. resulting in the formation of bridging alkylidenes (as i> found e.itperimentally).J(l Those few examples of terminal CR, cornpJexc, bound to group 8-lU metals all indicate carbene character (rTHbt of these examples involve CH 2, since the small 1A 1- 3B spillling (30) (ai For a comprehensive review. see: Herrmann. W A Adi (),g11110met. Chem. 1982. 20. 159. See also: (b) Theopold. K H : Bergman. R G. J. Am. Chem Soc. 1981. 103. 2489 (c) lsol:>e. K. Andrews. D G . ~lann. B. E.; Maitlis. P. M. J. Chem. Soc. Chem. Commun 1981. 809 (dJ Herrmann. W. A.: Bauer. C.: Plank. J.; Kalcher. W: Spelh. D Ziegler. \.I L Angew. Chem., Jnr. Ed. Engl. 1981. 20, 193. (e) Sumnec. C. E _Jr: Coll1er. J. A.: Pettit. R. 0Jl'ga1tom~1aJ/ics 19tll. J, 1350. (0 Lin, V C .. Cuhlbr~·.c J. C; Wreford, S.S. J. Am. Chem. Soc. 1983. 105. 1679 (g) Laws. W J., Puddepha11. R. J J. Chem. Soc .. Chem. Commun 1983, 1020 (hi Holmgren J. S.: Shapley, J. R. Organomtrallics 1985. 48 793 (i) Morrison. E D Geoffroy_ G. L; Rhcin8old, A L. J. Am Chem. Soc !9'!. Jl)7. ~S4 (3 l) Legzdins, P.: Re1tig. S. J.: Sanchez. L Organomerallics 1985. 4. 1470 (32) See. for example· Green. J C.: Payne. M P.: Teuben. J. H (),_ ganometallics 1983. 2. 203. -115Bonding in Transition-Metal Methylene Complexes makes the carbenc more acccssible). 206 in CH 2 for a strong metal-;;:arbenc bond, we require a singlet ground state (or low-lying singlet excited state) of the CXY ligand in order to form a u-donor /.--acceptor bond to the metal center. Whel) X or Y in the CXY ligand arc electronegative, the C-X/C-Y bonds utilize C p-orbitals, since the lower ionization potential of the C 2p allows more charge transfer to the electronegative substituents. More p character in the C-X/C-Y bonds stabilizes the nonbonding C u-orbital by introducing mores character into it. In addition, P"' lone pairs on X or Y may delocalize into the nonbonding C P"'· disfavoring p.- occupation by one of the carbon valence electrons. Both high electroncgativity and the presence of p.- lone pairs act to stabilize the u2( carbene) state of CXY 2.15b.33 To favor a stable metal-;;:arbenc. we would like either a late transition metal with doubly occupied d-orbitals to induce .-back-bonding [e.g., Cp(dppe)fe=CH 2+]26 or an early transition metal with ancillary closed-shell ligands that force the metal to be low-spin d" (e.g., (C0) 3Cr=C(0Mc)(Me)] 2 such that d..--p.back-bonding is possible. Examples of such mctal-;;:arbene complexes include many group 6 carbonyl alkylalkoxy carbenes as well as late transition metal CH 2, CF 2, CC1 1, and CF(OtBu) complexes, all exhibiting varying degrees of electrophilic character. 21 Strong preference for carbene bonding is expected in the first-row group 8-10 metals since the exchange loss incurred in forming covalent (alkylidene) bonds is particularly high (due to large K0.). However. for second- and third-row late transition metals. the more l!lOdcrate exchange losses lead to more competitive alkylidenc and carbene bonding when the CXY ligand has a small 'A 1-aB, splitting (namely. for CH 2), just as found for RuCH 2+ Bridging carbencs with electronegative substituents at carbon should be (and arc) rare. since donor/acceptor (terminal) bonding is preferred. 3o. Indeed, the M-C bonds in a µ-CF 2 complex should be weaker than those in a µ-CR 2 system by the singlet-triplet gap of CF 2 (57 kcal/mo!), since excitation to 3 B 1 CF 2 is necessary in order to form the bridged species. In sum, a desired bonding/reactivity scenario. be it carbene, alkylidene, or an intermediate case. can be designed by appropriate choice of both metal and ligand to meet the electronic requirements dictated by the character of each mode of bonding. VJ. Summary Ab initio electronic structure calculations on simple metal carbenes reveal the following conclusions. (i) Relative stabilities of metal carbencs vs. metal alkylidenes are predicted to De most sensitive to choice of metal for the first-row transition-metal CH 2 complexes (alkylidene state lowest for the early metals and the carbene state more favored for the late metals). (ii) Second- and third-row metals lead to situations where both states may be competetive and where the ground state may be determined by other factors (e.Q: .. substituents on CXY and/or ancillary ligands). (iii) M-CH 2 u-donor bonds are calculated to be worth 35-40 kcal/mo! while .--back-bonds are found to be -30 kcal/mo!. These values are ellpected to vary systematically depending on the c;l<:1,;uonegaLivity uf the metal .:u111pic;<.. with the u l.Juml \Jc;coming stronger and the ,,. bond becoming weaker as the metal becomes more electrophilic. (iv) The above ideas are utilized in formulating a general design prescription for the svmhesis of L.M(CXY) compleJ(es. based on quantitative electronic properties. For example, terminal CXY groups will be favored by electronegative substituents at carbon (X, Y "' F. Cl, OR. NR 2). while bridging CXY will be favored when X and/or Y are elcctropositive (X, Y "' R, H. SiR 3). VU. Cakulational Details A. Buis Sets. All atoms were described with all-electron valence double-I ( VDZ) basis sets. The Four's level VDZ basis >ets" were used (33\ Carter. E. A.: Goddard. W. A., Ill. unpublished results. J. Am. Chem. Soc .. Vol. 108. No. 16. 1986 4753 for Cr. contracted ( l0s8p5d/5s4p2d). and for Ru. contrac1ed ( l6sl 3p7d/6s5p3d).'.. The standard Huzinaga-Dunning VDZ bases" for C (9s5p/ls2p) and H (4s/2s) were used. with one set of d-polariz.ation funcuons (f, 0.69) 1' added to the carbon basis set. B. w..cfunctions. The generalized valence bond (GVB) method "as used m all calcuiat1ons. The GVB perfect pairing "avefunction is an MCSCF (mu\ticonfigurational self-consistent field) wavefunction in which each bond pair is described with two GVB one-electron orbitals = whose shapes are optimized. As a bond 1s broken. the overlap, S,,. of the two GVB orbitals describing the bond goes to zero. but for a strong bond near R,. or for a lone pair, the overlap is near unity. In the limit that S,, ·- l, the GVB description degenerates to the HF description Generally it is only necessary to use the GVB descripuon for elec1ron pairs where the overlap differs significantly from unity. This applies most strongly to M-X bonds in which the mismatch in orbital sJZes result5 in overlaps ranging from 0.3 to 0.7 between metal and ligand orbitals, while the doubly occupied core orbitals and C-H bonds (each pair with near:} unit overlap) are treated at the Hartrcc-Fock level. Thus, the general wavefunction has the form Al<l>coRe(<l'1,'l'1• + <l'1•<l'1,H"'2."'2• + >P:z•"'2.) ... xs•1Ni (I) where the doubly oe<:upicd O<bita\; a<c in <ilcoRE b111 caku\ated se\f- consistently with the GVB orbitals (,,,,.,.., 1,), (op,.,..,,.), etc. In order to indicate how many electrons are correlated, we denote the wavcfunction as GVB(n/m) = where n is the number of GVB electron pairs and m (usually m 2n) is the total number of natural orbitals wnhin the GVB space. The wavefunction (I) is denoted as PP (for perfect pairing) because the electrons in orbitals op 1, and ,, 1, have thCLr spins coupled into a singlet. the electrons in orbitals "'2. and ""'have their spins coupled into a singlet. etc. C. Geometry Optimization. The geometry of the 6 A, state of CrCH( was optimlled at the GVB-RCI( I /2)*5,. 1 level (generalized valencebond-restricted configuration interaction times all singie excitations from all valence orbitals to all virtual orbitals). The GVB-RCI( I /2) description allows a full Cl within the pair of natural orbitals de~cribing the Cr-C u bond, resulting in three spatiai configurations. For 6 A 1 CrCH/ these three configurations have eight associated spin eigenfunctions (SEFs}, while for the •0 1state, the GVB(2/4)-RCI descnpuon (two bond pairs wah four natural orbitals to describe both a and "bonds) bas nine configurations with 34 associated SEF's. The physical interpretation of the RC! wavefunct1on involves inclusion of imerpair correlation and high-spin coupling on the metal atom. Single excitations from the valence orbitals to all virtuals o.llows orbital shapes to rela:>1. us the geometry is optimized. Note we kept the C-H bond distance fixed at 1.078 A. while optimizing the H-C-H angle and the Cr-C distance O. Bond Energies. The bond energies for the 'A, state of CrCH( were calculated at the GVB( I /2J·PP, GVB-RC1(2). GVB-RCl( cl' D,. GVB RCI*S,. 1, ond GVB RCl(:?)*Sn, + GVB RCl(:?)*D, ieveb Since the PP, RC!, and RCl'S levels are explamed above, we will nov. ou1line the two calculations which allow double excitations to the virtual space. While the GVB-RC! wavefunction generally leads to a good description of potential surfaces as bonds are formed and broken. "e find that it is systematicully low for bond energie$. The reason is that '-lt Re there are a number of ways that the electrons correlate their motion. only part of which can be described with the two GVB orbitals (per bond pa.r). Thu;, to obtain good bond energieli. we must allow the two eiectrons of the bond pair to use any orbital of the basis (double excitations out oi the bond po.ir are thus r•quir.d). Thls CJ, denoted .:i.s GVB .. JlC}(2)*D.,., includes all single and double excitations from the Cr-C a bond pair starting from the set of RCI configurations. The other (higher level) calculation 1s just a sum of the RCI•s and the Rcr•o, calculations We calculate the energy to dissociate to ground-state er• (6S) and excited state CH, ( 1A, ). since this procei:s corresponds. to the experimentally observable met'.al- carbene dissociation pathway in which no electronic relaxation from singlet fragments is expected (e.g .. for low-valent M(C0) 1 and hcterocarbene fragments) Al infinite Cr-C separation. we allow the CH 2 cr pair to use a .-·correlating orbital as a second natural orbital. since this (34) (a) Rappe, A. K.: Goddard, W. A .. lll, unpublished resuits. The<e basis sets were optimized for 1hc d" configuration of the metal as laid out 1n: Rappe. A K.: Smedley. T. A.: Goddard, W A., Ill J. Phys Chem. 1981. 85. w:n. (\>)The Ru bas\• 11<.1 may i:>e fo11nd in r~( \\>. P'J \a) Huz1naga. s. I Chem. l'h}'S. 1'6~. 42, ;293 (\I) Dunning. T H., Jr. Ibid. 1970. 53. 2823 -1164154 provides the best correlation for singlet CH 1 described as a GVB( 1/2) orbital pair. (The CH 1 a pair at R,(Cr-C) prefers a a-correlating orbital.) We now discuss the Li's in terms or their dissociation limns. ( l) GVB( I /2)-PP and GVB-RC1(2) both dissociate to Hartrec-Foek (Hf) er+ (total energy -1042.004 30 hartrcc) and GVB(l /2)CH, (total energy= -38.901 64 hartrcc) {We calculate an HF bond energy by dissociating to Hf er• and HF CH 2 (total energy ~ -38.88098 hartrcc).) (2) RCl(2)"0, dissociates to HF er• and RC1(2) 0 D, CH, (total energy -38.916 49 hartree; 45 spatial configurations/ 45 spin eigenfunctions). (3) RCl(2l"S,., dissodatcs to HPS., Cr• (equivalent to Hf here) and RCJ(Z)•s.,1 CH 2 (lotal energy• -38.90764 haIL1cc, 34 •pdlio.I configurations/37 spin eigenfunctions). The RCl*S,.._. CJ in general not dissociation-consistent, but due to the equivalence of HF to H F*S fords er•. this Cl. as arc all the ones discussed here, is indeed dissoci· ation-consistent. 1 (4) RCl(2)•s,.. + RCJ(Z)•D, Ji>w<io.te> to !Jr (or <quivalcntly, Hf*S,.,) Cr• and IRC)(2)'S., 1 + RCl(2)*D,I CH 2 (total energy = -38.92249 hanrcc; 69 spatial configurations/72 spin eigenfunctions), 1 since the a bond localizes back on CH 2 at R E. Slate Splittinp. In order to preserve a balanced descnption of the A 1 and 4 8 1 states ofCrCH,•. we must allow the same degree of freedom 6 for both states in order lO ensure wc arc uc.1HinK Wth ::.l<Hc:i. c:yuivJk1nly (no artificial biases). We can accomplish this by maintaining the same number of occupied orbitals included in the SCF descriptior. of both states. The 6A 1 state. with a GVB( I /2) description. has a valence spa~ consisting of two C-H doubly occupied orbitals (treated as HF MO"s), one Cr--C bond pair with two natural orbital> (NO"s), and five singly occupied non bonding 3d-orbitals, for a total of nine orbitals in the valen~ spa~. The 4 8 1 state, with a GVB(2/4) description. has a valence space consisting of the two C-H HF MO"s, two Cr--C bond pairs (four NO'sl. and three singly occupied 3d-orbitals. for a total of nine orbitals again. Therefore we; hav~ a balao~od orbital description of the two :.ta.tes ut the two levels described above. F. Ru Carbetle Calcularions. All calculations on the various electron1c states of RuCH,+ arc described in paper 2 of this series." .<\~l<nnwi...tg..,..nt. Partial support of this work is lj!ratefully acknowledged from the Shell Development Co .. Houston, TX, and the National Science Foundation (Grant CHE83-J8041). -117- Chapter 2.D. The text of this section is an Article coauthored with William A. Goddard III and is to be submitted to the Journal of Chemical Phy~ic~. -118- Early versus Late Transition Metal-Oxo Bonds: the Electronic Structure of VO+ and RuO+ Emily A. Carter and William A. Goddard III* Contribution No. 7580 from the Arthur Amo.! Noye.~ Laboratory nf Chemical Phy.Jic.,, California Jn.,titute of Technology, Pa.,adena, California 91125 Abstract: We have carried out all-electron ab initio multiconfiguration self- consistent field with configuration interadion (MC-SCF /CI) calculations on two transition metal oxo cations MO+ (M = V, Ru). We find that accurate theoretical descriptions of the metal-oxo bonding are obtained only when important resonance configurations are included self-consistently in the wavefunction. The ground state of vo+ ( 3 :E-) has a triple bond similar to that of CO, with D~ak(V-0) = 128.3 kcal/mol [n:xpt(V-0) = 131±5 kcal/mol], while the ground state of RuO+ ( 4 ~) has a double bond similar to that of 0 2 , with D~alc(Ru-0) 67.1 kcal/mo!. Vertical excitation energies for a num.ber of low-lying electronic states of vo+ o.nd Ruo+ are also reported. These quantitative results indicate fundamental differences in the nature of the oxo ligand in early and late metal oxo complexes. We suggest that the differences in M-0 bond character are responsible for the observed trends in reactivity (e.g., the thermodynamic stability of early metal oxides versus the highly reactive oxidizing power of late metal-oxo complexes). -119- I. Introduction While the electronic structure of neutral transition metal oxides has been examined by several authors, 1 the only cationic transition metal oxide (TMO) which has been studied with correlated wavefunctions is CrO+ .2 With the growing availability of experimental bond energy and reactivity data for TMO cations, 3 physical descriptions of the molecular bonding in such systems are sorely needed. Hence we have undertaken an ab initio MCSCF /CI (multiconfiguration self-consistent field/configuration interaction) study of two TMO's, vo+ and RuO+, as representatives of early and late transition metal-oxo bonding, with the goal of understanding the differences in bonding and reactivity as one proceeds across the periodic table. Examination of empirical properties of transition metal oxides reveals that early metal-oxo compounds exhibit high stability, are relatively inert, and are characterized by very strong M-0 bonds, while late TMO's tend to be highly reactive oxidizing agents and possess much weaker M-0 bonds. 4 For example, while VQF is used as an inert ESR-active probe of protein reactive sites, 5 oxides such as Cr0 3 , Mn04, and Os0 4 rapidly oxidize olefins and alcohols to epoxides, diols, aldehydes, ketones, and carboxylic acids. 8 Late transition metal-oxo porphyrin complexes (modelis for active sites of enzymes) are effective oxygen atom transfer reagents 7 and are catalysts for hydrocarbon oxidation (cytochrome P-450 analogues). 8 The trends in reactivity are consistent with their relative thermodynamic stabilities, exemplified by the bond energies of metal-oxo diatomics (Table I). The early metal-oxo diatomics have bond strengths roughly twice as strong as their late metal counterparts. We believe that differences in the metal-oxo bond character are responsible for the sharp contrast in bond energies and reactivities of early and late transition metal oxo complexes. In the present work, we show that an oxo ligand is quite ver- satile: oxygen atom is capable of forming (at least) three distinct types of terminal metal-oxo bonds. 9 Experimental data for TMO cations include thermochemical measurements -120to obtain bond energies and heats of formation, 3 a-e photoelectron spectra to determine the equilibrium properties of ground and excited electronic states (e.g., vibrational frequencies, bond lengths, excitation energies, and ionization potentials), 3 f,g and gas phase studies of their chemical reactivity. 3 a,h-j Much attention has been focused on vo+, due to its presence in interstellar space 10 and its possible relationship to vanadium oxide-catalyzed hydrocarbon oxidations. 11 Aristov and Armentrout used guided ion beam techniques to directly measure the bond energy of VO+, obtaining D0 (V+-O) = 131±5 kcal/mol. 3 e These authors speculated that the ground state of vo+ might be 3 ~'similar to the ground state of Ti0. 1 c However Dyke et al. later recorded the photoelectron spectrum of VQ, 3 9 assigning the ground state of vo+ to be 3 :E- I with the 3 ~ state lying at least 1.15 eV higher in energy. From a Franck-Condon analysis of the vibrational fine structure o{ the VO+(X 3 E-) +- VO(X 4 E-) envelope, Dyke et al. uLLH.im:<l values of We = 1060±40 cm- 1 and Re = 1.54±0.01 A for vo+ (3:E-). From the first ionization potential of VO (7.25±0.01 eV), they derived an indirect value of D 0 (V+-o) = 138±2 kcal/mol. The reactivity of several metal-oxo cations (M = V, Cr, and Fe) has been studied by Freiser and co-workers 3 h,i and by Kang and Beauchamp. 3 a,j VO+ is found to be rather unreactive, with the strongly bound oxo ligand uninvolved in the chemi5try ob5erved. 3 ' Iu coutrl:L:st., FeO+, with its much weaker bond (Table I), is very reactive and nonselective, forming H 2 0 by hydrogen abstraction from alkanes. 3 h• 12 The reactivity of CrO+ is intermediate in nature,3 a,j reflecting its moderate bond strength. The oxo ligand in CrO+ is reactive, but selective, producing aldehydes from olefi.ns and alcohols from alkanes, without hydrogen abstraction. Ruo+ has not yet been observed experimentally. The only quantitative theoretical study which has been published concerns Cro+ ,2 where Ha.rri:sun predicts [from multireference singles and doubles CI calculations (MRCI~SD)] the ground state to be 4 II with the following properties: -121- De(Cr+-O) = 57.1 kcal/mol, We = 915 cm- 1 , and Re = 1.630 A. These results are in serious disagreement with the observations of the photoelectron spectrum of CrO. 3 / Franck-Condon analysis of the vibrational envelope yields We = 640±30 cm- 1 and Re = 1. 79±0.01 A for the ground state of CrO+, which was predicted by limited CI calculations to be 4 ~-. In addition, Harrison's bond energy is low from the best experimental determination of Ka.ng and Beauchamp 3 a by nearly 30 kcal/mol. Further examination of the electronic structure of CrO+ may be warranted, although it i:s nut the focm; of the work pre:seuted here. Normally when we consider how oxygen may form terminal bonds to other atoms, we think of double bonds consisting of one u and one 1T' bond (e.g., carbonyl groups within organic molecules). However, there are two other types of covalent bonding involving oxygen. First, triple bonds can be formed as in carbon monoxide, in which three valence bond (VB) resonance structures (two covalent bonds and one donor bond) participate in the bonding of C ( 3 P) to 0 (3 P) (1) c c 0 c 0 0 where we have indicated the locations of the valence p-electrons on carbon and oxygen in Eq. (1). 13 Second, double bonds can be formed as in 0 2 , in which two VB resonance structures (one u bond and two three-electron 7r bonds) contribute to the bonding between two ground state oxygen atoms (3 P). (2) + 0 0 0 0 -122- (Equivalently, molecular orbital theory describes the double bond in 02 as filled 7r bonding levels and half-filled 7r antibonding levels, leading to one u bond and two half-order bonds in the 7r system.) In the two next sections, we discuss MCSCF /CI predictions for properties of vo+ and Ruo+, drawing analogies from CO and 0 2 in order to understand the variations in metal-oxo bond charH.der. Section IV concludes with general predictions of properties and reactivity of transition metal-oxygen bonds from a :simple a1u1J.y:si:s u! the expected bond character (based on the electronic state of the metal center and the nature of its ancillary ligands). II.vo+ The outcome for metal-oxo bond character depends primarily on the electronic state of the metal center. Since v+ has a ground state valence electronic configuration of 3d4 , it has an empty cl-orbital similar to carbon's empty p-orbital. As a result, oxygen forms a. triple bond to v+ in the same manner as in CO, except that the oxygen p lone pair forms the third bond by donating into an empty dorbital on V instead of an empty p-orbital on C. The other two bonds are covalent in nature, i.e., each bond is composed of one electron from. each atom. Calcu.lational Detaila In order to treat the bonding in vo+ properly, it is imperative to include the three possible contributing resonance structures [Eq. (1)]. This is accomplished using an MCSCF approach in which all three resonance structures are optimized self-consistently at the GVB-RCI level. We begin with the GVB(3/6)-PP wavefunction [generalized valence bond with the perfect (singlet) pairing restriction] which allows each of the six electrons involved in the three bonds to occupy its own orbital, with each bond pair described by two orbitals. 14 The GVB{3/6)-RCI wavefunction includes, for each GVB bond pair, the configurations corresponding to the three possible occupations of two electrons in two orbitals (3 3 confi.gura.- -123- tions). Physically, the GVB(3/6)-RCI (opt) calculation solves self-consistently for the best orbitals of the resonating wavefunction, optimizing the spin-coupling between the electrons involved in the triple bond, the charge transfer effects, and the inter-pair correlations. For the purposes of calculating bond energies, the above wavefunctions for vo+ and CO dissociate to HF fragments (i.e., any correlation present at R.. is gone at R oo), where the fragments are ground state v+ (5 D), C (3 P), and 0 (3 P). Higher level correlations were also included self-consistently in the RCl(3/6)*Scorr (opt) calculation, in which one extra correlating orbital was optimized for each GVB bond pair by allowing single excitations to those correlating orbitals from the RCI reference states [keeping the RCI(3/6)(opt) valence orbitals fixed]. The largest CI expansion we carried out allowed all single excitations from all vn..le.nc-.e orbitals (e:xduding the. oxygen and carbon 2s orbitals) to all virtual (unoccupied) orbitals from the GVB-RCI(3/6)(opt) reference state, denoted a:s RCI(3/6)(opt)"'Sva1. Single:: excitations correspond to orbital shape changes,1 5 which are important for describing rehybridization effects which may occur during bond cleavage. The latter two wavefunctions dissociate to HF*Scorr and HF*Sval fragments at R = oo, since all other correlations present at Re disappear when the bond breaks. HF*Scorr is simply the HF wavefunction for the ground state atom, where single excitations to the (corresponding) correlating orbitals are optimized self-consistently, with the occupied orbitals fixed. HF*Sval involves all single excitations from all valence orbitals (excluding the 0 and C 2s) to all virtuals from the HF wavefunction. No higher levels of correlation were included beyond what the CI calculations described above. For example, double excitations to virtual orbitals were not allowed, since the bonds of VO and CO are partially donor/acceptor in character and thus do not dissociate correctly using a singles and doubles CI (i.e., CI-SD requires triple and quadruple excitations at Re)· -124- We used the Dunning valence double-( contraction 16 of the Huzinaga (9s5p) primitive gaussian basis set 17 for 0, augmented by one set of 3d polarization functions ((d = 0.95), 18 and the Rappe· and Goddard valence double-( basis set for vanadium (Table II).19 The ground state bond distance and the vertical excitation energies were optimized at the RCI(3/6)(opt) level. Re.sult.s The ground state of vo+ is predicted to be 3 :E-, with a bond length of Re(V+-o) = 1.56 A and We= 1108 cm- 1 , in excellent agreement with the experimental results of Dyke et al. [Re(V+-O) = 1.54±0.01 A and we= 1060±40 cm- 1 ]. 3 9 Two of the four d electrons on V are involved in bonding to the oxygen, with the remaining two nonbonding d electrons in o orbitals (to reduce electron repulsion). The bond character is found to be a triple bond, but Mulliken population analysis (1.46 electrons in each oxygen p11" orbital and 1.33 electron:s in the oxygen pc7 or- bital) suggests that the two resonance structures of Eq. (1) which have covalent er bonds (with an average of 1.5 electrons in each 0 p7r orbital and 1.0 electron in the 0 er orbital) dominate the bonding. If each of the resonance structures contributed equally, each oxygen p-orbital would have an occupation of 1 i electrons. Thus, since the occupations are inequivalent, the bonds in vo+ are best viewed as one covalent cr bond, one covalent 7r bond, and one donor 7r bond, (3) with 0.33 electron transferred from v+ to 0 in the <T system and 0.07 electron transferred back to v+ in the 11" system. This is consistent with the net charge -125- of -0.26 electron on oxygen. Similarly, Mulliken population analysis of CO finds 1.22 electrons in 0 pu and 1.46 electrons in each p-rr. Therefore, although all three resonance structures participate to some degree in both vo+ and co, the dominant resonance structures are those involving covalent u bonding. For a qualitative view of their triple bond character, the GVB-RCI(3/6)(opt) orbitals for vo+ and CO are compared in Fig. 1, where we see that the bonding in CO and vo+ is indeed very similar. 20 The triple bond character for both vo+ and CO results in very strong bonds. Table III compares their bond strengths as a function of increasing electron correlation. The correlation problem is much more severe for transition metals than for organic molecules, as is indicated by the disparity between the Hartree-Fock (HF) and the experimental values for De [ADe(VO+) = 142 kcal/mol whereas ADe(CO) = 88 kcal/mol]. vo+ is unbound by 11 kcal/mol a.t the HF level, due to the innbility of HF theory to describe the low overlap (-rr) bonds present in multiply-bonded metal-ligand complexes. 21 Once static correlation is built into the wavefunction, properly describing the low overlap 'It' bonds (S"' = 0.7) by the GVB-PP approach, vo+ is stabilized by almost 60 kcal/mol. Another large increase in stability occurs at the RCI level (53 kcal/mo! more stable than GVB-PP) in which proper spin coupling (important for high spin metal atoms )21 and all three resonance structures are taken into account. Including self-consistent optimization of the resonance and spin-coupling effects, along with single excitations to virtual orbitals to account for orbital shape changes along the dissociation pathway, leads to bond energies close to experiment for both CO and vo+. Since the bond energy of CO is known to far greater accuracy 22 than the bond energy of vo+, we can estimate the residual correlation error expected in vo+ by Acorr = n:xpt(CO) - D~ak(CO) 9.6 kcal/mol at the highest level of correlation, RCI(3/6)(opt)*Sval· Adding Acorr to De(VO+) at the same level of theory yields our best estimate for the V-0 bond energy, 118. 7 + -126- 9.6 = 128.3 kcal/mol, in excellent agreement with the experimental value of 131:::'..:5 kcal/mol. 3 e Finally, we examined two other triplet states at the predicted equilibrium bond distance for the ground 3 :E- state (Re = 1.56 A). We find a vertical excitation energy of 40. 7 kcal/mol to the 3 ~ state, which has a CO-type bond with only one resonance structure. (4) v 0 Two d electrons on v+ form 7f bonds to oxygen, with the nonbonding electrons residing in fi and <J' orbitals. The large vertical state splitting may be understood in terms of the difference in bond character between the 3 :E- and 3 ~ states. While the 3 :E- ground state forms one donor 71" bond, one covalent u bond, and one covalent 71" bond, the 3 A state is forced to form two covalent 71" bonds and one donor u bond. Covalent 7r bonds are weak relative to covalent u bonds, with the small 3d-orbitals of v+ enhancing this effect. Thus, the bond in the 3 A state is weaker than in the ground state because 0£ the tradeoff between covalent er and 7l' bonds. However, if the 3d-orbitals were more diffuse so that stronger 71" bonds could be formed (due to higher overlap), then the 3 A state might be competetive. Indeed, the ground state of the isoelectronic TiO is 3 ~, 1 c• 22 perhaps because the covalent 71" bonds are stronger for Ti(O) than for V(I). A 3 q, state is found to be only 1.9 kcal/mol above the 3 ~ state, with a nonbonding electron configuration of fi 1 71" 1 • This state has only a. double bond between v+ and 0 due to the presence of three electrons in one of the 7r planes. -127- (5) v 0 v 0 These vertical excitation energies are considerably higher than the 1.15 eV found by Dyke et al. 3 9 from the peak to peak distances in the photoelectron spec- trum of VO. However, we believe that the first IP of VO may be lower in energy than 7.25 eV as reported by Dyke, since the bond energy Dyke derives for vo+ (137.9±2.3 kcal/mol) is higher than the directly measured value (131±5 kcal/mol) 3 e by ,...,, 7 kcal/mol. The direct vo+ bond energy implies an adiabatic IP for VO of 6.95 eV (7 kcal/mol lower than Dyke's 7.25 eV), resulting in a higher experimental 3A - 3 E- state splitting for vo+ (33±5 kcal/mol), in closer agreement with the theory ( 40. 7 kcal/mol). However, an analysis of the ionization thresholds and an optimization of the excited state potential curves are necessary for any quantitative statement concerning adiabatic state splittings. Since we are primarily concerned with ground state properties of metal oxides, we will eschew this issue for the present. III. Ruo+ Group VIII transition metals have doubly-occupied cl-orbitals for all lowlying electronic states. The lack of empty cl-orbitals decreases the favorability of forming triple bonds to oxygen (unless the metal is in a low spin electronic state). The presence of doubly-occupied cl-orbitals makes metallaketone structures with covalent <J' and 71' bonds unlikely due to electron-electron repulsion between a doublyoccupied metal d71'-orbital and the doubly-occupied oxygen p7r-orbital. For Ru, the large 4d71' orbital overlaps the 0 2p11' orbital to such an extent that the "metallaketone" type of double bond is 16.9 kcal/mol higher in energy than the ground 128- state. Instead of triple or traditional double bonds in RuO+, we find a 4 A ground state with a biradical double bond analogous to the bond in 0 2 • Four of the delectrons in high spin d 7 Ru+ are involved in the 3 r:- type bonding to oxygen (as in ground state 02), forming a. covalent u bond and two three electron 7r bonds. (6) + Ru 0 Ru 0 Since the Ru du and d'll" orbitals are involved in bonds to oxygen, the other three Ru 4d electrons occupy the dS orbitals. High spin coupling of the 3 "E- Ru-0 bonding and the 63 nonbonding electrons on Ru gives rise to the ground 4 A state. However, just as in 02, there are other low-lying electronic states (1 Ag and 1 r:t for 0 2 ) with resonance structures containing conventional double bonds (one u and one 7r). These 02-type bonding configurations, when coupled high spin or low spin to the 63 Ru electrons, give rise to the spectrum of states shown in Table IV. Calculational Detaila The resonance present in Ruo+ necessitates an MCSCF treatment similar to vo+ in which both resonance structures of Eq. (6) are optimized self-consistently. This GVBCI(opt) calculation consists o{ a self-consistent RCI(l/2) treatment of the Ru-0 <T bond, a full six electron CI among the four orbitals of the Ru-0 7r system and simultaneous inclusion of the two possible configurations of the three electrons in the Rufi orbitals_ The GVRCI(opt) waveiunction, with its full CI in the 71" system, is capable of describing any electronic state that is determined by the occupo.tiou and spiu-coupliug of the 7r orbitals. Thus the vertical excitation energies to just such states ( 3 r:;, 1 Ag, and 1 Et bonds) were calculated at this level (Table -129- IV). One higher level MCSCF calculation was performed in which the valence orbitals from the GVBCI( opt) calcUlation were kept fixed, while allowing single 11" -+ 11"*, 6 -+ 6*, u -+ u* excitations from the GVBCI reference states. This GVBCI*Scorr( opt) calculation optimizes the shapes of seven important, low-lying correlating orbitals (with <Tz', 11"uz, 11"uy, rr92 , rr 911 , Ozy, and Oz,-y, symmetries). Moss and Goddard used an analogous CI treatment to accurately predict the bond energy and the electronic state spectrum of 0 2 •24 Three CI calculations involving excitations to the whole virtual space were performed. First, single excitations from all valence orbitals (excluding the oxygen 2s) to a.11 virtuals from the GVBCI(opt) wa.vefunction, GVBCI(opt)*Sva1' allows the orbital shape changes important during bond rupture. Second, the presence of a covalent er bond allows a dissociation consistent 1 ::;,n, 2 :s• 20 calculation to be performed, in which all single and double excitations from the u bond pair to all virtuals are allowed from the GVBCI reference states. This CI incorporates full correlation of the two electrons involved in the breaking bond. We have carried out these single and double excitations (using the GVBCI reference states) from both the GVBCI*S..., u(opt) wavefunction (denoted GVBCI*[S 0 00 ,... + SD.,.]) and from the GVBCI( opt) wavefunction, where singles from the Ru 4d and 0 2p valence :!!pace we.i:c a.l.5o a.llowed (dcuoted GVDCI(opt)*[Sval + SDu)). This latter wavc- function has been shown to yield bond energies accurate to 1-5% for both organic and organometallic molecules .15 •21 •26 The wavefunctions described above dissociate to ground state Ru+ ( 4 F) and ground state 0 (3 P). The HF, GVB(l/2)PP, and GVBCI(opt) wa.vefonctions dissociate to HF fragments. The wavefunctions involving optimization of correlating orbitals dissociate to HF*Scom while the wavefunctions involving single excitations to virtuals from the valence space (excluding the 0 2s) dissociate to HF*Sval (~ee Section II). (Note that single and double excitations out of the breaking bond pair -130- dissociates to just singles out of a singly-occupied orbital on each fragment.) We used the same oxygen basis as described in Section II, along with the Rappe and Goddard valence double.:( basis for Ru. 19 a, 25 a The Ru-0 bond length was optimized for the ground 4 A state at the GVBCI{ opt) level. Re.mlta The ground state of RuO+ is predicted to be 4 A, with an equilibrium bond length of Re = 1. 75 A and an equilibrium vibrational frequency of We = 787 cm- 1 . Although Ruo+ has not yet been observed, these values may be compared with those of a terminal Ru=O porphyrin complex, in which the bond length is 1. 765 A and the Ru=O stretching frequency is 855 cm- 1 •27 The Ru=O bond is very covalent, with no charge transfer to the oxygen. In fact, the total electronic charge (from Mulliken population analysis) indicates 0.04 electron transferred to Ru+ from 0. The GVB-CI(opt) orbitals for both RuO and 0 2 are shown in Fig. 2, where we see that the Ru-0 u bond is just as covalent as the 0-0 u bond. The three electron 7r systems of both RuO+ and 02 look very similar, with the Ru-0 11"u and 11"g orbitals delocalized over both centers as in 0 2 • The vertical electronic state spectrum shown in Table IV reveals the same ordering of bond types as in 0 2, with the 4 A state with 3 :£- biradical bonding lowest in energy, followed by the 2 r state with 1 A metallaketone bonding (i.e., covalent u and 7r bonds) 16.9 kcal/mol up. This 1 A - 3 :£- splitting of 16.9 kcal/mol for Ruo+ may be compared with the 1 A 9 - 3 :£; splitting of 22.6 kcal/mol for 0 2.22 The energy splitting between these two states corresponds to twice the exchange term between the singly-occupied 1!"9 ~ and 7rn orbitals, K.., 11 ; thus we find K.,y(RuO+) = 8.45 kcal/mol and K:i: 11 (0 2 ) = 11.3 kca.1/mol. The exchange term is larger for 02 since e.xchl.l.llge euc:::rgy h; proportional to the square of the overlap between the two orbitals [Re(0-0) = 1.21 A versus Re(Ru-0) = 1.75 A]. The 2 A state with the 1 :£+ bonding configuration, which should be ,. . ., 4Kzy higher in energy than the 3 :E- bonding ground state, is 37.1 kcal/mol above 4 .6. -131- instead of "" 34 kcal/mol. A lower 2 A state, along with a nonequilibrium bond length, destabilizes the high-lying 2 A state. In sum, the ordering of states in the 0 2 -type manifold is determined by a combination of two factors: (i) lower electronelectron repulsion favors 3:£- over 1 a and 1 a over 1 :E+ and (ii) high-spin coupling between the Ru-0 bond and the nonbonding 83 electrons is favored over low-spin coupling. Thus the low-lying states which have Ortype bonds are (in order of increasing energy): 4 A, 2 r, 2 A, 2 E±, and 2 A. We also calculated the energy of a 2 E+ state of RuO+ with a CO-type triple bond and a nonbonding d8 4 configuration on Ru+. This state involves only one resonance structure of Eq. (1) [~~-~r Ru (7) 0 since the other resonance structures would require promotion of Ru+ to an intermediate spin s 1 d 6 excited state. We did not investigate 2 II CO-type bonding, in which three electrons in one 7l' plane would destroy the triple bond. While Eq. (7) has three electrons in the u system, the triple bond may still form, since do- orbitals rehybridize away from the donor bond more easily (mixing ins-character) than d7l' orbitals (mixing in higher energy p-character). At the GVB-R.Cl(2/4)(opt) level, 28 this state lies 29. 7 kcal/mo! above the ground state. As expected, the lack of empty cl-orbitals on the metal destabilizes triple bonds to oxygen, and the biradical double bond is preferred. The bond energies for the ground state of RuO+ ( 4 A) and the ground state of 0 2 (3:Eg-) a.re shown in Table V as a function of increasing electron correlation. We see that HF and GVB-PP are inadequate descriptions of metal-ligand multiple -132- bonds. Although it is only a valence level calculation, the GVBCI( opt) description stabilizes both RuO+ and 0 2 considerably. As single and (selected dissociationconsistent) double excitations are included in the wavefunction, we converge to a bond energy for 02 of 115.5 kcal/mol at the GVBCI(opt)*[Sval + SDO'] level, 4.7 kcal/ mol lower than the experimental value of 120.2 kcal/ mol. 22 The analogous calculation on RuO+ yields De(Ru+=O) = 62.4 kcal/mol. Using the difference in the experimental and predicted De(O=O) = 4.7 kcal/mol as an estimate of the correlation error endemic to this level of calculation, we obtain De(Ru+=O) = 67.1 kcal/mo! as our best estimate for the bond energy of RuO+. Although the bond energy of Ruo+ is not known, it is very close to the measured bond energy of Feo+ [D 0 (Fe+=O) = 69±3 kcal/mol]. 3 d Bond strengths are usually thought to increase going down a column of the periodic table, although measurements of Fe+ and Ru+ bonds to hydrogen and methyl have recently disputed that intuitive notion, with second row bond energies found to be about 15 kcal/mo! weaker than their first row counterparts. 29 Since the bond strengths in 0 2 -type bonds are dependent on lowering the electron-electron repulsion in the 7r system, we might have expected Ruo+ to have a weaker bond than FeO+, since the 4d orbitals of Ru may cause more 7r repulsion than the small 3d orbitals of Fe. IV. Discussion and Summary We have presented results of ab initio calculations on representative early and late transition meta.I oxo cations, in a.n effort to understand the fundamental nature of their bonding and reactivity differences. The contrasts in ground state properties of vo+ and RuO+ are fully evident in Table VI. The early meta.I forms a CO-type triple bond with no unpaired electrons on the oxygen ligand, while the late metal forms a biradical 02-type double bond with one unpaired electron on the oxo group. The charge on oxygen in the two systems reflects the tendency toward ionic bonding for early meta.I oxides and toward more covalent structures for the late metal oxo compounds. The equilibrium properties of the ground state -133- of vo+ are in excellent agreement with the values derived from the photoelectron spectrum of V0. 3 9 The ground state properties for Ruo+ are in accord with both RuO porphyrin complexes 27 and FeO+. Jh The early metal oxide is characterized by a bond nearly twice as strong as the late metal oxide, with vibrational frequencies and bond lengths commensurate with their relative bond strengths. These contrasts in properties we have predicted for the simple metal-oxo diatomics a.re consistent with known reactivity and stability trends. The triplybonded oxygen of vo+ has no unpaired electrons on the oxygen and hence vo+ is expected to be relatively inert. Freiser and co-workers 3 i observed precisely this behavior, with the oxo ligand unreactive toward a variety of hydrocarbon substrates. Further testimony of the unreactive nature of a triply-bonded metal-oxo is provided by the vanadyl cation, V02+, which is used as an ESR-active probe of proteins because it does not react with substrates. 5 On the other hand, we expect RuO species to be reactive due to the radical character on the oxygen. Consistent with this hypothesis, isoelectronic FeO complexes a.re known to oxidize hydrocarbons to a.lcohols,86 FeO+ in the gas phase forms H 2 0 from reaction with alkanes, 3 h 112 RuO bipyridyl complexes are active oxygen atom transfer catalysts, 7 and Ru0 4 is an exceedingly powerful oxidizing agent. 4 Sample reactions expected for RuO /FeO systems a.re shown below. (8) 7 R ---?--+ [Ru] + ROH -134- The reactivity discu:ssed above can be uu<lerl:ituo<l entirely in terms of the metal-oxo bond character. If we can predict the M-0 bond character as a function of the metal, then we can predict its reactivity. We divide the transition metals into three groups based on their expected behavior: (i) Due to their empty d-orbitals, early transition metals (e.g., Sc, Ti, and V) can form triple CO-type bonds in which all of the electrons at 0 are paired up with the metal, rendering the oxygen inert. The early metals cannot form the Lira<lical 02-type bun<l since they have no doubly-occupied d-orbitals necessary for resonance. (ii) The Cr and Mn triads have no empty cl-orbitals and no doubly-occupied orbitals. As a result, these metals have no choice but to form conventional double bonds involving one <J' and one 11" bond and are expected (and found experimentally3 a) to be moderate in their reactivity. 30 (iii) The group VIII metals cannot readily form triple bonds since they have no empty cl-orbitals for the oxygen lone pair to donate into. However, the group VIII metals can form the very reactive, biradical 0 2 -type double bonds since they have doubly-occupied cl-orbitals available for the 11" resonance. The Or type double bond should be preferred over conventional u and 11' bonds due to 1t'-1t' repulsion between doubly-occupied metal cl-orbitals and the doublyoccupied oxygen p~orbital. Thus we have shown that the reactivity of metal-oxo systems can be explained in a. simple manner by considering how the d-orbital occupation on the metal dictates the type of metal oxygen bond formed, with early metals forming strong unreactive triple bonds and late metals forming weak, reactive biradical double bonds. These are appropriate descriptions of terminal metal-oxo bonding only. Future research will focus on the bonding and properties of bridging oxides, the preference between terminal and bridging isite:s, a.nd the relationship between molecular and bulk oxides. -135- Acknowledgments. This work was supported by the National Science Foundation (Grant No. CHE83-18041) and the Shell Companies Foundation. EAC acknowledges a National Science Foundation predoctoral fellowship (1982-1985), a research grant award from the International Precious Metals Institute and Ge~ni Industries (1985-1986), and a SOHIO fellowship in Catalysis (1987). -136- References (1) a) K. D. Carlson and C. Moser, J. Chem. Phys. 44, 3259 (1966); b) S. P. Walch and W. A. Goddard III, J. Am. Chem. Soc. 100, 1338 (1978); c) C. W. Bauschlicher, Jr., P. S. Bagus, and C. J. Nelin, Chem. Phys. Lett. 101, 229 (1983); d) P. S. Bagus, C. J. Nelin, and C. W. Bauschlicher, Jr., J. Chem. Phys. 19, 2975 (1983); e) C. W. Bauschlicher, Jr., C. J. Nelin, and P. S. Bagus, J. Chem. Phys. 82, 3265 (1985); f) C. J. Nelin and C. W. Bauschlicher, Jr., Chem. Phys. Lett. 118, 221 (1985); g) M. Krauss and vV. J. Stevens, J. Chem. Phys. 82, 5584 (1985); h) C. W. Bauschlicher, Jr. and S. R. Langhoff, J. Chem. Phys. 85, 5936 (1986); i) M. Dolg, U. Wedig, H. Stoll, and H. Preuss, J. Chem. Phys. 86, 2123 (1987). (2) J. F. Harrison, J. Phys. Chem. 90, 3313 (1986); we note that 71" - t 71"* transitions using UHF (Unrestricted Hartree-Fock) wavefunctions for TMO cations have been examined by K. Yamaguchi, Y. Takahara, Y. Toyoda, T. Fueno, and K. N. Houk, preprint. (3) a) H. Kang and J. L. Beauchamp, J. Am. Chem. Soc. 108, 5663 (1986) and references therein; b) D. L. Hildenbrand, Chem. Phys. Lett. 34, 352 (1975); c) E. Murad, J. Geophys. Res. 83, 5525 (1978); d) idem, J. Chem. Phys. 73, 1381 (1980); d) P. B. Armentrout, L. F. Halle, and J. L. Beauchamp, J. Am. Chem. Soc. 103, 6501 (1981); e) N. Aristov and P. B. Armentrout, J. Am. Chem. Soc. 106, 4065 (1984); f) J.M. Dyke, B. W. J. Gravenor, R. A. Lewis, and A. Morris, J. Chem. Soc., Faraday Trans. 2, 79, 1083 (1983); g) J.M. Dyke, B. W . .T. Gravenor 1 M. P. Hastings, and A. Morris, J. Phys. Chem. 89, 4613 (1985); h) T. C. Jackson, D. B. Jacobson, and B. S. Freiser, J. Am. Chem. Soc. 106, 12~2 (1984); i) T. C. Jackson, T. J. Carlin, and B. S. Freiser, J. Am. Chem. Soc. 108, 1120 (1986); j) H. Kang and J. L. Beauchamp, J. Am. Chem. Soc. 108, 7502 (1986). (4) F. A. Cotton and G. Wilkinson, "Advanced Inorganic Chemistry" (Wiley, -137- New York, 1980). (5) a) J. SelLin, Coord. Chem. Rev. 1, 293 (1966); b) N. D. Chasteen, R. J. DeKoch, B. L. Rogers, and M. W. Hanna, J. Am. Chem. Soc. 95, 1301 (1973). (6) A. Streitweiser, Jr. and C. H. Heathcock, "Introduction to Organic Chemistry" (1facMillan, New York, 1976). (7) a) D. J. Gulliver and W. Levason, Coord. Chem. Rev. 46, 1 (1982); b) G. J. Samuels and T. J. Meyer, J. Am. Chem. Soc. 103, 307 (1981). (8) a) J. P. Collman, J. I. Brauman, B. Meunier, T. Hayashi, T. Kodadek, and S. A. Raybuck, J. Am. Chem. Soc. 107, 2000 (1985); b) M. J. Nappa and C. A. Tolman, Inorg. Chem. 24, 4711 (1985). (9) Covalent metal-oxo bonding configurations for Cr, Mo, and Fe complexes have been discussed previously by: a) A. K. Rappe and W. A. Goddard III, ::iature 285, 311 (1980); b) idem, J. Am. Chem. Soc. 102, 5114 (1980); c) ibid. 104, 448 (1982); d) ibid. 104, 3287 (1982); e) W. A. Goddard III and B. D. Olafson, Ann. New York Acad. Sci. 367, 419 (1981). (10) H. Spinrad and R. F. Wing, Annu. Rev. Astron. Astrophys. 7, 249 (1969). (11) R. A. Sheldon and J. A. Kochi, "Metal Catalyzed Oxidations of Organic Compounds" (Academic, New York, 1981). (12) A preliminary study of the reactions of FeO+ appeared earlier: M. M. Kappes and R.H. Staley, J. Am. Chem. Soc. 103, 1286 (1981). (13) This type of triple bond has been proposed for Cr and Mo oxo bonds by Rappe and Goddard (see Ref. 9). (14) The details of the genernlized valence bond methu<l mi:l.y Le found in: (a) vV. J. Hunt, T. H. Dunning, Jr., and W. A. Goddard III, Chem. Phys. Lett. 3, 606 (1969); ·vv. A. Goddard III, T. H. Dunning, Jr., and \V. J. Hunt, Chem. Phys. Lett. 4, 231 (1969); W. J. Hunt, W. A. Goddard III, and T. -138- H. Dunning, Jr., Chem. Phys. Lett. 6, 147 (1970); W. J. Hunt, P. J. Hay, and W. A. Goddard III, J. Chem. Phys. 57, 738 (1972); F. W. Bobrowicz and W. A. Goddard III in "Methods of Electronic Structure Theory", H.F. Schaefer, ed., Plenum Publishing Corporation, 1977, pp 79-127; (b) L. G. Yaffe and W. A. Goddard III, Phys. Rev. A 13, 1682 (1976). (15) E. A. Carter and W. A. Goddard III, Chem. Phy.J. Lett., submitted for publication. (16) T. H. Dunning, J. Chem. Phys. 53, 2823 (1970). (17) S. Huzina.go., J. Chem. Phys. 42, 1293 (1965). (18) The oxygen cl-exponent was optimized for H 2 0 by R. A. Bair and W. A. Goddard III, submitted for publication. (19) a) A. K. Rappe and W. A. Goddard III, to be published. This basis set was optimized for the d" configuration of the metal as discussed in A. K. Rappe, T. A. Smedley, and W. A. Goddard III, J. Phys. Chem. 85, 2607 (1981). b) The HF 5 F - 5 D state splitting for v+ with this basis is 7.3 kcal/mol, which may be compared with the NHF value of -3.5 kcal/mo! [R. L. Martin and P. J. Hay, J. Chem. Phys. 75, 4539 (1981)] and the experimental value (averaged over J-states) of 7.6 kcal/mol (C. E. Moore, "Atomic Energy Levels", NSRDS-NBS-35, 1971). (20) We obtained one-electron orbitals from the RCI-MCSCF natural orbitals by freezing all orbitals other than GVB pairs and running one GVB-PP iteration to obtain the GVB-PP CI coefficients which tranform the natural orbitals to one electron orbitals. We did not allow any mixing to occur between GVB pairs. (21) E. A. Carter and W. A. Goddard III, J. Phys. Chem. 88, 1485 (1984). (22) K. P. Huber and G. Herzberg, "Constants of Di1domic Mnlt~cnles" (Van Nostrand, New York, 1979). -139- (23) J. Sugar and C. Corliss, J. Phys. Chem. Ref. Data 7, 1191 (1978). (24) B. J. Moss and W. A. Goddard III, J. Chem. Phys. 63, 3523 (197~). (25) a) R. A. Bair and W. A. Goddard III, submitted for publication; b) R. A. Bair, Ph. D. Thesis, California Institute of Technology, 1981. (26) a) E. A. Carter and W. A. Goddard III, J. Am. Chem. Soc. 108, 2180 (1986); b) ibid., to be submitted. (27) a) C.-M. Che, K.-Y. Wong, and T. C. W. Mak, J. Chern. Soc., Chem. Commun., 546 (1985); b) C.-M. Che, T.-W. Tang, and C.-K. Poon, J. Chem. Soc., Chem. Commun., 641 (1984). (28) The GVB-RCI(2/4)(opt) wavefunction for the CO-type bonding in Ruo+ (2:E+) is a self-consistently optimized RCI within the two GVB 7r pairs (two natural orbitals per pair), simultaneously allowing both occupations of the three O" electrons in the Ru dO" and the 0 pu orbital. This level of calculation maintains the same degrees of freedom (e.g., the same number of orbitals and the same correlations) as the GVBCI(opt) wavefunction for the 02-type bonding in Ruo+. (29) M. L. Mandich, L. F. Halle, and J. L. Beauchamp, J. Am. Chem. Soc. 106, 4403 (1984). (30) !:£metals from the Cr or Mn triads are oxidized, it is then possible to form triple bonds due to the vacated metal cl-orbitals. See Ref. 9. -140- Table I. First Row Transition Metal-Oxo Bond Strengths (kcal/mol).a metal D0 (M+-o) D0 (M-O) Sc Ti 159±7 161.5±3 161±5 158.4±2 v 131±5 146±4 Cr Mn Fe Co Ni 85.3±1.3 110±2 57±3 85±4 69±3 93±3 64±3 87±4 45±3 89±5 a) Taken directly from Ref. 3a. -141- Table II. The Valence Double-( Basis Set (Ref. 19) for Vanadium: Cartesian Gaussian Functions with Exponents (a,) and Contraction Coefficients (Ci)· type ai Ci s 6713.0 0.0201562 ~ 1013.0 0.1395721 s s 228.5 62.12 0.4823097 0.4967414 !S 88.72 -0.1201452 13.91 5.277 8.688 1.517 0.5481 0.8189 0.07869 0.03017 281.1 65.29 19.81 6.575 4.293 1.928 0.5894 0.4562692 0.6323929 -0.2174606 0.5246311 0.6086236 -0.3913214 1.1016545 1.0000000 0.0313639 0.1952724 0.5207761 0.4320400 0.0553142 0.5331482 0.5245114 1.462 ·-0.2289701 0.09538 0.02774 21.18 5.566 1.753 0.5256 0.1336 1.0105803 1.0000000 0.0416242 0.2040699 0.4524271 0.5663618 1.0000000 s s s s s s s s p p p p p p p p p p d cl cl d cl Table III. Comparison of Adiabatic Bond Energies (De) for vo+ and CO (kcal/mol).a total energies (hartrees) calculation vo+ ( 3 :E-) co (1:E+) 0 (lP)b De(V+ :=O)c De(C=O)d HF -lOHi.38880 (1/1) -1016.48099 (6/6) -1016.56530 (27 /126) -1016.57823 (27/126) -1016.59051 (81/582) -1016.59666 (747/4778) -112.75712 -74.80059 -11.1 170.6 (1/1) (1/l) -112.81849 (6/6) -112.87721 (27 /37) -112.87909 (27 /37) -112.88198 (81/139) II 46.8 209.1 II 99.7 246.0 II 107.8 247.2 -74.80148 (5/9) -74.80161 (33/53) 115.0 248.4 GVB(3/6)-PP GVB-RCI(3/6) GVB-RCI(3/6) (opt) RCI(3/6)*Scorr (opt) -112.88343 (351/649) N I 118.7 249.2 Experiment 131±5e 258.81 De + ,6.~orr 128.a RCI(3/6)( opt )*SvaI I ...... +>- a) Calculational details are given in Section II. The corresponding number of spatial configurations/spin eigenfunctions for each wavefunction is listed beneath each total energy. b) Total energies for ground state 0 (3 P) are calculated at the level consistent for R == oo for each calculation: HF, HF*Scorr, and HF*Sval· c) The wavefunctions for vo+ all dissociate to HF ground state V' ( 5 D) (total energy = -941.60584 hartrees). d) The wavefunctions for CO all dissociate to HF ground state C ( 3 P) (total energy::.__: -37.68462 hartrees). e) Ref. 3e. f) Ref. 22. g) .6.corr = n:xpt(CO) - D~ak(CO) = 9.6 kcal/mol. -143- Table IV. GVBCI( opt) Vertical. Excitation Energies for Re( 4 .6. RuO+) = 1.75 A (kcal./mol).a RuO+ at state characterb total energy (hartrees) .6.E 2.6. (1E+ bond)x(Ru 83 ) -4511.97615 37.1 -4511.98788 29.7C (1.6. bond) x (Ru 8 ) -4511.99187 27.2 low spin ( 3 :E- bond)x(Ru <5 3 ) + (1E+ bond)x(Ru 83 ) -4512.00239 20.6 (1.6. bond) x (Ru 63 ) high spin (3 I:- bond)x(Ru 15l) -4512.00828 16.9 -4512.03521 0.0 +low spin ( 3 :E- bond)x(Ru 83 ) 2:£+ 2I;+ ' 2.6. 2r 4 .6. CO-type bond 2:E- 3 a.) Calcula.tional. details a.re given in Section III. b) Character of each state describes the coupling between the Ru nonbonding electrons (83 ) and the Ru-0 bond (described by the analogous state of 0 2 to indicate the type of Ru-0 bond). The dominant character for each 2 .6. state is shown in boldface. c) The consistent calculation for the CO-type bond in RuO+ is the RCI(2/4)(opt) calculation described in Ref. 28. Table V. Comparison of Adiabatic Bond Energies (De) for RuO+ (4 A) and 0 2 ( 3 'E;) (kcal/mol). 4 total energies (hartrees) calculation Ruo+ ( 4 ~) 02 (3E;) Ru+ {4 F) 6 0 (3P) 6 De(Ru+=O) De(O=O) HF -4511.91327 (1/1) -4511.96279 (2/2) -4512.03521 (22/40) -4437.18354 (1/1) -74.80059 (1/1) -44.5 17.2 II II -13.4 34.8 ti II 32.1 83.7 -4512.07610 (288/916) -4512.08099 (1218/3964) -149.62855 (1/1) -149.65663 (2/2) -149.73456 (6/10) -149.77879 (54/130) -149.78138 (154/390) -4437.18429 56.7 110.3 59.5 111.8 GVBCI*[Scorr(opt) + SDu] -4512.08316 (1990/5300) -149.78571 (378/846) GVBCI(opt)*[Sn.1 + SDu} -4512.08549 (2656/7616) -149.78736 (426/966) -74.80148 (5/9) -74.80161 (33/53) -74.80148 (5/9) -74.80161 (33/53) GVB(l/2)-PP GVBCI(opt) GVBCI*Scorr( opt) GVBCI( opt )*Sval (5/11) -4437.18450 (21/48) -4437.18429 (5/11) -4437.18450 (21/48) ..;::. I 61.l 114.7 62.4 115.5 120.2c Experiment De + A:orr ..,,. !--' 67.1 a) Calculational details are given in Section III. The associated number of spatial configurations/spin eigenfunctions for each calculation is given in parentheses under each total energy. b) Total energies for the fragments are calculated at levels consistent for R = oo for each calculation (Section III). c) Ref. 22. d) Acorr = D:xpt(0 2 ) - D~ 11k(02 ) = 4.7 kcal/mol. -145- Table VI. Comparison of Properties of vo+ and RuO+. vo+ property ground state bond order Ruo+ theory ... expt theorya 3E- 3E-b 4~ 3 3c: 2 expt net charge on oxygend -0.26 Re(A) 1.56 1.54±0.01 b 1.75 1.765e w.,(cm- 1 ) 1108 1060±40b 787 g55e De(kcal/mol) 128.3 131±5c 67.1 +0.04 a) This work. b) Ref. 3g. c) Ref. 3e. d) Based on Mulliken populations of the RCI(opt) for vo+ and GVBCI(opt) for Ruo+ wavefunctions. e) The experimental R(Ru=O) and w(Ru=O) are from a Ru=O porphyrin complex (Ref. 27). -146- Figure Captions Fig. 1. The GVD one-electron orLitals fur the a an<l uue 7r Luml (the:: utht:r i~ identical) of vo+ ( 3 ~-) and CO (1~+): a) the V-0 u bond; b) the V-0 71" bond; c) the CO er bond; and d) the CO 71" bond. Contours are from -0.6 to 0.6 a.u. incremented by 0.06 a.u. Fig. 2. The GVB one-electron orbitals for the u bond, a doubly-occupied 11"u orbital, and a singly-occupied 11"g orbital of Ruo+ (''~)and 0 2 ( 3 :E;): a) the Ru-0 u bond; b) an Ru-0 11"u orbital; c) an Ru-0 1rg orbital; d) the 02 u bond; e) an 0 2 1ru orbital; and by 0.06 a.u. f) an 0 2 1f'g orbital. Contours are from -0.6 to 0.6 a.u. incremented -147 w z 0 6 I 0 - .... V\l w z 0 f ..... • ... .., .... I .. ..- I / 0 z 0 m \ ... ~·";'\I \ \ ~I I / ".,. - ' --. ,, '' ~\ ~Ill " / "' ' + u - ... ' ,. ,.... ,,,,.--.. -0 w z b w 0 0 I z 0 z 0 CD ~ ~ 0 I u u ,I -- ,....., ~ ~ -c u Q) 1'-< ::s Cl.() ' "" ;.i... w w 0.z z 0 , ... ... ' . \ ~\I I ,,,111 I ,-_., , ..,,,.~ ,......_ - . ® /'.~~' I V\l -+ ti) 0 > w z 0 ---~ I,- . . \ \ I ... ~~I\ I :I'.. c 0 z 0 m b 0 I 0 z "*O 0 ~ ~ \ I > ..-..0 m 0 I > -148- w z 0 0 z I -w ' - I I b ,. 0 0 :;, I O'I \ r0 0 I) \ - ,-.,, ... ... I , 0 0 - ... I . - ,. ...., - ...,,' \ .... 1''111 I 0 z 0 z 0 co ""', f' t::: "1\1 I ~II I 0 CD -- /,:;.~\ I \II~ ':::: ~l1. ~ \ ...-"' ' 1 I I , 0 f- z <[ * ~ 0 0 - - ( ,,'\:,... 1J' ' f- 0 ... - z co z (\j ~ w I t 0 w I '+- Q.) - -0 N <ll ~ ;::l bl} ..... w [..I.. z 0 0 -<J 0 - z I '7·~.l' q- + 0 z z en 0 0 w b 0 0 ::::J 0 0 co !::: z 0 .... J ~ - \ ' 1 tu \ ,,'<*- '.:- ..... c co f- z <[ I 0 ::J 0::: I ::J 0::: - z 0 *t::: 0 I ::J 0:: w - ..c - (.) 0::: -149- Chapter 2.E. The text of this section is an Article coauthored with William A. Goddard III which has been submitted to the Journal of the American Chemical Society. -150- Rela:tionships between Bond Energies in Coordinativcly Un- saturated and Coordinatively Saturated Transition Metal Complexes: A Quantitative Guide for Single, Double, and Triple Bonds Emily A. Carter and William A. Goddard III* Contribution No. 7567 from the Arthur AmoJ Noye& Laboratory of Chemical Phy&ic&, California [nJtitute of Technology, Pa&adena, California 91125 Abstract: A prescription is presented for converting M+-X bond energies (from experiment or theory) in un&aturated complexes to M+ -X bond energies appropriate for coordinatively &aturated organometallic compounds. The theoretical basis for the predicted conversion factors originates from quantitatively evaluating the consequences of: (i) the loss of high spin coupling (exchange energy) between va- lence electrons on the unsaturated transition metal ion subsequent to the formation of covalent metal-ligand bonds; (ii) the cost (promotional energy) of bonding to a low-lying excited state ofthe metal ion (either 8 1 d"- 1 or d") instead of the ground electronic state; and (iii) the loss of high spin coupling in coordinatively saturated transition metal complexes upon bond formation (assuming a d" valence electron configuration). These predictions should be most useful for covalent metal-ligand bonds in complexes where the metal has at least a +1 oxidation state and where the ligands of interest have electronegativities comparable to carbon or hydrogen. This method is not appropriate for prediction of bond strengths where the bonds are primarily of ionic or donor-acceptor character. -151- I. Introduction Thermochemical data for organotransition metal compounds are sparse, especially for the coordinatively saturated complexes which are often the important players in transition metal-catalyzed reaction chemistry. However, a growing list of metal-ligand bond energies is becoming available for gas phase metal ions with one ligand attached (M+-X). 1 - 4 The bond energies have been determined in a variety of ways, including: (i) the translational energy dependence of endothermic reactions in ion beam experiments; 1 (ii) ion cyclotron resonance (ICR) measurements of proton affinities to derive metal-hydrogen bond d.rengths; 2 (iii) brar.keting bond energies by using Fourier Transform mass spectrometry (FTMS) to study chemical reactiums;~ and (iv) photodissociation studies which yield bond energies from photoappearance thresholds. 4 While bond energies derived f'rom the above techniques are useful for interpreting the chemistry of gas phase, highly unsaturated, metal ion complexes, it is unclear how these values can be used for predicting the thermochemistry of the majority of organometallic species, namely for coordinatively saturated, "18-electron" complexes. In order to clarify this relationship, we present a prescription for the conversion of the experimentally or theoretically observed values for coordinatively un.5aturated transition metal-ligand bond energies to those appropriate for coordi- natively .5aturated transition metal-ligand bond strengths, based on examining the differential exchange and promotional costs (vide infra) inherent to bond breaking/making events. For main group X-H bond energies, Goddard and Harding 5 showed that a similar approach using only differential exchange leads to excellent quantitative predictions of trends in the bond strengths of XHn as a function of n. We commence with some background on the energetics of bonding to high spin metal ions, concentrating on the costs due to loss of high-spin coupling between valence electrons on the metal center. We also consider whether it is energetically feasible to form bonds to low-lying excited states of the metal ions (either s 1 dn-l -152- or dn). Tht: t:ut:rgdic:-; iuvulvt:d iu furmiug isiugle, double, und triple bundis to first and second row transition metals (Sc-Ni and Y-Pd) are computed from ab initio calculations of intraatomic exchange integrals and from experimental excitation energies for both the s 1 dn-l and dn states of M+. We then predict, taking the lowest cost for a given metal and a given bond multiplicity, the quantity AK which must be added to bond energies found for the completely unsaturated M+-x species D'at = Dunsat M-X M-X + /::,.K (1) in order to obtain estimates for the corresponding bond energies in coordinatively saturated organometallic complexes. Finally, we conclude by comparing our predictions from this method with some of the few metal-ligand bond energies available for 18-electron complexes. II. Description of the Method In a recent paper, Carter and Goddard 6 compared the M=CH 2 bond energy found for a completely unsaturated molecule, RuCHt, with that of a (model) cu- ordinatively saturated complex, (Cl )(H)Ru1 CH 2 • While the metal-carbon bond character is essentially identical in both complexes, the bond energies for the unsaturated and saturated complexes are predicted to differ by 16 kcal/mol. This is typical; as discussed below, the correction term AK can be as large as 60 kcal/mol, yet we find that changes in metal valence electron spin coupling and (possible) promotional energies adequately account for the trends in transition metal-ligand bond energies. For isolated metal ions (or atoms), the ground electronic state always has the singly-occupied valence orbitals coupled to form the highest spin state, as predicted by Hund's rule (e.g., Ru+ in its ground state configuration of 4d 7 has S = ~ ). The quantitive basis for Hund's rule is the energy lowering contributed by exchange interactions in the electronic energy expression: 7 Eex = - L Kia,;a i>; (2) 153These exchange terms arc only nonzero between electrons of the same spin. There- fore, the lowest energy state of M+, whether it be s 1 dn-l or dn, is always high spin. Form high spin-coupled electrons, there are m(7;-l) exchange terms, each leading to a lowering of the electronic energy. However, upon covalent bond formation, some of this exchange energy is lost, weakening the intrinsic metal-ligand bond. This loss of exchange energy results from necessarily singlet-coupling the electrons in ear.h mP.bt.l-ligand hond pair. On average 1 then, the metal electrons involved in covalent bonding have a (up) spin half of the time and f3 (down) spin half of the time. This results in partial quenching of intra.atomic exchange stabilization. The magnitude of this effect depends on the number of other (non-bonding) singlyoccupied orbitals on the metal (as well as the magnitude of each exchange term) and therefore it depends on the degree of saturation at the metal center. For example, a two electron triplet (X•pin = aa) has one exchange term (-K) in its energy expression. Making a single bond to one of these electrons changes the spin coupling between the two formerly high spin electrons to 1 Xapin = 2[aa + af3], (3) due to the averaged spin of the bonding electron. This spin function results in an exchange contribution of only -fK and a net energy destabilization of +~K. A three electron quartet (Xapin = aaa) has a -3K exchange energy. Forming a single covalent bond to the quartet results in the spin function 1 Xapin = [aaa + aaf3], 2 (4) with an exchange energy now of only -2K, a destabilization of +lK. Thus, we see that the exchange loss grows as the number of unpaired electrons grows (or as the degree of unsaturation grows). In this manner, it is easy to compute the loss of exchange energy upon covalent bond formation for single, double, and triple bonds by merely considering the effect -154- of averaged i:;pin-coupling for bonding dectruus. In the case of transition metals, d-d exchange terms are nearly always much larger than s-d exchange terms. Thus, for metals with a high spin dn ground state, it may be advantageous to promote an electron from a valence cl-orbital to the valences-orbital (forming the s 1 dn-l state), since bonding to an s-electron will result in less exchange loss. Therefore, we shall consider the costs for forming single, double, and triple covalent bonds to the first and second row metal ions in both the high spin s 1 dn-l and dn electronic states. Table I symbolically displays the cost of covalent bond formation in these cases, where E10 .t is the sum of the exchange and any promotional (excitation) energy destabilization. Exchange loss pee.ks in the middle of ee.ch row e.nd hence we expect the Cr and Mn triads to have the weakest bonds (in completely unsaturated metal ion complexes), consistent with many experimental 1 - 4 and theoretical 8 - 10 observations. Table II provides ab initio values of sd = K:;a and dd = K~~g from averaged-field Hartree-Fock calculations on each ion (Sc+-Ni+ and y+ _pd+) 11 and excitation energies, Ep(s 1 dn-l-+ dn and~-+ s 1 dn-l). 12 These numbers are used to evaluate each entry in Table I, with the results displayed in Table III. For the remaining discussion, we will utilize the values in boldface, which represent the lowest energy cost to form a particular bond to a particular metal ion. In order to predict metal-ligand bond strengths for saturated systems, we first must define an intrinJic (exchangeless) bond energy D.int -_ nun•at + Eunsat lost l (5) where nunsat is the observed bond strength of the unsaturated complex and E1ost is ta.ken from Table III. Dint is the bond energy one would observe if no promotional or exchange losses were incurred. To obtain the bond energy of a corresponding saturated complex, n•at, we must subtract from D1nt the exchange and/ or promotional costs associated with forming covalent bondi;. in t.he .rnforated ;,ydem. Therefore, we obtain -155- eat D int - E lost = Duneat +AK. (6) In order to calculate Ei;:t' we a.:ssw.m:: thti.t the metal prefers a d" configura- tion in a saturated complex, since repulsive interactions between the metal and its ligands should disfavor occupation of the valence s-orbital. Bonding to a d" configuration in a saturated complex leads to the following exchange losses (and no promotional costs since we assume ad" ground state): (7) Using Eq. (7) and the values listed in Table III, we can calculate ~K of Eq. (6) to determine the conversion factors which transform unsaturated bond energies into saturated bond energies, for each bond multiplicity and for each first and second row transition metal. These differential exchange energies are listed in Table IV. Adding these values to gas phase M+-X bond energies allows one to estimate metal-ligand bond strengths in 18-electron, coordinatively saturated complexes (or in singlet states of unsaturated complexes). To this end, Table V lists observed unsaturated bond strengths and predicted saturated bond strengths for a number of M+-H, M+=CH 2 , and M+ ::CH bonds. We have not included values for gas phase M+ -CH3 bond energies, which are much larger than those expected :£or aa.turated M-CH3 bond strengths. This i-e:mH hti.s been attributed by Mandich et al. 1 d to the anomalously large stabilization of the metal methyl cation due to the high polarizability of the (approximately spherical) methyl group. In contrast, we believe that the planar CH2 and CH ligands are not as easily polarizable and no extra stabilization is expected in the bare metal cation complexes. The gross trends in Table V are correct for the saturated systems, with the bond energies -156- decreasing as we go across a row and increasing as we go down a column. Some exceptions exist, but given current experimental uncertainties we believe that these discrepancies tag systems worthy of additional experimental study. The predictions for saturated bond energies mostly await experimental verification. However, a few bond energies have been measured, and these are compared to our predicted values in Table VI. The agreement is generally quite good, but as this model does not account for changes at the metal center due to the electron withdra.wing or electron-dona.ting ch6.racter of the ancillary l.igand:s, we ::;ee variations in the experimentally observed bond strengths as the ligand set is altered. The largest discrepancies occur for (CO)sFe+-H and (C0) 4 Ni+-H, where the most recent experiments yield 72.4±3.6 and 52.8±2.2 kcal/mol, respectively, whereas the theory yields 57.0±4 and 38.5±1.4 kcal/mol. On the other hand, the binary carbonyl hydride bond energies for Cr and Mo agree well with our predictions (55.9±2.4 versus 60. 7±2 kcal/mo! for Cr and 63.1::::2.2 versus 67.8±3 kcal/mol for Mo). Experimental bond energy determinations in these cationic systems rely on the accuracy of the ionization potentials (!P's) of the neutral carbonyls. Experimental IP data always provide upper bounds to the true adiabatic !P's, since structural relaxation of the resultant cations is not always observed on the time scale of the experiments. (If vibrational fine structure is observed, it is still difficult to determine the 0-0 transition.) Thus, for those cations which have the ability to relax geometrically, the observed !P's of the corresponding neutrals are upper bounds, leading to upper hounrls on the hond energies. Since Cr( CO )o and Mo( CO ) 6 are low spin octahedral with (t 2 g) 6 configurations, they are unlikely to change geometries upon ionization. Hence, the measured !P's are close to the adiabatic !P's, leading to adiabatic bond energies. For Fe(CO)s and Ni(C0) 4 , however, structural relaxation upon ionization is likely, due to the change in occupation of cl-orbitals overlapping the ligands [in contrast to Cr(C0) 6 and Mo(C0) 6 ]. Indeed, recent analysis of the photoelectron spectrum of Ni( CO )4 led to a decrease in the experimental (C0) 4 Ni+ -H bond energy by 7.4 kcal/mol (due to the decrease in the measnrert TP) -157and revealed a distortion from Td to D2d symmetry upon ionization. 13 With such structural relaxation occurring, the observed IP's are upper bounds, leading to bond energies which are also upper bounds for Fe and Ni carbonyl hydride cations. To bring the experimental values in line with the theoretically predicted bond energies would require decreasing the observed IP's of Fe(CO)s and Ni(C0)4 by 0.67 eV and 0.62 e V, respectively. III. Summary A simple method has been derived which accurately predicts bond strengths in coordinatively .wturated organotransition metal complexes from values currently available for coordinatively unsaturated M+-x bond strengths. The analysis is based on calculating the differential exchange and promotional losses which necessarily accompany covalent bond formation. The assumptions made in the derivation are: (i) that exchange and promotional energy effects dominate orbital hybridization and overlap contributions to the determination of bond strength conversion factors (inaccuracies in the method are no doubt due to this simplifying assumption) 14 and (ii) that metal centers in coordinatively saturated complexes have dn electronic ground states. The prescription as outlined above should be appropriate for 18-electron (or singlet states of even electron) metal complexes with oxidation states of at least +1. The approach is designed for predicting metal-ligand bond energies where the ligand is either a hydrocarbon moiety or hydrogen (i.e., where covalent bonding prevails). It is not designed to predict bond strengths for ionic (e.g., cyclopentadienyl, oxo~ halide) or donor-acceptor (e.g., CO or Fischer carbene) metal-ligand interactions. -158- Acknowledgments. This work was supported by the National Science Foundation (Grant No. CHE83-18041) and the Shell Companies Foundation. EAC acknowledges a National Science Foundation predoctoral fellowship (1982-1985), a research grant award from the International Precious Metals Institute and Gemini Industries (1985-1986), and a SOHIO fellowship in Catalysis (1987). We also thank J. L. Beauchamp for providing experimental data prior to publication. -159- References (1) a) Armentrout, P. B.; Beauchamp, J. L. J. Am. Chem. Soc. 1981, 103, 784; b) Armentrout, P. B.; Halle, L. F.; Beauchamp, J. L. J. Am. Chem. Soc. 1981, 103, 6501; c) Halle, L. F.; Armentrout, P. B.; Beauchamp, J. L. Organometallic.a 1982, 1, 963; d) Mandich, M. L.; Halle, L. F.; Beauchamp, J. L. J. Am. Chem. Soc. 1984, 106, 4403; e) Tolbert, M.A.; Beauchamp, J. L. J. Am. Chem. Soc. 1984, 106, 8117; £) Aristov, N.; Armentrout, P. B. J. Am. Chem. Soc. 1986, 108, 1806; g) Elkind, J. L.; Armentrout, P. B. lnorg. Chem. 1986, !5, 1078. (2) a) Beauchamp, J. L.; Stevens, A. E.; Corderman, R. R. Pure & Appl. Chem. 51, pp. 967-978; b) Stevens, A. E.; Beauchamp, J. L. J. Am. Chem. Soc. 1981, 103, 190. (3) Jacobsen, D. B.; Freiser, B. S. J. Am. Ch.em. Soc. 1985, 101, 5870. (4) a) Hettich, R. L.; Jackson, T. C.; Stanko, E. M.; Freiser, B. S. J. Am. Chem. Soc. 1986, 108, 5086; b) Hettich, R. L.; Freiser, B. S. J. Am. Chem. Soc. 1986, 108, 2537. (5) Goddard III, W. A.; Harding, L.B. Ann. Rev. Phy.a. Chem. 1978, 29, 363. (6) Carter, E. A.; Goddard III, W. A. J. Am. Chem. Soc. 1986, 108, 2180. (7) The changes in electrostatic energy from configuration to configuration involve changes in both coulomb and exchange integrals and hence it is not strictly correct to imply that only exchange interactions are responsible for high spin ground states. However, use of averaged exchange terms (weighted by the number of terms of a given type, e.g., one 08 versus four 7rO) from averagedfield orbitals (see ref. 11 below), leads to sufficiently accurate results for our considerations (and keeps the method simple enough to apply easily). (8) Carter, E. A.; Goddard III, W. A. J. Phy.a. Chem. 1984, 88,1485. (9) Brusich, M. J.; Goddard III, W. A., unpublished results. (10) a.) Schilling, J. B.; Goddard III, W. A.; Beauchamp, J. L. J. Am. Chem. Soc. -160- 1986, 108, 582; b) idem, submitted. (11) Carter, E. A.; Brusich, M. J.; Schilling, J.B.; Goddard III, W. A., unpublished results. "Averaged-field" means we solve for equivalently-shaped cl-orbitals (i.e., if n is the number of cl-electrons, then each orbital is constrained to have an occupation of 'i electrons). (12) Excitation energies (weighted over J-values) are taken from Moore, C. E. Atomic Energy Levela, NSRDS-NBS-35, 1971. (13) Reutt, J. R.; Wang, L. S.; Lee, Y. T.; Shirley, D. A. Chem. Phy.!. Lett. 1986, 1£6, 399. (14) A possible improvement to this method would involve a quantitative assessment of the relative preference for d versus s bonding to each metal, based on the intrinsic (exchangeless) bond strengths. However, such intrinsic bond strengths for s versus dare difficult to extract accurately (see ref. lOb ), and application of the method would be considerably more complicated. Table I. Symbolic Exchange and Promotional Costs for the Formation of Single, Double, and Triple Covalent Bonds to 81 d"- 1 and d!' Metal Ions.a M+ ground state Eloat (single bond) Eioat (triple bond) sldn-1 d" E1oat(double bond) Jld"-1 d" s1cri-1 d" Sc-+ .sl dl lsd 2 Ep + tdd 18d 2 Ep + tdd y+ 82 1 Ep(8 d ) + ~sd Ep(d2) + tdd Ep(s d 1 ) + tsd Ep(d2) + !dd Ti+, Zr+ 1 s d2 18d Ep + ldd lsd + ldd Ep + ~dd l8d + tdd Ep + ~dd v+ Nb+ a' Ep + ~8d !dd 2 Ep + ~sd + ldd 2 ~dd Ep + ~8d+ ~dd 3dd Cr-, Mo+ d5 EP + 28d 2dd Ep + 2sd+ ~dd 1dd 2 Ep + 28d + ~dd 2 Mn+, Tc+ 81d5 2 ~sd EP + ~dd isd + 2dd Ep + idd 2 + 1dd 2 EP + 3dd Fe-+ sld6 2sd Ep + ldd 2sd + ~dd Ep + ~dd 2sd + ~dd EP + ~dd Ru+ d} Ep + 2sd ldd Ep + 2sd + ~dd !dd 2 Ep + 2sd + ~dd !dd 2 Co+ Rh+ d8 Ep + !sd ldd 2 Ep + ~sd + ldd ldd Ep + ~sd + ~dd Ni+ Pd+ d9 Ep + lsd Odd Ep + lsd + tdd ' ' ' 1 1 2 ~sd ~dd EP + lsd + tdd a) E1ost = total energy lost upon forming single, double, or triple bonds to the high spin valence states of M+, in the form of promotional energy (Ep) and exchange energy K. 4 = sd and Kdd = dd. I >-' Q\ >-' I 162- Table II. Exchange (K::• and K:') and Promotional (Ep) Energics in 1 1 d"- 1 and d" Metal Ions (kcal/mol). 11 M+ state Sc+ ao 3F Ti+ 4F 4p v+ sn Cr+ Mn+ Fe+ co+ Ni+ y+ Zr+ Nb+ Mo+ !Sp as ,1d1 d2 ,1d2 d3 15 ,1d1 ao aF "F 4F ISD ISF as 1s •o 11.3 13.8 5.7 15.2 13.3 0.0 2.5 15.0 0.0 5.5 16.8 7.8 5.0 4.8 16.5 18.4 19.8 17.6 20.9 18.8 20.0 22.1 21.2 23.3 0.0 35.1 0.0 41.7 0.0 5.8 0.0 9.9 0.0 25.1 9.3 11.6 10.8 3.7 24.0 0.0 7.1 12.2 13.0 0.0 7.6 13.4 14.2 15.3 14.3 0.0 36.7 0.0 11.8 7.3 d8 ,1d8 5.0 d1 d' ,1d1 4.8 d8 ,1d8 4.8 ,1d1 d2 ,1d2 d3 d" ,1da di ,1d4 ,1dl5 d8 Ru+ 4p d1 ,1d8 Rh+ en aF ISp 20 "F Pd+ Ep d" a1d4 sn en 4F aF llF 2n 4F K~~'::.: dd K:?::.: sd a" ,1d3 en so Tc+ valence electron configuration 0.0 9.9 9.2 8.9 8.5 8.3 11.6 0.0 7.5 15.6 25.1 16.1 0.0 111J.1 7.5 17.1 49.1 d8 ,1d8 7.3 17.1 18.0 0.0 73.6 d' a) K~~· and K:' arc ab initio values for the sd and dd exchange integrals from averaged-field Hartree-Fock calculations (ref. 11). The dd exchange terms have been averaged over the five types of interactions (i.e., u6, (f"tr, 61C', 1C'i°, and 66). Ep is the (J-weighted) relative energy of the M+ excited state (ref. 12). -163- Table III. Exchange and Promotional Costs (kcal/mol) for the Formation of Single, Double, and Triple Covalent Bonds to .s 1dn-l and d" Metal Ions.a M+ ground state E101t (single) 81dn-1 d" E101t (double) 8 1dn-1 d" E101t (triple) 8 1dn-1 d" Sc+ 81d1 Ti+ sld2 3.7 5.7 19.5 17.8 3.7 13.3 19.5 22.5 13.3 22.5 v+ d4 16.1 22.5 32.9 37.5 41.3 45.0 er+ d5 45.1 33.0 72.7 57.8 91.1 74.3 Mn+ 81d5 12.0 68.1 51.6 85.7 81.3 94.5 Fe+ 81 10.0 24.6 41.4 34.0 62.3 34.0 co+ d!' d8 17.1 10.0 39.2 10.0 50.3 Ni+ d9 29.9 o.o 41.6 y+ 82 8.7 28.7 8.7 28.7 Zr+ sld2 9.2 17.9 us.o 23.3 15.0 23.3 Nb+ 21.0 18.3 34.0 30.5 40.5 36.6 Mo+ d'd5 53.7 26.8 75.0 46.9 89.2 60.3 Tc+ s1d5 20.8 33.3 51.4 74.4 54.7 Ru+ cJ:r 40.1 14.6 63.5 79.1 21.9 Rh+ d8 60.4 8.1 77.5 41.6 21.9 8.1 Pd+ ir 80.9 o.o 89.9 41.6 86.1 89.9 a) E1ost = total energy lost upon forming single, double, or triple bonds to the high spin valence states of M+ = Ep + K1ost (promotional energy and exchange energy losses). The values in boldface correspond to the least energy cost for M+ to form a given type of covalent bond. -164- Table IV. Predicted Differential Exchange Energies in kcal/mol (.6.K Eunaat Ki::t) for the Formation lost of Single, Double, and Triple Covalent Bonds in Coordinatively Saturated Metal Complexes." [Adding .6.K to unsaturated D(M+ -X) gives estimates for saturated D(M1-X).] .6.K = Eun1at 101t _ K•at lost M+ single bond double bond Sc+ 3.7 -2.0 Ti+ v+ 5.7 6.7 -6.7 16.1 25.4 18.8 er+ 33.0 49.6 49.6 Mn+ Fe+ 12.0 10.0 42.8 24.6 54.9 5.8 co+ 10.0 0.0 0.0 20.3 31.0 9.8 Ni+ y+ triple bond 8.7 9.2 4.1 9.6 -1.2 24.4 18.3 Mo+ 18.3 26.8 40.2 40.2 Tc+ 20.8 Ru+ 14.6 40.5 14.6 33.3 0.0 Rh+ 8.1 0.0 Pd+ 0.0 81.4 62.0 64.3 Zr+ Nb+ a) E~~~at values are taken from Table III. Ki::t 0 Kdd for a single bond, !Kdd for a double bond, and ! Kdd :£or a. triple bond ( a.:s:mw.ing the :sa.t urntt:tl complex has a local metal electron configuration of dn). Kdd values (for dn M+) are taken from Table II. Table V. Predicted Coordinatively Saturated M-X Bond Energies from Coordinatively Unsaturated M-X Bond Energies [D~~~d (M 1 --X) = Dunsat(M+-X) + ~K] in kcal/mol. -·· Mt Dunsat(M+-H) ·-- nsat (M+-H) pred nunsat(M+=CH2) nsat (M+=CH 2 ) pred nunsat(M+ =CH) nsat (M+ =:CH) prcd ----··· Sc+ 55.3±2" 59.0±2 97±6d 95±6 Ti+ 55.1±2" 60.8±2 85±6d 91.7±6 v+ 47.3±1.4a 63.4±1.4 76±2d 101.4±2 60.7±2 49.6,e52±3d 99.2,101.6±3 59.5±3.4 58.41 101.2 57.0±4 69.2/82±59 114±2d 132.8±2 93.8,106.6±5 101±79 106.8±7 100±79 120.3J::7 Cr+ 27.7±2 Mn+ Fe-I 47.5±3.4a Co+ 45.5±2.3a 55.5±2.3 84±59 84±5 Nit 38.5±1.4a 38.5±1.4 (86±6)h (117±6) 47.0±4 4 11 I ,__.. CT' V1 l y+ 58±3a 66.7±3 Zr+ 54±3a 63.2±3 Nb+ 53±3a 71.3±3 Mo+ 41±3a 67.8±3 Tc+ Ru+ 46.3 6 41±3c 67.1 55.6 L3 '73.6i 88.2 Rh+ 42±3c 50.1±3 94±5i 94±5 Pd+ 45±3c 45±3 a) ref. lg. b) ref. lOb. c) ref. ld. d) ref. lf. e) ref. 8. J) ref. 9. g) ref. 4b. h) ref. lb. The value is placed in parentheses to emphasize its uncertainty. i) ref. 6. j) ref. 3. -166Table VI. Comparison of Observed and Predicted Coordinatively Saturated (18-Electron) MetalLigand Bond Energies (kcal/mol). osat pred (M+ - X) = nunsat(M+ - X)" + AKC complex o•at (L n M+ obi (C0)11Cr+-H 55. 9±2.4, "58±3 1 60.7±2 (C0)11Mo+-H 63.1±2.2, "65±3 67.8±3 (C0)11(CHa)Mn+-H 64.8±2.6, •61 ±3' 59.5±3.4 (CHaC11H4)(CO)aMn+-H 68.6±3.1, •11±3 1 59.5±3.4 (CO)s(CHa)Re+-H 71.2±3.1,.73±3 4 67.11 (C0)11Fe+-H 72.4±3.6, d.7 4±5 11 57.0±4 Cp(CO):.i(CH 3 )Fe+-H 51.2±3.3, 4 53±311 57.0±4 X)• 1 Cp2Fe+-H 52.4±5, "54±5, 56±5' 57.0±4 Cp2Ru+-H 65. 7±3.6, "68±5, h79±5' 55.6±3 Cl(CH2)Ru-H 54.1' 55.6±3 Cp(C0)2Co+-H 57±5,"59.5±2.9, "73±5 1 55.5±2.3 [(CN)sCo-HJ!; 5gj 55.5±2.3 Cp{C0)2Rh+-H 55±5, "69.6±2.9, d80±5' 50.1±3 52.8±2.2,•60.2±2.2,"62±s• 38.5±1.4 (CO)&Mn+ =CH2 104±31 101.2 (Cl)(H)Ru=CH2 90.3' 88.2 (C0)4Ni+-H 11 a) Observed M+-x bond energy in coordinatively saturated complexes (cs). b) Observed M+-X bond energy in coordinatively unsaturated complexes (cu). c)AK =the differential cost in exchange and promotional energies between c1 and cu. d) Simoes, J. A. M.; Beauchamp, J. L., to be published. e) Stevens, A. E.; Beauchamp, J. L. J. Am. Chem. Soc. 1981, 103, 190. f) value for D~~!d(Tc+-H) which should be comparable to D~~d(Re+-H). g) Foster, M. S.; Beauchamp, J. L. J. Am. Chem. Soc. 1975, 91, 4814. h) revised version (Beauchamp, J. L., private communication) oheference e). i) theoretical value: Carter, E. A. and Goddard, W. A., in preparation. j) de Vries, B. J. Catal. 1962, 1, 484. k) revised according to new value of the adiabatic IP for Ni(C0) 4 from PES spectra (Reutt, J.E.; Wang, L. S.; Lee, Y. T.; Shirley, D. A. Chem. Phy1. Lett. 1986, 1£6, 399). l) Stevens, A. E., Ph.D. Thesis, California Institute of Technology, 1981. -167- Chapter 3 Modeling Fischer-Tropsch Chemistry: Kinetic and Thermodynamic Predictions -168- Chapter 3.A. The text of this section is a Communication coauthored with William A. Goddard III which appeared in the Journal of the American Chemical Society. -169- Reprinted Crom the Journal of the American Chemical Society, 1987, 109, 579. Copyright © 1987 by the American Chemical Society and reprinted by permission of the copyright owner. e (H-Ru-C), degrees Metbylidene Migratory Insertion into an Ru-H Bond 817 Emily A. Carter and William A. Goddard m• 700 600 55.0 500475450 400 131 Contribution No. 7409 Arthur Amos Noyes, Laboratory of Chemical Physics California Institute of Technology Pasadena, Callfarnta 91 I Z5 450 Received May 5, 1986 The migratory insertions of CH, fragments into transition· metal-hydrogen and transition-metal-alkyl bonds have long been proposed as chain initiation and propagation steps In the Pisch· er-Tropsch synthesis of hydrocarbons. 1 Particularly for ruthenium, an effective heterogeneous catalyst for the production of high molecular weight polymethylenes, 2 there is strong indirect evidence that the chain growth mechanism involves methylidcne insertion into growing alkyl chains. 1•3 Several experiments on homogeneous systems point to the facility of direct CH 2 insertions into both M-H and M-R bonds! Thorn and Tulip5• proposed that acidification of a hydrido hydroxymethyliridium complex proceeds via a hydridvmethylcncirio.lium inlcrmcdiatc wbi1.;h un· dergoes CH 2 insertion into the Ir-H bond to yield an iridium methyl complex. Upon hydrogen abstraction from mononuclear metal dimethyl complexes, Thom and Tulip, 5b as well as Cooper. 6 Maitlis. 7 and Wemer. 8 have ~tulated the intermediacv of methyl methylidene metal complexes which insert CH 2 into M-CH 3 and then /j-hydride eliminate en route to the formation of ethylene hydride romplexes. Thus these studies suggest that both the chain initiation and propagation steps in Fischer-Tropsch synthesis may be facile even at a single metal ocntcr. As a model for these important elementary reactions, we have used ab initio quantum mechanical techniques to investigate the migratory insertion of CH 2 into an adjacent Ru-H bond. To our knowledge, these calculations provide the first quantitative description of the energetics of such a reaction, including evaluations of both the activation barrier to insertion as well as the relative stabilities of the reactant and product. The reaction pathway is depicted below - 40.0 0 E '350 0 u ,,. 30.0 ~ 25.0 UJ ~ 20.0 UJ :> 15.0 ~...J 10.0 UJ ex: 5.0 0.0 0.45 0.50 0.55 0.60 R(Ru-H) R(Ru-H)+R(C-H) Flgure J. Reaction coordinate for the insertion of CH, into Ru-H in I to form CIRu(CH 3) (2) at the HF. GVB-PP(3/6). GVB-RC!(3/6J. GVBCI(3/6), and GVBCI(3/6)-MCSCF levels. Energy (kcal/moll 1s plotted relative to the total energy for 2 vs. R(Ru-H)/[R(Ru-Hl + R(C-H)] (normalized reaction coordinate). Also shown at the top are the corresponding H-Ru-C angles (deg). The full GVBCl·MCSCF leads simultaneously to a proper description of both the reactan1-like and product-like configurations important at the transition state and hence to a smooth potential curve. Some lower level calculations lead 10 a less smooth transition. the wave function being less capable of simultaneous description of both reactant and product channels. the other ligands to form rovalent bonds to unpaired d-electrons (or to form donor bonds into empty metal valence orbitals). Thus ligands with large electron aflinities 10 such as Cp (17 5-C 5H 5 ) and Cl form rather ionic bonds with the metal valence electrons. while neutral >:·donor ligand> (e.g., •·ar)l>) and pho>phinc• 1cqu11 c 2 where J is a model for 18-electron romplexes such as (C 5H 5)(PPh3)Ru(R)(CH2) (3) or [(C 6 Me6 )(PPh 3)Ru(CH 3l(CH 2 W (4), the intermediate postulated by Werner. 3 As discussed previously,9 1 conforms to the valence bond (VB) view of oxidation states in which electronegative ligands may remove no more than two units of charge from the metal (the easily ionized s-electrons). leaving (1) Biloen. P.; Sachtlcr, W. M. H. Adv. Cata/. 1981, JO, 165. (2) (a) Anderson. R. B. In Catalysts: Emmett, P.H .. Ed.: Reinhold: New empty metal valence orbitals. Finally, ligands with unpaired electrons (and small electron affinities, e.g .. CH 2, CH 1, H, NO. etc.) require unpaired metal d-electrons with which to form covalent bonds. As a result, we believe the singlet state of 1 is a good model for 3 and 4, since all three complexes have a metal VB oxidation state of+ I. Ru(I) is d 7 , with three unpaired delectrons to form covalent bonds to R and CH 2 in I, 3, and 4. Consider the process of inserting the CH 2 ligand into the Ru-H bond to form an Ru-CH 1 species. We begin with an Ru-H bond and two Ru-C in-plane bonds (one Cf and one .-) which are converted to a C-H bond, one Ru-C bond and an Ru d lone pair. Notice that the presence of rhe in-plane 1f'-bond 11 suggests a York. 1956; Vol. IV, pp 237-242. (b) Pichler. H.; Buffieb, H. Brennst.-Chem. 1~411, ZI. ZYI, Z7.!, ZM5. (3) (a) Brady. R. C., III: Pettit. R. J. Am. Chem. Soc. 1980, 102. 6181. (b) Ibid. 1981, 103. 1287. (c) Baker. J. A.; Bell, A. T. J. Cata/. 1982, 78, 165-181. (4) The first observation of general alkylidene insertions into M-R bonds was by: Sham. P. R.: Schrock. R. R. J. Organnm.r. Ch•m. 1979. 171. 43 (5) (a) Thorn. D. L.: Tulip, T. H. Organometa/lics 1982. I. 1580. (b) Thorn, D. L.; Tulip. T. H. J Am. Chem. Soc. 1981, 103. 5984 (6) Hayes, J.C.: Pearson. G. D. N.: Cooper, N. J. J. Am. Chem. Soc 1981, 103, 4648. (7) lsobc. K.; Andrews, D. G.; Mann, B. E.; Maitlis, P. M. J. Chem. Soc .. Chem. Commun. 1981. 809. (8) Kletzin, H.; Werner. H.; Serbadh, 0.; Ziegler, M. L. Angew. Chem., Int. Ed. Engl. 1983. 22, 46. 0002. 7863/87;1509-0579$0 uo;o (9) Carter. E. A.: Goddard, W. A .. Ill J. Am Chem. Soc. 1986, 108, 2180. (10) The electron affinities ofCp and Cl are 2.2 eV (Rosenslock. H M.; Draxl, K.; Steiner, B. W.; Herron. J. T. J. Phys. Chem. Ref Data 1977. 6. 736-772) and 3.62 eV (Hotop, H.: Lineberger. W. C. J. Chem Phys. Ref Data 1975, 4, 539~576). respectively. ( 11) This conformation is !he lowest energy orien1ation for I Carter. E A.; Goddard, W. A .. Ill. manuscripl in preparation © 1987 American Chemical Society -170580 the highest level of theory considered (the bottom curve of Figure I), we optimize the six active orbitals (the orbitals actively involved in the insertion, namely, the Ru-H and the Ru-C u- and 1r-bond pairs) self-consistently for a full six-electron CI within those six orbitals (all occupations of six electrons in six orbitals-the GVB(3/6)CI-MCSCF level). This level allows a balanced de•cription of the three bond pairs changing during the reaction. bl Ru-C Sigma Bond Pair ONE c) Ru-C P1 Bond to Ru d1T Lone Pair ONE (@) -.. ~"· . . ..·.· ·..·. ····I I ~··· ";'. F1gure 2. GVB(3/6)PP one-electron orbitals near the transition state (0(H-Ru-C) = 50.0°). (a) Orbital pair describing the Ru-H bond of the reactant 1 and the C-H bond of the product 2; (b) orbital pair describing the Ru-C 11-bond for both I and l; (c) orbital pair describing the Ru-C r-bond of I and the Ru dr lone pair of 2. Contours arc shown at intervals of 0.05 au. smooth transition from an Ru-H to a C-H bond may be possible, since the in-plane carbon p-orbital is oriented correctly for formation of the in-plane C-H bond. Indeed, at the highest level of theory examined, we find that the CH 2 insertion into Ru-H proceeds with a low activation barrier (11.5 kcal/mo!) and is thermodynamically favorable, with an exothermicity of 7.1 kcal/mol, as displayed in the reaction coordinate of Figure I. Notice that the transition state occurs approximately halfway between reactants and products, as expected for a reaction which is nearly thermoneutral (Hammond postulate). Figure 2 shows the orbitals near the transition state [0(HRu-C) 50°]. Here we see that the Ru-H bond smoothly converts into the; C-H bond (rigurc; 2a), while: the Ru-C u-bond (Figure 2b) does not change significantly. At the transition state, the Ru-C -x--bond (Figure 2c) has begun to move out of the way of the incipient C-H bond and already has substantial Ru d lone-pair character. 12 The Ru-C and Ru-H bonds at the transition state have lengthened significantly from their values in 1, increasing from 1.87 to 1.93 A for Ru-C and from 1.65 to 1.77 A for Ru-H. The exothermicity, activation barrier, and transition-state ge- = ometry were calculated at five levels of theory, as shown in Figure 1. 13 The geometries along the reaction coordinate were predicted by analytic gradients of Hartree-Fock wave functions, 14 with all geometrical parameters optimized at each H-Ru-C angle. 1i In Higher level, extended basis dissociation-consistent CI calculations16 on various dissociation processes involving these species 13 suggest that the true exothermicity is 10.4 kcal/mo!, in good agreement with our MCSCF calculations. In conclusion, we have shown that alkylidene migratory insertions can be quite facile, proceeding with a low activation barrier. These calculations provide the first quantitative evidence for the feasibility of this elementary reaction (previously postulated based on experimental results,H but never directly observed). These results suggest that for Ru, the reverse reaction of a-hydrogen elimination is subject to a barrier of 18.6 kcal/mo!. This is consistent with the fact that a-H eliminations most often occur for the early transition metals. Work in progress on the related reaction of CH 1 insertion into an Ru-alkyl bond suggests an cxotbermicity of 4.9 kcal/mo!. The activation barrier will probably be higher than that for H due to the necessary reorientation of the alkyl upon migration from Ru to CH 2. 17 The alkyl migration differs primarily from the hydride energetics because the incipient C-C bond is weaker than the incipient C-H bond. While our calculations suggest that late transition metals undergo CH 2 insertion with relative ease, early metal alkylidenes have been observed that do not insert into M-R bonds. We believe that this is due to the much greater strength of the M-C -x--bond for the early transition metals. 18 • Acknowledgment. This work was supported by the Shell Development Co., Houston, TX, and the National Science Foundation (Grant CHE83-J8041). E.A.C. gratefully acknowledges the support of a National Science Foundation Predoctoral Fellowship (1982-1985). (12) By the point at which 0(H-Ru-C) • 40.0", the Rud lone pair is fully formed. (The equilibrium geometry of CIRuCH, has an H-Ru-C angle of 23.2°.) (13) Full details to be p\lbhshed elsewhere. A valt11nco dol.lbie t' quality basis was used. (14) Hartrcc-Fock (Hf) calculations arc known to predict a=rate geometries. As a test, we optimized the geometry of l at both the HF and GVB-RCl(3/6) levels and found that the two geometries were very similar (e.g., all bond lengths and angles differed by at most O.QJ A and 11.9°, n::af'Cl\'tivt:Jy); M:1; ref 11. ( 15) The geometries of I and l were optimized with no restrictions except the retention of C, symmetry (lower symmetry cases were found to be higher in energy; ref 11 ) . (16) Bair, R. A.; Goddard, W. A., Ill, unpublished results. Bair, R. A. Ph.D. thesis, Caltech, 1980. Carter. E. A.: Goddard. W. A.. Ill J. Phi's. Chem. 1984, 88, 1485. Reference 9. (17) Low. J. J.; Goddard, W. A., III Orga11ome1a/lics 1986, 5, 609. (18) Carter, E. A.: Goddard, W. A.. III J. Am. Chtm. Soc. 1986, 108, 47-«i. -171- Chapter 3.B. The text of this section is an Article coauthored with William A. Goddard III and is to be submitted to OrganometallicJ. -172- Modeling Fischer-Tropsch Chemistry: the Thermochemistry and Insertion Kinetics of ClRuH(CH2) Emily A. Carter and William A. Goddard III"' Contribution No. 7583 from the Arthur Amo" Noye" Laboratory of Chemical Phy&ic.,, California Jn.,titu.te of Technology, Pa.,adena, California 91125 Abstract: The insertions of metal-bound CHx into M-H and M-CH 3 bonds have been proposed as the chain initiation and propagation steps, respectively, in the Fischer-Tropsch reductive polymerization of CO to form alkanes. As a model for this important elementary reaction, we have examined the properties and migratory insertion reactivity of a prototypical coordinatively saturated complex ClRuH( CH 2 ) using ab initio methods (generalized valence bond + configuration interaction). The Ru=CH 2 double bond is covalent, with De(Ru=C) = 84.7 kcal/rnol. The optimum geometry has the CH:a plane perpendicular to the ClRuH plane, with a. i·utatiuna.l bauier of !::13.6 kca.1/mol. The lowest energy conformer of the 1 A' state of ClRuH( CH 2 ) has an in-plane rr bond, which facilitates the insertion of the CH 2 ligand into the adjacent Ru-H bond. Using analytic gradient techniques combined with MCSCF wavefunctions to find the minimum energy pathway, we find that the insertion proceeds with a moderate barrier (11.5 kcal/mol) and is exothermic by 7.1 kcal/mol. From a thermodynamic cycle designed to probe basis set and electron correlation deficiencies, we estimate an actual barrier to insertion of 10.9±1.7 kcal/mol and an e:x:othermicity of 10.5±1.0 kcal/mol (using predicted values of De(Ru-H) = 54.1 kcal/mol, De(CH2-H) CH3) 54.3 kca.l/mol). 112.9 kcal/mol, and De(Ru- -173- I. Introduction Ruthenium complexes containing hydrido, alkyl, alkylidene, and alkylidyne ligands have been proposed as intermediates in metal-catalyzed heterogeneous and homogeneous C-H and C-C bond forming processes. In homogeneous reactions, both CH 2 insertion into M-H and M-R bonds to make new metal alkyls 1 and intra.molecular alkylidene coupling in binuclear Ru systems to make olefins, have been observed. 2 Catalytic reduction of CO to methanol, ethanol, and ethylene gly- col by soluble Ru complexes have also been observed. 3 In the particular heterogeneous case of the Fischer-Tropsch (FT) synthesis of hydrocarbons from CO and H 2 , Ru metal is the most active undoped catalyst, readily producing high molecular weight polymethylenes. 4 The insertions of metal-bound CHx fragments into metal-hydrogen and metal-alkyl bonds are thought to be responsible for the chain initiation and growth steps of the FT reaction. 5 (1) The mechanism shown in eq 1 is particularly applicable to Ru catalysts since polymethylene may be produced simply through repeated CH2 insertions into a growing alkyl cha.in. While methylene on the clean Ru( 001) surface has been observed in bridging coordination sites at low temperature, 6 the actual insertion step of eq 1 may well require both reacting species to be coordinated to the same metal atom. Indeed, Thorn and Tulip 1c,l/ have provided evidence for both H and CH3 migration to CH 2 at an Ir(I) center, while Cooper, 1 a,b,g,i,j Ma.itlis, 1 e and Werner 1h have proposed methyl methylidene metal complexes as intermediates during dimethyl rearrangements to olefin hydrides (subsequent to hydrogen abstraction). These studies suggest that both chain initiation and growth may be -174- achieved at a single metal center. Hence, we ha.ve !'ltudied a model for the first step of eq 1, in which CH 2 inserts into an adjacent Ru-H bond to form a metal-methyl bond, in the mononuclea.r urga.uumetallic complex shown in eq 2. (2) 2 As outlined previously,7 the electronic structure of 1 may be understood using the valence bond (VB) description of oxidation states in which electron-withdrawing ligands such as Cp (715 -C 5 H5 ), Cl, or oxo may collectively ionize the metal center up to a. ma.ximum uf two units of charge (i.e., only the easily ionized valence selectrons), with the rest of the metal valence d-electrons forming covalent bonds to less electronegative ligands such as alkyl, aryl, or hydrogen. Donor-acceptor bonds involve donation into empty metal valence d, &, or p orbitals, in order to saturate the metal to eighteen electrons. These bonding rules imply that Cl and Cp will form ionic bonds, ?r-aryls, phosphines, and CO will make donor bonds, and open shell ligands such as R·, :CH 2 , H·, and ·NO will form covalent bonds to unpaired metal d-electrons. Thus, the singlet state of C1Ru(CH 2)H (1) is a model for 18-electron, coordinatively saturated complexes such as Cp(PR3)Ru(R)(CH 2), in which the Cp and PR3 groups are mimicked by the Cl and the low spin state of 1 (the metal must be low spin so that PR 3 and Cp- have four empty metal orbitals to donate into). [(CGMc,i)(PPh 3 )Ru(CH3)(CH2)]+ (3) ls a.nuther cumplexfor which low spin 1 serves as a prototype, where the phosphine and the ?r-aryl group again force the metal to a low spin state in order to have empty orbitals available for ligand donation and where the positive charge is mimicked by the chlorine ligand in 1. Complex 3 has been postulated as an intermediate in the isomerization of a ruthenium dimethyl complex to a ruthenium ethylene hydride via the insertion of CH2 into an adjacent 175- Ru-CHa bond. 1h + ~ ~u ..... Ph,P /' " -¥Ru--.-[Ru+] Insertion CH 1 CH, CH Ph,P/' ' CH 1 proposed 1 /CH, ,G-H ellmlnallon >H, ----~[Ru•] H ~ ~H (3) 1solo1ed While CH 2 insertions into adjacent M-H(R) bonds have been indirectly observed for a number of homogeneous organometallic system11, 1 direct ob:serva.tiuu has eluded researchers until very recently. Magnetization transfer experiments of Bercaw and co-workers 8 directly monitored the insertion of CH 2 into the Ta-H bond of Cp2Ta(H)( CH2) above room temperature, yielding the 16-electron Cp2Ta-CH 3 complex. The VB oxidation state 7 of Ta in this complex is +2, since the Cp* ligands (Cp• = T/ 5 -CsMe 5 ) form ionic bonds to Ta (achieving the aromatic structure of Cp-), leaving three unpaired d-electrons on Ta to form covalent bonds to H and CH2. The situation is a.na.log011R in 1, where we find that the Cl of Cl-Ru ties up approximately one valence electron from the Ru in an ionic bond, leaving the Ru in a d 7 Ru(I) configuration having three singly-occupied d orbitals available for bonding to H and CH 2. To date, no direct measurements of kinetic parameters or thermodynamic properties for the migratory insertion of CH 2 into M-H have been reported. Thus, the goal of this work is to examine the nature of this reaction at one metal center, characterizing the qualitative features of the metal-ligand bonding which favor (or disfavor) migratory insertions of CH2 and predicting the quantitative aspects of the insertion potential energy surface (e.g., the activation barrier and the exothermicity). In the next section, we discuss the equilibrium properties of the hydrido methylidene 1. Section III presents detailed theoretical results on the migratory insertion itself, 9 while Section IV discusses an independent way of estimating the energetics of the insertion event. Using the newly-developed method of correlation-consistent configuration interaction (CCCI), 10 we obtain the exothermicity and activation barrier to -176- insertion as a function of both basis set and level of electron correlation via a thermodynamic cycle which utilizes metal-ligand bond energies obtained from CCCI calculations. Section V concludes with some speculations regarding other insertion steps in FT chemistry, while Section VI provides the calculational details. II. Properties of CIRu(CH2)H To understand the electronic structure of the 1 A' state of 1, we consider how the ClRu fragment may bond to H and CH2. As mentioned in the Introduction, the Cl ligand of ClRu( CH 2 )H ties up the Ru a-electron (the ground state of Ru atom is s 1 d 1 ) in an ionic bond, leaving a high spin d7 electronic configuration on Ru. Classifying the five d orbitals with respect to the final molecular plane as <T or 7r, there are two important configurations of ClRu, and Two high symmetry conformers of 1 exist: 11 a twisted structure la and a planar structure lb. H H I I Cl-Ru~ Cl-Ru~ ~··H la ~c--H lb \ Geometry la has all three M-H and M-C bonds in the H-Ru-C plane, requiring the ClRu cr 3 configuration, while geometry lb has an out-of-plane M-C 7r bond, requiring 7rcr 2 ClRu. 12 The one-electron generalized valence bond (GVB) orbitals for both conformers are shown in Figures 1 and 2, where we see that the Ru-H and Ru-C bonds are quite covalent, with each bond pair involving one electron localized in an Ru d -177- orbital spin-paired with one electron localized on the ligand. ln both cases, the CH 2 fragment is best viewed as a neutral triplet CH 2 having one electron in each of the u and 7r nonbonding orbitals Ru CH2 spin-paired with singly-occupied du and d7r (or dit, for the in-plane 11" bond) orbitals on Ru, forming an Ru=C covalent double bond as in ethylene. 7 The GVB orbital overlaps, metal orbital hybrid character, and electron populations for the metal and the ligand for the three correlated bond pairs for both geometrics a.re liljted in Table I. We see that the metal bonding orbitals have 74 to 983 4d character, with less than 113 ionic character in each bond pair. 13 Approximately 0.5 electron is transferred from the Ru 5s to the Cl in both la and lb, so that one should visualize the Ru-Cl bond as partially covalent, involving 5s-5p hybrid character on Ru. The orbital overlaps for all three bonds in geometry la are larger than the overlaps in geometry lb. These differential overlaps are not due to changes in bund length, since the optimum bond lengths for both la and 1 b are very similar (Table II). Geometry la is expected to be more stable than geometry lb, since bond overlaps should correlate with stability. Indeed, we find that geometry la ( u 3 bonding) is favored by 13.6 kcal/mol with respect to geometry lb (u 2 7r bonding). Thus we predict a lower limit of 13.6 kcal/mol on the Ru=CH 2 rotational barrier. Denoting the Ru=C and Ru-H axes as z and y, the Ru-Cit bond (Tr bond in the plane) in la involves the 4d11 z orbital, while the Ru-C <1' and Ru-H bonds involve orbitals that are mainly 4dz' and 4d11 ,. Since the it bond involves the 4dyz orbital, we expect a 90° H-Ru-C bond angle so that the Ru-H and Ru-C u bond orbitals will be orthogonal to the Ru-C it bond. The optimum structural parameters 14 for geometry la are listed in Table II -178- and dl;!picted below: 1.65A)0 H 90.3° 145.1° Ru \r n ~v 1.9sA 1.,.-H c~'\ 120.0° 1.90.B. ~ H Cl ri.,· As mentioned in the Introduction, d3 Ta(II) should form bonds similar to d7 Ru(I), since both metals have three unpaired d-electrons which can bond to H(R) and CH 2. Thus, the Ru-H and Ru=CH2 bonds in la should be quite analogous to the Ta-CH 3 and Ta=CH 2 bonds in Schrock's complex Cp 2Ta(CH 3 )(CH 2 ) (4). 15 In fact, the Ru=C bond length, the H-Ru-C bond angle, and the perpendicular orientation of CH2 ligand, all compare well with the values R(Ta=C) = 2.03 A, 8( CTaC) = 95.6°, and the out-of-plane orientation of the CH 2 ligand found in 4. 15 Another electronically similar complex to 1 is Cl(NO)(PPh 3 )20s(CH 2 ) (5), in which the NO and PPh3 ligands a.re simulated by the H ligand and the low spin state in 1. The X-ray structure of 5 reveals an Os=C bond length of 1.92A and an orientation for the CH2 ligand which is perpendicular to the N-Os-C plane, 16 in excellent agreement with our results for 1. The Ru=CH:i stretching frequencies a.re in the range of 740-800 cm- 1 , which may be compared with 623.6 cm- 1 for matrix-isolated FeCH 2.17 (No other M=CH 2 vibrational frequencies have been identified.) The Ru=C stretching frequency of lb is larger than in la by ,...., 50 cm- 1 • This may be understood in terms of the larger steric repulsions in lb relative to la, since the methylidene hydrogens are coplanar with the rest of the molecule in lb, whereas they are out of the plane in la. Such steric repulsions induce a harder inner wall of the local potential, leading to an increased Ru=C vibrational frequency. The decrease in the Ru-H vibrational frequency going from la to lb may be attributed to the decrease in the overlap in the Ru-H bond (Table I), indicating a shallower potential and thus a lower vibrational frequency in lb. The calculated rotational barrier of 13.6 kcal/mol for la-> lb is smaller than -179- the lower bound of 21.4 kcal/mol estimated for 4. 15 This is to be expected, since the Cp ligands in the Ta complex should destabilize the 11' orbitals required to make the out-of-plane 71'-bond in 4, thereby increasing the rotational barrier. In the Ru case, the d7r's are accessible in energy, leading to a lower rotational barrier for the. Ru complex. In a related system, Brookhart 18 has measured the rotational barrier in Cp(Ph2PCH2CH2PPh2)FeCHt (Ph= C6Hs) to be 10.4 kcal/mol, in reasonable agreement with our results. The structural coordinates and vibrational frequencies for geometry 1 b (see Table II) are similar except that the H-Ru-C angle opens up to 111. 7°, and the H-Ru-Cl angle drops to 93.6°. In this case, there is a doubly-occupied du orbital bisecting the H-Ru-C bond angle (see Figure 2), and the Ru-H and Ru-C du orbitals must stay orthogonal to this orbital, forcing a larger H-Ru-C bond angle. The Cl ligand must also stay orthogonal to the in-plane do- orbital and thus moves away, resulting in a smaller Cl-Ru-H angle. As the Ru-C bond distance is increased to break the Ru=CH2 bond, la correlates with the ClRuH complex 6a in the (u 1 ) 1 ( u2 ) 1 triplet state 3 A' ( u 3 configuration of ClRu), while lb correlates with 6b in the (o-1 ) 1 (11') 1 triplet state 3 A 11 (7ru 2 configuration of ClRu). H I Cl-Ru«(0 0 6a H I Cl-Rucr-::\ 6~ 6b These states of ClRuH are separated by at least 4.2 kcal/mol, with 3 A" lower. 19 Thus, even though the lowest triplet state of ClRuH is 7r0" 2 , 11 the favored geometry -180- of ClRuH(CH 2 ) ( 1 A') corresponds to the u 3 state. This means that the stabilization enjoyed by the u 3 state of la over the u 2 7!" state of lb is determined by the RuC Lun<ls ra.ther tha.u by the intrinsic energies of the ClRuH fragment. That is, the in-plane 7f bond of la versus the out-of-plane 71" bond of lb contributes to the stabilization of la over lb. Consistent with this idea, Table I indicates that the most dramatic increase in orbital overlaps occurs for the out-of-plane 7r bond ( 1 b) converting to an in-plane 7f bond (la). Another factor which destabilizes lb relative to la is the higher steric (or nuclear) repulsion in lb, since all of the atoms are coplanar. III. Migratory Insertion Kinetics Fur the wethylideue imsertiuu tstep (1) releva.ut tu Fischer-Tropsch catalysis, we find the structure la, with the in-plane 71" bond, to be the relevant conformation. Consider the transformation of the Ru-H bond and the Ru=C double bond (prior to insertion) to a C-H bond, an Ru-C single bond and an Ru 4d lone pair. We envision a sequence involving the rearrangement of the three in-plane bonding pairs, 20 .o cr-JJ! Cl~·····\., ~C~·HH .... ·· ....@\c'2. H H - where the Ru-C 1f bond must be mixed with the Ru-Hu bond in order to make the new C-H u bond and an Ru 4d lone pair. Structure la (u 3 ) has a carbon p-orbital in the H-Ru-C plane (part of the 7f bond) which is oriented such that a smooth conversion from Ru-H to C His possible, whereas structure lb (u 2 7i) has a 1r bond perpendicular to the H-Ru-C plane such that the carbon p-orbital needed for the incipient C-H bond is orthogonal to the insertion pathway. This suggests that only ayatema containing alkyli.denea oriented perpendicular to adjacent bonda (with an in-plane 1t' bond as in la) will have low barriers to migratory insertion. In a. preliminary report of this work, 9 we showed that the insertion reaction of eq -181- 2 (involving la with its in-plane 7T' bond) is indeed favorable, proceeding with a low barrier of 11.5 kcal/mol and an exothermicity of 7.1 kcal/mo!. Figure 3 displays the five levels of theory for which the reaction path was calculated. Analytic gradients of Hartree-Fock (HF, variational molecular orbital theory) wavefunctions were used to optimize the geometries at the nine points shown along the insertion pathway. The H-Ru-C angle was taken to be the reaction coordinate, with each successive H-Ru-C angle held fixed while all other geometrical parameters were optimized (within C 3 symmetry). The geometries of ln and 2 were optimized using HF gradients with no constraints except the retention of C, symmetry. 11 •21 Table III, in conjunction with Figure 3, displays the trends in exothermicity and activation energy as a function of increasing electron correlation. Notice that Hartree-Fock theory, while reliable for structural predictions, 21 is in serious disagreement with the highest quality wavefunction, GVBCI-MCSCF (see Section VI), where reaction energetics are concerned. HF predicts a highly exothermic reaction (.6.Erxn = -38.9 kcal/mol) with no barrier, while GVBCI-MCSCF predicts a much more moderate exothermicity of 7.1 kcal/mol and a moderate barrier of 11.5 kcal/mo!. The reason HF describes the reaction energetics so poorly is due to the inability of HF theory to properly describe transition metal-ligand multiple bonds. As explained previously, 22 the restriction in HF which forces all orbitals to be doubly-occupied results in a charge-separated species, which is very high in energy. Thus, the metal-carbene bond in la is ill-described and the reactant is therefore highly destabilized, leading to an artificially large exothermicity. HF-Slater transition state theory predictions of large exothermicities for migratory insertion of CH 2 into a Mn-H bond must therefore be considered suspect. 23 Recent HF predictions of the energetics of CO insertion at Mn should also be interpreted with caution. 24 Once each of the six electrons involved in the insertion reaction (two in the Ru-H bond and four in the Ru=C bond) are allowed the freedom to each occupy their own orbitals [as in all of the GVB(3/6) wavefunctionsJ, the description of metal-ligand multiple bonds improves tremendously. 7122125 Thus, we find a large -182- reactant stabilization relative to HF, leading to a decrease in the exothermicity by 17.2 kcal/mol and the appearance of a barrier (9. 7 kcal/mol), even with the lowest level of GVB theory (GVB-PP). Another significant drop of 11.4 kcal/mol in the exothermicity, with a concomitant increase of 7 kcal/mol in the activation barrier, occurs when the spin-coupling restriction of the perfect singlet pairing (GVB-PP) wavefunction is lifted and interpair correlation terms are included by the GVB-RCI calculation, allowing a reasonable description of the metal-carbon double bond. 7 •22 The exothermicity drop:s still further when these :six electrons a.re allowed full free- dom within the six active orbitals involved in the insertion in the GVBCI(3/6) calculation (a full valence Cl, i.e., all occupations of the six electrons in the six orbitals). The activation barrier now drops at the GVBCI level, since the six active orbitals are now allowed to overlap in the transition state. Optimizing the orbitals self-consistently at the GVBCI level reduces the barrier and the exothermicity to their final values of 11.5 and -7.1 kcal/mol, respectively. Figures 1, 4, and 5 show the progression of the six active orbitals from reactant la in Figure 1 through the transition state in Figure 4 to product 2 in Figure 5. The Ru-C <T bond does not change very much during the insertion, but the other two bond pairs change smoothly from reactants to products, converting the Ru-H bond of la into the C-H bond of 2 and the Ru-C 1f bond of la into the Ru 4d lone pair of 2. At the transition state, the Ru-C 7i' bond (Figure 4c) is beginning to move out of the way of the incipient C-H bond, with some 4d lone pair character evident. The barrier to reaction is kept moderate by the ability of the active orbitals to maintain high overlap in the transition region so that no bonds are weakened significantly. 26 Finally, we note that the orbitals in Figure 5 [O(H-Ru-C) = 40.0°] are presented as product orbitals, merely to emphasize that once past the transition region, the orbitals quickly adopt the characteristics of product, even just 10° past the transition state geometry [O(H-Ru-C)t "" 50°]. (The H-Ru-C "bond angle" in the product 2 is 23.2°.) The changes in the geometry as the insertion proceeds are shown in Table IV. -183- The Ru-H bond length smoothly increases from 1.65 A in la to 2.63 A in 2, while the incipient C-H bond decreases smoothly in length from the nonbonded distance of 2.33 A in la to the equilibrium distance of 1.10 A in 2. The Ru=C double bond length of 1.87 A in la also smoothly increases to the Ru-C single bond length of 2.06 A. Other geometrical parameters change also, but with less marked differences. In the next section, we discuss higher level calculations aimed at determining the effect of extended basis sets and of higher electron correlation on the barrier a.nd cxothcrmicity of the insertion process. IV. Insertion Thermochemistry Theoretical calculations usually produce predictions with no independent means of estimating the associated error or degree of accuracy. In addition to the five levels of theory used above to map out the potential energy surface of the insertion shown in eq 2, we have undertaken a study using a larger basis set than used for the work of Section III, along with the inclusion of higher order correlations in the configuration interaction (CI) calculation. The goal of the work presented in this section is to provide an independent assessment of the activation barrier and exothermicity for the insertion reaction. Calculating the bond energies for the metal-ligand bonds in la and 2, we can construct a thermodynamic cycle to predict the exothermicity of eq 2, as shown in Figure 6. The energetics for each step in the cycle were calculated using the CCCI method 10 (see Section VI) within both a valence double-( (VDZ) basis and polarized VDZ bases (VDZD, VDZP and VDZDP). The CCCI method has proven to be an extremely accurate technique for the prediction of energetics, predicting single and double bond dissociation energies and excitation energies for both organic and organometallic molecules to within 5 kcal/mol of the experimental values. 10 •25 •27 We have calculated the steps leading to ClRu ( 2 A') + H (2 S) + CH 2 ( 3 B 1 ) at the top of Figure 6, starting from the reactant la at the bottom left or from the product 2 at the bottom right and following the cycle upward, in order to obtain -184- the re~ative energies of la and 2. Tables V - IX display results for De(Ru=C), LlEsT(ClRuH), De(Ru-H), De(Ru-C), and De(H2C-H), as a function of basis set and increasing level of electron correlation. The CCCI results listed in each table correspond to the values shown in Figure 6. Table V lists the adiabatic Ru=C bond energies in ClRuH(CH 2) (la), dissociating the optimized geometry of la (Table II) to the optimum structure for the 3 A' state of ClRuH [Re(Ru-H) = 1.64 A, Re(Ru-Cl) = 2.38 A, and Be(Cl-Ru-H) 104.8°] and the equilibrium geometry of CH 2 ( 3 B 1 ) [Re(C-H) = 1.08 A and Be(H-CH) = 133°]. We see that HF theory grossly underestimates the Ru=C bond strength, consistent with the discussion in Section III regarding the inability of HF theory to describe multiple metal-ligand bonds properly. The GVB-PP wavefunction stabilizes the Ru=C bond by 32 kcal/mol (VDZ basis), indicating the importance of allowing each electron in the Ru=C bond to occupy its own orbital (allowing for less than unit overlap in the bond pair). Higher order CI calculations up through CCCI serve to increase the bond strength by allowing up to full correlation of each breaking bond pair and allowing for valence orbital shape readjustments important !or :fragment rehybridiza.tion which occurs upon bond cleavage. The:: final CCCI value within the VDZD basis, De(ClHRu=CH2) = 84.7 kcal/mol, should be representative of Ru=CH 2 bond energies in coordinatively saturated systems. 7 •28 Our best estimate for De(ClHRu=CH2), and hence Ru=C bond energies in other coordinatively saturated (or low spin unsaturated) complexes, is 89.6±2.5 kcal/mol, based on the correlation error inherent to the CCCI description of double bonds (4.9±2.5 kcal/mol). 1 0 Table VI displays the adiabatic singlet-triplet splittings [LlEsT = E(1 A 1 ) E( 3 A")] for ClRuH. The equilibrium geometry of the 3 A" state of ClRuH is listed above and the equilibrium structure of the 1 A' state of ClRuH is found to be Re(RuH) = 1.59 A, Re(Ru-Cl) = 2.35 A, and Be(Cl-Ru-H) = 101.3°. LlEsT changes only slightly among all the levels listed, with the final CCCI result of 16.9 kcal/mol found to be the same for polarized and unpolarized basis sets. -185- Table VII presents f\.Oll-l.hl-l.t.i.c. Rn-H honil energies for C1RuH ( 1 A'), using the equilibrium geometry described above for ClRuH and the equilibrium bond distance of 2.39 A for RuCl (2 A'). At the highest level of correlation (CCCI) and basis (VDZP), we find an Ru-H bond energy of 54.1 kcal/mol. Since the model complex is low spin and does not suffer exchange losses during bond formation, this value should be representative of coordinatively saturated Ru-H bond energies. 28 Furthermore, De(ClRu-H, 1 A') should be higher than the bond energy in the coordinatively unsaturated complex Ru+-H by 14.6 kcal/mol, 28 leading to a predicted bond energy for De(Ru+-H) = 39.5 kcal/mol, in excellent agreement with the experimental value of 41±.3 kcal/mol 29 a.nd in good agreement with a. theoretical va.lue of 34.5 kcal/mol. 30 Adiabatic bond energies for ClRuCH3 (1 A') (2) are shown in Table VIII, using the equilibrium geometry for 2 shown in the last column of Table IV, the optimum bond length for ClRu (2 A') of 2.39 A, and the experimental geometry for CH 3 ( 2 A") of Re(C-H) = 1.079 A and Be(H-C-H) = 120.0°. 31 At the CCCI level, the bond energy is 54.3 kcal/mol within the VDZD basis, essentially identical to the Ru-H bond energy. While this result is contrary to the trends in coordinatively saturated complexes, where M-CHa bond strengths are thought to be weaker than the corresponding M-H bond energies by 10-15 kcal/mol, 32 the result is in excellent agreement with the experimental Ru+-CH3 bond energy of 54±5 kcal/mol. This agreement is probably due to a cancellation of two effects: (i) the differential exchange loss incurred when bonds are formed in a saturated versus an unsaturated complex7128 (leading to a bond weakening of"' 15 kcal/mol going from saturated to unsaturated Ru complexes) and (ii) the extra stabilization of RuCHt due to the polarizability of the methyl ligand (resulting in a. bond strengthening, relative to a neutral system, of "'15 kcal/mol). 29 Thus, the Ru-CH 3 bond energy predicted here should be representative of coordina.tively saturated (or low spin unsaturated) RuCHa bonds. 28 -186- The adiabatic C-H bond energies in CH3 are shown in Table IX for three different basis sets and five levels of theory. As we have seen for all of the bond energies calculated herein, the bond strengths increase dramatically upon the inclusion of electron correlation. The final value for the CCCI C-H bond strength with the VDZDP basis is 112.9 kcal/mol, in good agreement with the experimental De(CH2-H) = 115.8±1.4 kcal/mol. 33 The exothermicities calculated using the CCCI values from Tables V - IX are shown at the bottom of Figure 6 for three different basis sets. The VDZ basis set result of AErxn = -9.4 kcal/mol is in good agreement with the GVBCI-MCSCF result of -7.1 kcal/mol (Table III), suggesting that the dominant correlations important in the reaction are already included at the valence level (GVBCI). Considering the number of calculations required to complete the thermodynamic cycle of Figure 6, the agreement is excellent. Increasing the basis as well as the electron correlational level serves to increase the exothermicity slightly, to a final value of AErxn = -11.5 kcal/mol. Figure 6 yields thermodynamic estimates for the feasibility of eq 2, but yields no kinetic information a.bout the height of the barrier. For an independent prediction of the barrier height as a function of electron correlation, we carried out CCCI calculations (Section VI) on the reactant la, the transition state geometry [O(HRu-C)t = 50°), and the product 2, for both the VDZ and the VDZDP basis sets. The results are shown in Table X, where we see an across-the-board decrease in the activation energy and an increase in the exothermicity going from VDZ to VDZDP bases. A slight overall decrease in the activation energy and the exothermicity is seen going from the valence level CI [RCI(3/6)) to the higher order Cl's. Onr bef>t. estimates for Ea and AErxn are obtained simply by averaging the results from the two higher order Cl's within the extended basis (VDZDP). Thus we have used two different techniques to arrive at independent estimates of the energetics of the migratory insertion reaction of CH 2 into an adjacent Ru-H bond. The exothermicities and activation barriers are in close agreement from all -187three methods [.6.Erxn --=- -7.1 (GVBCI-MCSCF), -11.5 (Figure 6), and -10.6±1.0 (Table X) kcal/mo!; Ea= 11.5 (GVBCI-MCSCF) and 10.9±1.7 (Table X) kcal/mol], lending credence to the reliability of these methods for the prediction of energetics in organometallic systems. V. Discussion and Summary The migratory insertion of a terminal CH2 ligand into an adjacent rutheniumhydrogen bond is predicted to be exothermic by 10.5±1.0 kcal/mo! and to proceed with a small barrier {10.9±1.7 kcal/mo!), with a preferred orientation of the CH2 ligand perpendicular to the bond into which it will insert. We have thus demonstrated the feasibility of the FT chain initiation step (eq 1) to occur at one metal center. Group VUI metals are by far the most active for F'T synthesis; perhaps another reason for their higher activity (aside from their ability to readily dissociate carbon monoxide) is this low barrier for chain initiation. Early metals are not good catalysts for FT synthesis, presumably because the M=CH2 bond strength is too strong, leading to an endothermic process. 34 The analogous insertion of CH2 into an adjacent Ru-CH3 bond can be predicted using the bond energies and excitation energies in Figure 6, along with an estimate for the C-C bond strength of ethyl radical. The methyl migration thermodynamic cycle will be identical to that of Figure 6, except for two steps: (i) instead of the Ru-H bond in ClRuH ( 1 A') breaking, we now break an Ru-CH3 bond in the 1 A' state of ClRuCH 3 [De(Ru-CH 3 ) = 54.3 kcal/mol; see Figure 6] and (ii) instead of breaking the C-H bond of methyl radical, we break the C-C bond of ethyl radical [De(H3C-CH 2 ·) = 105.8±3.4 kcal/mol35 ]. We a5sume here that the singlet-triplet splittings of ClRuH and ClRuCHa are the same (we expect that the singlet-triplet splitting is more a function of the metal than of the ancillary ligands) and that De(Ru-Et) is the same as De(Ru-Me). Given these two assumptions, we find that the insertion of CH2 into an Ru-CHa bond -188- is downhill by 4.2±3.4 kcal/mol. This insertion is less exothermic than for the insertion into an Ru-H bond because the incipient C-C bond is 7.1±3.4 kcal/mol weaker than the incipient C-H bond. Furthermore, steric factors would suggest that De(Ru-Et) should be less than De(Ru-Me), which would lead to an even less exothermic reaction (perhaps even endothermic). A higher barrier is expected for methyl migration over hydrogen migration due partly to the smaller exothermicity (the Hammond postulate) and partly to the essential reorientation of the methyl group (with its directed sp 3 hybrid orbital) during the migration from Ru to CH 2 (H has no such reorientation problems due to the spherical nature of its ls orbital). 36 Hence we predict that chain propagation should be the rate-determining step in FT synthesis. Indeed, for some group VIII meta.ls (e.g., Ni), the chain propagation step is so unfavorable that the only product of FT synthesis is methane. 37 The present work yields the following conclusions: {i) methylidene insertions into metal-hydrogen bonds should be facile, with low barriers ("' 10.9 kca.l/mol) and moderate exothermicities ("' 10.5 kcal/mo!) for late transition metals (since the M::::;:C double bonds are relatively weak compared to those of early metals) only if the orientation of the CH2 ligand iJ perpendicular to bond into which it will in.aert; (ii) the reverse reaction of a-hydride elimination is predicted to be uphill by ,. ., , 21 kcal/mol, consistent with the lack of evidence for a-hydride eliminations among late transition meta.ls; (iii) The analogous insertion of CH2 into a Ru-CH3 bond is predicted to be less exothermic {6.Erxn ,..., -4 kcal/mol) than for insertion into Ru-H, due to the weaker incipient bond formed (C-C versus C-H). The activation barrier should be higher due to the lower exothermicity and the reorientation of the sp 3 hybrid on CH3 during its migration; and (iv) the implications for FT synthesis from (i) and (iii) are that chain initiation should proceed readily with a low barrier while chain propagation is predicted to be the rate-determining step for late transition metals. -189- VI. C~lculational Details All of the electrons of Ru, C, and H were treated explicitly, while the Cl atom was described using the SHC effective potential to represent the core electrons 384 and a valence minimal basis molecularly contracted for TiC1 4 •38 b The VDZ basis consisted of a valence double-( basis for Ru, 7 •39 the Dunning valence double-( contractions 40 of the Huzinaga (9s5p) and (4s) primitive gaussian bases for carbon and hydrogen 41 (exponents for H scaled by 1.2). The VDZP basis added one set of unscaled 2p-polarization functions for the migrating hydrogen to the VDZ basis. The VDZD ha.sis added one set of carbon 3d-polarization functions ((d 0.64) to the VDZ basis. The VDZDP basis added the two polarization functions above to the VDZ basis. The geometries of la, lb, and 6a were optimized at the GVB-RCI level [RCI(3/6) for la and lb; RCI(l/2) for 6a, leaving the Ru-Cl bond at the HF level]. The RCI (restricted configuration interaction) starts from the GVB-PP wavefunction (generalized valence bond with perfect-pairing restriction) in which each correlated bond pair (Ru-H, Ru-Cu, Ru-Orr) is described with two orbitals, so that each electron involved in the insertion process has its own orbital. All other electron pairs were left uncorrelated (but solved for self-consistently). The GVB-RCI wavefunction allows all configurations arising from the three possible occupations of two electrons in two orbitals for each GVB bond pair. [The rotational barrier in 1 was calculated at the GVB-RCl(3/6) level.] The geometries of 2, the 1 A' state of ClRuH, and the 2 A' state of Ru Cl were optimized using Hartree-Fock (HF) gradient techniques. The reaction pathway was followed at the HF, the GVB-PP(3/6), the GVBRCI(3/6), the GVDCI(3/6), a11d the GVBCI(3/6)-MCSCF levels. The GVBCI(3/6) allows a full CI within the six "active" orbitals (e.g., the Ru-C bond pairs and the Ru-H bond pair), while the GVBCI(3/6)-MCSCF self-consistently optimizes the orbitals for the GVBCl(3/6) wavefunction. -190The bond o.nd excitation energies of the various species in Tables V - IX were calculated at the HF, GVB-PP, GVB-RCI, and higher order CI levels described below: (i) RCI*Sval allows all single excitations from all valence orbitals (except Cl) to all virtual (unoccupied) orbitals from the RCI reference configurations. (ii) RCI*[SDpair 1 + SDpair 2 + · · ·] allows all single and double excitations to all virtuals from pair 1 and pair 2, etc. (but not simultaneously) from the RCI reference configurations. (iii) CCCI adds the configurations of (ii) to the configurations of (i), allowing for full correlation of the changing bonds (RCI*SD) along with orbital shape readjustments ior the other valence orbitals (RCI*Svai). 10 Acknowledgments. This work was supported by the National Science Foundation (Grant No. CHE83-18041) and the Shell Companies Foundation. EAC acknowledges a National Science Foundation predoctoral fellowship (1982-1985), a rese1trch gr1tnt award from the International Precious Metals Institute and Gemini Industries (1985-1986), and a SOHIO fellowship in Catalysis (1987). -191- References (1) (a) Cooper, N. J.; Green, M. L. H. J. C. S. Dalton TranJ. 1979, 1121; (b) Hayes, J.C.; Pearson, G.D. N.; Cooper, N. J. J. Am. Ch.em. Soc. 1981, 103, 4648-4650; ( c) Thorn, D. L.; Tulip, T. H. ibid. 5984-5986; (d) Canestrari, M.; Green, M. L. H. J. C. S. Dalton TranJ. 1982, 1789; (e) Isobe, K.; Andrews, D. G.; Mann, B. E.; Maitlis, P. M. J. Chem. Soc., Chem. Commun. 1981, 809; (f) Thorn, D. L.; Tulip, T. H. Organometallic.! 1982, 1, 1580; (g) Hayes, J. C.; Cooper, N. J. J. Am. Chem. Soc. 1982, 104, 5570; (h) Kletzin, H.; Werner, H.; Serhadli, O.; Ziegler, M. L. Angew. Chem. Int. Ed. Engl. 1983, %!, 46; (i) Jernakoff, P.; Cooper, N. J. J. Am. Chem. Soc. 1984, 106, 3026; (j) J ernakoff, P.; Cooper, N. J. Organometallic.! 1986, 5, 74 7; (k) Thorn, D. L. ibid. 1897. (2) (a) Cooke, M.; Davies, D. L.; Guerchais, J. E.; Knox, S. A. R.; Mead, K. A.; Roue, J.; Woodward, P. J. Chem. Soc., Chem. Commun. 1981, 862; (b) Herrmann, W. A. Adv. Organomet. Chem. 1981, !O, 249. Other C-C couplings atµ - CH 2 Ru 2 centers include: Colborn, R. E.; Dyke, A. F.; Knox, S. A. R.; MacPhersuu, K. A.; Orpen, A. G. J. Organomet. Chem. 1982, 239, C15 and Adams, P. Q.; Davies, D. L.; Dyke, A. F.; Knox, S. A. R.; Mead, K. A.; Woodward, P. J. Chem. Soc., Chem. Commun. 1983, 222. (3) (a) Bradley, J. S. J. Am. Chem. Soc. 1979, 101, 7419; (b) Dombek, B. D. ibid. 1980, 10!, 6855; (c) Daroda, R. J.; Blackborrow, J. R.; Wilkinson, G. J. Ch.em. Soc., Chem. Commun. 1980, 101; (d) Knifton, J. R. ibid. 1981, 188; (e) Warren, B. K.; Dombek, B. D. J. Catal. 1983, 79, 334. ( 4) ( o.) Anderson, R. B. "Catalysts for the Fischer-Tropach Synthesis'', in "Cataly- sis: Hydrocarbon Synthesis, Hydrogenation, and Cyclization", Emmett, P. H., Ed.; Reinhold Publishing Corporation: New York, 1956; Vol. IV, pp 237- 242; (b) Pichler, H.; Buffl.eb, H. Brenn.at. Chem. 1940, 21, 257, 273, 285. (5) (a) Biloen, P; Sachtler, W. M. H. Adv. Catal. 1981, 30, 165; (b) Brady, R. C., III; Pettit, R. J. Am. Chem. Soc. 1980, 102, 6181; (c) ibid. 1981, 103, -192- 1287; {d) Baker, J. A.; Bell, A. T. J. Cata!. 1982, 78, 165. (6) George, P. M.; Avery, N. R.; Weinberg, W. H.; Tebbe, F. N. J. Am. Chem. Soc. 1983, 105, 1393-1394. (7) Carter, E. A.; Goddard, W. A., III J. Am. Chem. Soc. 1986, 108, 2180. (8) van Asselt, A.; Burger, B. J.; Gibson, V. C.; Bercaw, J.E. J. Am. Chem. Soc. 1986, 108, 5347. (9) A preliminary account of the insertion results has already appeared: Carter, E. A.; Goddard, W. A., III J. Am. Chem. Soc. 1987, 109, 579. (10) (a) Carter, E. A.; Goddard, W. A., III Chem. Phya. Lett., submitted for publication; (b) idem, J. Chem. Phya., submitted for publication. (11) The lowest energy structure of la retains C. symmetry (i.e., lower symmetry structures for both la and lb were found to be higher in energy) but the CH 2 ligand is bent 4.1° out of the idealized RuCH 2 plane, toward the Cl ligand. However, the cost to make Ru and the CH2 ligand coplanar is only 0.08 kcal/mo!, and hence we consider the RuCH2 unit to be coplanar for simplicity. (12) Complexes la and lb are taken to be singlet spin states as models for coordinatively saturated organometallic complexes. Similar low spin models with only a few ligands have recently been used in ab initio studies of CO insertion (Dedieu, A.; Saka.ki, S.; Strich, A.; Siegbahn, P. E. M. Chem. Phya. Lett. 1987, 133, 317). Since 1 A' spin states are used for 1, we consider only the triplet spin states of ClRuH (obtained when the bond of Ru=C bond is broken). However, the actual ground state of ClRuH( CH2) is a 3 A" state wherein all three bonds to H and CH 2 are maintained. The singlet "u3 " state we have chosen to examine lies (at least) 16.8 kcal/mol higher in energy at the GVBCI(4/8) level of theory (which consists of a full CI among the six orbitals of the three bond pa.i.rs o.nd the two high spin orbitals for ClRu(CH2)H ( 3 A"), and of a. full CI among the eight orbitals corresponding to the three bond pairs plus the singlet Ru 4d lone pair for C1Ru(CH 2)H (l A')]. We did not optimize the structure of the 3 A" state of ClRu( CH 2 )H, so that 16.8 kcal/mol is a lower bound on the -1931 A' - 3 A" energy difference. The 3 A" ground state of ClRu(CH2)H may be understood as follows. In the 1 A' state, the u and it bonds to H and CH 2 (choosing the H-Ru-C plane as yz) utilize 4dy., 4d.,, 4dy2, and some 5s character on the metal, while 4dx, character is not used at all. In the triplet state, the 4dx2 and 4du orbitals are singly-occupied, gaining favorable exchange terms between the high spin electrons without losing any of the metal-ligand bonding, leading to a triplet ground state. Correspondingly, the ground state of ClRuH is actually a linear 5 .6.. state, derived from the (excited state) s 2 d6 valence electron configuration on Ru. (13) The electron populations were calculated by summing over Mulliken populations for the first and second natural orbitals of each GVB pair. The electron transfer to the Cl was calculated by summing over Mulliken populations of the Cl Hartree-Fock orbitals. (14) All angles and bond lengths were optimized at the GVB-RCI(3/6) level (Section VI) in complexes la and lb, except for R(C-H), which WM fixed at 1.08 A. (15) Guggenberger, L. J.; Schrock, R. R. J. Am. Chem. Soc. 1975, 97, 6578. (16) Hill, A. F.; Roper, W. R.; Waters, J. M.; Wright, A. H. J. Am. Chem. Soc. 1983, 105, 5939. (17) Chang, S.-C.; Kafafi, Z. H.; Hauge, R. H.; Billups, W. E.; Margrave, J. L. J. Am. Chem. Soc. 1986, 107, 1447. (18) Brookhart, M.~ Tucker, J. R.; Flood, T. C.; Jensen, J. J. Am. Chem. Soc. 1980, 101, 1203. (19) The optimum geometry [at the GVB(l/2)-PP level] of 3 A' has 0 (Cl-Ru-H) = 104.8°, R(Ru-H) = 1.64 A, and R(Ru-Cl) = 2.38 A. The 3 A' 3 A" energy splitting of 4.2 kcal/mo! is a lower bound since the geometry of the 3 A" state was kept fixed at the optimum geometry for the 3 A' state (only the equilibrium geometry of the 3 A' state was needed in later calculations). (20) For spin-conserved processes, the resultant insertion product is 1 A' ClRuCH 3 , -194- not 3A' ClRuCH3. (21) HF wavefunctions are reliable for predicting accurate geometries. The HF and the RCI(3/6) optimum geometries of la are very similar, with the Ru-Cl, RuH, and C-H bond lengths identical for both levels of theory. The other HF geometrical parameters for la are R(Ru=C) = 1.87 A, O(H-Ru-C) = 82. 7°, B(H-Ru-Cl) = 157.0°, and B(H-C-H) = 113.3°. These values differ from the RCI(3/6) optimum geometry by no more than 0.03 A and 11.9° (where the latter difference is large due to the flat potential felt by the Cl ligand). The HF energies for these two geometries are: -4936.36310 and -4936.35958 hartrees for the HF gradient and the RCI(3/6) optimizations, respectively. These small changes in energy (2.2 kcal/mol) and structure between the two geometries support the use of HF gradient-optimized geometries in this study. Future work using gradients of correlated wavefunctions will be necessary to test this assertion. (22) Carter, E. A.; Goddard, W. A., III J. Phya. Chem., 1984, 88, 1485. (23) Ziegler, T.; Versluis, L.; Tschinke, V. J. Am. Chem. Soc. 1986, 108, 612. (24) Axe, F. U.; Marynick, D.S. Organometallica, 1987, 6, 572. (25) Carter, R A.; Goddard, W. A., III 1. Chem. Phy.•., submitted for publication. (26) (a) Steigerwald, M. L.; Goddard, W. A., III J. Am. Chem. Soc., 1984, 106, 308; (b) idem, submitted for publication. (27) Hanratty, M.A.; Carter, E. A.; Beauchamp, J. L., Goddard, W. A., III Chem. Phya. Lett. 1986, 11.3, 239. (28) The difference in Ru-H bond energies in singlet ClRuH and triplet Ru+ -H may be attributed to differential exchange loss suffered by Ru when the Ru-H bond i1:> formed. Here the difference amounts to one d-d exchange term, Kctct(Ru+) = 14.6 kcal/mol. (Carter, E. A.; Goddard, W. A., III J. Am. Chem. Soc., submitted for publication.) (29) Mandich, M. L.; Halle, L. F.; Beauchamp, J. L. J. Am. Chem. Soc. 1984, -195- 106, 4403. (30) Schilling, J.B.; Goddard, W. A., III; Beauchamp, J. L. J. Am. Chem. Soc., submitted for publication. (31) Herzberg, G. Proc. Roy. Soc., 1961, A262, 291. (32) Martinho Simoes, J. A.; Beauchamp, J. L. Chem. Rev., submitted for publicati on. (33) (a) The total energies for CH2 differ slightly from the values listed in Table V, due to one change in the basis set between complex 1 (where the 3s combination of the 3d-polarization functions on carbon was included in the calculation) and CH3 [where the 3s combination was omitted (ref lOa)]; (b) the experimental De was derived from AH/,o in "JAN AF Thermochemical Tables", NSRDS-NBS 1971, 37 and supplements to JANAF in J. Phy&. Chem. Ref. Data 1915, 4, 1; ibid., 1982, 11, 695, with zero point energy corrections from Jacox, M. E. J. Phy&. Chem. Ref. Data 1984, 13, 945 for CH 3 and from Bunker, P. R.; Jensen, P.; Kraemer, W. P.; Beardsworth, R. J. Chem. Phy&. 1986, 85, 3724 for CH2. (34) Carter, E. A.; Goddard, W. A., III J. Am. Chem. Soc. 1986, 108, 4746. (35) De(H3C-CH2') was estimated from D298(H3C-CH2·) = 101.3±2.2 kcal/mol [AH/, 298 was taken from JANAF (ref 33b) for :CH2 (92.35±1 kcal/mol) and CH3 · (34.82±0.2 kcal/mol) and AH/, 298 for C2Hs · (25.9±1 kcal/mol) was taken from McMillen, D. F.; Golden, D. M. Ann. Rev. Phy&. Chem., 1982, 33, 493]. Temperature corrections for the heat capacity changes going to T = 0 K were taken equal to 4RAT = 2.4 kcal/mol, leading to D 0 (H3C-CH 2·) = 98.9±2.2 kco.l/mol. Finally, De(H 3 C- CH:.i-) = 105.8±3.4 wa.:s obtained from zero point energy corrections to Do ( AZPE = 6.9±1.2 kcal/mol from ref lOa and references therein). (36) Low, J. J.; Goddard, W. A., III Organometallic&, 1986, 5, 609. (37) Kelley, R. D.; Goodman, D. W. in "The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis" (Elsevier, Amsterdam, 1982) Vol. 4, 427-453. -196- (38) (a) Rappe, A. K.; Smedley, T.A.; Goddard, W. A., III J. Phy.,. Chem. 1981, 85, 1662; (b) Rappe, A. K.; Goddard, W. A., III, unpublished. (39) a) Rappe, A. K.; Goddard, W. A., III, to be published. This basis set was optimized for the dn configuration of the metal as discussed in A. K. Rappe, T. A. Smedley, and W. A. Goddard III, J. PhyJ. Chem., 1981, 85, 2607. (40) Dunning, Jr., T. H. ibid. 1970, 59, 2823. (41) Huzinaga, S. J. Chem. PhyJ. 1965, 42, 1293. -197- Table I. Orbital overlaps, metal orbital hybridization, and bond populations for the GVB bond pairs in la and lb.a Ru bond hybridization populo.tionsb complex bond overlap % 5sp % 4d Ru x la (cr 3 ) Ru-C er 0.73 18.8 81.2 0.96 1.03 II Ru-C 1t' Ru-H 0.50 0.69 4.4 95.6 0.88 25.6 74.4 1.10 1.02 Ru-C <T Ru-C 1t' 0.71 17.8 82.2 0.93 1.03 0.41 2.2 97.8 1.07 0.93 Ru-H 0.63 15.6 84.4 1.08 0.91 II 1 b ( cr 2 1t') " II 0.95 a) Ref. 13. b) A perfectly covalent bond has a bond population of 1.00 for Ru and 1.00 for X (X = CH 2 or H). -198- Table II. Optimized structural parameters and harmonic vibrational frequencies for la and lb.a complex la ( u 3 ) complex 1 b ( u 2 7r) Re(Ru-C) (A) 1.90 1.92 Re(Ru-H) (A) 1.65 1.63 Re(Ru-Cl) (A) 2.42 2.43 Be(H-Ru-C) (deg) Oe(H-Ru-Cl) (deg) 90.3 111.7 145.1 93.6 Be(H-C-H) (deg) parameter 120.0 121.1 1 we(Ru=C) (cm- ) 740 798 we(Ru-H) (cm- 1 ) 2013 1825 we(Ru-Cl) (cm-l) 420 353 we(HCH scissors) (cm- 1 ) 1487 1416 a) Optimized at the GVB-RCI(3/6) level (Section VI). Table ID. Energetics (kcal/mol) for the CH 2 insertion into the Ru-H bond in ClRuH(CH2) within a VDZ basis." total energies (hartrees )0 spatial config./ calculation SEFC la T.S.d 2 LlErxn Eae 0(H-Ru-C)te HF (1/1) -4936.36311 -4936.36311 -4936.42511 -38.9 0.0 82.7° GVB(3/6)-PP (8/8) -4936.43966 -4936.42443 -4936.47422 -21.7 9.7 5i.2° RCI(3/6) (27 /37) -4936.46372 -4936.43708 -4936.48020 -10.3 16.7 47.7° GVBCI(3/6) (141/175) -4936.46940 -4936.44821 -4936.48174 -7.7 13.4 45.2( GVBCI(3/6)-MCSCF (141/175) -4936.47118 -4936.45301 -4936.48242 -7.1 11.5 48.8° a) Calculational details are provided in Sections III and VI. b) 1 hartree = 627 .5096 kcal/mol. c) The number of spatial configurations/ spin eigenfunctions associated with each calculation. d) T.S. = transition state. The total energies listed I under T.S. are values for points calculated nearest the true T.S. and its associated 9(H-Ru-C)t (i.e., HF energy is for ot ....... = 82.7°, GVB-PP for 50.0°, RCI for 47.5°, GVBCI for 45.0°, and GVBCI-MCSCF for 50.0°). e) The proper method I of calculating the activation barrier is by fitting the data points to a potential maximum; the values listed for E,. and 9(H-Ru-C)t are obtained in this manner. Using the differences in total energies for the nearest points to the T. S. leads to a decrease in E,. by 0.1 kcal/mol for the GVB-PP and the two GVBCI calculations. <.O <.O Table lV. Changes in the Hartree- Fock geometry along the reaction coordinate. 8(H-Rll-C) (deg) 82.7" 70.0 60.0 55.0 50.0 47.5 45.0 40.0 23.2° Rc(Ru-H) (A) 1.65 1.68 1.72 1.75 1.77 1.83 1.85 1.94 2.63 Rc(C-11) (A) 2.33 2.05 1.82 1.70 1.57 1.51 1.45 1.33 1.10 R .. (Ru-C) (A) 1.87 1.89 1.91 1.92 1.93 1.93 1.93 1.94 2.06 Rc(Ru-Cl) (A) 2.42 2.41 2.40 2.40 2.38 2.39 2.38 2.37 2.36 Rc(C-11')" {A) 1.09 1.08 1.08 1.08 1.09 1.08 1.08 1.08 1.09 8.,(H'CH 1 ) (deg) 113.3 112.4 112.2 112.2 110.9 112.4 112.5 112.5 108.6 8.,(Cl-Ru.. C) (deg) 120.3 130.~ 134.3 138.9 142.0 135.4 135.5 132.1 105.4 8.,(H'-C-Ru) (deg) 123.4 123.7 123.7 123.8 124.4 123.8 123.6 122.9 110.5 I N a) The optimum angle for la at the HF level. b) The optimum angle for 2 at the HF level. c) Unprimed hydrogen is the migrating hydrogen. 0 0 I Table V. Adiabatic Ru= CH 2 Bond Energies (De) in 1 A' CIHRu=CH 2 (kcal/mol).• - calculation basis set 6 total energies (h)e 1 A' CIRuH(CH 2 ) 3 A' ClRuH 3 E1 CH2 De(Ru=C) VDZ -4936.35958 (1/1) -4897.42464 -38.91349 (1/1) (1/11 13.5 GVB-PP " -4936.44192 (8/8) -4897.45542 (2/21 II 45.8 RCI II -4936.46669 (27/37) -4897.45736 (3/51 II 60.1 RCI*Sval II -4936.51258 (1899 /3997) -4897.46850 -38.92067 (117 /295) (14/28) CCCI' u -4936.51676 (4979/9725) II VDZD -4936.45422 (8/8) -4897.45542 (2/21 -38.92331 (1/1) 47.4 -4936.477 49 (27/37) -4897.45736 (3/51 " 60.8 -4936.50089 (5465/9619) -4897.46142 (67 /1U9) .. 72.9 -4936.53849 (7127 /13895) -4897.46850 (117/295) HF GVB-PP RCI RCI*[SDRu-Cu + SDRu-c,.-] CCCI .. II . .. -38.93503 (:.:2/44) 77.4 80.1 I N 0 f--' I 84.7 a) Details of the calculations are provided in Section VJ. b) VDZ: Valence double-( bases were used for all atoms except Cl [treated using an SHC-EP for the core electrons and an MBS (minimum basis set) description of the valence electrons]; VDZD: same basis set as VDZ except one set of d-polariliation functions was added to the C basis ((= 0.64). See Section VI. c) 1 h = 1 hartree = 627.5096 kcal/mol. The number of spatial confignrations/spin eigenfunctions associated with each calculation is given in parentheses under each total energy. d) CCCI ::=: RCC*[SDRu-cu + SDRu-Cor + Sv,,:J· -202- Table VI. Adiabatic Singlet-Triplet Splittings (AEsT) in ClRuH (kcal/mol).a calculation b GVB-PP basis setc VDZP total energies (h) iA' 3A' -4897.42851 (4/4) -4897.45650 (2/2) AEsT 17.6 RCI II -4897.42855 (9/10) -4897.45841 (3/5) 18.7 RCI*SDRu du's II -4897.43829 (389/490) -4897.46436 (348/550) 16.4 CCCid II -4897.44504 (555/760) -4897.4 7204 (408/778) 16.9 CCCI VDZ -4897 .44320 (425/581) -4897 .47013 (304/584) 16.9 a) AEsT = Esinglet Etriplet. b) Calculational details provided in Section VI. c) VDZP: VDZ Ru, SHC-EP + MBS Cl, and DZP H; VDZ: same as VDZP but the unscaled p-function on H was removed (Section VI). d) CCCI::::: RCI*(SDRu du's + Sval)• -203- Table VII. Adiabatic Ru-H Bond Energies (De) in 1 A' ClRuH (kcal/mol).a calculation basis setb total energies (h )c 2 ClRuH A' ClRu 1 A' De(Ru-H) 23.0 VDZ -4897.39340 (1/1) -4896.85740 (1/1) GVB-PP II -4897.42733 (4/4) -4896.86188 (2/2) 41.5 RCI II -4897.42737 (9/10) -4896.86188 (3/4) 41.5 RCI*SDRu-H " -4897.43014 -4896.86197 43.2 (289/361) (32/42) -4897.44147 -4896.86258 (425/581) (76/152) -4897.39505 -4896.85740 (1/1) (1/1) HF CCCid HF II VDZP 50.0 24.1 GVB-PP II -4897.42851 (4/4) -4896.86188 (2/2) 42.3 RCI II -4897.42855 (9/10) -4896.86188 (3/4) 42.3 RCI*SDRu-H II -4897.43616 (389/490) -4896.86197 (32/42) 47.0 CCCI II -4897.44812 (555/760) -4896.86258 (76/152) 54.1 a) Calculational details provided in Section VI. b) See Table VI, footnote c. c) The total energy of the H atom within the DZ (and DZP) basis is -0.49928 hartree. d) CCCI ;;:: RCI*(SDRu-H + Sv..1]- -204- Table VIII. Adiabatic Ru - CHa Bond Energies (De) in 1 A' C1Ru-CH 3 (kcal/mol). calculation" basis setb 1 total energies ( hartrees) 2 2 A' ClRuCHa A' ClRu A~ CHa De(Ru-C) VDZ -4936.42511 (1/1) -4896.85740 -39.54946 (1/1) (1/1) 11.5 GVB-PP II -4936.47422 (8/8) -4896.86188 -39.56471 (2/2) (2/2) 29.9 RCI II -4936.48019 (27 /37) -4896.86188 (3/4) -39.56620 (3/4) 32.7 -4936.48672 (1843/3191) -4896.86197 -39.56943 (32/42) (6/8) 34.7 II -4936.52800 (3457 /7113) -4896.86258 (711/152) -39.58120 (42/104) 52.9 VDZD -4936.43668 (1/1) -4896.85740 (1/1) -39.56032 (1/1) 11.9 II -4936.48692 (8/8) -4896.86188 -39.57549 31.1 (2/2) (2/2) HF RCI*SDau-c cc ere HF GVB-PP .. RCT II -4936.49312 (27/37) -4R96.86188 -39.57677 (3/4) (3/4) 34.2 RCI*SDau-c II -4936.50339 -4896.86197 -39.58737 33.9 (254::1/4402) CCCI II -4936.54580 (4510/9272) (32/42) (25/44) -4896.86258 -39.59667 (76/152) (58/143) 54.3 a) Calculations discussed in detail in Section VI. b) See Table V, footnote b. c) CCCI::::: RCI*[SDRu-c + S,.,.1]. -205Table IX. Adiabatic CH2 - H Bond Energies (De) in 2 A~ CH 3 (kcal/mo!)." total energies (h )c calculation HF basis set11 VDZ GVB-PP II RCI II RCI*SDc-H " CCCI4 II HF VDZD GVB-PP II RCI II RCI*SDc-H II CCCI II HF VDZDP GVB-PP II RCI II RCI*SDc-H II CCCI II CH a 3 B1 CH2 -39.54946 (1/1) -39.56471 (2/2) -39.56620 (3/4) -39.57066 (36/60) -38.91349 (1/1) 85.8 II 95.3 II 96.3 " 99.1 -39.58487 (65/140) -39.56032 (1/1) -39.57549 (2/2) -39.57677 (3/4) -39.58743 (61/104) -39.60548 (102/215) -38.92067 (14/28) -38.92254 (1/1) 103.5 II 96.4 II 97.2 II 103.9 -38.93425 (20/40) -38.92254 (1/1) 107.9 II 97.7 II 98.5 II 108.7 -38.93425 (20/40) 112.9 -39.56282 (1/1) -39.57750 (2/2) -39.57874 (3/4) -39.59498 (80/138) -39.61340 (130/271) 86.9 88.5 115.8±1.4 a) Calculational details provided in Section VI. b) VDZ a.nd VDZD: see Table V, footnote b; VDZDP: one set of unscaled p-pola.rization functions for the hydrogen atom involved in the breaking C-H bond was added to the VDZD basis. c) The total energy of the H atom within the DZ (and DZP) h1tsis is -0.49928 hartree. d) CCCI::: RCI*[SDc-H + Sva1]. e) Ref. 33. Table X. Direct calculations of the insertion activation barrier (Ea) and exothermicity ( .1.ErXll) within both VDZ and VOZDP bases as a function of electron correlation (k:cal/molj.• total energies (hartrees) VDZ basis" E. VDZDP basis" .1.Erxn ,..- -···~ RCI(3/6)" la -4936.46372 T.S. 4 -4936.44119 2 -4936.48020 la -4936.47494 T.S. -4938.45713 2 -4936.49508 VDZ 14.1 RCI(3/6)*SDI -4936.48731 -4936.47086 -4936.49752 -4936.51191 -4936.49718 -4936.52711 CCCI• -4936.51729 -4936.49542 -4936.53167 -4936.54521 -4936.52510 -4936.56373 calculation best estimate,. VDZDP 11.2 VDZ -10.3 10.3 9.2 -6.4 -9.5 13. 7 12.6 -9.0 -11.6 10.9±1.7 VDZDP -12.6 -10.6 ± 1.0 a) Details of the calculations are provided in Section VI. b) VDZ: See Table V, footnote b. c) VDZDP: VOZ +one set ofd-polarization functions on C ((= 0.64) and one set of unscaled p-polarization functions on the migrating H. d) T. S. =geometry at transition state where 9(11-Ru-C)l = 50.0 degrees (Section III). e) 27 spatial configurations/37 spin eisenfunctions. /) RCI(3/6)*SD = RCI(3/6)*[SDRu-H bond/C-H bond+ SDRu-C a bond + SDRu-C .,.. bond/Ru 4d lone pair]· VDZ: 5475 spatial configurations/9499 spin eigenfunctions; VDZDP: 9034 spatial configurations/16048 spin eigenfunctions. g) CCCI= [SDRu-H bond/C-H bond + SDRu-C a bond + SDRu-C ... bond/Ru 4d lone pair + s....:]. VDZ: 6501 spatial configurations/12337 spin eigenfunctions; VDZDP: 10488 spatial configurations/19950 spin eigenfunctions. h) Based on tle average of the RCI(3/6)*SD and CCCI values using the VDZDP basis. I N 0 °' I -207- Figure Captions Fig. 1. GVB(3/6)PP one-electron orbitals for la, the o- 3 state of C1Ru(CH 2 )H at its optimum geometry: (a) the Ru-H bond; (b) the Ru-Co- bond; (c) the Ru-C ft bond; (d) the Ru doubly-occupied 4dxs orbital; and (e) the Ru doubly-occupied 4dxy orbital. Long dashes indicate zero amplitude and the spacing between contours is 0.05 a.u. Fig. 2. GVB(3/6)PP one-electron orbitals for lb, the o-2 7r state of C1Ru(CH 2 )H at its optimum geometry: (a) the Ru-H bond; (b) the Ru-Co- bond;(c) the Ru-C 7r bonds; ( d) the Ru doubly-occupied 4d.2 orbital; and ( e) the Ru doubly-occupied 4dxy orbital. Fig. 3. Reaction coordinate for the insertion of CH 2 into Ru-H in la to form 2 at the HF, GVB(3/6)-PP, GVB-RCI(3/6), GVBCI(3/6), and GVBCI(3/6)-MCSCF levels of theory. Energy (kcal/mol) is plotted relative to the total energy of 2 vs. the normalized reaction coordinate R(Ru-H)/[R(Ru-H) + R(C-H)]. The corresponding H-Ru-C angles (deg) are indicated at the top. The full GVBCI-MCSCF wavefunction yields simultaneously a proper description of reactant, transition state, and product, resulting in a smooth potential curve. Some lower level wavefunctions lead to less smooth transitions, since they are less capable of describing both reactant and product channels. Fig. 4. GVB(3/6)PP one-electron orbitals near the transition state [O(H-Ru-C)t = 50.0°): (a) orbital pair describing the Ru-H bond of reactant la and the C-H bond of product 2; (b) the Ru-C o- bond; ( c) orbital pair describing the Ru-C ft bond of la and the Ru 4d lone pair of 2. (Nodal lines have been omitted for clarity.) Fig. 5. GVB(3/6)PP one-electron orbitals in the product channel [O(H-Ru-C)t 40.0°]: (a) the C-H bond of product 2; (b) the Ru-C <1' bond; (c) the Ru 4d lone pair of 2. (Nodal lines have been omitted for clarity.) -208- Fig. 6. The thermodynamic cycle used tu uc::s:ive ~Erxn (kcal/mul) for eq 2. The bond and excitation energies shown are from CCCI calculations (Sections IV and VI) using the VDZ, VDZD, and VDZDP basis sets (Table V, footnote band Table VI, footnote c; Section VI). The predicted exothermicities (~Erxn) are shown at the bottom. -209- )-. x a) RuH CT Bond ONE y ONE PAIR y-:_~·\ ~\" \ \ l.- ) \ z b) Rue CT Bond ONE -........., I y I~ ___ ..... \ ..... , ONE ~ I ;: IL_. ~;;) . I PAIR \...,: ::-~: 2) ~ :...---; - ..:- .., '..__/ _,,,,. / .... \ \+ - ·~;- .. ,,... ....._._.· ... .,../ ,_... ·... -· ....... .. ~ \ /'· ; / ;~·:.:; ~ \ z c) Rue ff Bond y z d) Ru 4dxz Lone Pair e) Ru 4dxy Lone Pair TWO TWO r-... x _cj.j__ o~~') /-... ....\ ! : t~"".,:' x __ "'L ... \• z ) ... ·;-· "-._,.1 ..__/ y Figure 1. ,·.-. - r::·; ' 1 .. -210- x )-. a) RuH er Bond I I ONE t \\I). L/~.'\. ~\.-- t + +\ z b) Rue o- Bond y z cl Rue .,,. Bond x z d) Ru 4dz 2 Lone Pair el Ru 4dxy Lone Pair TWO TWO ()~~j.:\-\ }~'\ ·; :;:. ) y / .. / .... ... ::;...-" ) c~~, ,_ z y Figure 2. -211 8 ( H-Ru-C), degrees 82.7 70.0 60.0 55.0 50.0 47.5 45.0 40.0 23.2 45.0 - 0 E ~ 0 40.0 35.0 (.) .:.:.. 30.0 >- <.!::> 0:: lJ.J 25.0 zlJ.J 20.0 w > 15.0 J-- <! _J lJ.J 0:: 10.0 5.0 0.0 0.45 0.50 0.55 0.60 R(Ru-H) R(Ru-H)+R(C-H) Figure 3. 0.65 0.70 -212- [Cl~?Hr a) Ru-H Bond to C-H Bond Pair ONE ONE ONE ONE + I " \,,, \'t \ '' -' I b) Ru-C Sigma Bond Pair , -, I \ ~y + I ""~""" I ' ' .,.,,, I ' \ ' _. ;' ',; I ' -, I c) Ru-C Pi Bond to Ru d;r Lone Pair ONE + ONE + Figure 4. -213- a) C H Bond Ru -C Bond c) Ru d Lone Figure 5. THERMODYNAMICS OF CIRu(H)(CH 2 )~ CI Ru(CH 3 ) AS A FUNCTION OF BASIS SET* fi + H• + CI - Ru 547 De(Ru-H)=50.0(VDZ) ~ \3 ""H <D>C~ /H 9 ,~··H Cl -Ru<'.il + e!>C't A H @_} '-H & De (C-H)= 103.5 (VDZ) 107.3 ( VDZDI 112.9 (VDZDP) 6E 5 T(CIRuH)= 15.9 (VDZ) 15.9(VDZP) I Cl - /H \3 .. H Ru-cD + <!>C-."' ~ 6E= 970(VDZ) IOl.6 ( VDZO) IOl.6(VDZDP) N ,..,. ..,. I 6"-H €l~H Cl- "Ru<!) '+ H- i'-H De(Ru=C)=80.I (VDZ) 84.7(VDZD) De 1Ru-C)=52.9 (VDZ) 54.3 (VDZD) I/ H Cl_ Ru~ .,,.. H C'-.H ~ /Ru 6Erxn= *Energy in kcal/mo! -9.4 (VDZ) -10.6 (VDZD) -11.5 (VDZDP) Figure 6. Cl I H --c~·H '-H -215- Chapter 4 Chemisorption of Oxygen, Chlorine, Hydrogen, Hydroxide, and Ethylene on Silver Clusters: A Model for the Olefin Epoxidation Reaction The text of this chapter is an Article coauthored with William A. Goddard III and is to be submitted to Surface Science. -216- Chemisorption of Oxygen, Chlorine, Hydrogen, Hydroxide, and Ethylene on Silver Clusters: A Model for the Olefin Epoxidation Reaction Emily A. Carter and William A. Goddard III* Contribution No. 7582 from the Arthur Amo& Noye& Laboratory of Chemical Phy&ic&, California ln&titu.te of Technology, Pa&adena, California 91125. Abstract: The mechanism of the silver-catalyzed olefin epoxidation reaction is still far from understood, despite extensive experimental investigation. In order to sort out the feasibility of various postulated pathways, we have undertaken an ab initio quantum mechanical study of the key role players in this reaction. In particular, we have predicted preferred binding sites, geometries, vibrational frequencies, and binding energies for 0, 0 2 , Cl, H, OH, and C 2 H4 on Ag 3 , a model for Ag aggregates present on actual supported catalysts. A primary prediction of this work is the ex- istence of two near-degenerate states of Oad, with binding energies of 77.8 and 78.7 kca.l/mol [in excellent agreement with TDS data for O/Ag(llO) and O/Ag(lll)j, but with only one predicted to be active for olefin epoxidation. These states are proposed to be unique forms of oxygen occupying distinctly different adsites on Ag. Implications for other mechanistic aspects of this reaction (e.g., the role of promoters and the combustion pathway) are discussed, with new interpretations offered of recent single-crystal studies of the epoxidation reaction in terms of monatomic oxygen as the active oxidizing agent. -217- I. Introduction The selective oxidation of ethylene to ethylene oxide (EO) is an exceedingly important industrial catalytic reaction, providing the feedstock chemical for the production of ethylene glycol, which is in turn used to synthesize antifreeze and polyesters. 1 The industrial reaction is usually carried out at pressures of 10-12 atm and at temperatures of about 540°K, with a catalyst consisting of silver dispersed on a-alumina, 0 Ag/Al 2 0 3 - 270 °C ·"" 111 /\ ' C--C 111 "'"" + C0 2 + H 2 0 ~ (1) with trace quantities of chlorine (usually in the form of 1,2~dichloroethane), cesium (in the form of aqueous solutions of CsOH, CsN0 3 , or Cs 2C0 3 2 ), and other promoters added in order to increase the activity and selectivity of the catalyst. Total combustion of the olefin to C02 and H2 0 is a competetive process, with alkali metals and chlorine (as well as other electronegative elements) known to inhibit this latter route. The unique aspects of this partial oxidation are the following: 3 - 5 (i) silver is especially active, with other transition metals yielding only products of total combustion; (ii) chlorine, calcium, potassium, and cesium are among the known promoters of the reaction; and (iii) epo:x:ida.tion il5 only efficient for ethylene, with higher olefins com.bul5ted to CO:i and H20. It is not known why silver is so exceptional nor is it fully understood why olefins other than ethylene are combusted rather than epoxidized. In addition, despite the -218- relative simplicity of this system, there remains great controversy over the precise nature of the active form of oxygen (atomic versus molecular 3 - 6 ) and over the mechanism by which alkali metals and chlorine act to promote the formation of E0. 7 Much emphasis has been placed on achieving maximum selectivity to EO (i.e., minimal combustion), since the production of EO from ethylene is such a lucrative industry. Proponents of molecular 0 2 ,ad as the active species claim that selectivities higher than 6/7 are unattainable, due to a postulated mechanism in which an adsorbed peroxy radical reacts with ethylene, forming EO with the outside oxygen and forming C02 with the oxygen which remains behind. The stoichiometry of the two competing reactions would then fix the maximum selectivity at 6/7: 6 (2) (3) (Thie echeme aseumee thn.t the outer oxygen exclueively forme EO n.nd the :surface- bound oxygen exclusively combusts ethylene.) A mechanism involving atomic oxygen, however, sets no maximum on the selectivity to EO. While unpromoted catalysts normally achieve selectivities in the range of 453, 6 a recent report indicates selectivities as high as 85-873 (at or slightly above the theoretical maximum from the above mechanism) when NaCl was added to the catalyst. 8 Thus it is not at all clear whether 6/7 is a true theoretical limit on the selectivity of the partial oxidation of ethylene. Detailed experimental data exist to support either Oad or 0 2,ad as the active precursur to ethylene uxide. 7 1,9 - 13 Huwever, all evideuce :suppurtiug 11mlecul1u uxy- gen is indirect, 7 /, 9 - 12 while there does exist direct evidence for the evolution of EO in the presence of Oad· 13 The most recent experiments to be interpreted in terms of molecular oxygen as the active agent a.re due to Campbell, 7 f,l 2 who found no direct correlation between the steady-state coverage of monatomic oxygen (by varying the crystal face, the temperature, or the coverage of chlorine) and the rate of EO -219- production. He concluded from these negative results that diatomic oxygen must be the active species for epoxidation. We have a different interpretation consistent with his data (Section IV), invoking Oad as the active site for expoxidation. The most convincing evidence to date supporting monatomic oxygen was recently reported by van Santen and de Groot. 13 1 16 0 2 was initially adsorbed on Ag powder at high temperature (475°K) to produce monatomic 16 0ad [e.g., 02 a.d:sorb:s dissociatively above 150°K on Ag(110) 14 ], with an adsorbed oxygen to surface Ag ratio of ,. . ., 1. (Separate experiments showed that this precovered oxygen surface yielded epoxide when reacted with ethylene.) Then a mixture of gaseous 18 0 2 and C 2H4 was introduced at room temperature to the 16 0-precovered surface, and the temperature was increased at a rate of 2.3°K/min. Under conditions where gaseous oxygen scrambling was slow, ethylene first reacted to form exclusively C2H 4 16 0, followed later by the 18 0 analog. Unless the oxygP.n ada.toms recombine immediately prior to reaction (which has not been ruled out), these experiments indicate that Oad ia the direct precursor to EO. The promoters which have been studied most thoroughly experimentally are Cl and Cs. 7 •8 Since they observed an increase in rate of EO production at high Cl coverages, Campbell and Koel have concluded that Cl promotes EO formation by site-blocking, with C02 production suppressed due to its site requirement for formation presumed larger than for EO formation. 1 a-c While this may be one service Cl provides, we believe it is the apecific aitea blocked by Cl which are crucial to the formation of the oxidant active for EO synthesis (Section IV). Concerning Cs and other alkali metals, Lambert has demonstrated that Cs inhibits isomerization and hence the secondary combustion of EO on Ag(lll). 7 Y•h,lS On the same surface, Campbell found that cesium is converted to a surface cesium oxide with the approximate composition Cs0 3 , under the reaction conditions for producing EO. Again, Campbell proposes a site-blocking mechanism for the role Cs plays as a promoter. 7 d We prefer (Section IV) to consider the electronic rather than the steric effect that cesium may induce when aggregated with oxygen. -220- The present work is concerned with calculating qualitative features (e.g, the nature of the adsorbate-silver bond) and quantitative features (e.g., binding energies, vibrational frequencies, and equilibrium geometries) of the interaction of a silver cluster with various adsorbates postulated or known to play a role in the epoxidation chemistry. We have focused this first study on Ag 3 , as a model for the dose-packed (111) plane of silver, which should be the primary surface on sup- ported catalysts (due to its thermodynamic stability). We begin by discussing the qualitative aspects of bonding atomic and molecular species to the Ag 3 cluster in Section II. Reported in Section III are results for H, Cl, 0, 0 2 , OH, and C 2 H 4 interacting with the 1-fold (lF), 2-fold (2F), and 3-fold (3F) sites of Ag 3 • Section IV discusses these results in terms of their impact on interpreting experimental data from extended surfaces and on the various controversial mechanisms outlined above. We propose our own view of the epoxidation reaction, in terms of the active oxygen species, the role promoters play in stabilizing it, and other contributions by promoters which enhance the production of EO. Section V concludes with a summary of the cluster findings and their impact on the mechanistic details of the epoxidation reaction over Ag. Section VI provides calculational details. II. Qualitative Bonding of X to Ag 3 When an gaseous atom or molecule adsorbs on a perfect surface, the infinite two-dimensional periodicity is broken, with the subsequent interactions expected to be localized. Thus we believe that the chemical bonding between an adsorbate and a substrate is a localized phenomenon, and therefore may be well-represented by the interaction of an adsorbate on a finite cluster. The cluster model we have chosen is three silver atoms in an equilateral triangle with a Ag-Ag distance equal to the nearest neighbor distance in bulk Ag [R(Ag-Ag) = 2.89A]. The cluster geometry is kept fixed, while the adsorbate degrees of freedom are optimized, in order to mimic the interaction of an adsorbate with an unreconstructed surface. With a valence electron configuration for Ag of 4d10 5s 1 , the closed shell Ag d- -221- electrons do not participate directly in metal-metal bonding, while the s-electrons on Ag form the Ag-Ag bonds. Ag 3 has three valence s-electrons, with the ground 2E' state (D 3h symmetry) having two electrons spin-paired to form the Ag-Ag bond, leaving one s-electron in a singly-occupied orbital. The valence orbitals for one component of the 2E' state are shown in fig. 1 ( 2A 1 for this C 2v resonance structure). We find, as in alkali metals, 16 that the electrons localize in interstitial sites, bond midpoints in this case, due to the greater strength of one-electron bonds over two-electron bonds in systems where the orbitals have low overlap (S'""'0.4) [e.g., D 0 (Lii) = 1.44 eV whereas Do(Li2) = 1.05 eV]. These localized electrons then spinpair to form a low spin ground state, often causing geometric distortions. 16 However, since we are not concerned here with predicting the ground state structure of JahnTeller-distorted Ag 3,17 but instead are interested in modeling a surface, we constrain Ag 3 to the equilateral triangle geometry to model the (111) face. The presence of the radical orbital on Ag3 (fig. la) is in contrast to the electronic structure of bulk Ag, which is diamagnetic (no unpaired spins). Thus, we expect that adsorbate-cluster bonds in the 2F site (where the radical orbital has the greatest amplitude) will be especially strong, with binding energies larger than that expected for an extended surface. On an actual surface of Ag, some coupling energy (probably fairly small) will have to be expended in order to unpair Ag spins (breaking Ag-Ag bonds) so that bonds to the adsorbates may be formed. The lF site on Ag3 is generally next lowest in energy, since the radical orbital has considerable amplitude there. The 3F site should give a lower bound to the binding energy of most species, since the electron density of this cluster is centered around the bond midpoints, leaving the center of the cluster (the 3F site) electron-deficient. Fig. 2 schematically depicts the binding of H, Cl, and 0 to the 2F site of Ag 3 • Both H ( 2S) and Cl ( 2P) have one unpaired electron which can be spin-paired to the Ag3 radical electron, as shown in figs. 2a and 2b. The bond to Cl is in reality very ionic, so fig. 2b is not meant in any way to imply that covalent bonding occurs (see Section III.B). Oxygen atom ( 3 P), with its two unpaired electrons can either -222- :form one <r and one 7r bond (fig. 2c) to the 4 A2 state of Ag 3 (30.1 kcal/mol above the ground 2 A 1 state) or it can form ionic bonds to the 2 A 1 state, pulling the radical electron off the cluster to form Agto-. o- ( 2 P) has two possible orientations with respect to the C 2 axis, with either the unpaired electron along the C 2 a.xis (denoted 2 :E in fig. 2d) or with the unpaired electron perpendicular to this axis (denoted 2 n in fig. 2e ). Similar bonding configurations are found for adsorbate bonding in the lF site (retaining C 211 symmetry) and in the 3F site (C3 11 symmetry). The bonding of the molecular adsorbates (OH, 0 2 , and C 2 H4 ) is somewhat more complex and discussion of them is deferred to the next section. III. Results Although configurations involving adsorption in the lF site are of theoretical interest, they are less important for comparison to experimental results than the ground states of each Ag 3 X system, along with the 3F binding sites expected to be prevalent on aggregated Ag. Hence we will emphasize results for the ground state of each complex and for the electronic states arising from interaction of the adsorbate with the 3F binding site. The simplest adsorbate to interact with the Ag 3 cluster is hydrogen. The three adsorption sites are shown schematically below, for the singlet states of Ag 3 H. Ag-Ag ©:f (4) Ag I H lF 2F 3F Predicted properties are listed in Table I for Ag 3 H as a function of adsorption site and electronic state. The ground state ( 1 A1 ) involves hydrogen bonding to the radical orbital on Ag 3 (fig. 2a), leading to the planar 2F site as the lowest energy -223- configuration (nonplanar configurations of the cluster were found to be higher in energy). The Ag 3 -H bond strength of 56.8 kcal/mol is similar to second row, late transition metal-hydrogen diatomic bond strengths (54 - 59 kcal/mol1 8 ) presumably because of the similarly large amounts of metals-character involved in both the bond to the cluster and to the metal atom in M-H (903 s-character in the Aga radical orbital). 18 The one-electron GVB orbitals for the Ag-Ag and Aga-H bonds are shown in fig. 3, where we see that the Ag-Ag bond (fig. 3b) has moved out of the way of the 2F site to avoid interaction with the Ag 3 -H bond. Fig. 3a indicates that the Ag3 -H bond is essentially covalent, with one electron localized on the cluster and one electron in a ls orbital on hydrogen, spin-paired to form the Ag 3 -H bond. The degree of ionic character is assessed quantitatively in Table II, where Mulliken population analysis indicates that hydrogen actually pulls 0.2-0.4 electron off of the cluster, resulting in a substantial dipole moment for Hin the lF and 3F sites. The dipole moment is nearly zero for the 2F site because the negative image charge on the "bulk" Ag atom (the atom not directly attached to the adsorbate) cancels out the effect of the charge shift to H. We have also indicated the shift expected in the Ag 4d-band upon adsorption of H, with the 3F H(ad) shifting the d-band the most (downward by 0.4 eV). The large charge transfer to hydrogen is due to the small vertical ionization potential (IP) for Ag 3 of 4.18 eV (in good agreement with 4.26 eV for the work function of bulk Ag 19 ). Examining the excited states in Table I, we see that the lF binding site lies above the ground state by 4.4 kcal/mol. In the lF geometry, the H is attached to only one of the Ag atoms, within the plane of the cluster. Although the distance to the cluster, Ri., is shorter for the 2F site, the actual Ag-H distance is longer for 2F [R(Ag-H) = 2.02 A] than for lF [R(Ag-H) = 1.77 A], leading to a lower vibrational frequency for the 2F Ag3 -H. The binding energy for the lF site is found to be weaker than the 2F binding energy by 6 kcal/mol. (The relative total energies reported are from GVB-PP calculations, whereas the bond energies are calculated -224- a.t the CCCI level; this results in slightly different energy splittings when comparing the two levels of calculation.) Two triplet states lie next highest in energy, with the 1 A' state of the 3F site lying 39.1 kcal/mol up from the 2F (1 A 1 ) ground state. The binding energy of H to the 3F site is less than half that predicted for the ground state of the cluster [D(Ag-H) = 28.5 kcal/mol for the 3 A" state and D(Ag-H) = 19.5 kcal/mo! for the 1 A' state]. For adsorbates such as H, where covalent bonding is expected, the 3F site suffers from n. la.ck of electron deneity in the center of the clueter, lea.ding to low overlap in the Ag 3 -H bond, and hence a low binding energy. On an extended surface, however, we expect much larger electron density in the 3F hollows, 16 with larger binding energies as a result. Thus the 3F binding energy for H is a lower bound on the actual Ag surface-H bond energy. Dissociative adsorption of H2 has not been observed on Ag and is known to be activated on Cu and Au. 20 Therefore, either the process is activated or endothermic (and thus activated) on Ag. If it is an endothermic reaction, then the binding energy of H to Ag must be less than 52 kcal/mol (half of the bond energy in H 2 ). Consistent with this expectation, the 2F site bond energy of 56.8 kcal/mol is an upper bound, since no unpairing energy present on an extended surface is incurred for Ag 3 • However, the 2F site binding energy may reflect the stability of H bound at a step or kink, where unpaired Ag electrons may be present (as in Ag3). The Ag-H binding energy is thus bracketed to an upper bound of 57 kcal/mol near sites of unsaturation and a lower bound of 20 kcal/mol for a 3F site. We expect that larger clusters will have higher binding energies to 3F sites as a result of more density present in the 3F fa.ces. Indeed, results for tetrahedral Ag4 from pseudopotentia.1 local density functional (LDF) calculations 21 indicate binding energies to the 3F face of 49.8 kcal/mol and to the 2F bridge of 54.6 kcal/mol, the latter in good agreement with our CCCI result of 56.8 kcal/mol. (We have also calculated the binding energy of H to the 2F bridge site of tetrahedral Ag4 using CCCI methods, yielding a binding energy of 55.2 kcal/mol, again in good agreement with the LDF -225- work ,of ref. 21.) B. Ag3 Cl The three possible high symmetry adsorption sites for Cl on Ag3 are shown below. Ag-Ag ~ Ag Cl Ag_J_Ag Cl ~g c1 ~ Ag Ag~ lF 2F 3F 1 (5) Ag Table III lists predicted properties of Cl bonding to both the 2A, ground state of Ag3 and to the 4 A2 excited state (30.1 kcal/mol up), resulting in a spectrum of lowlying singlet e.nd triplet states. Unlike H, the singlet states a.re all lower in energy than the triplet states. The bond between Ag 3 and Cl is much more ionic (Table II) than the Ag3-H bond. Thus the relative stabilities of the triplet and singlet states of Ag3Cl are due primarily to the triplet-singlet splitting in Agt (D..EsT 50.5 kcal/mol). The ground state has Cl in the 2F site (1 A 1 ), with a Ag-Cl distance of 2. 72 A (R.L = 2.23 A), an Ag 3-Cl vibrational frequency of 211 cm- 1 and a bond energy of 91.0 kcal/mol. The bond distance is very close to that observed for Cl on Ag(lll) from SEXAFS experiments, in which the Cl was found to reside in 3F sites with R(Ag-Cl) = 2.70±0.0lA. 22 Although Cl;a dissociates readily on Ag, no binding en- ergies for Cl on Ag have been reported, primarily because there is some uncertainty as to whether Cl desorbs as Ch or as AgCl. 23 The orbitals for the ground state of Ag3Cl (fig. 4) indicate a large amount of ionic character in the Ag3-Cl bond, with the Ag-Ag bond again moving out of the way of the Ag3-Cl bond (as for Ag 3H). Table II supports the assertion that the bonding is ionic, with approximately 0.6 electron removed from the cluster by Cl for all three sites. Significant dipole moments and d-band shifts a.re predicted 226- for all three sites of Ag 3Cl, with a very large dipole moment of 12.5 de bye and d-band shift of 0.8 eV predicted for the lF site. The dipole moments as a function of adsite for electronegative groups such as Cl and 0 (vide infra) show the following trend: lF exhibits the largest dipole moment, 2F a moderate dipole moment, and 3F the smallest dipole moment. Since the lF site has the most dispersive charge distribution, with the adsorbate negatively-charged and all three Ag atoms positively-charged, it exhibits the largest dipole moment. The 2F site has the next most wide-spread charge distribution, but the small negative image charge on the "bulk" Ag atom induces a dipole moment less than half the size of the lF dipole moment. The closest approach of the adsorbate is in the 3F site, leading to the smallest dipole moment. A trend is also apparent in the d-band shifts: for clusters where the "bulk" Ag atoms are positively-charged, the d-band shifts are quite large (i.e., for the lF site). Decreasing the occupation of the sp-band (the valence Ag orbitals) stabilizes the d-band by lowering electron-electron repulsion. The lF site lies 9.3 kcal/mol above the 2F site, with the 3F site 22.0 kcal/mol up (Table III). The 3F site has an Ag-Cl bond length of 2.90 A (R..L = 2.38 A) and a bond energy of 79.7 kcal/mol. This is 0.18 A longer than for the 2F site and 0.20 A longer than the experimental value for Cl/ Ag(lll). This suggests that Cl adsorbed on Ag(lll) is held more tightly than the theoretical 3F site properties would imply. The bond energy of Cl to Ag3 in the 3F site is therefore expected to be a lower bound on the surface-Cl binding energy (as with Ag 3H). Thus, we have been able to brar.ket the Ag-Cl surface bond energy to within ,..._, 10 kca.l/mol, since the Ag-Cl bond for the 2F site (91.0 kcal/mol) should be an upper bound (see Sectiun II) a.nd the Ag-Cl 3F site provides the lower bound of 79. 7 kcal/mol. Since no experimental values are available, these values may only be compared to results from semi-empirical SW-Xa calculations for Cl on an Ag5 cluster, which yielded a binding energy of 72.2 kcal/mol. 24 -227- The luw-lyi11g stales uf ox.ygeu uu Ag3 ausurLeu 011 a 2F site are i111.lict1.Leu i11 figs. 2c - e, while we show the three low-lying states of oxygen on a 3F site of Ag3 below. Ag~A: '~ Ag 21J D Ag~~ ~Ag di-0' /Ag Ag~+ "~ (6) Ag 2n Instead of a C1 and 7r double bond as found for the lF and 2F sites for 0 / Ag 3 (fig. 2), we obtain two equivalent er bonds for the double-bonded state of the 3F site, denoted as di-0' bonding. Table IV displays the properties for the three low-lying states of Ag 30 binding to all three sites. Again, the 2F site is favored, with the ionic bonding configurations of figs. 2d and 2e separated by only 2.7 kcal/mol, while the <nr double-bonded state lies 29.8 kcal/mol higher in energy. The ground state has an Ag-0 bond length of 2.26 A (R.L = 1.74 A), an Ag 3 -0 vibrational frequency of 332 cm- 1 , and a bond strength of 92.9 kcal/mol. Again, this bond energy is expected to be an upper bound to the surface-0 binding energy, because both the slightly smaller (vertical) IP of Ag 3 ( 4.18 eV) relative to the bulk work function of Ag (4.26 eV) and the localized hole (positive charge) on the cluster work to create a stronger ionic bond. The 2 II state (2. 7 kcal/mo! up) has a longer bond length [R.L = 1.91 A or R(Ag-0) = 2.515 A], a smaller vibrational frequency (289 cm- 1 ), and a slightly smaller bond energy (90.2 kcal/mo!) than the ground state. This is due to the doubly-occupied 0 pC1 orbital which prevents a close approach of 0 to the cluster. The ground state, on the other hand, can form a shorter, stronger bond to the cluster because the 0 pu orbital is singly-occupied. In contrast, the lF 2 II state is much lower in energy (3.1 kcal/mol above the ground state) than the lF 2 E state (23.4 kcal/mo!). The -228- bonding for lF resembles AgO diatomic, since the oxygen is bound to only one Ag atom. AgO has a similar ordering of states, with a 2 II ground state and a 2 :E excited state ,...., 15 kcal/mol higher. 25 The two lowest states of oxygen in the 3F site are of primary importance to the discussion in Section IV, since they represent the most realistic binding site on .Ag 3 to compare with an extended surface. We see from Table IV that the two lowest states in the 3F site are nearly degenerate, separated by 0.9 kcal/mol (up 14 kcal/mol from the 2F ground state). These near degenerate states have very different properties, however, with the 2 :E radical state exhibiting a long bond length (R.L = 1.80 A) and a small vibrational frequency (299 cm- 1 ), while the di-u state (0.9 kcal/mol higher) has a much shorter bond length (R.L = 1.37 A) and a higher vibrational frequency (412 cm- 1 ). The vibrational frequency for 0 / Ag(llO) is known from electron energy loss spectroscopy (EELS) to be 315 cm- 1 , in good agreement with the 3F radical state. 26 The bond energies for the two 3F states are predicted to be 78.7 and 77.8 kcal/mol. This is in excellent agreement with thermal desorption data from 0/ Ag(llO) and 0/ Ag(lll) where 0 desorbs at temperatures between 565 and 600°K (depending on the crystal face and the coverage), implying a surface-oxygen binding energy of,...., 80 kcal/mol. 26 •27 Our results are in contrast to Hartree-Fock calculations reported for 0 on Ag 26 , where, although good agreement was obtained for the vibrational frequency and distance from the surface, a Ag-0 bond energy of 9 kcal/mol was predicted for the 4-fold bridge site on Ag(ll0). 28 The 2 II radical state in the 3F site is ,....,5 kcal/mol higher than the two 3F states discussed above, with the oxygen much less tightly bound, as indicated by the long bond length (R.L = 1.92 A) and the low vibrational frequency (252 cm- 1 ). Even higher in energy are the 2 :E radical state for the lF site and the two <T7r doublebonded states for the lF and 2F sites. The <T'lr double-bonded states in the 2F and lF sites are destabilized because they involve very weak 7r bonds due to the low overlap between the cluster valence b 2 orbital and the oxygen p7r orbital: for the 2F site (discussed below), the 71" bond resolves this problem by ionizing the cluster, -229- while the 7r bond in the lF site involves two weakly-coupled singly-occupied orbitals with an overlap of 0.06! This explains why the lF <1'7r double-bonded state is so high in energy (53.9 kcal/mol up). The 3F analog, the di-<1' state, forms ionic <1' bonds (1.60 electrons on 0 in each bond) with some back-donation bonding from the 0 lone pair, leading to a large stabilization of the di-<1' state over the <1'7r double-bonded states. In sum, we predict that the radical states are preferred for the lF and 2F sites, while twu very different :;tate:s [with :st1:1rk cuutra:st:s iu Luth predide<l prvve1·tit::s am.l reactivity (Section IV)] are competetive for the 3F site, one with radical character on oxygen and one with the 0 2p electrons tied up in bonds to the cluster, leaving no unpaired electrons on oxygen. The orbitals for the three states of 0 on Ag3 in the 2F site are shown in figs. 5 - 7. Fig. 5 shows the ground state (2 A 1 ) of Ag 30, with fig. Sa depicting the singly-occupied 0 2p radical [oriented perpendicular to the cluster "surface" (i.e., the two Ag atoms)], fig. Sb shows the in-plane, doubly-occupied 0 2p7r lone pair, and fig. 5c displays the Ag-Ag bond. Fig. 6 shows the 2 B2 excited state, in which the radical orbital (fig. 6b) now is oriented parallel to the cluster surface, with the doubly-occupied 0 2p orbital perpendicular to the surface. Comparison of the Ag-Ag bonds in figs. 5c and 6c reveal that the Ag-Ag bond delocalizes towards the surface of the 2F site more in the 2 A 1 (or 2 'E) radical state than in the 2 B 2 (or 2 II) radical state, presumably because the 0 2p orbital of the 2 A 1 radical is only singly-occupied. This delocalization may explain why the 2 'E orientation is preferred over the 2 II orientation for the 2F site. The orbitnls for the "o-11" double-bonded" sto.te (nlso 2 A 1 ) o.re shown in fig. 7, where we see that the 7r bond (fig. 7b) is very ionic and strongly resembles the doubly-occupied oxygen p7r in the 2 A1 ground state (fig. ob). Hence, although this 2A 1 excited state is derived from a <1'7r double bond, the 7r bond is extremely ionic (with 1.67 electrons on the oxygen and only 0.33 on the cluster). This excited state is very high in energy (29.8 kcal/mol up), since the Ag-Ag bond has been broken -230- in the cluster. It is also destabilized because it must be orthogonal to the ground state, which has the same symmetry ( 2 Ai). The major difference between these two 2 Ai states is the location of the unpaired electron: the ground state has a radical electron on the oxygen, while the excited state has radical character on the cluster. In Table II we see that all of the low-lying states of oxygen pull 0.6 - 0. 7 electron off the cluster, leading to large dipole moments which follow the same trend as discussed above for Cl and H (i.e., the lF site has the largest dipole moment due to the larger distance over which charge is distributed, the 2F states have more moderate dipoles due to the negative image charge on the "bulk" Ag atom, and the 3F states have the smallest dipoles since they have the most compact charge distributions). The Ag d-band is largely unaffected by adsorption of 0, except for the lF site, where the large polarization of the s-electrons induces the d-band shift, as discussed for Cl. The two lowest energy configurations for 0 2 on Ag 3 are shown below, with the ground state having the parallel o; structure (denoted as 17 2 to indicate that both oxygen a.toms are bound to the surface), with the 17i peroxy (only one oxygen bound to the surface) lying 4.1 kcal/mol higher. o-o-:- Ag-Ag ~+ Ag 0 /o. Ag_l_Ag ~ Ag (7) Except for the 2F peroxy species, only high symmetry orientations of 0 2 on all three sites were considered (Table V). For the 2F site, we examined the following orientations: (i) 17 2 !-fold. o; is bound parallel to the 2F surface a.nd in the Aga plane (ground state); (ii) 17 1 perozy. One oxygen is bound to the surface with the other oxygen free [the -231- optimum c. symmetry geometry, assuming the attached oxygen binds above the Ag-Ag bond midpoint, has R-1(Ag 2 -0) = 2.24 A, R(0-0) = 1.33 A, and the outer oxygen displaced by 1. 7° degrees off the horizontal and toward the cluster) (4.1 kcal/mol up); (iii) TJ 1 end-on. All atoms are coplanar with one oxygen bound to the surface, and the 0-0 axis perpendicular to the Ag-Ag 2F site and along the C2 axis of the molecule (9.8 kcal/mol up); and (iv) TJ 2 %-fold .L bridge. The 0-0 axis is perpendicular to the Ag-Ag axis, with the oxygen atoms above and below the Ag 3 plane (the 0-0 bond midpoint is coplanar with Ag 3 and lies on the C2 axis of the molecule) (16.2 kcal/mol up). Two orientations were examined for each of the lF and 3F sites: (v) T/ 2 1-fold. All atoms are coplanar, with the 0-0 axis parallel to the two "bulk" Ag atoms and the 0-0 bond midpoint lies along the C2 axis, with the 0 atoms equidistant from the "surface" Ag a.tom (13.2 kcal/mol up); (vi) T/ 1 end-on 1-fold. All atoms are coplanar, with the 0-0 axis perpendicular to the "bulk" Ag atoms and along the C2 a.xis 0£ the molecule (25.9 kcal/mol up); (vii) TJ 2 3-fold. The 0-0 axis is parallel to the Ag 3 plane, lying directly above a perpendicular bisector 0£ the Ag3 triangle, with the 0-0 bond midpoint directly above the center of the cluster (26.4 kcal/mol up); and (viii) T/ 1 end-on 3-fold. The 0-0 axis is perpendicular to the Ag 3 plane and directly above the center of the cluster (29.7 kcal/mol up). The properties ,of geometries (i) - (viii) are listed in Table V. The ground state ( 2 A 2 ) has an 0-0 bond length and vibrational frequency of 1.32 A and 1264 cm- 1 , respectively, with a very large bond energy of 46.9 kcal/mol. The peroxy state, which has been proposed as a possible intermediate in the synthesis of EO, has a similar 0-0 bond length of 1.33 A but with a lower vibrational frequency of 921 cm- 1 and a smaller bond energy of 36.3 kcal/mol. These values differ sharply from observed binding energies for 0 2 on Ag (ranging from 11 - 13 kcal/mol, 14 •27 b depending on crystal face) and from the observed 0-0 vibrational frequency of 639 -232- cm- 1 on Ag(ll0). 26 •29 For all geometries examined, we find that the bond between 02 and Ag 3 is very ionic (e.g., 0. 70 electron is transferred from the cluster to 0 2 in the ground state). Thus Ag 3 0 2 is best thought of as AgtOi, with binding energies much larger than those found on extended surfaces because the localized positive charge on the cluster (not present on the surface) induces an anomalously strong ionic bond. The average 0-0 vibrational frequency of all the geometries listed in Table Vis 1036 cm- 1 , which is close to the 0-0 stretch in 02 (we= 1090 cm- 1 ). 30 The 0-0 bond length for 0 2 on Ag(llO) has recently been estimated from NEXAFS experiments to be 1.47±0.05 A, 31 very close to the bond length of 1.48 A in (CH 3)3CO-OC(CH 3)3, 32 but very much longer than the 1.32 - 1.39 A range which we find for 02 on Ag3. While our model clearly does not describe the states of dioxygen observed on extended Ag eur!a.cee, we a.t lea.et ma.y conclude tha.t 02 prefcre a. eymmetric configuration rather than 11 1 peroxy or end-on orientations. This is consistent with XPS data for 02 on Ag(llO), in which only one sharp 0 ls peak is observed, indicating that the 0 2 is lying parallel to the surface. 33 A recent XPS study of 0 2 on Ag(lll) indicates the oxygens may not be equivalent, 34 which could be interpreted either as 02 being tilted with respect to the surface (as in the 11 1 peroxy species) or as the 0 2 lying parallel to the surface but with each oxygen sitting over inequivalent sites. In order to successfully model the interaction of dioxygen with the Ag(llO) surface, at least four Ag atoms will be needed to mimic the 4-fold trough site. Future work will require examining 0 2 on a bent rhombus Ag 4 cluster in order to model the four-fold site of the (110) face. E. AgaOH Table VI displays properties for OH binding to the lF, 2F, and 3F sites on Ag 3. We find that OH prefers to bind in a linear fashion, rather than bent or tilted with respect to the surface. This is due to the ionic character of the Ag3-0H bond, -233- in which 0.6 - 0.8 electron (depending on the site) is transferred to OH from the cluster. Therefore the bonding in Ag 3 0H is best viewed as OH- interacting with Agt. The 2F site is again lowest in energy, with the bond energy of 78.9 kcal/mol providing an upper bound to the bond energy on an extended surface. The 3F site is 18.8 kcal/mol higher in energy, with the bond energy of 59.1 kcal/mol expected to reflect that of OH bound in a 3F site on a single crystal face of Ag. The lF site lies slightly higher in energy (20.2 kcal/mol up) and has a bond energy of 69.4 kcal/mol. As before, the relative energies are calculated at a different level than the bond energies (Section VI). Since the bond energies were calculated using CI methods and the relative energies shown in Table VI are from the lower level GVB-PP calculations, it may be that a more reliable ordering of states is obtainable from the rP.lative bond energies_ This would lead to the 3F site being 19.8 kcal/mol a.hove the 2F site (in good agreement with the GVB-PP result) and to the lF site being ouly 9.5 kcal/mol above the ground state. The GVB-PP energies !or lF and 3F are close in energy, so that the dynamic correlations included in a CI calculation could very well change the ordering of the excited states. The vibrational frequencies for AgaOH may be compared to values for OH adsorbed on Pt(lll), 35 where the 0-H stretch is 3480 cm- 1 and the Pt-0 stretch is 430 cm- 1 • The predicted Ag 3 -0 stretch in the lF site (445 cm- 1 ) is closest to the experimental value, while the 0-H stretch in the 3F site (3637 cm- 1 ) most closely resembles the experimental result. A strong intensity bending frequency is also observed on Pt, which was interpreted as a tilted OH group on the surface. However, if the OH group is linear and perpendicular to the surface, the bending (or frustrated rotational) mode is dipole allowed, so that our findings are still consistent with the observations on Pt(lll). Since OH is valence isoelectronic with Cl, and Cl is known to sit in 3F sites on Ag{lll), we suggest that OH also adsorbs in 3F sites. The binding energy of OH to the 3F site (59 kcal/mol) along with the predicted binding energy of Oad (79 -234- kcal/mol) may then be used to estimate the thermodynamics of hydroxyl disproportionation to H2 0 ad + 0 ad. Assuming a binding energy for water in the presence of 0 on Ag(llO) of 15 kcal/mol (H 20 desorbs at 240°K under such conditions 36 ) and assuming that the 0-H bond strength in adsorbed water is the same as the 0-H bond strength in adsorbed OH (vide infra), we estimate that hydroxyl disproportionation is endothermic by "'24 kcal/mol. This is in good agreement with recent work by Madix and co-workers who followed the kinetics of hydroxyl disproportionation on oxygen-covered Ag(llO) and found an activation energy of 22.2..L0.3 kcal/mol. 37 Thus our binding energy for the 3F site of 59.1 kcal/mol provides a good estimate of the true binding energy of OH to Ag. Calculations on ethylene interacting with neutral Ag3 yielded only repulsive potential curves. This is consistent with the low probability for adsorption of ethylene on clean Ag surfaces. 38 On oxygen-precovered surfaces, however, the more electrophilic Ag atoms readily adsorb C 2 H4 •38 As a model for these electrophilic sites, we have examined five high-symmetry orientations of ethylene bound to Agt, shown schematically in fig. 8. They are listed in terms of decreasing energy, with the 3-fold bridge being the least-favored and with both 1-fold sites being nearly degenerate in energy, so that the ground state should have essentially no barrier to rotation about the Ag-C2 H4 bond. Table VII shows the properties predicted for these five orientations, with the primary result being the prediction of an 8. 7 kcal/mol bond energy for ethylene in the 1-fold site. This is in excellent agreement with the experimental heat of adsorption of ""10 kcal/mol for C2H4 adsorption on an oxygen precovered Ag(llO) surface. 38 (It is known that ethylene binds directly to Ag, since no change in the Ag-0 stretch is observed in the EEL spectrum; thus this is heat of adsorption for ethylene on Ag, not ethylene on Oad·) The good agreement between experiment and theory for the Ag-(C 2 H 4 ) bond energy suggests that C 2 H 4 may prefer to bind -235- in 1-fold sites on the Ag surface (as found for the cluster). The bond lengths for the five adsorption sites increase for less favored binding sites, with the vibrational frequencies tracking the bond lengths consistently. Only a 71"-bonded form of ethylene was considered, since EEL spectra for C 2 H4 and C 2 D 4 on Ag(llO) reveal no change in the out-of-plane bending vibrations when compared to the gas phase values. This indicates that no substantial rehybrid.ization occurs upon adsorption. 38 " In sum, the predictiunis of thiis :section are mostly in good agreement with experimental data, lending credence to the use of a metal cluster to represent the localized interactions present on an extended metal surface. IV. Implications for Olefin Epoxidation In this section we will a.<l<lress the major reaction steps involved in the par- tial oxidation of ole:fins, predicting both the thermodynamic feasibility and the qualitative nature of each reaction. We will develop a perspective which allows a reinterpretation of a series of experimental studies, leading to a global view of the types of oxygen which exist on the surface, how promoters work to stabilize the active form of oxygen, and how decomposition pathways occur. Thermodynamic.s of Olefin O:r:idation on Silver From the experimental and theoretical heats of adsorption of oxygen, we conclude that 02 dissociation is facile, proceeding through a chemisorbed 02 species (heat of adsorption ,...., 10 kcal/mol 27 b) which decomposes above 170°K to form a monatomic oxide. 26 From the results of Section III.C, we predict that two neardegenerate states of oxygen can populate high coordination sites on Ag surfaces. One we refer to as "di-u" bonding, with both singly-occupied 2p-orbitals on 0 ( 3 P) spin-paired to the surface, forming two u bonds. The other we refer to as " 2 ~ radical" bonding, to indicate the presence of a singly-occupied P" orbital on o-. -236- ~ u / di-a- (8) ~//~//# I The di-u species is predicted to have a short bond length (R..L = 1.37 A), a vibrational frequency of 412 cm- 1 , and a binding energy of 77.8 kcal/mo!. Since all of the electrons of the di-u oxygen are intimately involved with the surface, we expect this species to be relatively inert and it should not be active for the formation oi EO. In contrast, the 2 :E radical species is expected to have a much longer bond length (R_.L = 1.80 A), a smaller Ag-0 vibrational frequency (299 cm- 1 ), but essentially the same binding energy to the surface (78.7 kcal/mol). We propose that the radical character of the 2 :E oxygen nominates this species as the active oxidizing agent for EO formation. The oxygen radical orbital can easily break into the C=C 71" bond of an olefin, forming a radical center on the outer olefinic carbon, followed by rapid collapse to the epoxide. (The extra electron on Oad i:s tran:sferred to the Buda.ct: upon reaction, i.e., the surface is reduced when the olefin is oxidized). (9) The mechanism shown in eq. 9 implies a loss of stereochemistry at one of the carbon atoms. In fact, stereospeci:fic ethylene-1,2-d 2 does randomize (although not 1003) when oxidized to EO under actual catalytic reaction 1conditions, 39 lending support to the above mechanism. The production of epoxide is predicted to be thermodynamically favorable for both ethylene and propylene ( D..Hrxn = -6 and -8 kcal/mol for C 2 H4 and C 3 H6, respectively), where we have used the theoretical -237- value for the Ag-0 binding energy (79 kcal/mol) in conjunction with the heats of formation of the olefins (6.H/, 298 12.5 kcal/mol for C2H4 and 4.9 kcal/mol for C 3 H6), epoxides [6.H/, 298 = -12.6 kcal/mol for EO and -22.6 kcal/mol for propylene oxide (PO)], and oxygen atom (6.H/, 208 = 59.6 kcal/mol) to predict the heats of reaction. 40 Although the reaction is thermodynamically fovora.blc, it is well-known tha.t PO is produced in yields ranging from 0 - 53 from propene over Ag catalysts. 41 PO is formed in such small amounts due to the competing reaction of total combustion to C0 2 and H 2 0. The rate-limiting step for total oxidation is presumably the first hydrogen atom abstraction from the olefin to form 0 Had on the surface, since the subsequent olefinic radical should be highly reactive and decompose rapidly. Hydrogen abstraction from ethylene is endothermic by "'28 kcal/mol, inhibiting combustion. 42 (10) For propylene, however, the hydrogen abstraction reaction is predicted to be exothermic by "' 3 kcal/mol. 43 Combustion of propylene competes significantly with partial oxidation, while ethylene combustion is unfavorable. The difference in energetics is merely due to the differenr.P. in C-H bond strengths for the two olenns. In the case of ethylene, the vinylic C-H bond strength is extremely strong, recently determined by Lee and co-wurkers42 tu be D 0 = 116. 7±1.2 kcal/mol (D298 = 118 kcal/mol 42 ), whereas the allylic C-H bond is much weaker (D2 98 = 87 kcal/mol 43 ). The difference in C-H bond strengths may be understood in terms of the stability of the subsequent radical formed: in the case of C 2H4 , a highly unstable vinyl radical would be formed, while for C 3 H6, a resonance-stabilized allyl radical is formed, as shown below. -238- (11) Thus any olefin with allylic hydrogens will combust; this explains why the epoxidation reaction over Ag is specific to ethylene. It would be interesting to know whether blocking the allylic sites, such as in styrene or t-butylethylene, leads to greater selectivity. Certainly such experiments would help determine whether the hydrogen abstraction occurs preferentially from the olefin or whether subsequent intermediates in the partial oxidation reaction are more susceptible to combustion. After hydrogen abstraction from the olefin occurs to form surface-bound hydroxyls (Had is not formed, since the incipient Ag-H bond is weaker than the incipient 0-H bond), water is produced as one of the final products of combustion. As discussed in Section III.E, the energetics for the formation of H20 from surfacebound hydroxyl groups can be predicted from the theoretical values for the binding energies of OH (59 kcal/mo!) and 0 (79 kcal/mo!) and an estimate for the heat of adsorption of H 2 0 on Ag("" 15 kcal/mol). 36 We assumed that the 0-H bond strengths do not change significantly going from H 20 to OHad· This assumption is reasonable, since the average bond strength in water is 110.8 kcal/mol40 and the bond strength in OH- (similar to adsorbed OH, as discussed in Section III.E) is 110.6 kcal/mol. 30 These values lead to a predicted endothermicity of 24 kcal/mol to disproportionate two surface-bound hydroxyls to one adsorbed oxygen atom and one adsorbed molecule of H20. This is in good agreement with the activation energy of 22.2±0.3 kcal/mo! observed for OH disproportionation on Ag(ll0). 37 Identification of the Active Ozygen As discussed in the Introduction, many investigations have been carried out to try to determine the nature of the oxygen which produces epoxide, in order to find 239- ways to optimize its concentration. Van Santen's recent labelling study involving an Ag surface pre-covered with 16 0 ad and exposed to a gaseous mixture of C 2 H 4 and 18 0 2 provides compelling evidence that adsorbed oxygen atoms are responsible for the production of EO, since initially only 16 0-labeled EO is formed. 13 1 However, Campbell has shown that the rate of EO production is uncorrelated with the overall concentration of atomic oxygen, a conclusion based on the following two focts: (i) for low coverages of oxygen ( 80 :::; 0.5), the probability for dissociative adsorption is about two orders of magnitude smaller on Ag(lll) than on Ag(llO) at 490°K. 27 b Thus the steady-state coverage of Oad is a factor "" 18 smaller on Ag(lll) than on Ag(llO), while the activities for EO production on the two surfaces differ only by a factor of two; 12 c and (ii) coadsorption of Cl and 0 on Ag(llO) and Ag(lll) produced EO at rates dependent on chlorine coverage but independent of the steady-st.Rte c.nnc.Pnt.rat.ion of Oad. 7a-c Since the rate was found tu Le imlqJt:llUt:ut of the overall coverage of monatomic oxygen, Campbell concluded that diatomic oxygen must be the active precursor to EO. Herein we present a new interpretation of the kinetic trends discussed above, in terms of atomic oxygen as the active species for epoxidation. The difference in steady-state coverages of Oad between the (110) and (111) faces of Ag is due to the presence of more than one binding site for 0 on Ag(llO). While the close-packed (111) surface has only 3-fold binding sites available (assuming the energy differences between the hep and fee sites are negligible), the corrugated (110) surface has two diJtinetly different binding 3ite3 with undoubtedly different tJtabilities. These two sites are shown in fig. 9, in which fig. 9a depicts the 4-fold site in the bottom of troughs (between the first and second layer Ag atoms), while fig. 9b displays the 3-fold site located on the side of the troughs. This 3-fold site is analogous to the 3-fold site present on the (111) plane of Ag. At oxygen coverages below 0.5, p(n x 1) (n decreasing continuously from 7 to -240- 2 as the oxygen coverage increases) low-energy electron diffraction (LEED) patterns form, which have been interpreted as oxygens residing in the 4-fold sites of the troughs. 6 •44 At a pressure of 50 torr and a temperature of 485°K, a new high coverage (Bo = 0.67) form of oxygen has been recently observed on the (110) surface, exhibiting a c(6x2) LEED pattern. 27 " This high coverage form was shown to be reactive for CO oxidation to C02, but once the oxygen coverage dropped to 0.5 [p(2xl) LEED pattern], the reaction probability for CO oxidation dropped precipitously. Several conclusions may be drawn from these observations: (i) the 4-fold site on Ag(llO) (fig. 9a) is filled first and thus is probably the most stable site for oxygen adatoms; (ii) higher dosages of oxygen allow another site to fill which we interpret to be the 3-fold site (fig. 9b ); and (iii) the 4-fold site is less reactive than the 3-fold site as indicated by the CO titration studies.27a Thus the difference in coverage of Oad between Ag(llO) and Ag(lll) is due to the fact that the unreactive 4-fold sites on Ag(llO) fill first, followed by filling the reactive 3-fold sites on Ag(llO). Ag(lll) only has 3-fold sites and therefore the activity per adsorbed oxygen atom is higher than that found for Ag(llO). We believe that the crucial concentration is not the overall concentration of Oad but rather the concentration of Oad in 3-fold sites, and that perhaps these latter concentrations are similar on both crystal faces, resulting in similar activities for the formation of EO. We predict 011 the basis of the present ab initio study that the oxygen species in the 3-fold site has the 2 !J radical o- character shown in eq. 8, since this species is predicted to be the most stable (by 1 kcal/mo!) type of oxygen in the 3-fold site of Ag 3 • This radical oxygen is set up to react with olefinic substrates, as indicated in eq. 9. The oxygen in the 4-fold site is expected to have di-u-type bonding (eq. 8), resulting in an unreactive oxide, since all of the oxygen electrons are tied up with the -241surface. The oxygens in the 4-fold hollows of Ag(llO) have binding energies of,...., 82 kcal/mol, whereas the 3-fold oxygens on Ag(lll) are bound by ,...., 80 kcal/mol. 27 b Thus the di-CT bonding in the 4-fold site is slightly stronger than the di-CT bonding in the 3-fold site of Ag3 (77.8 kcal/mol). The o- radical in the 3-fold site of Ag 3 has a binding energy of 78. 7 kcal/mol, in excellent agreement with the stability found for oxygen in the 3-fold sites on Ag(lll) and Ag(ll0). 27 In sum, a key to increasing the activity of the catalyst is to saturate the 4-fold, unreactive sites, and then maximize the oxygen concentration in the reactive 3-fold sites. Consistent with this idea is the observation that a 1:1 ratio of 0 /Ag is needed to obtain EO on Ag powders; 13 f i.e., a high coverage of oxygen is necessary to form the active oxygen species. The Role of Promotera Chlorine is the prototypical promoter for a reaction in which other electronegative elements also act to increase the activity and selectivity to EO formation. 3 - 5 Campbell and Koel have observed that high coverages of Cl (Om 2:: 0.4) inhibit the formation of C0 2 •7 b They have interpreted this result as an ensemble effect, where the number of open surface sites required for total combustion is presumed higher than the number of sites necessary for epoxidation. While the relative site requirements may indeed differ, we believe there is significant evidence that it is the apecific aitea blocked by chlorine which increaae the activity of the catalyat. In particular, a p(2xl) structure is observed by LEED above Om = 0.4 on Ag(llO), coinciding with the dramatic increase in reactivity towards ethylene. A comparison of the ab initio binding energies of Cl versus 0 indicate (Tables III and IV) that Cl may be slightly more stable than O, with predicted binding energies of 79.7 kcal/mol for Cl and and 78.7 kcal/mo! for 0 in 3-fold sites. Thus Cl may displace O, binding to the most stable site on the (110) surface (the 4-fold site in the troughs). The p(2xl)-Cl LEED pattern is consistent with this analysis, since the p(2xl)-O LEED pattern is interpreted as binding in those 4-fold sites. Furthermore, Winograd and co-workers used angle-resolved secondary ion mass -242- spectrometry (SIMS) to show that as the Cl coverage increases, the surface-Cl distance decreases significantly, indicating that Cl probably falls into the troughs (occupying the 4-fold sites) at high coverage. 45 Our interpretation of Campbell and Koel's results is that Cl saturates the 4fold hollows, forcing 0 to occupy the slightly less stable but reactive 3-fold sites. Thus the role of Cl (or S, Se, Br, etc.) is simply to block the unreactive 4-fold hollows to increase the population of reactive oxygen species in the 3-fold sites. Salts of alkali metals and alkaline earths are also known promoters of the EO reaction. 3- 5 Cesium is one of the most common dopants and has been studied on single crystals by both Lambert and Campbell. 7 d,e,g,h Thermal desorption and LEED studies of the coadsorption of Cs and 0 on Ag(lll) have revealed that aggregates are formed with the approximate stoichiometry Cs0 3. The promotional effect of Cs was attributed in this work by Campbel1 7 d to be exactly analogous to the role he proposed for Cl: that of a site-blocker such that C0 2 formation was suppressed. As in the case of Cl, we offer a new interpretation of the role of Cs, based on our results for the interaction of ethylene with Ag 3 and Agt. Since Cs (and the other electropositive promoters) are added as salts, they are likely to be present as Cs+. Aggregates such as Cs+o 3 should be favorable, since the oxygen adatoms are partially negatively charged (Section III.C). Ethylene binds only weakly to the clean Ag surface, 38 consistent with our results of a repulsive interaction with the neutral Ag3 cluster (Section III.F). However, we find that the positively-charged Ag 3 cluster does bind ethylene with a bond energy of,...., 9 kcal/mol. We propose that Cs+ sits on top of the oxygens present in the 4-fold trough sites (since they may be more negatively charged than the radical oxygens in the 3-fold sites), and then helps to direct olefins down to the Ag surface via a Lewis acid-Lewis base interaction, increasing the overall sticking probability for ethylene to Ag. If ethylene adsorption occurs on Cs+ in the troughs, nearby oxygen radicals in the 3-fold sites on the sides of the troughs may be more readily accessible to the ethylene, increasing the rate -243- of reaction, as shown schematically below for a generic surface. (13) In this section we have addressed many of the issues involved in the olefin epoxidation reaction as catalyzed by silver. In the next section we summarize our findings. V. Conclusions Ab initio GVB-CI calculations of the interaction of various adsorbates on Ag 3 indicate the following: (i) all adsorbates except ethylene (which prefers 1-fold coordination) favor binding to the 2-fold, in-plane site of the cluster, with bond energies much stronger than those expected for adsorbate surface bond energies. The unpaired electron on this cluster helps to preserve the Ag-Ag bonds (bulk diamagnetic Ag should incur some Ag-Ag bond weakening upon adsorption); and {ii) adsorbate binding energies to the 3-fold site of the cluster provide realistic estimates of the actual binding energies on an extended surface, with values reported for H {29 kcal/mol as a lower bound), Cl {80 kcal/mo!), 0 (79 kcal/mol), 02 (17 kcal/mol as an upper bound), and OH {59 kcal/mol). The binding energy of ethylene to Agt waR found to be 9 kcal/mol in the 1-fold site. The values for C2 H4 and 0 are in excellent agreement with experiment. Implications from this work for understanding the detailed mechanistic aspects of the Ag-catalyzed olefin epoxidation reaction are as follows: -244- (iii) two near-degenerate states of Oad are predicted to have drastically different properties and reactivity, with a 2 :E radical o- species predicted to be the active precursor to epoxide. This suggests that the control of cataly"t activity iJ directly related to the relative population" of the reactive oxygen radical and the inactive, di-u-bound ozygen; (iv) these two oxygen species are used in Section IV to propose new interpretations of the trends observed in single crystal studies of EO formation, with the result tha.t the ra.dica.1 oxygen i::s predicted to re::side on 3-fold ::sites on both Ag(lll) and Ag(llO), while the unreactive di-u oxygen is expected to prefer the 4-fold binding site in the valleys of the (110) surface; (v) the role of electronegative promoters such as Cl is attributed to blocking the 4-fold sites, forcing the formation of the radical oxygen, while the role of electropositive promoters is to enhance the probability for adsorption of ethylene; (vi) epoxide formation is exothermic for both ethylene and propylene, but olefins larger than ethylene combust due to the ease with which allylic hydrogens may be abstracted from the olefin to form surface-bound hydroxyl groups. This disproportionation of OHad to adsorbed 0 and H 2 0 is predicted to be endothermic by 24 kcal/mol, in good agreement with experiment; (vii) the combustion of ethylene may actually occur after EO is formed, since the primary C-H bonds in EO are weaker than the vinylic C-H bonds of ethylene; and, lastly, (viii) we suggest that the reason Ag is the only transition metal which successfully catalyzes the selective oxidation of ethylene is because ethylene dehydrogenates rapidly on most other transition metal surfaces. 46 Indeed, the low affinity of the Ag surface for ethylene and the low binding energy of H to Ag must play a significant role in inhibiting ethylene decomposition on Ag. -245- VI. Calculational Details BaJiJ SetJ The eleven valence electrons of Ag (4d10 5s 1 ) were treated explicitly within the (3s3p4d/3s2p2d) gaussian basis of Hay and Wadt, with the core electrons represented by an effective core potentia.1.. 47 The Dunning valence double-( cont.cactiuu:s 48 of the Huzinaga gaussian primitive bases 49 for hydrogen ( 4s; exponents scaled by 1.2), oxygen (9s5p ), and carbon (9s5p) were used, with a 3d-polarization function added to oxygen ((d = 0.95). For Ag 3H, the more extensive triple-( contraction of Huzinaga's 6s primitive basis 49 along with a 2p-polarization function ((P = 0.6) were used on H. Cl was described using the SHC effective core potential and valence double-( basis set of Rappe et al., 50 along with one 3d polarization function ((d = 0.6) and one set of sand p diffuse functions((• = (P = 0.49). For Ag 3 0 and Ag 3 OH, one set of s and p diffuse functions 51 was added to the 0 basis described above((• = 0.088 and (P = 0.60) and the (6s/3s) basis used on Hin Ag 3H was also used on Ag30H. GVB and CCCI Calculationa All geometries and vibrational frequencies were optimized for all molecules [with the Ag3 cluster constrained to be an equilateral triangle with side length 2.89A (the nearest neighbor value in bulk Ag 52 ) and the ethylene molecular geometry fixed at the experimental geometry 53 ] at the GVB-PP level (two pairs were correlated for Ag3H, Ag3Cl, Ag30H, Ag 3 0:,a, while three bond pa.ir:s were correlated for 0 a.ml C2H 4 bound to Ag3). 54 The relative energies reported in each table were calculated at the GVB-PP level. The bond energies for H, Cl, and the doubly-bonded states of 0 were calculated using the correlation-consistent configuration interaction (CCCI) approach, 55 which allows full correlation (single and double excitations) from the bond that is breaking, along with single excitations from all valence orbitals to all unoccupied orbitals, to account for orbital shape changes important during bond breakage. These excitations are allowed from the RCI reference states, in which -246- all three occupations of two electrons in the two orbitals of each GVB pa.ir are included. The doubly-bonded states of Ag 30 dissociate diabatically to the 4 A 2 excited state of Ag3. We calculate the diabatic bond energy, then subtract the 4 A 2 - 2 A 1 energy splitting in Ag 3 [30.1 kcal/mol at the GVB(l/2)PP level] to obtain the adiabatic bond energy. The bond energies for the ionic radical states of 0 on Ag 3 were determined indirectly by subtracting or adding the GVB-PP energy difference between the radical state and the double-bonded state for each adsite. The binding energies for 02 to Ag3 were determ..ined using a. va.ltmce lc:::vd CI to describe the resonance in the 71" orbitals of 02. Since 02 on Ag 3 is best described as 02, we calculated the ionic bond energy, then subtracted the theoretical IP(Ag 3) = 4.18 eV and added the experimental EA( 02) = 0.44 eV30 to obtain a covalent bond energy. The valence level CI consisted of an RCI within the Ag-Ag and 0-0 u bond pairs simultaneous with both configurations of the o; three-electron 71" system ( 71"~ Tr! and 71"! 71";). The bond energies for Ag3 0 H were calculated by allowing all single and double excitations out of the 0 s and p lone pairs from the RCI configurations for the 0-H and Ag-Ag GVB bond pairs, dissociating to the ionic limit, followed by subtracting the cluster IP and adding EA(OH) = 1.83 eV. 56 The ethylene binding energies to Agt were calculating at the GVB(3/6)-PP level (Ag-Ag and the two C-C bonds were correlated as GVB pairs). Acknowledgments. This work was supported by the National Science Foundation (Grant No. CHE83-18041) and the Shell Companies Foundation. EAC acknowledges a National Science Foundation predoctoral fellowship (1982-1985), a research grant award from the International Precious Metals Institute and Gemini Industries (1985-1986), and a. SOHIO fellowship in Catalysis (1987). -247- References (1) A. M. Brownstein, "Trends in Petroleum Technology" (Petroleum Publishing Co., Tulsa, 1976). (2) (a) R. P. Nielsen and J. H. LaRochelle, Shell Oil Co., U. S. Patent 3 962 136; (b) M. M. Bhasin, P. C. Ellgen and C. D. Hendrix, Union Carbide, U. K. Patent Application GB 2 043 481 A; (c) W.-D. Mross, Catal. Rev. - Sci. Eng. 25 (1983) 591. (3) H. H. Voge and C. R. Adams, Adv. Catal. 17 (1967) 1515. (4) X. E. Verykios, F. P. Stein and R. W. Coughlin, Catal. Rev. - Sci. Eng. 22 (1980) 197. (5) W. M. H. Sachtler, C. Backx and R. A. van Santen, Catal. Rev. - Sci. Eng. 23 (1981) 127. (6) M. Barteau and R. J. Madix, in: "The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis", Vol. 4, Eds. D. A. King and D. P. Woodruff (Elsevier, Amsterdam, 1982), Ch. 4. (7) (a) C. T. Campbell and M. T. Paffett, Appl. Surf. Sci. 19 (1984) 28; (b) C. T. Campbell and B. E. Koel, J. Catal. 92 (1985) 272; (c) C. T. Campbell, J. Catal. 99 (1986) 28; (d) C. T. Campbell, J. Phys. Chem. 89 (1985) 5789; (e) C. T. Campbell and K. A. Daube, Surf. Sci., in press; (f) C. T. Campbell, in: "Catalyst Characterization Science", Eds. M. L. Deviney and J. L. Gland (American Chemical Society, Washington, D. C., 1985), ACS Symposium Series, No. 288, p. 210; (g) R. B. Grant and R. M. Lambert, J. Catal. 93 (1985) 92; (h) R. B. Grant and R. M. Lambert, Langmuir 1 (1985) 29. (8) (a) A. Ayame, N. Takeno, and H. Kanoh, J. Chem. Soc., Chem. Comm. (1982) 617; (b) A. Ayame, T. Kimura, M. Yamaguchi, H. Miura, N. Takeno, H. Kanoh, I. Toyoshima, J. Catal. 79 (1983) 233. (9) W. Herzog, Ber. Bunsenges. Phys. Chem. 74 (1970) 216. (10) R. B. Clarkson and A. C. Cirillo, J. Catal. 33 (1974) 392. -248- (11) P. A. Kilty, N. C. Rol, and W. H. M. Sachtler, Proc. 5th Int. Cong. Cata!., Palm Beach (1972) paper 64. (12) (a) C. T. Campbell and M. T. Paffett, Surface Sci. 139 (1984) 396; (b) C. T. Campbell, J. Vac. Sci. Technol. A2 (1984) 1024; (c) C. T. Campbell, J. Cata!. 94 (1985) 436. (13) (a) E. L. Force and A. T. Bell, J. Cata!. 38 (1975) 440; (b) E. L. Force and A. T. Bell, J. Cata!. 40 (1975) 356; (c) C. Bach:, J. Moolhuysen, P. Geenen, R. A. van Santen, J. Cata!. 72 (1981) 364; ( d) R. B. Grant and R. M. Lambert, J. Chem. Soc., Chem. Comm. (1983) 662; (e) R. B. Grant and R. M. Lambert, J. Cata.l. 92 (1985) 364; (f) R. A. van Sa.nten and C. P. M. de Groot, J. Catal. 98 (1986) 530. (14) M. A. Ba.rteau and R. J. Madix, Surface Sci. 97 (1980) 101. (15) R. B. Grant and R. M. Lambert, J. Ca.ta!., submitted for publication. (16) (a) M. H. McAdon and W. A. Goddard III, J. Non-Cryst. Solids 75 (1985) 149; (b) M. H. McAdon and W. A. Goddard III, Phys. Rev. Lett. 55 (1985) 2563; (c) M. H. McAdon and W. A. Goddard III, J. Phys. Chem., in press. (17) Distortion irom D3h symmetry lea.ds to a.n obtu5e-a..ugle geo111etry for the 2 B2 state and an acute-angle geometry for the 2 A 1 state of Ag 3 • ESR studies have yielded conflicting results, with the 2 B 2 state lower in a C 6 D 6 matrix [J. A. Howard, K. F. Preston, and B. Mile, J. Am. Chem. Soc. 103 (1981) 6226], while the 2 A 1 state prevails in an N2 matrix [K. Kernisant, G. A. Thompson, and D. M. Lindsay, J. Chem. Phys. 82 (1985) 4739], indicating that all three structures a.re very close in energy. [The equilateral triangle is the low-lying saddle point (,...,, 400 cm- 1 ) between these two near-degenerate, C 2 v symmetry structures.] For a recent theoretical study of this distortion, see S. P. Walch, J. Chem. Phys. 85 (1986) 5900. (18) M. A. Tolbert and J. L. Beauchamp, J. Phys. Chem. 90 (1986) 5015. (19) "CRC Handbook of Chemistry and Physics", R. C. Weast, Ed. (CRC Press, Boca Raton, 1981), E-79. -249- (20) (a,) M. Balooch, M. J. Cardillo, D . .H.. Miller, and R. E. Stickney, Surface Sci. 46 (1974) 358; (b) A.G. Sault, R. J. Madix, and C. T. Campbell, Surface Sci. 169 (1986) 347. (21) J. Flad, G. Igel-Mann, M. Doig, H. Preuss and H. Stoll, Surface Sci. 163 (1985) 285. (22) G. M. Lambie, R. S. Brooks, S. Ferrer, and D. A. King, Phys. Rev. B15 34 (1986) 2975. (23) (a.) M. Bowker and K. C. Waugh, Surface Sci. 134 (1983) 639; (b) D. E. Taylor, E. D. Williams, and R. L. Park, preprint. (24) T. Zeng-ju, Z. Kai-ming, and X. Xi-de, Surface Sci. 163 (1985) 1. (25) E. A. Carter and W. A. Goddard III, unpublished results. (26) C. Backx, C. P. M. de Groot, and P. Biloen, Surface Sci. 104 (1981) 300. (27) (a) C. T. Campbell and M. T. Paffett, Surface Sci. 143 (1984) 517; (b) C. T. Campbell, Surface Sci. 157 (1985) 43. (28) R. L. Martin and P. J. Hay, Surface Sci. 130 (1983) L283. (29) B. A. Sexton and R. J. Madix, Chem. Phys. Lett. 76 (1980) 294. (30) K. P. Huber and G. Herzberg, "Constants of Diatomic Molecules" (Van Nostrand, New York, 1979). (31) D. A. Outka, J. Stohr, W. Jark, P. Stevens, J. Solomon, and R. J. Madix, Phys. Rev. B15, in press. (32) J. Marsden, L. S. Bartell, and P. Diodati, J. Mol. Struct. 39 (1977) 253. (33) K. C. Prince, G. Paolucci, and A. M. Bradshaw, Surface Sci. 175 (1986) 101. (34) C. T. Campbell, Surface Sci. 173 (1986) 1641. (35) P. R. Norton, in: "The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis", Vol. 4, Eds. D. A. King and D. P. Woodruff (Elsevier, Amsterdam, 1982), Ch. 2. (36) (a) E. J. Stuve and R. J. Madix, Surface Sci. 111 (1981) 11; (b) I. Pockrand, Surface Sci. 122 (1982) L569. (37) S. W. Jorgensen, A. G. Sault, and R. J. Madix, Langmuir 1 (1985) 526. -250- (38) (a) C. Backx, C. P. M. de Groot, and P . .l:Eloen, Appl. Surface Sci. 6 (1980) 256; (b) C. Backx, C. P. M. de Groot, P. Biloen, and W. M. H. Sachtler, Surface Sci. 128 (1983) 81. (39) (a) A. L. Larrabee and R. L. Kuczkowski, J. Catal. 52 (1978) 72; (b) N. W. Cant and W. K. Hall, J. Catal. 52 (1978) 81. (40) !::i..H/, 298 are taken from "JAN AF Thermochemical Tables", J. Phys. Chem. Ref. Data 14 Suppl. 1 (1985) and from S. W. Benson, "Thermochemical Kinetics" (Wiley, New York, 1976). (41) M. A. Barteau and R. J. Mad.ix, J. Am. Chem. Soc. 105 (1983) 344, and references therein. (42) 6.Hrxn = +27.6 kcal/mo! for hydrogen abstraction from ethylene is derived from D2 98 {C2Ha-H) = 118.2 kcal/mol [obtained by correcting D 0 by 1.5 kcal/mol (~RT) for finite temperature, where Dg = 116. 7±1.2 kcal/mol is from H. Shi- roma.ru, Y. Achiba., K. Kimura., and Y. T. Lee, J. Phys. Chem. 91 (1987) 17)), D~ 98 (0-H-) = 110.6 kco.l/mol (obtained from temperature correcting D 0 from ref. 30 by 0.9 kcal/mol (JRT)], and the theoretically-predicted binding energies of OH and 0 to the Ag surface (59 and 79 kcal/mol). ( 43) 6.Hrxn = -2.8 kcal/mo! is derived from the same quantities listed in ref. 42 except that the C-H bond energy in propene of 87.8 kcal/mol was obtained from ref. 40. ( 44) H. A. Engelhardt and D. Menzel, Surface Sci. 57 (1976) 591. (45) D. W. Moon, R. J. Bleiler, and N. Winograd, J. Chem. Phys. 85 (1986) 1097. (46) M. M. Hills, J.E. Parmeter, C. B. Mullins, and W. H. Weinberg, J. Am. Chem. Soc. 108 (1986) 3554, and references therein. (47) P. J. Hay and W.R. Wadt, J. Chem. Phys. 82 (1985) 270. (48) T. H. Dunning, J. Chem. Phys. 53 (1970) 2823. (49) S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. (50) A. K. Rappe, T. A. Smedley, and W. A. Goddard III, J. Phys. Chem. 85 (1981) 1662. Note that the second p exponent for the Cl basis listed in Table -251- I of this reference should read 0.641, not 0.691, and the s orbital energy for Cl in Table IV of this reference should read -1.0675, not -0.1068. (51) R. A. Bair and W. A. Goddard III, submitted for publication. (52) N. W. Ashcroft and N. David Mermin, "Solid State Physics" (Holt, Rinehart, and Winston, Philadelphia, 1976). (53) M. D. Harmony, V. W. Laurie, R. L. Kuczkowi;ki., R. H. Sc.hwendeman 1 D A. Ramsay, F. J. Lovas, W. J. Lafferty, and A. G. Maki, J. Phys. Chem. Ref. Dato. 8 (1979) 619. (54) (a) W. J. Hunt, T. H. Dunning, Jr., and W. A. Goddard III, Chem. Phys. Lett. 3 (1969) 606; W. A. Goddard III, T. H. Dunning, Jr., and W. J. Hunt, Chem. Phys. Lett. 4 (1969) 231; W. J. Hunt, W. A. Goddard III, and T. H. Dunning, Jr., Chem. Phys. Lett. 6, (1970) 147; W. J. Hunt, P. J. Hay, and W. A. Goddard III, J. Chem. Phys. 57 (1972) 738; F. W. Bobrowicz and W. A. Goddard III in "Methods of Electronic Structure Theory", H. F. Schaefer, P.d., (PlP.num, New York, 1977) pp 79-127; (b) L. G. Yaffe and W. A. Goddard III, Phys. Rev. A 13 (1976) 1682. (55) E. A. Carter and W. A. Goddard III, Chem. Phys. Lett., submitted for publication. (56) P. S. Drzaic, J. Marks, and J. I. Brauman in: "Gas Phase Ion Chemistry", Vol. 3 (Academic, Orlando, 1984) Ch. 21. -252- Table I. Properties of Ag 3 H as a function of adsite and electronic state. site relative energyb (kcal/mol) Rl.,e(A)c w1 (Aga-H) (cm- 1 ) D. (kcal/ mol)" B2 1-fold 41.3 1.75 1411 l A' 3-fold 1.63 482 a A" aB2 3-fold 2-fold 39.1 37.4 21.4 21.6 19.5 1.19 1.21 809 1012 28.5 42.8 1 Ai 1-fold 1357 50.8 A1 2-fold 4.4 0.0 1.77 1 1.41 913 56.8 state" 3 a) Electronic state symmetry of the GVB wavefunction. b) GVB(2/4)-PP energy relative to the ground state total en~rgy of -112.82983 hartrees (1 hartree 627.5096 kcal/mo! 27.21162 eV). c) R.L the perpendicular distance from H to the center of the cluster site (e.g., to the Ag-Ag bond midpoint for the 2-fold site, to the Ag atom for the 1-fold site, and to the center of the triangle for the 3-fol<l 11ite). d) Adiabatic bond energies from CCCI calculations (Section VI). = = = Table II. Charge transfe1 to atomic adsorbate X on AS3, as a function of adsite and bond character. -- state/bond x character• H 1 Jl1 c excess charge" dipole site x Agsurrace Agbulk moment (de bye)" d-band shift (e V)" -0.22 0.08 +0.10 7.60 +0.09 -0.W 2.06 -0.39 .. 2-fold -0.30 +0.26 H 1-fold -0.23 +0.03 H lA' 3-fold -0.39 +0.13 Cl t Aic 2-fold -0.61 +0.36 -0.12 5.19 -O.:J6 Cl .. 1-fold -0.64 +0.38 +0.13 12.50 -0.80 Cl 1A1 3-fold -0.5~ +0.18 - 3.61 -0.44 0 2 1: radicalc 2-fold -0.70 +0.40 -0.09 4.14 -0.(]5 0 2 11 ra.dical 2-fold -0.69 +0.41 -0.13 3.95 -0.(]5 0 2 II ra.dical 1-fold -0.61 +0.39 +0.11 10.83 -0.51 0 2 1: radical 3-fold -0.60 +0.20 1.75 +0.CJ4 0 di-a- double bond 3-fold -0.78 +0.26 - 3.03 +0.02 a) See Table IV for Ag 3 0. b) Obtained from Mulliken populations. "Surface" Ag = Ag atoms directly attached to adsorbate and "bulk" Ag = Ag atoms beneath the surface atoms. c) Magnitude of the dipole moment along bond a.xis. d) Averaged shift of Ag d-orbital energies upon adsorption. e) Ground state. I N (J1 tN I -254- Table III. Properties of Ag 3 Cl as a function of adsite and electronic state. site relative energya (kcal/mol) B2 1-fold 50.7 3 A" 3-fold 3 B2 state 3 we(cm- 1 ) De(kcal/mol)b 2.43 258 50.0 44.4 2.21 203 55.2 2-fold 35.1 2.15 230 61.8 iA' 3-fold 22.0 2.38 161 79.7 1 A1 1-fold 9.3 2.45 246 85.0 1 Ai 2-fold 0.0 2.23 211 91.0 a) GVB(2/4)-PP energy relative to the ground state total energy of -571.82622 hartrees. b) See Table I, footnote d. -255- Table IV. Properties of Ag 3 0 as a function of adsite and bond character. bond character" site relative energyb (kcal/mol) R.L,a(A) w,(cm- 1 ) D,(kcal/moW double 1-fold 53.9 2.11 41:5 39.0 bond cnr double 2-fold 29.8 1.54 380 63.1 2 1:: radical 1-fold 23.4 2.13 378 69.5 2 II radical 3-fold 3-fold 19.9 1.92 72.8 14.9 1.37 252 412 3-fold 1-fold 2-fold 2-fold 14.0 3.1 2.7 1.80 299 78.7 2.14 1.91 1.74 399 289 332 89.8 90.2 92.9 tr'lr bond di-u double bond 2 E radical 2 II radical 2 II radical 2 :E radical u.u 77.8 a) Bond character refers to either two bonds from 0 to Aga (cr11" or di-cr) or an ionic bond between o- and Agt C'E for radical electron along the symmetry axis or 2 II for radical electron perpendicular to the symmetry axis); see Section III.C. b) GVB(2/4)-PP energy relative to the ground state total energy of -187.10445 hartrees. c) Bond energies for the double-bonded states are from CCCI calculations {Section VI); bond energies for the radical states are obtained by adding the difference in relative GVB-PP energies (column 3) of the radical and double-bonded states (for a given adsite) to the CCCI bond energy for the double-bonded sto.te. Table V. Properties of Ag302 as a function of adsite and orientation. we(cm- 1 ) 0-0 Ag3-02 site relative energy• (kcal/mol) R.i,e(A)" R(0-0) (A) 711 end-on 3-fold 29.7 1.85 1.39 195 8~6 17.1 7/2 3-fold 26.4 2.24 1.34 211 912 20.4 711 end-on 1-fold 25.9 2.10 1.35 303 1005 20.9 712 l. bridge 2-fold 16.2 1.99 1.34 226 1179 30.6 7/2 1-fold 13.2 2.22 1.33 290 1200 33.7 1 2-fold 9.8 1.76 1.37 251 949 37.1 2-fold 4.1 2.22 1.33 306 9:21 36.3 0.0 2.18 1.32 286 1264 46.9 bond orielltation 4 71 end-on 1] 1 7/2 peroxy 2-fold De(kcal/mol) 4 a) High symmetry orientations except for 711 perox:y (see Section IIl.D. for details of peroxy geometry). 111 a!ld 112 refer to the number of o:xygen atoms directly bound to the cluster. End-on has only one oxygen bound to the cluster, with 0 2 oriented straight up from the 1-, 2-, or 3-fold sites. 1- and 2-fold Aga02 orientations are aU planar except for the 2-fold perpendicular bridge (0 2 in 2-fold site, oxygens equivalent with 0-0 axis perpendicular to Ag-Ag axis). b) GVB(2/4)-PP energy relative to the ground state total energy of -261.94443 hartrees. c) Perpendicular distance from the center of the cluster site to the bond midpoint of 02 for 1]2 and to the nearest 0 for 711 • d) Adiabatic bond energies from a valence level CI (Section VJ). I N tn Q\ I -257- Table VI. Properties of Ag 30H as a function of adsite. 4 we(cm- 1 ) Ag3-0 0-H site relative energyb (kcal/mol) RJ.,e(A)c R(O-H) (A) 1-fold 20.2 2.07 0.96 445 3796 69.4 3-fold 18.8 1.72 0.97 295 3637 59.1 2-fold 0.0 1.70 0.96 363 3740 78.9 De(kcal/mol)d a) Linear geometries for OH are global minima, with tilted OH orientations found to be higher in energy. b) GVB(2/4)-PP energy relative to the ground state total energy of-187.75179 hartrees. c) RJ.,e perpendicular distance from the center of the cluster site to 0. d) Adiabatic bond energies from CCCI calculations (Section VI). Table VII. Properties of Agt(C 2H4} as a function of a.dsite and orientation. orientation'" site relative energy• (kcal/mol) R1,,,(A)c w,,(Aga-C2H4} (cm- 1 ) D,,(kcal/mol) 4 C-C II C-C ..L 3-fold 7.6 4.95 21 1.0 2-fold 6.1 3.64 34 2.5 C-C I! 2-fold 5.8 3.58 37 2.8 C-C II C-C ..L 1-fold 0.1 2.71 107 8.6 1-fold 0.0 2.70 110 8.7 a) Gives orientation ofC-C axis relative to the Ag3 plane, wht:re the C-C bond midpoint lies in the Ag 3 plane for the 1- and 2-fold sites. b) GVB(3/6)-PP energy relative to the ground state total energy of -190.157[)5 hartrees. c) R.L,• = perpendicula1 distance from tlie center of the cluster site to C-C bond midpoint. d) Adiabatic bond energies from GVB(3/6)PF calculations (Section VI). I N (Jl 00 I -259- Figure Captions Fig. 1. The GVB one-electron valence orbitals of Ag 3 (2 A1 ): (a) the Ag3 singlyoccupied orbital and (b) the Ag-Ag bond pair. Contours range from -0.5 to +0.5 a.u., incremented by 0.01 a.u. Fig. 2. Schematic of possible bonding configurations for X/ Ag 3 (the 2-fold bridge site): (a) X = H; (b) X = Cl; (c) X = 0 (O' and 71" double bond); (d) X = 0 (ionic 2 E state); and (e) X 0 (ionic 2 II state). Fig. 3. The GVB one-electron orbitals of Ag 3H (iA 1 ) (for the 2-fold bridge site): (a) the .Ag3-H bond pair and (b) the Ag-Ag bond pair. Fig. 4. The GVB one-electron orbitals of Ag3Cl (1 Ai) (for the 2-fold bridge site): (a) the Ag 3 -Cl bond pair; (b) the Ag-Ag bond pair; and (c) the Cl doubly-occupied, in-plane p-orbital. Fig. 5. The GVB one-electron orbitals of ground state Ag 30 (2 Ai) with 2 'E ocha.ra.cter (for the 2-fold bridge site): (a) the 0 2p0' radical; (b) the 0 in-plane 2p lone pair; and (c) the Ag-Ag bond pair. Fig. 6. The GVB one-electron orbitals of Ag 30 (2 B2) with 2 II o- character (for the 2-fold bridge site): (a) the 0 2p<T pair; (b) the 0 2p7r radical; and (c) the Ag-Ag bond pair. Fig. 1. The GVB one-electron orbitals of excited state Ag3 0 (2 A 1 ) with U7r double bond character (for. the 2-fold bridge site): (a) the Ag3-0 bond pair; (b) the Ag3-0 7r bond; and ( c) the Ag3 singly-occupied orbital. Fig. 8. Adsorption sites for C2 H4 on Agt: (a) the 3-fold site; (b) the 2-fold perpendicular bridge site; (c) the 2-fold parallel bridge site; (d) the 1-fold parallel site; and ( e) the 1-fold perpendicular site (the ground state). The + signs for Agt have been omitted for clarity. Fig. 9. The two high-symmetry adsorption sites on Ag(llO): (a) the 4-fold site down in the trough and (b) the 3-fold site along the sides of the trough. -260- Ag 0 Ag 'V a) ------ --:.:.::=.:~:.. ,,. .., ,,,,, """ .... .... .... ' ..... ' ,, 1 ,';-"""I~-":.,- ......... , ' I I I I I I I I I I Ii-•,..:: \ ,1 -t_ '1 ' ,. ' I I , 1\ '1'1''~11:,,,,, A -"""':"""--:.,.._ .. I I I I "' ,. -.,. I I ',,, 11 1 1 ' I I \ \ 1 \\\'_,..,/I \ l I \ \ ' ' ' , ....,, - - : ., " ,1 I I I I Ag RADICAL b) Ag-Ag BOND Figure 1. \ -261- b) c) Ag 6 + + . Ag-Ag Ag-Ag d) \t e) Figure 2. ~ Ag -262- Ag H 3 ( 1A ) 1 ONE ONE a) IPAIRI Ag -H BOND 3 ONE ONE ,,, ,. ... I b) IPAIRI Ag-Ag BOND Figure 3. j -263- , ,.. ........... , ,,,;:',\ a) • ,,• - ;""-.... ~-: .... , ONE I I ',,,. - ' 11, ':,~ \ \ ONE t "\ 11,;;-,.,,, 11t I •,,- IDJ IOI II • • -• Ag:3CI BOND ONE ONE 0 ,-• ' -,' 0 ,-., •,_, ' ' b) IPAIRI Ag-Ag BOND c) • Cl 2p LONE PAIR Figure 4. -264- A~g­ ~ + Ag ONE a) • 0 2p O" RADICAL ONE ONE ,": ~ ~ ;;~, -~ ' ,, b) :,',~ ,,• "\)..,., ,:'1 0 o'' / //<',~"~~ \ ,' ', '~,,,J: I :• 0 o~:' IPAIRI ~ ; -...... ..: , 1 '--'-?:/ . -, ,' • • 0 2p LONE PAIR ONE ONE -,:,-- ,,. : ... ~:~..' c) 1 1- · I ... IPAIRI Ag-Ag BOND Figure 5. -265- ~­ Ag 0 3 2 ( 8) 2 u tf Ag-Ag + ONE ONE ,• a) .,• •, • 0 2pcr PAIR ONE b) • 0 2p rr RADICAL ONE ONE Q_ ..'1 '.. :.' I• ' c) Ag-Ag BOND Figure 6. -266- ~ Agp AJ; (2A1) Ag 0 .. -...... ONE ONE a) • ONE ONE b) • • Ag -0 1T' BOND 3 ONE c) Ag 3 RADICAL Figure 7. -267- Ag a) H 'C,,..H I H,,,,C, H Ag Ag b) c) H e) Figure 8. -268- 0 -269- Conclusions of the Thesis This thesis has presented an ab initio method for the prediction of accurate energetics for events of chemical interest. The correlation-consistent configuration interaction (CCCI) technique is based on the generalized valence bond (GVB) first order wavefunction, whose orbitals form the basis for the CCCI calculation. The uniqueness of the method is due to the choice of the CI expansion, which incorporates the same electron correlations at both endpoints of a process, but includes only the dominant correlations dictated by the physics (or chemistry) of the system. This results in a rapid truncation of the CI expansion, so that the energetics for processes involving fairly large molecules can be easily assessed by this approach. The accuracy of the CCCI method has been demonstrated by predicting the following quantities (for both organic and inorganic compounds): (i) chemical bond dissociation energies; (ii) electronic excitation energies; (iii) activation barriers for chemical reactions; and (iv) thermochemical heats of formation and heats of reaction. The goal of this thesis was not merely to provide quantitatively accurate energetic information, but also to use these quantities to distill simple conceptual rules for predicting the relative stabilities and reactivity of organic and transition metal-containing molecules. In particular, we have shown that: (a) the dominant contribution to the relative bond strengths in substituted olefins and methanes is the singlet-triplet energy splittings of the substituted carbenes from which they are comprised; (b) the relationship between molecular bond energies and electronic excitation energies in the subsequent fragments establishes a new connection between thermochemistry and spectroscopy; ( c) the ground electronic states of substituted carbenes are determined by the electronegativities of the substituents (relative to carbon), the presence of p7r -270- lone pairs on the substituents, and the size of the substituents, with highly electronegative groups with p7r lone pairs favoring singlet ground states, while bulky electropositive groups favor triplet ground states; ( d) the bond character, reactivity, and stability of transition metal carbenes is dictated partially by whether the ground state of the carbene is singlet or triplet, with singlet carbenes [e.g., CF2, CCb, CR(OR')] preferring a. terminal configuration involving a donor/acceptor bond and triplet carbenes [e.g., CH 2 , CRR', CR(SiR~)] favoring covalent alkylidene bowling; (e) the bond character, reactivity, and stability of transition metal carbenes is also determined by the valence electronic configuration at the metal, with early metals favoring covalent, terminal alkylidene-type bonding (since the 7r bonds are strong for early metals) and late metals favoring donor/acceptor carbenetype bonding or bridging alkylidene bonding (since the 7r bonds are weak and doubly-occupied orbitals on the metal allow for 7r-backbonding); (f) the character, reactivity, and stability of transition metal oxygen buuds may be predicted solely by knowing the valence electronic state of the metal, with early metals forming inert triple bonds as in CO (since an empty metal dorbital allows 0 to be a four-electron donor) and late metals forming reactive biradical double bonds as in 0 2 (since the doubly-occupied cl-orbitals on the metal allow an 0 2 -type 7r resonance); (g) coordinatively unsaturated (cu) metal-ligand bonds are generally weaker than coordinatively saturated (cs) metal-ligand bonds, because the coordinatively unsaturated metal prefers to be high spin (resulting in maximum exchange losses upon bonding); and (h) additive conversion factors for converting from cu M-X bond strengths to cs M-X bond strengths have been derived, so that organometallic chemists will be able to estimate the thermochemistry of cs metal complexes. Finally, we have used CCCI to elucidate mechanistic information about two very important catalytic reactions, the Fisr.hn-Tropsch reductive polymerization of -271CO and the Ag-catalyzed selective oxidation of ethylene, with these results: (i) the chain initiation step of the Fischer-Tropsch synthesis of hydrocarbons is found to be exothermic by ,..., 10 kcal/mol and possess a barrier of ,..., 11 kcal/mol, while the chain propagation step is predicted to be less exothermic (l:.Erxn ~ -4.2 kcal/mol) and possess a higher barrier; (j) control of epoxidation catalyst activity is related to deactivating 4-fold sites on Ag(llO) facets and adsorbing oxygen in 3-fold sites (the oxygen species in the 3 fold site has radical o- character and should be active for ethylene epoxidation); and (k) electronegative promoters are predicted to £.114-fold hollows so that increasing concentrations of active oxygen will form in 3-fold sites, while electropositve promoters are expected to enhance the probability for adsorption of ethylene. In sum, the CCCI method is a powerful, general approach which, when combined with physically reasonable models, yields both accurate energetics and new qualitative insights regarding bonding and rear.tivity for a. diverse group of chemical systems. -272- Appendix 1 The text of this appendix is a Letter coauthored with M. A. Hanratty, J. L. Beauchamp, W. A. Goddard III, A. E. Illies, and M. T. Bowers which appeared in Chemical PhyJicJ LetterJ. -273- Volume I 23, numbet 4 CHEMICAL PHYSICS LETTERS 17 January I 986 ELECTRONIC STATES OF CHROMIUM CARBENE IONS CHARACTERIZED 8\' HIGH·RESOLUTION TRANSLATIONAL ENERGY LOSS SPECTROSCOPY M.A. HANRATTY. E.A. CARTER. J.L. BEAUCHAMP. W.A. GODDARD Ill Arthur Amos Noyrs la~ratory of Chrm1ca/ Physics 1, Caltforma Jnmtuu of Trchnolog:.-. P1JJadena, CA 91/}J, USA A.J. ILLIES and M.T. BOWERS Drpartmrnt of Chrm1s1ry. Unwt:rsuy of California. Santa Barbara, CA 93106. USA Received 4 November I 985 The electronic states of the unsaturated organometallic carbene CrCHi are investigated using high·resolution translauonal energ) Joss spectroscop). The observed energy loss feature (1.05 ±0.2 eV) is in good agreement with theoretical calculat1om which predict two higher lying stam. 6 8 1 and 6A 1 at 0.78 and 0.82 eV respectively. above the ground state of CrCH; •e, 1. Introduction Rapid progress in experimental methodology has made it possible to generate and study highly reactive organometallic fragments in the gas phase. While experimental investigations have focused mainly on the reactivity and thermochemical stability of such species [ 1-7), parallel developments in ab initio theory have provided descriptions of the molecular and electronk structures of the$C molc~ules (8-10). Transi· tion metal carbenes, species which contain a divalent carbon bonded to a transition metal center, are an example of reactive organometallic fragments which have been the subject of both experimental and theoretical investigations. Ion beam (J-3) and ion cyclotron resonance (4-7) techniques have recently been used to investigate the energetics and reactions of both the coordinately satu· rated and "bare" transition metal carbenes. In the latter category it has been observed (1,4) that the chromium carbcne ion, CrCHi, can be generated by reaction of electronically excited er+ with methane: Cr++ CH 4 .... CrCtti + H2 • 1 (1) Reaction (I) is 45 kcal/mo! endothermic for ground· state Cr+ (6S derived from the ds configuration) [ J l], but is 12.5 kcal/mo} exothermic if the er+ ion is in the 4D excited state. Several experimental results (1,4) suggest that it is, in fact, the 4p state (derived from the sld4 configuration and 2.5 ~v highn in PnPrgy than the ground state) [ 11] which is responsible for the production of CrCHi by reaction (1). Recent ab initio calculations of the low-lying electroni~ )tate~ of C1 CHi by Canc:r and Goddard [8 J predict that the ground state ofCrCHi is a 4 B1 state, with a directly calculated bond dissociation energy De = 44 kcal/mo! and an estimated exact bond dissociation energy of Dcou = 50 kcal/mol. This can be compared with the experimentally determined [I] bond energy of 65 ± 7 kcal/mo!. Earlier CI calcula· tions by other workers (9] suggested that the CrCHi ground state is the 6B 1 state, with a significantly weak· er bond, while Carter and Goddard (8) found the 6B 1 state to be 18 kcal/mo! higher in energy than the 4B1 1tatc. In an attempt to rcwlvc the situation, we have employed high-resolution translational energy loss spectroscopy to investigate the electronic states of CrCtti. Contribution No. 7320. 0 009·2614/86/S 03.SO ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) 239 -274- Volume 123, number 4 17 January 1986 CHEMICAL PHYSICS LETTERS 2. Experimental The theory and instrumentation for translational energy loss spectroscopy have appeared in detail elsewhere [ 12,13] and will be described only briefly. Ex· periments were performed at UCSB using a double focusing mass spectrometer (VG ZAB-2F). A variable temperature ion source was operated at 330 K with 6.5 X 10- 3 Torr total pressure. Chromium ions are formed from 150 eV electron impact ionization of Cr(C0) 6 . Reaction of excited-state Cr+ with eH 4 (reaction (I)) produces CrCffi. Ions extracted from the source are accelerated to 8 kV, mass selected by a magnetic sector and focused into a collision cell. Typically, l o-3 Torr of helium is used as the collision gas. Translational energy analysis of the unscattered main [12]. For transition metal systems, it is not uncorn· mon to have numerous electronic states of the same or different spin multiplicity close in energy to the Fig. I. Translational ellll!ll!Y loss spectrum of er• scattered from helium {PHe" 6 X 10-3 Ton). ion beam .and its scattered components is accom· ground state. In order to determine the relative mag. plished with an electrostatic analyzer, located after the collision chamber and collinear with the incident ion beam axis. In the absence of a collision gas, the nitudes of the collisional excitation cross sections for transition metal ions, the high-resolution translational energy loss spectrum of er+ scattered from He was energy resolution of the: main bc:am (Cr+ or CrCHz) investigated (fig. 1). The: main p<::a.k at z.ero tnmsla· was 0.2 eV (fwhm). During the collision between a neutral target and an ion, which has been accelerated to several kilovolts, the internal energy of the ion may be altered in this situation, peaks at higher and/or lower energies than the unscattered ion beam (corresponding to de-excita· tion and excitation, respectively, of ionic states) are observed. The reported experiments are sensitive to collisions occurring at small scattering angles, for which translational energy losses of the ion correspond to changes in the ion internal energy [ 13]. Ions with the same nominal mass as the ion of interest may also appear in the spectrum but are easily identified with the high-resolution capabilities of the instrument. In the case of chromium carbene (5 2 CrCtfi), other ions of mass 66 were also observed in the high-resolution energy loss spectrum but did not occur in a region which would obscure the predicted electronic transitions. tional energy loss in fig. I corresponds to the unseat· tered er+ beam. Two smaller features occur 1.45 eV lower and higher in energy than the main beam. As shown in table 1, this energy change corresponds to the spin allowed a 65 .... a 60 excitation and a 60 .... a 6s de-excitation, respectively. Also from table I, one can see th.at this is the only transition involving the 65 ground state which would occur below 2 eV. Transitions between the quartet states of Cr+, speci· fically the a 4 0 .... b 4p and the a 4 G ..... b 4 P, would appear at 1.17 and l.23 eV, respectively. and may in fact be present but obscured by the 6 S .... 6 D transi· tion. Transitions between the a 40 and a 6s states at Table 1 Low-lying electronic states of chromium ion State s 3. Results and discussion Although collisional excitation can generate states that are difficult to prepare by optical methods, processes which are optically "allowed" are generally ob· served to have a larger cross section for collisional ex· citation than those which are optically "forbidden" 240 Confljluration Enell!Y (eV) a) . -----·--·-- a6 a6 D 3d 5 3d4 s1 a'G 3d5 3d~ 2.11 b"D b'P 3d 5 3.10 3d4 s1 32p 3d 5 3.71 3.74 a•o a"P 4 1 3d s 0.00 1.48 2.42 2.S4 a) Data taken from ref. { 11 J refer to lowest J state. -275- CHEMICAL PHYSICS LETIERS Volume 123, number 4 17 January 1986 Table 2 Low-lying elecuonic states of Cr CH; ion State 4 B1 6 B1 •A1 _, 0 "'°"'to''°"°' £rwi;n iev Conf1&urat)On J:.nergy (cV) cr•( 6S) + 3B1 CH2 0.00 cr•( 6S) + 3B1 CH2 Cr•( 6 S) + 1 A1 CH2 O.llZ •2 peaks or metastable transitions are observed. The other two peaks indicated in fig. 2 ("B" and "C") result from S4 crc• and s0 crcH:, which have the same nominal mass as 52CrCHi, but which otherwise have no bearing on the present study. The recent ab initio calculations of Caner and Goddard [8] for the electronic states of CrCHi can be used to assign the transitions observed in the translational energy loss spectrum of CrCff'i. The authors predict a 4B 1 ground state, which is best envisioned as a high-spin 65 er+ forming a covalent double bond with a 3B 1 CH 1 fragment. Two low-lying excited states were calculated: a 6B 1 state, consisting of a single covalent o bond between ground-state (6 S) er• and CH2, with the Cr+ and CH2 11' electrons high-spin 1 52 Fig. 2. Translational energy loss spectrum of CrcH; scat· tered from helium (PHe" 6 x 10-3 Torr). The feature marked "A" is from 52 crctt;, while "B" and "C" are from mass im· purities. 2.42 eV were not observed. The apparent collisional cross sectiort for these excitation processes is small. This could be due to either a small value of the tr an· sition matrix elements linking these states, a small population of the initial states, or both [12,13). The translational energy loss spectrum for CrcH; scattered from He is displayed in fig. 2. An excitation peak labeled "A" appears 1.05 eV lower in energy than the main beam. No superelastic(higher-energy) -- ---------- ------------t 575 0.78 CHlA 1) GJ>c( .. -,..0 E ..... 0 v :! .,.,... c'r--c>c"'·" (l.(:) 1\ 1 'Q.. .. C:c'7 c:c'7 <6e (1 t> ()';, 188 18.0 11 ~•Q..B>C''' iic IAJ (\.~,, 00 C>C•<3l....JZ>C'" (1 b 6':. . . t;•l.'1 2 I 8 11 Fig. 3. Adiabatic electronic state correlation diagram for low-lying states of 52 CrCHi. Data from refs. (8,14). 241 -276- Volume I 23, numl-er 4 CHEMICAL PHYSICS LETTERS coupled to the other valence d electrons, lies 18.0 kcal/mo! (0.78 eV) above the 48 1 ground state, and the 6 A1 state [ 14), composed of a single a donor bond between the ground·state (6S) Cr+ and excited· ~tate (1A 1) CH2, cakulaml 1u lie 18.8 k1,;al/mol (0.82 eV) above the 48 1 ground state ofCrCHi. These results are summarized in table 2 and shown with schematical descriptions of the bonding orbitals in fig. 3. The experimentally observed translational energy loss feature at 24.2 kcal/mo! (I .05 ± 0.2 eV) obtained 17 Janua.ry 1986 Acknowledgement This work was supported by the National Science Foundation under Grants No. CHE-8318041 (WAG), CHE-8020464 (MTB) and CHE-8407857 (JLB). Support from the Shell Development Company (WAG) and the Atlantic Richfield Foundation (MAH gradu· ate fellowship) is gratefully acknowledged. EAC acknowledges a National Science Foundation pre· doctoral fellowship ( 1982-1985). in this investigation is in good agreement with the the- oretical predictions for electronic excitation of the 4B 1 ground state to either 68 1 or 6A 1 states of CrCHi. The calculations of Carter and Goddard [8] indicate that vibrational exc1tat1on (U.4 eV for the C-H stretch of the 4 8 1 ground state and 69 1 excited state) coulq also be resolved with this technique. There is no evidence for vibrational excitation of either the ground or excited state at this SIN ratio. In contrast to the translational energy loss spectrum of er+ ions, where only spin allowed transitions are readily apparent. the CrCH1° excitations are attributed to spin forbidden transitions, and the small cross section in· ferred from the weak signal is consistent with this as· signment. Unsaturated metal species such as CrCHi are of interest as prototypes for organometallic species im· plicated in numerous catalytic reactions. This study suggests that high-resolution trandational energy loss spectroscopy can be successfully applied to investiga. tions of the excited electronic states of a wide range of reactive organometallic species which can be formed in the gas phase. It Is also encouraging that, In this case, the agreement between the experimental deter. mination and the theoretical predictions is quite good. 242 References [I) L.F. Halle, P.B. Armentrout and 1.L. Beauchamp, J. Am. Chem. Su~. l 03 (198 l) 962; P.B. Armentrout and J .L. Beauchamp, 1. Chem. Phys. 74 (1981) 2819. (2 I N. Aristov and P.B. Armentrout, 1. Am. Chem. Soc. 106 (IQR4) 406~ (3 J M.L. Mandich, L.F. Halle and J.L. Beauchamp, J. Am. Soc. 106 (1984) 4403. ( 4 I D.P. Ridge, private communication. (5 J D. Jacobson and B.S. Freiser, J. Am. Chem. Soc. 107 (1985) 4373. (6) D. Jacobson and B.S. Freiser, J. Am. Chem. Soc. 107 (1985) 4379. [ 7] A.E. Stevens and 1.L. Beauchamp, J. Am. Chem. Soc. 100 (1978) 2854, 101 (1979) 6449. (8 I E.A. Carter and W.A. Goddard !II, J. Phys. Chem. 88 (1984) 1485. (9) M.A. Vincent, Y. Yoshioka and H.F. Schaefer Ill, J. Phys. Chem. Rli (I QR2) ~QO~ (JO] A. Rappe and W.A. Goddard Ill. J. Am. Chem. Soc. 104 (1982) 448. ( 11] C.E. Moore, NS RDS NBS 35 (1971) l 0. [ 12 J A.J. lilies and M.T Bowers. Chem. Phys. 65 ( 1982) ~8 l. ( 13 l R.G. Cooks, ed., Collision spectroscopy (Plenum Press, Ne11. York. 1978). [ 14 I E.A. Carter and W.A. Goddard Ill, submitted for publication.