Theoretical Studies of Oxidative Addition and Reductive Elimination Citation Low, John James (1985) Theoretical Studies of Oxidative Addition and Reductive Elimination. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XR1N-CM33. https://resolver.caltech.edu/CaltechTHESIS:10232009-095454256 Abstract Chapter 1: Ab initio calculations (Hartree-Fock, generalized valence bond, and configuration interaction), utilizing relativistic core potentials, have been used to follow the oxidative addition of H 2 to Pt(PH 3 ) 2 . We find an activation barrier of 2.3 kcal/mol and an exothermicity of 15.9 kcal/mol. From examination of the geometries and wavefunctions, we find that up to the transition state the H-H bond is still intact. The role of the Pt s 1 d 9 and d 10 states in oxidative addition is described, and the effects of including electronic correlation are discussed. The implications for reductive elimination of the dimethyl and hydridomethyl complexes are also discussed. Chapter 2: Ab initio calculations have been carried out on MR 2 complexes (where M = Pd or Pt and R = H or CH 3 ) to model concerted reductive coupling from MR 2 L 2 complexes (where L is a substituted phosphine). The results of these calculations support the following two conclusions. (1) The differences in the driving force for reductive elimination from Pd(II) and Pt(II) complexes with the same R groups is very close (0-4 kcal/mol) to the difference in the s 1 d 9 -d 10 state splittings of these elements (32 kcal/mol). Thus reductive elimination is exothermic from Pd complexes (since Pd prefers d 10 ) and endothermic from Pt complexes (since Pt prefers s 1 d 9 ), where the metal product is in its d 10 state. This supports the conclusion, derived from qualitative considerations of generalized valence bond wavefunctions, that Pt(II) and Pd(II) complexes have their metal atoms in a s 1 d 9 configuration and the metal atoms in Pt(0) and Pd(0) complexes are in a d 10 configuration. (2) The activation barriers for C-C coupling are approximately twice that for C-H coupling. There are essentially no barriers for processes involving H-H bonds. The origin of this trend is the directionality of the methyl sp 3 orbital, which destabilizes the transition state for the case where an M-C bond is being converted to a C-C or C-H bond. Conversely, the spherical H 1s is orbital can form multicenter bonds easily, allowing it to break M-H bonds while forming an H-H bond and leading to low intrinsic barriers. These results are consistent with the experimentally observed trends. Chapter 3: Ab initio calculations were carried out on Pt(CH 3 ) 2 (Cl) 2 (PH 3 ) 2 and on various Mt(R 1 )(R 2 )(PH 3 ) 2 complexes (where Mt = Pd or Pt; R 1 , R 2 = H or CH 3 ) in order to elucidate the differences in reductive H-C and C-C coupling from Pd(II), Pt(II), and Pt(IV) complexes. These studies explain why (1) reductive C-C coupling is facile for Pd(II), favorable for Pt(IV), and unobserved for Pt(II) systems, while (2) reductive H-C coupling is facile for Pt(II) and Pd(II) systems, and (3) oxidative addition is favorable only for addition of H 2 to Pt(0) systems. Chapter 4: Ab initio calculations were carried out on CH x and NH x molecular fragments on small clusters of Ni atoms (Ni 13 and Ni 14 ), as a model for chemisorption on the Ni(100) surface. The results presented here show that these species make strong π bonds to the surface which cause methylidyne and imidogen to be the most stable CH x and NH x , species on this surface. The results have also been used to estimate ∆H 0 f for various intermedates important for methanation and ammonia decomposition on Ni surfaces. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Theoretical Study; Addition Reaction; Oxidation Elimination; Chemical Reduction; Chemical Coupling; Ab initio Method; Platinum Organic Compounds; Platinum Complexes; Chloro Complex; Inorganic Ligand; Phosphine; Platinoid Complexes; Palladium Complexes; Reactivity; Chemical Bond; Hydrido Complex Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Gray, Harry B. Thesis Committee: Gray, Harry B. (chair) Goddard, William A., III Bercaw, John E. Weinberg, William Henry Defense Date: 5 May 1985 Record Number: CaltechTHESIS:10232009-095454256 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10232009-095454256 DOI: 10.7907/XR1N-CM33 Related URLs: URL URL Type Description https://doi.org/10.1021/ja00335a010 DOI Article adapted for Chapter 1. https://doi.org/10.1021/om00135a001 DOI Article adapted for Chapter 2. https://doi.org/10.1021/ja00280a003 DOI Article adapted for Chapter 3. Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 5324 Collection: CaltechTHESIS Deposited By: Tony Diaz Deposited On: 18 Nov 2009 00:26 Last Modified: 20 Dec 2019 19:57 Thesis Files Preview PDF - Final Version See Usage Policy. 7MB Repository Staff Only: item control page

. Theoretical Studies of Oxidative Addition and Reductive Elimination Thesis by John James Low In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1985 (Submitted May 27, 1985) -ii- © 1985 John James Low ALL RIGHTS RESERVED -iii- Acknowledgment First of all I would like thank Bill Goddard for providing me the opportunity to do research in Quantum Chemistry. We did not always -aggree but he allowed me to make many of my own decisions and mis- takes. I do appreciate the faith he showed in me and that he trusted me enough to give me important tasks and responsiblities. I hope that | did not and will not disappoint him too often. I would also like to ack- nowledge my high school instructor in chemistry, Mr. Gerad A. Kass. He first kindled my interest in understanding chemistry at a fundamental level. I would to thank my parents for providing me with the talents and for raising me the way they did. I am sure that I would not have persevered for as long as | have, if it was not for the good start they gave me. I have appreciated the help that various Goddard group members have given me. Most of all, I would like to thank Tony Rappé, Ray Bair and Tom Upton for helping me get started in research and Mike Stiegerwald for many helpful discussions. A special thanks goes to Adria McMillan not only for her secretarial skills, but for her encouragement and for remind- ing me that there is life after Cal. Tech. I would like thank Horia Metiu and Dick Messmer for their encourage- ment, advice and helpful discussions. They showed me that one could be a good scientist and a good person as well. I have made a few good friends here (Steve Witt, Greg Voth, Dan Zirin Mark Brusich, Tom Gibson, Bill Finch, The Lynches, Walther Ellis, Eric Hood, Mike Weimer, and Heidi Tanicar). They have gotten drunk with me (except Eric) and made me laugh on many occasions. I thank the Weenies for competitive softball and the Sierra Club for many relaxing excursions. -iv- A special thanks goes to the Blankenburgs for always being suppor- tive and providing a retreat for me to regain equilibrium. I acknowledge Tikoes for his many loans and for being a good friend, Aunt Eleanor for ‘good food and lots of beer, and Annette and Debbie (a future Blanken- burg) for proofreading assistance. I would like to acknowledge One West and Chippendales for many exciting friday nights. I finally would like thank Claudia Troesch. She was a good companion at a time when I needed a lot of support. -V= ABSTRACT Chapter 1: Ab initio calculations (Hartree-Fock, generalized valence bond, and configuration interaction), utilizing relativistic core poten- tials, have been used to follow the oxidative addition of H, to Pt(PH,) 2 We find an activation barrier of 2.3 kcal/mol and an exoth- ermicity of 15.9 kcal/mol. From examination of the geometries and wavefunctions, we find that up to the transition state the H-H bond is still intact. The role of the Pt s'd® and d!° states in oxidative addition is described, and the effects of including electronic correlation are discussed. The implications for reductive elimination of the dimethyl and hydridomethyl complexes are also discussed. Chapter 2: Ab inifio calculations have been carried out on MRg com- plexes (where M = Pd or Pt and R = H or CHs) to model concerted reductive coupling fromm MReL2e complexes (where L is a substituted phosphine). The results of these calculations support the following two conclusions. (1) The differences in the driving force for reductive elimination from Pd(II) and Pt(II) complexes with the same R groups is very close (0-4 kcal/mol) to the difference in the s'd9—d!° state splittings of these elements (32 kcal/mol). Thus reductive elimina- tion is exothermic from Pd complexes (since Pd prefers d!°) and endothermic from Pt complexes (since Pt prefers s'd®), where the metal product is in its d! state. This supports the conclusion, derived from qualitative considerations of generalized valence bond wavefunctions, that Pt(Il) and Pd(Il) complexes have their metal atoms in a s'd® configuration and the metal atoms in Pt(0) and Pd(0) complexes are in a d!° configuration. (2) The activation barriers for @vi- C-C coupling are approximately twice that for C-H coupling. There are essentially no barriers for processes involving H-H bonds. The origin of this trend is the directionality of the methyl sp® orbital, which destabilizes the transition state for the case where an M-C bond is being converted to a C-C or C-H bond. Conversely, the spheri- cal H 1s orbital can form multicenter bonds easily, allowing it to break M-H bonds while forming an H-H bond and leading to low intrin- sic barriers. These results are consistent with the experimentally observed trends. Chapter 3: Ab initio calculations were carried out on Pt(CHs)a(CYe(PH3)g and on various Mt(R,)(Re)(PH3)zg complexes (where Mt = Pd or Pt; Ry, Rg = H or CH) in order to elucidate the differences in reductive H-C and C-C coupling from Pd(Il), Pt(II), and Pt(IV) complexes. These studies explain why (1) reductive C-C cou- pling is facile for Pd(II), favorable for Pt(IV), and unobserved for Pt(II) systems, while (2) reductive H-C coupling is facile for Pt(II) and Pd(II) systems, and (3) oxidative addition is favorable only for addi- tion of Hz to Pt(0) systems. Chapter 4: Ab initio calculations were carried out on CH, and NH, molecular fragments on small clusters of Ni atoms (Nig and Ni,,), as a model for chemisorption on the Ni(100) surface. The results presented here show that these species make strong 7 bonds to the surface which cause methylidyne and imidogen to be the most stable CH, and NH, species on this surface. The results have also been used to estimate AHP for various intermedates important for methanation and ammonia decomposition on Ni surfaces. -vii- Table of Contents Chapter 1: Theoretical Studies of Oxidative Addition and Reductive Elimination: Hg + Pt(PH3)2g > Pt(H)a(PH9)a ........ccccccceccceeeccreecreeeenseenenere I. Imtroductio4n ...........cccccceeccceseceeeeecen ee sesene essen eeceeueeseeaeeseee reese eseeag eens eesennegs I]. Surmmary of Results 20.0... ieee cceceee eee ceeeeee ee cee eee eeeeeeeaeneseeneereeeeeeeteesana TIL. RESUItS 20... eccecccecceeeeeeeen een eeeeeeueeecepenaageeeeseneeeeeeeaeeesescueeesnseneeesees TV. Calculational Details 20.0... cece e eee nnee eee e cece tere ee nese a neeeneneee ere ti ee Chapter 2: Theoretical Studies of Oxidative Addition and Reductive Elimination: II. Reductive Coupling of H-H, H-C, and C-H Bonds from Pd and Pt Complexes ..............ccceecccsecce cece ccnneeeseee scene eeenaneseanecueneees 1. Introduction bocce cae e eee ceenenececeneaeceeeeeeaesetaceeeceenneeee esse eeeneeeeeesea nena eneeeeesiane tl. Summary of Results sscsesesesssesssussstsestissessatstisissisteistasisetseseaseseasee dese eceeees III. Comparison With Experiment................. ccc ccc cee ceee cece eeeee eter e eee settee IV. Comparison With Other Theoretical Work...............ccecceee cee ce cece ee enee eee V. Calculational Details 2.0.00... ee cceee reece eee rere eeeeeaseeeeeeneeeenieeeeeeeees FN 2) 0) 3016 0b. 0. Cane eS APPendix Bho... ie eee cceeeceeceeeecececceeeeeeeaeesegeaaeeeseeeeeeeeessee essen eeseneseeeeesegs References and Notes .........cccccccccccecesevcccvscsecuceeesueeseneeseeeneetenessenerseeeas - Chapter 3: Theoretical Studies of Oxidative Addition and Reductive Elimination: III. C-H and C-C Reductive Coupling from Pd and Pt Bisphosphine Complexes...............ccccec ccc ceseee cece ene ece en neeeten anes TI. Imtroduction ..0......0...ccccceccc ccc eecc eee ceeeneseeeeeeeseseaeeeeeeeeecesen essa eaaeeesenseeueegease II. Summary of Results ............ccccceeeeececc cece cae eneeseeeeecaeseaaauavaaeseresaeeneaeawenseess TIL. DiSCUSSION ......c0.ccccccccecccecececccuceuecceceevavaeuseesaveccuevaneesenevaneereueeanarneeeneetensea 30 TV. Calculational Details... ccc cseceneeseeneeeceeneeceeeseeeeeeseeseeessneesesuess 121 References and Notes 0.0.0... ccccseeceseeseceteeccaneneeeenaeaeseceeeaeceeeeeeaaeeserees 126 No) (1 eee 134 FIZ UTES... ee cece cece cee ce ee eecceeeeeeeeneeeeseeeseeeeeeeeeeeeeneeeeeseeeeese eee seeeersaeeeeeeee 149 Chapter 4: Theoretical Studies of CH, and NH, Species Chemisorbed on Ni Clusters 2.0.0... cece ee seeeceeee ener eeteaeneenes 160 T. Imtroduction .0....... ccc cececeeeccceeeeeeececueeeeeceeeeeeceeeeeeeeeeeeeeeeeregaeeaaeeageeneeeees 161 TI. Results... cece ccceceeceeeceeeeceneceseeeceneesseeesaceeaeceseeegaeeeaeeeeaeneeeeseeraneseeeesea 163 TH. Calculational Details... ec cecc cece neceeeceeeceeeeeeeecseeeeesaeeeneeseeseaees 174 TV. Conclusions. ...........cceccceeececeeeeccnneeeceeeeecaeeeecececeeeuesseuersceeaeeseueseeacesecaeaes 178 APPendix AL... ee cece cece ence neceeeeeeeeneeceenaecaeeeeeeneeeseceeseneeaeearees sen eeeesennees 179 References ..........ccccesecceeeceeeecesecneeeseeecenecaueeseaecseeeeeeeseeeesaeeeeeecseesneseeseeegs 186 Table «20.2... ceceeeceeecceeeenaeecnaeceneeeenscrenseneeceeuceeansesaecesecesaeceaeseetetenersaess 191 CHAPTER 1 Theoretical Studies of Oxidative Addition and Reductive Elimination: Hz + Pt(PHs)2 > Pt(H)2(PHs)e2 The following chapter has appeared in the Journal of the American Chem- ical Society, 1984, 106, 6928-6937. ~2~ Reprinted from the Journal of the American Chemical Society, 1984, 106, 6928. Copyright © 1984 by the American Chemical Society and reprinted by permission of the copyright owner. Theoretical Studies of Oxidative Addition and Reductive John J. Low and William A. Goddard III* Contribution No. 6995 from the Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91125. Received March 5, 1984 Abstract: Ab initio calculations (Hartree-Fock, generalized valence bond, and configuration interaction), utilizing relativistic core potentials, have been used to follow the oxidative addition of H, to Pt(PH;).. We find an activation barrier of 2.3 kcal/mol and an exothermicity of 15.9 kcal/mol. From examination of the geometries and wave functions, we find that up to the transition state the H-H bond is still intact. The rote of the Pt s'd® and d’° states in oxidative addition is described, and the effects of including electronic correlation are d. The impli pi are also di d. 1. Introduction Oxidative addition and reductive elimination are important steps in many organometallic reactions.' In particular, the oxidative addition of a hydrogen molecule to a PtL, complex (where L is a substituted phosphine) has been observed for a number of different ligands, L {e.g., P(c-CgHj,)3, P(i-Pr)s].>_ H,PtL, complexes have been observed to undergo many types of reactions, including insertion,* e.g., trans-H,Pt[P(c-C,Hj,)3]2 + CS, > trans-HPt(S,CH)[P(CsH)1)3}2 dimer formation,’* ¢.g., 2cis-H2Pt{(t-Bu),P(CH,);P(t-Bu).} 2H, + [Pt(t-Bu),P(CH2);P(¢-Bu)2]2 metaillation,’ ¢.g., 2trans-H2Pt[P(t-Bu)3]2 > rT H, + [((¢-Bu),PC(CH;),CH2) PtH], and oxidative addition followed by reductive elimination of H,,2310-12 e.g, trans-H,Pt[P(c-C,H;,)3]. + SiH, > HPt(SiH;)[P(c-CgH11)3]2 + He Such species have also been proposed as intermediates in the catalysis of the water—gas shift reaction! and of alkene hydro- genation.” (1) Collman, J. P.; Hegedus, L. S. “Principles and Applications of Orga- ition Metal Chemistry”; University Science Books: Mill Valley, CA, 1980; Chapter 4. (2) Yoshida, T.; Otsuka, S. J. Am. Chem. Soc. 1977, 99, 2134-2140. (3) Fornies, J.; Green, M.; Spencer, J. L.; Stone, F. G. A. J. Chem. Soc. Dalton Trans. 1977, 1006-1009. (4) Albinati, A.; Museo, A.; Carturan, G.; Strukel, G. Inorg. Chim, Acta 1976, 18, 219-223. (5) Immirzi, A.; Musco, A. Inorg. Chim. Acta 1977, 22, L35-L36. (6) Clark, H. C.; Goel, A. B.; Wong, C. S. J. Organomet. Chem. 1978, 152, C45—C47. (7) Yoshida, T.; Yamagata, T.; Tulip, T. H.; [bers, J. A., Otsuka, S. J. Am. Chem. Soc. 1978, 100, 2063-2073. (8) Tulip, T. H.; Yamagata, T.; Yoshida, T., Wilson, R. D.; Ibers, J. A.; Otsuka, S. Inorg. Chem. 1979, 18, 2239-2250. (9) Clark, H. C.; Goel, A. B.; Ogini, W. O. J. Organomet. Chem. 1978, 157, C16-C18. (10) Ebsworth, E. A. V.; Maranian, V. M.; Reed, F. J. S.; Gould, R. O. J. Chem. Soc., Dalton Trans. 1978, 1167-1170. (11) Clark. H. C.: Goel, A. B.: Billard, C. J. Organomet. Chem. 1979, 182, 431-440. (12) Paonessa, R. S.; Trogler, W. C. Organometallics 1982, 1, 768-770. (13) Yoshida, T.; Ueda, Y. Otsuka, S. J. Am. Chem. Soc. 1978, 100, 3941-3942, 0002-7863 /84/1506-6928501.50/0 ions for reductive elimination of the dimethyl and hydridomethy! Asa first step in gaining a better understanding of the formation of covalent bonds through reductive elimination and the scission of bonds via oxidative addition, we have examined the process PHs H3P oH | H \/ Proo+ | — Ptr a | H af \ Pts H, H Of particular interest in analyzing these results will be to explain why (i) the addition of hydrogen to PtL, occurs at room tem- perature, but reductive elimination is quite slow;?*" (ii) the reductive elimination of methane from (H)(CH;)Pt(L), proceeds at room temperature;'> but (iii) Pt(I1) diakyl complexes tend be stable with respect to forming carbon-carbon bonds through reductive elimination. Thus, diakyl complexes will disproportionate through 8-hydride elimination \ Se Pt /\ Lo CHeCHs ———=— Pt + HeC==CHe, + CoHe (2) rather than reductively eliminate when they thermally decom- pose.'*20 Only for Pt(II) diary! complexes, where 8-elimination is impossible, have carbon-carbon bonds been formed through reductive elimination at high temperatures.”"_ On the other hand, (iv) Pd(ID dimethyl complexes are quite unstable with respect to reductive elimination to yield C-C coupling.” In this paper we develop a relatively simple model of reaction I by examining the energetics, geometries, and wave functions along the reaction coordinate. These results indicate that oxidative addition of H, to PtL, depends crucially on the relative positions of the 5d!° and 6s!Sd° states of the platinum atom. The resulting energetics explain the observed differences regarding oxidative (14) Paonessa, R. S.; Trogler, W. C. J. Am. Chem. Soc. 1982, 104, 1138-1140. (15) Abis, L.; Ayusman, S; Halpern, J. J. Am. Chem. Soc. 1978, 100, 2915-2916. (16) Whitesides, G. M.; Gaasch, J. F.; Stedronsky, E. R. J. Am. Chem. Soc. 1972, 94, 5258-5270. (17) Nuzzo, R. G.; McCarthy, T. J.; Whitesides, G. M. J. Am. Chem. Soc. 1981, 103, 3404-3410. (18) McCarthy, T. J.; Nuzzo, R. G.; Whitesides, G. M. J. Am. Chem. Soc. 1981, 103, 1676-1678. (19) McCarthy, T. J.; Nuzzo, R. G.; Whitesides, G. M.; J. Am. Chem. Soc. 1981, 103, 3396-3403. (20) Komiya, S.: Yoshiyuki, M.; Yamamoto, A.: Yamamoto, T. Organo- metallics 1982, 1, 1528-1536. (21) Braterman, P. S.; Cross, R. J; Young, G. B. J. Chem. Soc., Dalton Trans. 3976, 1310. (22) Gillie, A.; Stille, J. K. J. Am. Chem. Soc. 1980, 102, 4933-4941. © 1984 American Chemical Society Oxidative Addition and Reductive Elimination H H & $ wee Left Pt-H Bond Pair Hsp PHs % One % Pt 633 Gp 5a 44 Pt 657 6p 5H? Right Pt-H Bond Pair One & One % Pt 6s" ep 5a°H°7 Pt 63 6p'5ahH* Oe \ | y| Figure 1. GVB orbitals for the Pt-H bonds of H,Pt(PH;), at equilib- rium. Hybridization for each singly occupied GVB orbital is shown on each plot. Each contour represents a change of 0.05 in amplitude. Solid lines represent positive amplitude. Dashed lines represent nodes. Dotted lines represent negative amplitude. Asterisks represent the position of atoms. addition/reductive elimination in Pt and Pd complexes. II. Summary of Results The details of the calculations are described in section FV. Here we will emphasize the main lessons from the theoretical studies. In the ground state of the reactants, the lone pairs of the phosphines make strong Lewis base bonds to the Pt atom, stabilizing the (d!°} configuration and leading to a linear complex. The oxidative addition product is square-planar, HsP OH \/ wae! Na zr with an HPtH angle of 79.4° and a PPtP angle of 99.9°. Despite the terminology “oxidative addition”, we find that there is ¢s- sentially no charge transfer from the Pt to the H’s. Instead, we find that the Pt in II corresponds to a (6s)'(5d)? configuration of Pt, allowing the formation of two covalent bonds to the H atoms. The generalized valence bond (GVB) orbitals for these bond pairs are shown in Figure 1 where each bond involves one electron in an H1s-like orbital and one electron in a 6s~5d hybrid (60% d) pointing at the H. The net exothermicity of reaction } is calculated to be 16 kcal/mol, so that one can consider the two Pt~H bonds of II to J. Am, Chem. Soc., Vol. 106, No, 23, 1984 6929 PH, PHy \ | H PA Pt | “ | 4 PHs Py G D . mol —» kcal 15.95 I 240 fi ‘ 1 L 1 SSO S220 | 255 28 RRS ROTATE PH, OUT OF WAY NOW CONVERT BOND H» AS LEWIS BASE s'q? pave df? Pt To NO Hz ACTIVATION. STRONG srt START FORMING Pt-H BONDS P1-H BONDS H, P-PI-PHy oor He 153° 176° 180° H-H 193A LtoA 074A 0.734 0.744 PI-H 150A 1664 245A 3.198 Figure 2. Potential energy curve along the reaction coordinate. be worth 60 kcal/mol each. [If the geometry of the Pt(PH,), fragment were kept fixed, then the average Pt~H bond energy would be 72 kcal/mol.] The next question is how do the orbitals change as the system goes from I to II? This process is orbital symmetry allowed”? and indeed we find in Figure 2 that the reaction has only a 2.3-keal/mol barrier. In examining the po- tential curve in Figure 2, three distinct phases in the process of oxidative addition are discerned. (i) Lewis Base /Lewis Acid Bonding of H, to Pt(PH;), (D — C in Figure 2). Since the platinum atom is in a d'® state, the Pt 6s orbital is empty and can serve as an electron acceptor. As the hydrogen molecule approaches the diphosphine complex, the Hy electrons utilize the Pt 6s orbital, making a Lewis acid /Lewis base bond. As this occurs, the phosphine ligands bend back (a) to lower steric interactions between the hydrogen molecule and the phosphine ligands and (b) to increase the overlap between the Pt 6s orbital and the H-H bonding orbital. The overlap between the Pt 6s and H-H bonding orbitals increases because the Pt 6s orbital polarizes away from the phosphines (hybridizes with the 6p orbital) to get orthogonal to the phosphine lone-pair orbitals. By the transition state, the P-Pt—-P bond angle has decreased from 180° to 153°, but the H~H bond length remains essentially constant (changing by only 0.003 A). The overall energy increase is 2.3 kcal/mol, whereas to bend the P-Pt-P angle the same amount in the diphosphine complex would cost 9 kcal/mol. Therefore we can consider the H.-Pt Lewis base/Lewis acid interaction to be worth 7 kcal/mol at the transition state. (ii) Electronic Promotion of the Piatinum Atom (C — B in Figure 2). Once the H, molecule has passed the transition state (point B in Figure 2), the platinum atom begins to build in some d°s! character. As the phosphines bend back from 153° to 113°, this becomes more favorable because the splitting between the d'° (14,) ground state and the lowest s'd® state (*B,) decreases as the P-Pt~P angle decreases. Thus, as the P-Pt~P angle de- creases from 180° to 140° and then to 90°, this splitting decreases from 107 kcal/mol, to 63 kcal/mol, and then to 20 kcal/mol. The mixing of the d’s! and the d’® states occurs mainly through the delocalization of the H, electrons into the Pt 6s orbital and the back-donation of the Pt 6d,, electrons into the H~H antibonding (23) Tatsumi, K.; Hoffmann, R.; Yamamoto, A.; Stille, J. K. Bull. Chem. Soc. Jpn. 1981, 54, 1857. 6930 J. Am. Chem. Soc., Vol. 106, No. 23, 1984 orbital. As these electronic changes occur, the H~H bond lengthens from 0.74 to 0.87 A. (iii) Covalent Bonding (B — A in Figure 2). By point B in Figure 2, the platinum atom is in the ds! state, allowing it to form two covalent Pt-H bonds. As the Pt--H bonds decrease from 1.72 A to their equilibrium bond lengths (1.50 A), the energy decreases rapidly. In this region the P-Pt-P bond angle changes from 113° to 100° and the H-H distance increases from 0.87 to 1.93 A. An important point from the calculations is that the final bonds are covalent; thus the oxidative addition of H, to Pt is not oxi- dative. Rather, the electronic state of the Pt is promoted from d'° to s!d° because the d!° state cannot make covalent bonds, while the s'd® state can make two covalent bonds. Therefore one might denote these states as Pt® and Pt", respectively, where the su- perscript indicates not oxidation state but rather maximum co- valency (maximum number of covalent bonds). Substantiation of this idea that H, addition is not oxidative is given by the observed promotion of H, addition to Ir(I) complexes by elec- tron-withdrawing substituents (opposite of the expected trend if one has assumed significant charge transfer to the hydrogens). A second point of the calculations is that a low barrier for the H, oxidation requires that the adduct (H.,) must be a sufficiently good Lewis base that it can activate the Pt by pushing back the phosphine ligands while forming a Lewis acid-base bond. The activation of the Pt corresponds to the stabilization of the s'd® (Pt) state that can form the covalent bonds. Implications for other systems are as foilows. Preliminary calculations for HP OCH \pe 4 A Nets Big indicate an average Pt~C bond energy of Dac = 36 kcal/mol, whereas the work presented here leads to Dp, = 60 kcal/mol. Extrapolating the same bond energies to H(CH;)Pt(PH;), gives the following energetics: Pt(PH3). + H;C-CH; — (PH;),Pt(CH,), AF = +19 kcal/mol Pt(PH;). + H-CH; — (PH;).Pt(H)(CH,) AE = +9 kcal/mol Pt(PH;). + H, — (PH;),PtH, AEF = -16 kcal/mol The above energetics can be used to explain the relative en- ergetics of hydridomethy!platinum(II) and of dihydride complexes. The platinum dihydrides are stable under 0.5 atm of hydrogen at room temperature and decompose slowly under vacuum.'* The only known cis-hydridomethylplatinum(II) complex decomposes quickly at room temperature.!5 Since the Pt(II) dimethyl! compiex has been calculated to have a larger driving force for reductive elimination, and it is known experimentally that these complexes are more stable than the hydridomethylplatinum(IT) complex, there must be a larger barrier to reductively eliminate ethane than to reductively eliminate methane. This is plausible since the directional character of the Pt-C bond requires that the methyl groups must rotate away from the Pt in order to overlap each other in forming the C-C bond. In contrast, for H, thes orbital used in the Pt—-H bond can also be used in the H~H bond. Thus, for reductive elimination of ethane directly from L,Pt(CH3),, it is plausible that a barrier exists even if the process is exothermic. (Preliminary calculations on this process for a Pd complex confirm these expectations.25) On the other hand, in the hydridomethy! complex, the hydrogen orbital can overlap both the carbon sp’ orbital and a Pt sd hybrid Low and Goddard Table I. Pt Atom State Splittings (in kcal/mol) GVB--RCI-—sGVBCI- state expt’, «= HF = (5/10)® 5/10)" (5/10) psa)? 0 0.0 0.0 0.0 'S(d") HO 314 270 12.3 12.2 Rd?) 147 B84 11.2 18.5 14.2 “See Calculational Details section. *The total energies of the ?D state are -27.506 19 hartrees at the HF level, -27.51933 hartrees at the GVB-PP level, and -27.551 29 hartrees at the RCI(5/10) level (using the relativistic effective core potential of ref 37). ‘The energies in this column are actually the average of experimentally observed j states derived from each Russell-Sanders term. orbital as methane reductively eliminates. This should lead to an activation barrier for reductive elimination of methane from hydridomethylpiatinum(I]) complexes that is intermediate between those for breaking H~H and forming C~C bonds, in agreement with the observed reactivities of hydridomethyl complexes.!5 We find that oxidative addition of H, to Pt(PH;), proceeds with a small activation barrier (2.3 kcal/mol) and the overall reaction is sufficiently exothermic that the products should be stable with respect to reductive elimination. This is in agreement with the results of Paonessa and Trogler.'* They have prepared the di- hydrides of the sterically unhindered Pt(PMe;), and Pt(PEt;), and found these complexes to be stable under 0.5 atm of H; and to decompose slowly under vacuum. The singular difference between Pd and Pt is that the Pd atom prefers the d!° configuration by 22 kcal/mol,” while Pt prefers the d°s' configuration by 11.0 kcal/mol.” Thus Pd has a total bias of about 33 kcal/mol in favor of the d!° configuration. Since the reductive eliminations con- sidered here involve mostly changing from s'd? to d'®, this means that the increased splitting should make the Pd(II) complexes considerably (about 34 kcal/mol) less stable than their Pt counterparts. This is in agreement with observed reductive elimination of ethane from Pd(CH;)2L, complexes” (where L = PPh;, PPh,CH;; L, = PPh,PCH,CH,PPh,) and the fact that hydrogen will not oxidatively add to a Pd diphosphine complex but does add for the corresponding platinum complex.” TH. Results A. Platinum Atom. The changes occurring during oxidative addition are partly determined by the electronic structure of the Pt atom. As with Ni and Pd, the platinum atom has three low- lying states, 3D(s'd®), 'S(d'°), and 2F(s?d®), We find that the Pt complexes tend to have the character of one or another of these atomic states and that the chemistry is dominated by this atomic character. In Table I, we summarize the relative energies of these states for various levels of calculations and experimental results.?’ Clearly, Hartree-Fock (HF) calculations are strongly biased against the d*° state. In the jargon of theorists, electron correlation is far more important if the two electrons are in a 5d orbital than if the electrons are in different orbitals (5d or 6s). A simple way to account for the major electron correlation errors implicit in the HF or molecular orbital (MO) description is the use of the GVB wave function, which allows each electron to have a dif- ferently shaped orbital and allows the orbitals for singlet-coupled electrons to overlap. Thus, in GVB each doubly occupied valence orbital of the HF wave function is described by a pair of over- lapping GVB orbitals. For an atom with a doubly occupied d orbital in the HF wave function, the GVB wave function converges to one tight d orbital (near the nucleus) and one diffuse d orbital (farther from the nucleus). We have chosen to describe the doubly occupied s orbital of the °F state by tight and diffuse s orbitals in order to be consistent with the correlation included in the GVB pairs describing d electrons.” (26) Moore, C. E. “Atomic Energy Levels”: National Bureau of Standards: Washington, DC, 1971; Vol. III (averaged over j states to cancel out spin-orbit ling). (24) Crabtree, R. Acc. Chem. Res. 1979, 12, 331-388. (25) Low, J. J.; Goddard, W. A., IE J. Am. Chem. Soc., submitted for publication. (27) Herzberg, G. “Molecular Spectra and Molecular Structure, Part EI. Electronic Spectra and Eiectronic Structure of Polyatomic Molecules”; D. Van Nostrand Co., Inc.: Princeton, NJ, 1966. Oxidative Addition and Reductive Elimination Pt (PH,), 90 T ‘ ‘ L -~Equiibrium bond 70 t angie from H,Pt{PHs), = ‘ ™~ 1 = ‘ S sor } = a H z ' t 5 30 ‘ ut 7 1 ‘ ior ' ‘a, : Fi : H aa 3 4 4 90 105 120 135 150 165 «180 P-Pt-P Angie (deg} Figure 3. Potential energy curves for the low-lying states of Pt(PH;)2 as a function of P-Pt-P angle. In many systems, electron correlation plays an important chemical role only for certain orbitals. In the platinum atom most of the electronic correlation important for state splittings occurs in the Pt 5d and 6s orbitals. Thus, if all ten d electrons in the Pt 'S(d!°) state are correlated in the GVB wave function, we denote this wave function as GVB(5/10) [here the 5 is the number of singlet-coupled electron pairs, while the 10 is the number of orbitals used to describe the five pairs]. If only one pair of electrons were to be correlated (i.c., for the bonding pair of electrons in Pt-H), we would use a GVB(1/2) wave function. When there is more than one pair to correlate, there are ad- ditiona] options in describing the wave function. The simplest description is for each pair to have singlet spin coupling as a simple valence bond (VB) wave function. This is denoted as GVB-PP and is the usual form in which the orbitals are calculated. However, for a system with five pairs of electrons (ten VB orbitals), there are 42 VB structures or spin couplings that should all be included in calculating the final wave function. In addition, there are interpair correlation effects, wherein if the two electrons in the d,, orbitals are at some instant closer to the nucleus, the two electrons in the d,, orbital will at that instant tend to be farther from the nucleus. These spin coupling and interpair correlation effects are included by carrying out a configuration interaction (CD) calculation in which the two electrons in each pair of orbitals are simultaneously allowed all possible occupations of those two orbitals, leading to what is termed a GVB-RCI wave function. Thus, for a GVB-PP(5/10) wave function, there are 3° = 243 configurations in the GVB-RCI wave function. The most complete wave function that can be described with just the GVB orbitals is to carry out a full CI with use of all possible occupations of these orbitals. This is termed GVB-CI, and for a GVB-PP(5/10) wave function, this leads to 8953 configurations. Since the GVB-RCI and GVB-CI are based on GVB orbitals, we can interpret these CI wave functions in terms of simple VB concepts. As is evident from the results in Table 1, the GVB-RCI wave function gives results that are as consistent as the GVB-CI results but with significantly fewer configurations. For the purposes of this paper, the GVB-RCI provides the best combination of accuracy and simplicity. B. Pi(PH;),. When two phosphines are added to a platinum atom, the major effect is to raise the energy of the platinum 6s orbital relative to the Pt 5 d orbitals. This occurs because the phosphine fone pair makes a Lewis acid~base bond by overlapping with (donating into) the Pt 6s orbital. The net result is that the ground state of P1(PH;), is a singlet (A,) state derived from the 1$(d!°) state of the platinum atom. In this state, the phosphines minimize their steric replusions by increasing the P-Pt—P bond angle to 180°. The low-lying tripiet states of Pt(PH3)2 are both je J. Am. Chem. Soc., Vol. 106, No. 23, 1984 6931 % DM re PHs 5 dyz orbital 6s~6p hybrid orbital One i ¢ ra Nar 4 | a ae \ 1 Figure 4. Open-shell orbitals for the °B, state for bent (100°) Pt(PHs)2. Table H. State Splittings for the d'° and d°s' States of Pt(PHs)2 state splittings PH,-Pi-PH, (kcal/mol) state angle, deg HF GVB(5/10) RCI(5/10) ‘Af 180.0 0.0 0.0 0.0 7B, 180.0 81.9 89.2 106.5 JA, 180.0 65.7 53.3 69.6 3B, 99.0° 28.5 35.2 $1.5 TA, 99.0° 22.8 22.1 24.6 3A, 99.0° 72.9 58.0 75.3 “The total energies for the 'A, are -712.170592 hartrees at the HF level, -712.199127 hartrees at the GVB-PP(5/10) level, and ~712.260738 hartrees at the RCI(5/10) level. #99.0° is the optimum bond angie for the *B, state. derived from the °D(s'd°) state of the platinum atom. When two hydrogen atoms make bonds to Pt(PHs)2, we find that the Pt atom changes from d’° to s!d° character in order to make covalent Pt-H bonds. In making these bonds, there is a major change in the P-Pt-P angle of PtL,. In order to assess the role of this geometric change upon the energetics of the Pt d’° and s!d° states, we show in Figure 3 the energies of the Pt(PH;), complex as a function of P-Pt-P bond angle. [The internal coordinates of the phosphine were frozen at the internal coordinates of free phosphine” (H-P-H angle = 93.3°, PH bond distance = 1.420 A). The Pt-P distance was chosen to be 2.268 A. The H-P-Pt angles were fixed (at 122.9°) so that the C; axis of the phosphine groups would pass through the platinum atom.] The lowest excited state of Pt(PH;), is the *B, state with an s'd° configuration. This state has a singly occupied 5d,, orbital and a singly occupied 6s orbital. The phosphines would prefer to have their lone pairs overlap the singly occupied d,,. orbital as much as possible, which would imply a bond angel of 90° or 180°; however, the 90° geometry allows the 6s pair to hybridize away from the phosphines, stabilizing this geometry. Steric interactions of the phosphines cause the bond angle to open up slightly, leading to an optimum bond angle of 99.0° (HF). A plot of the singly occupied orbitals for the *B, state is shown in Figure 4, where we note that the singly occupied 6s orbital has been polarized away from the phosphines. This occurs because the 6s orbital must be orthogonal to the phosphine lone pairs. In Tabie I, we show the state splittings at various levels of calculation for several states. The 2A, state has a singly occupied Pt d, orbital and a singly occupied Pt p orbital (see Figure 5). In this case a bond angle of 180° is favored since the phosphines can both overlap the singly occupied d,: orbital while simultaneously minimizing their steric (28) The best (lowest energy) two-orbital description of the 6s pair of electrons would be in terms of two sp hybrid orbitals, ¢, = ce, + cog, and Wp = Cit, — Crt. as for Be, Mg, Za, etc"? (29) Goddard, W. A., Hil; Harding, L. B. Annu. Rev. Phys. Chem. 1978, 29, 363-396. (30) Noell. J. O.; Hay, P. J. J. Amt. Chem. Soc. 1982, 104, 4578~4584. 6932 J. Am. Chem. Soc., Vol. 106, No. 23, 1984 =6~ Low and Goddard Table 111. Summary of Results for Pt-H dipole De total energy,’ w,? moment‘ Mulliken Mulliken RA kcal/mol hartrees cm! Debye pop. on Pt pop. on H HF 1.516 37.3 28.065 612 2027 2.52 10.07 0.93 GVB-PP(1/2) 1,526 $1.6 28.088 370 1948 1.89 10.10 0.90 GVB-PP(S/10) 1.530 58.1 28.098 619 1930 1.88 10.10 0.90 RC1(5/10) 1.544 48.9 28.128 813 1914 1.86 10.11 0.89 GVB-CI(5/10) 1.549 52.8 28.136 407 1909 1.90 10.10 0.90 pel Lsi¢ 60.6 experiment* 1.528 <79.3 2260 * Huber, K. P.; Herzberg, G. “Molecular Spectra and Molecular Structure. IV. C of Di ic Molecules”; Van Nostrand-Reinhold Co.: New York, 1979. *Frequencies were obtained from the curvature at R, which was obtained from a cubic spline fit. “The positive sign implies PttH™. “This calculation was only carried out at this bond distance. ‘All total energies are reported for R = 1.51 A. te t H,P—P!— PH, HP —G2PKB— PH, Pt 6p hybrid orbital Pt dz? orbital Figure 5. Open-shell orbitals for the 7A, state for linear Pt(PH;). interactions. However, in this geometry the s orbital cannot as easily polarize out of the way of the phosphine Ione pairs, leading to a higher energy. In fact, for this state the Pt s electron has been promoted to the p orbital?! (see Figure 5). The *B, state is the best triplet because it allows both phosphines to overlap the singly occupied d orbital, while allowing the platinum s orbital to polarize out of the way of the phosphine lone pairs. Comparisons between Pd and Pt complexes are useful because both atoms have low-lying d°s' and d!° atomic states but yield different ground states. In palladium the atom has a d’® ground state (22.9 kcal/mol below the d°s! state), while in platinum the d°s! state is the ground state (11.0 kcal/mol below the d’° state). This should lead to d'™s'd? splittings for the Pd diphosphines that are 33.9 kcal/mol larger (disfavoring oxidative addition to Pd) and hence should result in much weaker Pd¢-H and Pd-C o bonds for Pd diphosphine complexes than for the corresponding Pt complexes. Consistent with these expectations, hydrogen has not been observed to add to PdL, while it has for PtL, [e.g., L = P(c-CgH,,);, PG-Pr)3}.2 In addition, Gillie and Stille” have observed reductive elimination of ethane from Pd(II} dimethyl complexes, while Pt(II) dimethyl complexes are much more stable. These cases demonstrate how the d'*s!d? splittings for these ML, complexes affect the driving forces for reductive elimination and oxidative addition. C. Pt-H. Caiculations were performed on the platinum hydride diatomic molecule to determine how the energetics of the Pt-H bond are affected by the level of the calculations. These studies also help demonstrate the nature of the Pt-H bond. Five levels of calculation have been performed: HF, GVB(1/2), GVB(5/10), RCI(5/10), and GVB-CI(5/10). The results of these calculations are shown in Table [II where we see that bond distance (R,), bond energy (D,), and vibrational frequency (w,) are fairly insensitive to the level of calculation once the Pt~H bond pair was correlated. Thus, description of the Pt-H bond at the GVB(1/2) level provides a quite adequate description of the bond and should be a suitable level for use in the Pt~H bonds in H,Pt(PH;), and in reductive elimination from this complex. g% % CHOOH Pt 6s-5Sd hybrid orbital Hydrogen orbital One ¢ [One ‘ % Pt 523 y0%q56, 10 | Pi P pq! 478 Figure 6. GVB orbitals for diatomic PtH. Experimental characterization of PtH includes the bond length and vibrational frequency but only an upper bound for the bond energy. This compares well with the experimental geometry (1.5% long) but is 15% low for the vibrational frequencies. The best theoretical bond energy of 60.6 kcal/mol was obtained from a dissociation-consistent configuration interaction (DC-CI) calcu- lation. This calculation involves all single and double excitations from the active space defined by the Pt-H bond pair from a GVB-PP(1/2) calculation times all single excitations from the semiactive space defined by the remaining platinum valence electrons. This calculation was carried out at only a single point (1.51 A), so a vibrational frequency is not reported for this level of calculation. This calculated bond energy is 20 kcal/mol smaller than the experimental upper bound of 80 kcal/mol. The calculated Mulliken populations and dipole moments show that the PtH bond is essentially covalent. This is consistent with the small difference in Pauling electronegativities of Pt (2.2) and H (2.1).? However, detailed comparison of the dipole moment and Mulliken populations appears to give conflicting results. The dipole moment indicates a transfer of 0.26 e- to the hydrogen atom, while the Mulliken populations indicate a transfer of 0.10 ¢- from the H. This apparent conflict is partly due to the Pt part of the bond orbital being a Pt sd hybrid with some Pt p character so that is is polarized toward the hydrogen. This polarization contributes to the dipole moment but not to the Mulliken charge transfer. To obtain a qualitative measure of the polarization taking piace, we have calculated the dipole moment of the platinum orbitals from a GVB(1/2) calculation on PtH. This calculation included the localized Pt GVB orbital from the Pt~H GVB bond pair and the other five Pt-like nonbonding sd orbitals (four doubly occupied and the singly occupied d,2_» orbital), where in each case any hydrogen character was deleted (and the orbitals were renor- lized). This calculation on the Pt atom yields a dipole moment of 1.08 D, over half the total dipole moment of Pt-H. Subtracting (31) We have used C,, symmetry to classify the states in this discussion. At a P-Pt-P angie of 180° the P1(PH,), complex would actually have D,, symmetry. The *A, state would be one component of the *E’ state. (32) Bair, R. A.; Goddard, W. A., HI J. Chem. Phys., submitted for publication. Bair, R. A. Ph.D. Thesis, California Institute of Technology, 1981. Oxidative Addition and Reductive Elimination Table IV. Geometries along the Reaction Coordinates 1-13 J. Am. Chem. Soc., Vol. 106, No. 23, 1984 6933 1 2 3 4 5 6 7 8 9 10 il 12 13 Rei’ 1.166 1.417 1.542 1.667 1.792 1.917 2.042 2.167 2.417 2.667 2.917 3.167 o Rr 2.447 2.417 2.387 2.372 2.356 2.335 2.336 2.348 2.35t 2.330 2.334 2.325 2.318 Rin 1.926 1.570 1,104 0.865 0.812 0.780 0.762 0.750 0.740 0.733 0.728 0.732 0.743 Revw 1.504 1.620 1.628 1.723 1.838 1.957 2.077 2.199 2.445 2.692 2.940 3.188 Rew, 1.525 1.522 1.519 1.524 1.525 1.525 1.526 1.529 1.530 1.525 1.518 1.526 1.527 Rew 1.529 1.526 1.526 1.526 1.525 1.526 1.525 1.527 1.526 1.525 1.522 1.527 1.527 Opm-p? 99.9 102.5 108.1 113.5 122.3 127.2 133.8 137.4 152.9 167.2 170.1 175.2 180.0 Oya 19.4 58.0 39.4 29.1 25.5 23.0 211 19.6 17.4 15.6 14.3 13.2 Oy py 96.6 96.8 95.9 95.3 95.0 95.2 94.9 94.8 95.1 95.6 94,3 95.7 96.2 95.5 95.5 95.5 94.9 94.7 94.8 95.2 95.0 95.5 95.7 95.8 95.8 96.2 Ce 119.3 120.2 121.2 123.8 123.1 124.4 124.8 124.8 124.9 120.7 122.9 121.4 120.7 ea 121.4 120.9 121.0 120.4 121.1 120.2 120.0 120.2 119.7 121.4 121.3 121.1 120.7 “All Rin A. *All 8 in deg. 8.0 8 ¢ Hartree-Fock — MP! (Phil, —™ Hy + Pt (PH), 2.00 $ 180 [HgPIKPHyh, ~~ Hp + Pt (Pry), e Lor H-H distance @ Fond 74 462 2 fo] . a & -agk GVB-C1(2/6) @ 3 8 . > aah |_P-P1-P bond | 4144 @ = RCI(4/8)* GVBCI(2/6) 2 angie 2 z 5 S ied 2 eel 4i26 2 a x 8 ' a 17.6 x a dios & 0.96 108 & a -24,9 r n 1 1 L 0.70 1 l fl r = 90 150 185 220 2,55 2.90 325 “1S L500 ««L85)—2.200 2.55 2.90 3.25 iS ; Pt-H, distance (A) Figure 7. Plot of energy along the reaction coordinate for HF, GVB- C1(2/6), and RCI(4/8)*GVB-Cl(2/6) wave functions. this dipole moment due to Pt atom polarization from the total dipole moment leads to a residual molecular moment of 0.81 D, corresponding to a transfer of only 0.11 ¢” to the hydrogen atom. Therefore, a large fraction of the dipole moment is due to po- larization of the Pt valence orbitals. The remaining discrepancy of Qy = 1.11 e° from the dipole moment vs. 0, = 0.90 ¢ from the Mulliken populations represents a deficiency in the Mulliken analysis, namely, the equal partitioning of overlap terms tends to underestimate the population on H. Summarizing, the charge transfer in the Pt-H bond is small so that the Pt~H bond should be described as covalent. The Mulliken populations for the GVB orbitals (see Figure 6) of the Pt-H bond show that the GVB orbital localized on the Pt atom is about 60% Pt d character and 40% Pt sp character. This hybridization of the Pt d,: orbital makes the density along the z axis larger than it would be for either a pure Pt 6s orbital or a pure Pt d, orbital. This increases the overlap (and contragra- dience) between the platinum orbital and the hydrogen orbital.* D. H,Pt(PH;),, The changes in the electronic structure that occur during oxidative addition can most easily be elucidated by following a reaction path from reactants to products. We used the distinguished coordinate method to find a good approximation to the reaction coordinate at various levels of calculation.*> The distinguished coordinate method freezes one internal coordinate of the system to be studied while optimizing all the others for lowest energy. By repeating this procedure for a number of values for the frozen coordinate, one can generate a potential curve that is only a function of one variable and changes continuously from products to reactants. These optimizations were performed at the HE level with use of an analytic gradient technique.* HF (33) Pauling. L. “The Nature of the Chemical Bond”, 3rd ed.; Cornell University Press: {thaca, New York, 1960; pp 88-98. Pt-H, distance (A) Figure 8. Changes in the P-Pt-P bond angie and H~H distance along the reaction coordinate. 3 C 2.0; a 10 a He & 1.6 Pt {Pl —~ H,+ PtP 3 E & 12k 2 a 2 40.0 8 a 08F oe So) a z 0.4 9.5 s he PF sp’ 0 rl 1 L 1 1 3.0 4S. 140 165 L930 2.45 240 2.65 Pt-H, distance (A) Figure 9. Muliken population along the reaction coordinate. provides accurate equilibrium geometries for various platinum complexes®” and leads to exothermicities and barrier heights similar to correlated wave functions. The geometries resulting from the distinguished coordinate method are listed in Table IV. For more details on how these calculations were carried out, see section IV. The distinguished coordinate used in these calculations was the Pt-H, distance. The HF potential as a function of Pt-H, distance is shown in Figure 7, As the Pt-H, distance was varied, only two other internal coordinates changed significantly. The P~Pt—P angle changed from 180° to 100° through the reaction path. The H-H distance increased a small amount as the hydrogen molecule approached the Pt(PH), complex up to a Pt-H, distance of 2.0 A. For PtH, (34) Steigerwald. M. L. Ph.D. Thesis, California Institute of Technology, 1983 5) Rothman, M. J; Lohr, L. L. Chem. Phys. Lett. 1980, 70, 405. (36) Low, 3. J.; Goddard, W. A., III, manuscript in preparation. (37) Noell, J. O.; Hay, P. J. Inorg. Chem. 1982, 21, 14-20. 6934 J. Am. Chem. Soc., Vol. 106, No. 23, 1984 distances less than 2.0 A, the H~H distance increased rapidly from 0.76 to 1.926 A. These geometry changes as a function of Pt-H, distance are shown in Figure 8. E. Charge Populations. The Mulliken populations of the Pt d, Pts and H, orbitals are plotted as a function of Pt-H, distance in Figure 9. This plot shows that the amount of Pt 6s character increases and the amount of Pt 5d character decreases as H, approaches the Pt(PH;)2 comp At the dis d limit, the Pt population has 9.51 d electrons and 0.38 s electrons. At equilibrium, the population has 9.10 d electrons and 0.96 s electrons. Although Mulliken populations are not truly quanti- tative measures for the character and locations of the electrons, as shown above for Pt-H, they can be used to provide qualitative ideas of how charge is distributed. At equilibrium, the Mulliken populations show that the platinum atom is in a d°s! state. At the dissociated limit and at the transition state, the platinum atom is in a state that is mainly d’° and singiet. In Noell’s population analysis,* charges are assigned to atoms by partitioning space. All charge within the covalent radius of the Pt atom was assigned to this center. The space outside this sphere was partitioned into cones with 45° angles of rotation about each ligand. The charge in a particular cone was assigned to the ligand that was contained in the cone. The remaining charge outside the covalent radius of the platinum atom was assigned to the platinum atom. This partitioning resulted in a positively charged platinum atom (1.22 7), negatively charged hydrogen atoms (-0.29 e°), and negatively charged PH; groups (-0.32 ¢). Noell feels that this is a more reasonable assignment because it is closer to the formal oxidation states of the platinum and hy- drogen atoms. One problem with Noell’s analysis is that a rel- atively large fraction of the platinum atom d basis (11%) and sp basis (37%) is outside the covalent radius of the platinum atom. When the platinum atom is in a s'd? state, this would result in 1.36 e* being assigned to the ligands! Clearly this is not a fair division of density. Comparing the Pauling electronegativities”* of platinum (2.2) and hydrogen (2.1), we see that the hydrogen atom should be slightly negatively charged. But such a small difference in the electronegativity should lead to a bond that is essentially covalent (less than 4% ionic by Pauling’s formula). The dipole moment of Pt-H indicates that the Pt~H bond is more polar than Pauling would predict, as discussed in section III. This is due largely to the polarization of the Pt valence electrons rather than to charge transfer. Although the Mulliken population leads to the wrong polarity (Pt"H’), it is paritcularly useful in determining the relative amounts of Pt s, p, and d character in a wave function. Quali- tatively, the Mulliken populations indicate that there is not a large amount of charge transfer, and this is in agreement with the dipole moments. F. Forms for the Wave Functions, In analyzing the character of bond orbitals, it is important to use wave functions that change smoothly as one goes from one extreme with a doubly occupied Pt d,, orbital and H—H bond pair to the other extreme with Pt-H bonds. The simplest wave function providing a good description of the Pt-H bonds is the GVB(2/4) wave function. This wave function contains one GVB pair for each Pt-H bond, as shown in Figure 1. These orbitals involve combinations of the platinum 5d,, and 6s orbitals and of the two hydrogen atomic orbitals. The best GVB orbitals at the dissociated limit are shown in Figure 10. These orbitals involve combinations of a tight Pt 5d,, orbital, a diffuse 5d,, orbital, and two hydrogen atomic orbitals. Thus the GVB(2/4) wave function is nor consistent throughout the reaction path because different types of correlation are required to describe the electrons localized on the platinum atom at the different limits. At the dissociated limit, the pair of Pt electrons involved in the Pt-H bonds are both in d,, orbitals and are cor- related in-out. In other words, one electron is in close to the platinum atom while the other is farther away. After the two Pt-H bonds are formed, the bonding Pt electrons are both in sd hybrid orbitals. A. more consistent wave function for this reaction would be to allow the Pt pair of bonding electrons to use a tight d orbital, a =8- Low and Goddard x *. and $ aS Left Hydrogen Orbital Right Hydrogen Orbital One % / | ? Figere 10. GVB orbitals for H, + Pt(PH;), near the transition state. Table V. Energies along the Reaction Path GVB-C1(2/6)- Rey HF, GVB-Cl(2/6), *RCKH(4/8), x" kcal/mol kcal/mol kcal/mol 1,166 16.21 -23.79 ~15.90 1.417 ~5.92 ~16.91 10.09 1.542 2.26 4.76 1.86 1.667 3.12 “LAL 0.56 1.792 3.42 0.55 0.51 1.917 3.69 0.13 0.13 2.042 4.00 0.86 0.70 2.167 4.04 1.25 1.40 2.417 3.47 1.96 2.34 2.667 2.37 L71 2.05 2.917 1.26 0.92 1.40 3.167 0.15 0.02 0.52 oe 0.0 0.0 0.0 *The total energies at the dissociated limit (#) are -713.330533 hartrees at the HF level, -713.363061 hartrees at the GVB-CI(2/6) level, and ~713.449 931 hartrees at the GVB-C1(2/6)*RCI(4/8) level. diffuse d orbital, and a Pt s orbital. This would allow this pair of electrons to have both in-out correlation and the optimum ds! mixture throughout the reaction. In order that the two GVB pairs involved in the bonding be treated equivalently, we have permitted each of them to have three natural orbitals (rather than two). At the dissociated limit, this corresponds to a Pt pair, as was described above, and to an H, molecule described at the GVB(1/3) level (in-out plus left-right correlation). In considering the effects of electron correlation on this reaction, we examined the HF, GVB~C1(2/6), and GVB-CI(2/6)*RCI- (4/8) wave functions. The GVB-CI(2/6) wave function includes electronic correlation terms differential in describing the Pt-H bonds. The GVB-CI(2/6)*RCI(4/8) wave function includes both the Pt-H bonding terms of the GVB-CI(2/6) level as well as the d-d correlations important in determining the d°s'~d’° splitting on the platinum atom. For more calculational details, see section IV. Oxidative Addition and Reductive Elimination Table VI. Transition State as a Function of Electronic Correlation for Pt(PH3)2 + H2 —> H,Pt(PHs)2 level of Pi-H, activation - electronic distance, energy, exothermicity, correlation A kcal/mol kcal/mol HF 2.199 4.04 16.21 GVB-CI(2/6) 2.417 1.96 -23.79 RCI(4/8)*GVB- 2.417 2.34 15.90 Cl(2/6) Table VII. Comparison of the HF Activation Barrier for Pt(PH;). + H, — P1(PH,).(H), and Important Geometric Parameters at the Transition State Obtained in Various ab Initio Studies SE, Rew » Opry kcal/mol x a deg Noell and Ha: 17.4 1.81 0.90 120 Kitaura et al. 5.2 2.066 0.766 147.7 this work 4.04 2.199 0.750 137.4 “Reference 30. *Reference 39. The potential curves are shown in Figure 7, and the calculated energies are tabulated in Table V. The main effect of correlating the Pt-H bonds at the GVB-CI(2/6) level is to increase the exothermicity of the reaction and to move the transition state to longer distances. Correlating the nonbonding d electrons at the GVB-CI(2/6)*RCI(4/8) level makes the exothermicity for the reaction smaller than for the GVB-Cl(2/6) level wave function, but gets essentially the same transition-state geometry and barrier. Correlating the nonbonding d electrons does not affect the long-range behavior of the Pt-H bonds. The GVB-C1(2/6) wave function (in which the nonbonding d electrons are doubly occupied) does as well as the GVB-CI(2/6)*RCI(4/8) wave function (which has the nonbonding d electrons correlated) near the transition state. This implies that this transition-state geometry is less sensitive to the s'd°-d'° splitting than is the exothermicity. Qualitatively, these potential curves all have similar shapes. The potential curves for the correlated wave functions can be divided into three regions similar to those for the HF surface. This implies that the HF level wave function could have been used to elucidate the electronic structure of the mechanism. Unfortunately HF yields orbitals that are delocalized and difficult to interpret, whereas the GVB types of wave functions lead to orbitals that are localized and easier to interpret. Also, the GVB wave function allows one to interpret the various types of correlation and to see how each one affects the wave function. The GVB-CI(2/6) wave function leads to an improved description of the long-range at- tractive terms in the wave function, leading to a lower activation energy and a longer Pt—H bond distance at the transition state. At the GVB-CI(2/6)*RCI(4/8) level, we also include interpair correlations of the nonbonding d electrons on the platinum atom. These correlations were not important at the transition state because the Pt atom still has a d'°-like configuration. On the other hand, these dd correlations have a big effect on the d!°-s'd? separation, and hence they have a big effect on the reaction exothermicity. These correlation effects stabilize d'° relative to s'd? and have led to a smaller exothermicity. In Table VI we present a summary of the energetics for oxidative addition at the different levels of calculation. G. Comparison with Previous Results. The previous two ab initio studies of this system gave different results for activation barrier and tr state. A parison of the results presented in this paper with the results from Noell and Hay and from Kitaura et al.>° is shown in Table VII. The transition-state geometry found in our studies and by Kitaura et al.2° is much closer to products than Noell and Hay’s” transition state. Also, our HF activation barrier (4.04 kcal) for oxidative addition is close to the value (5.2 kcal) found by Kitaura et. al2° Noell and Hay,” on the other hand, found a significantly (38) Noell, J. O. Inorg. Chem. 1982, 21, 11-14. aoe Kitaura, K.; Obara, S.; Morokuma, K. J. Am. Chem. Soc. 1961, 103, -2892. -9- J. Am. Chem. Soc., Vol. 106, No. 23, 1984 6935 larger activation barrier (17.4 kcal/mol). Since we have used the same effective potential as Noell and Hay*’ and completely op- timized the geometry for every fixed value of Pt-H, distance, Noell and Hay’s™ high activation barrier must be due to their partial optimization, which apparently did not converge to the lowest energy point along the reaction coordinate. The differences between our transition-state geometry and that of Kitaura et al.2° must be due to the different effective potentials and basis sets used. Our results should be more reliable for the following reasons. (1) We have used Noell and Hay’s’” Pt po- tential, which includes the f-projected terms required when f electrons are included in the effective potential, whereas the Kitaura et al.2° calculations used an effective potential with only sand p projections. (2) We have used a larger hydrogen basis than Kitaura et al.’ This larger basis includes the more diffuse character needed to describe the long-range Pt-H, interactions at the transition state. The energies of reaction found from HF calculations in these three studies were also very different. Our AE (-16.2 kcal/mol) is larger than that found by Noell and Hay” (-6.7 kcal/mol), but smaller than the AE(—36.9 kcal/mol) of Kitaura et al.°?> We obtain a larger AE than Noell and Hay for this reaction because we allowed the Pt~P bond lengths to change along the reaction path. Noell and Hay held this parameter fixed at a value closer to the optimum for Pt(PH;)2, which should favor the dissociated limit and give a smaller AE. The Pt potential used by Kitaura et al.29 is known to give Pt-H bonds that are 11.6 kcal/mol too strong.” Applying this correction factor to Kitaura et al.'s” AE leads to 2 corrected AE of 13.7 kcal/mol, which is very close to our value. Comparing geometries with the available X-ray structures, we see that our Pi-P bond distances are too long by 0.1 to 0.2 A. For Pt(PCy;)2, the experimental distance was found to be 2.231 AS while our calculated Pt~P bond distance for Pt(PHs), is 2.32 A. Typical Pt-P bond distances for Pt(II) complexes are 2.25 A for t-H,Pt(PCy;)3,” 2.268 A for t-PtHCI[P(CgH3)C2Hs]2." and 2.248 A for c-PtCl,(PMes3)2.47 Our calculated Pt-Pt bond distance for c-H,Pt(PH;), is 2.45 A, which is 0.2 A too long. This elongation of the Pt-P bond length was also found by Noell and Hay?’ when they optimized the geometry of Pt(PH;)2 and found a Pt-P distance of 2.36 A (using a different effective potential and basis set on the phosphorus). This effect appears to be systematic for phosphorus Lewis acid/Lewis base bonds treated at the HF level with a valence double-¢ basis. In BH;PH;, where phosphorus is making a similar Lewis acid /Lewis base bond, we find a B-P bond length of 2.180 Aat the HF level using a double-¢ basis“? When the geometry was optimized with polarization functions on both the phosphorus and boron,”? the B-P distance was found to be 2.055 A. The ex- perimental“ B-P distance in BH;PH; is 1.937 A. Therefore, approximately 0.1 A of the error observed in P Lewis acid /Lewis base bonds is due to the use of an unpolarized basis. Ahirichs and Koch*S have carried out calculations on BH;PH; using a smaller basis set with both HF and correlated wave functions (CEPA). The smaller basis set yields a shorter B~P bond distance of 1.99 A at the HF level. For the correlated wave function, their B-P bond distance is 0.04 A shorter than their HF results. This indicates a large part of the remaining discrepancy must be due to electronic correlation. Kitaura et al2? found Pt-P bonds that were short by 0.1 A, but this is most likely due to the small basis set (STO-2G) used to optimize their geometries, which would underestimate bond distances for Lewis acid~Lewis base bonds. (40) Immirzi, A; Musco, A.; Carturan, G.; Belluco, U. Jnorg. Chim. Acta 1975, 12, L13. (41) Eisenberg, R.; Ibers, J. A. Inorg. Chem. 1965, 4, 473. (42) Measmer, G. G.; Amma, E. L.; Ibers, J. A. Inorg. Chem. 1967, 6, 725. (43) Dunning, T. H.; Hay, P. J. In “Modern Theoretical Chemistry: Methods of Electronic Structure Theory”; Schaefer, H. F., IH, Ed.; Plenum Press: New York, 1977; Vol. 3, Chapter 1, pp 1-27. (44) Durig, J. R.; Li, Y. S.; Carreira, L. A., Odom, J.D. J. Am, Chem. Soc. 1973, 95, 2491-2496. (45) Ablrichs, R.; Koch, W. Chem. Phys. Lett. 1978, 53, 341-344. -10- 6936 J. Am. Chem. Soc., Vol. 106, No. 23, 1984 H Hag FY Ley HMM P Figure 11. Geometry of H,Pt(PH;), obtained by using a double-} basis on phosphines. Hoffmann and co-workers” have performed an analysis of reductive elimination reactions using the extended Hiickel method. Three major conclusions were presented in this work: (1) The better the o-donating capability of the leaving group, the more readily the elimination proceeds. (2) Stronger donor ligands trans to the leaving groups give a higher barrier for the elimination reaction. (3) A lower positioning of the MA, b, orbital facilitates the reductive elimination of R,. A lower MA, b, energy will be given by a lower metal d orbital energy. Our studies concur with the third conclusion of Hoffmann et al. A more stable d orbital implies a more stable d’° state of the metal relative to s'd? that will in turn increase the driving force for reductive elimination. This should also decrease the barrier for reductive elimination. Our results do not bear on the first two points since we have studied only the one system. Balazs et al.“* have also studied (1) using the SCF-Xa-SW approach. However, they do not report calculated geometries or transition states nor do they report calculated bond energies or activation energies; thus there is little with which to compare our work. The electronic densities from Xa agree with our results, indicating neutral H atoms (charge of -0.04 e). IV. Calculational Details A. Potentials and Basis Sets. On platinum atom we used the relativistic effective potential of Noell and Hay.>’ For the hy- drogen atoms bonded directly to the Pt atom we used a triple-f contraction of Huzinaga’s six-Gaussian basis.“’ For phosphorus we used the SHC effective potentials of Rappé et al. with a minimum basis contraction based on the atomic orbitals. The hydrogen atoms bonded to P were described with a minimum basis set based on Huzinaga’s four-Gaussian basis (unscaled). To determine whether the use of minimum basis phosphines affected the geometries or energetics for oxidative addition, we carried out geometry optimizations on H,Pt(PH;), and Pt(PH;), using full double-¢ basis sets on the phosphine ligands. The results are shown in Figures 11 and 12, The exothermicity calculated for this reaction with double-{ phosphines is 13.84 kcal/mol, only 2.47 kcal/mol! smaller than the result with minimum basis set phos- phines. This represents only a 1.25-kcal/mol error per Pt-H bond. B. GVB-PP (Generalized Valence Bond with Perfect Pairing Restrictions).4? {n this wave function each correlated pair of (46) Balazs, A. C.; Johnson, K. H.; Whitesides, G. M. Inorg. Chem. 1982, 21, 2162-2174. (47) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293-1302. (48) Rappé, A. K.; Smedley, T. A.; Goddard, W. A., III J. Phys. Chem. 1981, 85, 1662-1666. (49) Bobrowiez, F, W., Goddard, W. A., TI In “Modern Theoretical Chemistry: Methods of Electronic Structure Theory”; Schaefer, H. F., 11, Ed.; Plenum Press: New York, 1977; Vol. 3, Chapter 4, pp 79-127. Low and Goddard My a Bap H, Hilti Pa ts cant SI BE H # Figure 12, Geometry of H,Pt(PH;), obtained by using a minimum basis on phosphines. electrons is described as a spin singlet state y.@ + or. This description can be transformed to a natural orbital description Co ao where (+ @) _ W- @) e*ad+sy? @ Ga-sy? /e, = (1- S)/(1 +S), ¢:? + ¢,? = 1, and S = (g,[¢). These natural orbitals are then used in higher Jevel CI calculations. C. GVB~RCI (Restricted Configuration Interaction). The GVB-RCI calculation includes the configurations ¢,’, ¢,’, and 1, for each GVB pair. When the configuration ¢,¢, is multiplied by similar configurations in the other GVB pairs, more general spin couplings are included that will optimize the total spin ei- ion of the electronic wave function. This spin optimization can be important in describing the dissociation of multiple bonds and in describing the changes in the spin multiplicity in different atomic states. This wave function also includes interpair corre- lations important in the atomic d'~s'd? splittings. This type of wave function is useful because it still maintains orthogonal GVB pairs of electrons, facilitating the interpretation of the wave function. When ing singlet and triplet states of the platinum atom and of Pt(PH;),, we counted the two open-sheil orbitals as a GVB pair in the RCI(5/10) nomenclature. This is consistent since the triplet wave function contains all the configurations that the singlet contains except for those that have two electrons in one of the open-shell orbitals. D. GVB-CI (Generalized Valence Bond Configuration Inter- action). This type of CI is carried out by using all possible configurations that can be formed from the various occupations of the GVB orbitals from the GVB-PP calculation. This wave function includes all the terms of the RCI wave function plus terms that allow the GVB pairs to overlap and to change shape by allowing linear combinations between pairs. Such terms are particularly important near the region where the Pt-H bonds are just starting to form. Omission of such terms (as in a GVB-PP or RCI calculations) would fead to an artificial hump in the transition region. Figure 13 demonstrates the importance of full correlation among the four electrons that are involved with the oxidation/reduction process. The GVB-PP wave function can describe the two Pt-H bonds at equilibrium or the doubly occupied d orbital and H~H bond at the dissociated limit. Near the region where both of the above VB descriptions are important, the energy of the GVB-PP wave function becomes artificially high. This gives a transition state near 1.55 A for the GVB~PP wave function that disappears ~11- Oxidative Addition and Reductive Elimination 9,0 GVB-PP (2/6) — 24F 3S E = 8 -4.2r GVB~CI (2/6) = Pond 2 -10.8F a Cc iw ECS og HAP (PHL, —> Ho+ Pt(PHy), -24.0 2. 4 al 4. i iS 450185 2.200 2.55) 2.90 3.25 Pt-H, distance (A) 13. Comparison of energies along the reaction coordinate for GVB-PP(2/6) and GVB-CI(2/6) wave functions. for the GVB-CI wave function (which can describe both VB wave functions). Geometry Optimizations. All of the geometry optimizations were Couine! by using an analytic gradient procedure (GVBGRAD). This program was based on (a) the GvB2Ps‘? program to evaluate density matrices for restricted HF and GVB~-PP wave functions, (b) the HONDO” program to calculate derivatives of the ab initio terms in the energy expression, and (c) routines from the GAUSS 80°! program and the Los Alamos effective potential program’? to calculate the effective potential terms of the derivative. For the optimization of the geometries we used a relatively simple Newton-Raphson technique® in which the second derivative matrix is updated after every gradient calculation (except for the starting geometry). The end-on approach of H, to Pt(PH;), was not considered in this work since the side-on approach of H, to Pt(PH;) gave a low barrier. The end-on approach should give a higher barrier because it would require breaking an H-H bond (104 kcal/mol) and promoting PtL, to a triplet state (~50 kcal/mol) while only getting ~72 kcal/mol back in the Pi-H bond. [Kitaura et al. found that the C,, transition state is a true saddle point (i.c., there is only one negative root in the curvature matrix).] F. Hybrid Wave Functions. In examining the effect of elec- tronic correlation along the reaction path, we calculated a GVB-Cl(2/6)*RCI(4/8) wave function where the orbitals were optimized for the full 3360 confi iguration (8568 spin eigenfunc- tions) wave function by using the GvB3°? program. We used this wave function to examine the effects of correlating the nonbonding d electrons on the energetics along the reaction coordinate. The electrons in the Pt-H bonds were treated at the GVB-CI level for the reasons described above. The d nonbonding orbitals were treated at the RCI(4/8) level because this level was needed to get reasonable triplet-singlet splittings for the atom. The resulting wave function is therefore a product of the GVB(2/6) wave function for the Pt-H bonds and a RCI(4/8) for the nonbonding (50) Dupuis, M.; King, H. F. J. Chem. Phys. 1978, 68, 3998-4004. (51) Binkley, J. Ss; Whites: teside, R. A.; Krishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol. S. W.; Kaha, L. R.; Pople, J. A. “Gauss 80°, unpublished. (52) Hay, P. J.; Wadt, W. R.; ak Kahn, L. R., unpublished results. (53) Yaffe, L. G.; Goddard, W. A., Hl Phys Rev. A 1976, 13, 1682. J. Am. Chem. Soc., Vol. 106, No. 23, 1984 6937 8.0 Orbitals optunized at the RCI (4/8) « GVBI (2/6) level = 16 io} E = 3 -aab = & “u.2b Orbitals optimized at 2: GVB-PP (6/14) level ww ~17.67 HyPt(PHsL —> Hy+ PtPH), -24.0 ad L 4 L 4. 5 «50 852.20 2.55 2.90 3.25 Pt-H, distance (A) Figure 14. Comparison of energies along the reaction coordinate for RCK4/8)*GVB-Cl(2/6) and GVB-PP(6/14) wave functions. d electrons. This wave function was optimized self-consistently by using the GVB3 multiconfigurational self-consistent-field program®? because the nonbonding d natural orbitals did not change smoothly from equilibrium to the dissociated limit at the GVB-PP level uniess they were optimized at the CI level. Often it is sufficient to use the orbitals from the GVB~PP wave function for RCI or GVB—CI wave functions. For example, orbitals obtained at the GVB-PP level were adequate for the GVB-C1(2/6) wave function. Optimizing the orbitals at the GVB-CI level lowered the energy of the GVB—CI wave function by Jess than 0.002 hartree (1.255 kcal/mol) relative to the GVB-CI calculation by using orbitals obtained at the GVB-PP level. This energy lowering remained essentially constant along the reaction path. Thus, although the GVB-PP wave function yields an unreasonable potential curve in the transition region, it does provide orbitals yielding a proper description of Pt-H bonding formation. This occurs because the GVB-CI includes the recoupling of bonding electrons necessary in describing the reaction. However, for the GVB-CI(2/6)*RCI(4/8) wave function it is essential to self-consistently reoptimize the orbitals for the full wave function, as illustrated in Figure 14.. The upper potential curve was obtained from the fully self-consistent wave function, while the lower curve is for a wave function for which the orbitals were optimized at the GVB-PP level. Use of incompletely op- timized orbitals (GVB-PP) is biased against the Pt d'° state (the dissociated limit) and leads to an irregularly stepped potential curve. The reason for this behavior is that for Pt(PH;)2 the RCI wave function includes terms differential in the d'°~s'd? splitting. When the orbitals are optimized for a wave function including these terms, orbital shape changes occur that are differential for these state splittings. These differential terms affect the shape of the potential curve (and the transition state) because the platinum atom changes its electronic state during the reaction. Acknowledgment. This work was supported in part by a grant from the National Science Foundation (No. CHE80-17774). One of the authors (J.J.L.) wishes to acknowledge financial support in the form of a fellowship from Exxon. Registry No. Pt(H),(PH;)>, 76832-29-6; Pt(PH;),, 76830-85-8; H,, 1333-74-0. ~12- CHAPTER 2 Theoretical Studies of Oxidative Addition and Reductive Elimination: Il. Reductive Coupling of H-H, H-C, and CC Bonds from Pd and Pt Complexes The following chapter has been submitted for publication to Organome- tallics I. Introduction The concepts of oxidative addition A A M + —> "a (1) B >: and reductive elimination a M + | (2) -_> Np B are prevalent in the literature on organometallic chemistry.! Thus, cata- lytic hydrogenation of alkenes often requires oxidative addition of Hz to form the activated complex MHp,” e.g., He + CeHy ------- +> CoH, (3) RhCl(PPh)5 involves formation of Rh(H)2(Cl)(PPhs)3. Similarly, an important step in the H-D exchange in alkanes® is the oxidative addition of C-H bonds, e.g., CH, + D20 --------- + CH3D + HOD (4) may involve formation of Pt(H)(CHg)(Cl)¢. In addition, reductive coupling to form C-C bonds is an important step in the cross coupling reaction catalyzed by Ni(II) and Pd(ID),* e.g., Ar-Cl + RMgCl ---------— » Ar-R + MgCle (5) involves Ni(Ar)(R)Lz > Nilg + Ar-R. Because of the central role of oxidative addition/reductive elimina- tion in organometallic chemistry, a number of recent experimental stu dies have been directed toward elucidating the details of such reactions. 14. However, a number of puzzles remain and there is yet no unified theoreti- cal framework for understanding such processes for H-H,H-C, and C-C systems. The purpose of this paper is to add toward building this frame- work. Current experimental evidence relating to these reactions is as fol- lows. A. Experimental Evidence for Mechanism Mechanistic studies have been carried out on activation of Hg by Ir(I) complexes,” Hp + IrCl(CO)(PPhg)z > Ir(H)e(Cl)(CO)(PPhs)2 (6) C-H activation by Ir(1)§ and Rh(1)” complexes, CH, + Ir(CsMe;)(PMes) -» IrH(CH3)(C;Mes5)(PMes) (7) reductive coupling of C-H bonds from Pt(I)hydridomethyl] complexes,® PtH(CHs)(PPhs)2 ~ Pt(PPhs)g + CH, (8) and reductive coupling of C-C bonds from Pa(I)® Pd(CH3)a(PPh3)2 > Pd(PPh3)z + CgHg (9) and Ni(II)!° complexes. OM Mo e \ / \/ 4 z= Ni + MePh (10) p/ Ph L p/ \ Me, Me, In all cases there is good evidence that these H-H, C-H, and C-C coupling or activation processes are concerted. Some of the evidence is as follows. The activation of He by Ir(I) complexes, (6), is believed to be con- certed because (i) the oxidative addition of Hg to Ir(I) complexes almost always yields a cis-product;!! (ii) the kinetics of the addition reaction Sabd ond (iii) the entropy are first-order in both He and the Ir(I) complex; of activation AS? © -23 + 3 e.u. for oxidative addition of Hg is very close to the entropy of reaction, AS § -28 + 3 e.u. (which is dominated by the loss of the translational and rotational entropy of the Hz molecule).>> Activation of C-H bonds by Ir(I) complexes, (7), has been observed by a number of different research groups.® Janowics and Bergman® con- ducted crossover experiments and measured the relative rates of inser- tion in different types of C-H bonds. Their results appear to be most con- sistent with a concerted process. ' The mechanism of reductive elimination from Pt(II) hydridoalkyls, (8), has been studied by two research groups.® Abis, Sen, and Halpern®? used isotope labeling experiments to follow the decomposition of various Pt(H)(Me)Lg complexes and found that reductive elimination is 18° studied the decomposition of cis- intramolecular. Michelin et a Pt(H)(CHgCF3)(PPh3)2 [which decomposes at a slower rate than the hydri- domethyl Pt{II) complexes] and found that (i) the rate of decomposition is first-order in the reaction, and (ii) the reaction has low values for the entropy of activation As? (2-8 e.u.). These results are consistent with a concerted unimolecular reductive elimination. The mechanism of reductive elimination from Pd(II) dimethyl com- plexes, (9), has been studied by Stille et al.9° and by Ozawa et al.*4 The lack of crossover products in the decomposition of Pd(CHg)gle and Pd(CDs3)sle and the unimolecular kinetics observed in these experiments are consistent with a concerted process. Note, however, that the corresponding Pt complex will nof reductively eliminate ethane; LePt(CHs)e —X> LePt + CoH, (11) -16= it can, in fact, be sublimed before it will decompose. !# B. Theoretical Strategy Four issues we wish to address here are: (i) Are the processes concerted? (ii) What are the relative barriers for H-H, H-C, and C-C coupling (and activation)? (iii) | How does the nature of the metal affect the reaction? [Why is Pt(II) so different from Pd(II)7] (iv) What relation should there be between the processes for metal complexes versus those for metal atoms? For reasons to be discussed below, we wanted to consider two related classes of systems where one class has exothermic reductive coupling for all three cases of R,,Rg = H,CH3, and where the other class has exoth- ermic oxidative addition for all three cases. Consequently, we examined the following reactions: Pd(H)p «> Pd + Hp (12) Pd(H)(CHs) <> Pd + CH, (13) Pd(CHs)g «> Pd + CoH, (14) Pt(H)g «> Pt + Hp (15) Pt(H)(CHs) <> Pt + CH, (16) Pt(CHs)e «> Pt + CoH, - (17) where the first three are exothermic (to the right) while the last three are endothermic. The Pd-H, Pd-CHs3, Pt-H, and Pt-CHg3 bonds in these sys- ~17- tems should typify the M-H and M-C bonds of other organometallic com- plexes involving metals of comparable electronegativity and oxidation state. 3 From various previous studies, ! we concluded that the reactions L Na te i <—- * (18) L” Sr, i R, [where R,,Re = H, CHs and M = Pt(0), Pd(0)] involve a change in the effective electronic configuration of M from an s'd® configuration for M(R,)(Re)Le to a d)° configuration for Mlg. Since the ground state of the Pd atom is d!° (with the lowest s'd® state lying 22 kcal/mol higher),'* the Pd atom should be a fair model for facile reductive elimination from vari- ous low valent Group VIII transition metal complexes (18). On the other hand, the ground state of the Pt atom is s'd® (with the d!° state lying 11 kcal/mol higher), 4 favoring oxidative addition and making the Pt atom a good model for facile oxidative addition processes. The theoretical results for reactions (12)-(17) are described in Sec- tion Il, compared with experiment in Section II, and compared with other theoretical work in Section IV and Appendix A. Calculational details are described in Section V. Il. Summary of Results A. Electronic Promotion Versus Charge Transfer A major conclusion from these studies is that ozidative addition requires promotion of the metal from the d’° atomic configuration to the s'd® configuration. We find for R = H,CHg, that the M-R bonds are covalent for both M = Pd and Pt, with each bond involving one electron in an orbital on R and one electron in an sd hybrid orbital on the metal. The d?° configuration cannot make covalent bonds since all five d orbitals are doubly-occupied; however, the s'd® configuration with two singly-occupied orbitals can mix these two orbitals to form two sd hybrids capable of forming covalent bonds to the two ligands. Thus the metal atom is not oxidized during the oxidative addition of Hz, CHy, and CgHg to Pd and Pt. Rather, the metal is promoted from the d! state incapable of forming covalent bonds to the s'd® state capable of forming two covalent bonds. Generalized valence bond (GVB) orbitals for the complexes studied in this work are shown in Figures 1, 2, and 3, with the hybridization of each orbital indicated just above the lower boundary of each orbital plot (these populations of GVB orbitals are summarized in Table I). In each case the ligand GVB orbital has 0.80+0.03 electrons on the ligand with 0.17+0.02 electrons on the Pt atom. For the Pt complexes, the metal GVB orbital has 0.08+0.01 electrons on the ligand, 0.62+0.02 electrons in a Pt d orbi- tal, and 0.30+0.02 electrons in Pt 6s and 6p orbitals (94% s and 5% p). Thus the metal orbitals are sd* hybrids. In the Pd complexes there is more variety in the character of the GVB orbital describing the metal part of the metal-carbon bond pair, with 0.24 electrons on the CHg for Pd(CHg3)e, but 0.12 for Pd(H)(CH3). In addition, the sd hybrid character varies [from s'd1\? for PdHg to s'd‘5 for the Pd-H bond of Pd(H)(CHs) and -19. from sid°8 for the Pd-C bond of PdH(CHs) to s!d®® for Pd(CHs)z]. We do not believe that these variations are as significant as the general result that the GVB orbitals for both Pt and Pd use sd hybrid orbitals to form bonds to H and CHs groups. These sd hybrids are similar in all cases, with somewhat more d than s character. The carbon atoms in methyl groups bonded to the metal are tetrahedral (within 1°) and sp® hybridized (see Appendix B). From total Mulliken populations (see Table Il), the Pt com- plexes on the average have 9.03 d electrons and 1.06 s electrons, while Pd complexes have 9.23 d electrons and 0.69 s electrons (a difference expected from the preference of Pd for d electrons). The fact that Pd-H, Pd-C, Pt-H, and Pt-C bonds are covalent is con- sistent with the Pauling electronegativities: Pd(2.2) and Pt(2.2) versus H(2.1) and C(2.5).1° Crabtree et al.°ti have also suggested that the addi- tion of Hg to Ir(I) complexes is not oxidative based on observations that the oxidative addition of Hz to cationic Ir(I) cyclooctadiene complexes is promoted by electron-withdrawing ligands and inhibited by electron donors* and that an upfield shift of the vinyl carbon resonance occurs in the 13C NMR of Ir(COD)+ (COD = 1,5-cyclooctadiene) on addition of He.°€ Summarizing, the oxidative addition of Hz, CHy, and CgHg to d!° metal centers should be thought of in terms of promoting an electron from a doubly-occupied d orbital to an unoccupied s orbital in order to accorn- modate the formation of two covalent bonds rather than the transfer of one electron to each ligand. For Pd and Pt this promotion corresponds to the electronic transition from d!° to s!d® instead of ionizing two electrons from d!° M(0) to form a d® M(II). ~20- B. Reaction Energetics and Bond Energies 1. Reaction Energetics Before discussing the details of the reactions, we will examine the overall energetics (see Figures 4 and 5). For Pd, H-H, H-C, and C-C cou- pling is exothermic (with AHagg!® of -4.0, -17.2, -19.0 kcal/mol resulting from AE’s of -3.6,-20.1, and -16.0 kcal/mol, respectively), while for Pt these processes are endothermic (with AHogg of 33.2, 19.0, 15.5 kcal/mol resulting from AE’s of 33.6, 16.1, and 18.3 kcal/mol AE, respectively; see Table Ill). (For Pt these energies are for the lowest spin-allowed process, leading to d!° Pt atom.) These differences between Pd and Pt are easily understood on the basis of relative atomic excitation energies. Reductive coupling changes the metal from s'd® to d!°, but for Pd the s!d® state is 22 kcal/mol higher than d!°, while for Pt the sid® state is 11 kcal/mol below d!°. Thus, reductive coupling from Pd should be favored by 33 kcal/mol (theoretical value 32 kcal/mol) over comparable reductive cou- pling from Pt. Indeed, we find the differences [AHzgg for (2)] to be 37.2 kcal/mol for the dihydrides, 36.2 kcal/mol for hydridomethyl complexes, and 34.3 kcal/mol for the dimethyl complexes. Thus the GVB model of bonding allows one to use atomic excitation energies and the relative energetics of reductive coupling for one metal complex to estimate the energetics for other metals. 2. Average Bond Energies For semi-quantitative comparisons of various systems, it is often use- ful to have an idea of average bond energies for various types of bonds. There are two simple ways of doing this: Method 1: Adiabatic Bond Energies The adiabatic bond energy is defined as Da(M-R) = }% [AHgog(MRz + M+ Rg) + AHygo9(Re > 2R:)]. The calculated reaction enthalpy for the reductive coupling is added to the Re bond energy’” for a free Rp, and then the total is divided in half to give the adiabatic bond energy. This leads to Da(Pt-H) = 69 kcal/mol, D,(Pt-C) = 53 kcal/mol, Ds(Pd-H) = 50 kcal/mol, and D,s(Pd-C) = 36 kcal/mol. As a check on the consistency of average bond energies, we can use the bond energies calculated from the AHagg of reactions (12), (14), (15), and (17) to predict AHggg for reactions (13) and (16). This yields predicted values of AHggg of -19 kcal/mol for reaction (13) and 17 keal/mol for reaction (16), which are both 2 kcal/mol lower than the cal- culated values of -17.2 and 19.0 kcal/mol. Overall, the Pd-R bonds are 19 and 17 kcal/mol weaker than the corresponding Pt-R bonds, which just represents the preference of Pd for d?° over s!d?. Method 2: Intrinsic Bond Energies In order to eliminate the effect of sid®—d! state splittings on the average bond energies, we define an intrinsic bond energy as where the final state of the metal atom is taken as the s'd® state. This is the intrinsic bond strength where the electronic state of the atom is not allowed to relax to a d! state. In this case, we obtain very similar bond energies for Pd and Pt, with D,;(Pd-H) = 60 kcal/mol and D,(Pt-H) = 62 keal/mol, while D;(Pd-CHg) = 45 kcal/mol, and D,(Pt-CHg) = 47 kcal/mol (see Table IV). Thus, these intrinsic energies plus atomic excitation ener- gies should be most useful in using results for one metal to predict ~22~ results for another. 3. Energetics on Metal Surfaces For metal surfaces, one might expect that metal-metal bonding would tend to keep the surface atoms for the Ni triad in s'd® states. If so then the D; should provide a reasonable estimate for the bond energy at metal surfaces. }8 (Band calculations for Pd and Pt have been interpeted in terms of an average s°4d®6 configuration, !® somewhat more d occupa- tion than in our complexes.) The predicted results for R,- R, R, R, are AHogg = -15 kcal/mol (Pd) and -20 kcal/mol (Pt) for Hg AHzgg = -4 kcal/mol (Pd) and -8 kcal/mol (Pt) for H-CH, AHgpg = -10 kcal/mol (Pd) and -14 kcal/mol (Pt) for H-CgHs and AHggg = O kcal/mol (Pd) and -5 keal/mol (Pt) for CHs—CH3. The experimental heats of adsorption for Hz on Pt and Pd surfaces are 20.8 keal/mol,”° on Pd(111), 24.4 keal/mol, on Pd(110),"° 9.5 keal/mol, on Pt(111),"! and 12 keal/mol on Pt[9(111) x (111)].*! Thus our one-center Pd numbers predict surface Pd-H bonds about 3 kcal/mol weaker than experiment, whereas our numbers for Pt indicate surface Pt-H bonds about 5 kcal/mol stronger than observed. Using the experimental results on Hg to calibrate the predictions for the other reactions leads to a=23e AH =-10 kcal/mol (Pd) and +1 kcal/mol (Pt) for H-CH3 AH = -16 kcal/mol (Pd) and -6 kcal/mol (Pt) for H-CgHs5 AH = -6 kcal/mol (Pd) and +4 kcal/mol (Pt) for CHs—CH3 As experimental data become available for such surface reactions, it will be interesting to see how energetics can be extrapolated between homo- geneous and heterogeneous systems. 4. Barriers for Reductive Coupling For the Pd(R,)(Rz) complexes, it is exothermic to reductively couple H-H, H-C, or C-C bonds; however, the barriers for these processes depend dramatically upon the nature of the ligands (see Figure 6): AE{_4 = 1.6 kcal/mol, AHdggy- = 0.4 kcal/mol AEZ_¢ = 10.4 kcal/mol, AHisg y-c = 9.5 kcal/ mol AEi_¢ = 22.6 kcal/mol, AHZgac-c = 23.6 kcal/mol. Similarly, for the corresponding Pt complexes (see Figure 7), the barriers for H-C and C-C coupling are far larger than the endothermicity Ei_¢ = 29.0 keal/mol, Héggy-c = 28.1 kcal/mol Eé_c¢ = 53.5 kcal/ mol, Hoe c-c = 54.5 kcal/mol. Such dramatically different barriers would explain why Pt(H)(CHs)(PH3)2 will reductively couple H-C bonds, whereas Pt(CHs)2(PHs)2 will not reduc- tively couple C-C bonds. However, the question now is why the dramatic differences in barriers? As discussed in more detail in Section II.6, the reductive coupling process starts with a configuration having two covalent bonds involving sd hybrids on the metal, ~24~—e (19) s'd® Resonance Configuration and converts this to a wavefunction with one covalent bond between the ligands and a doubly-occupied d orbital on the metal, QV 20) CKw d?° Resonance Configuration At the transition state geometry, both configurations must come into the wavefunction, wherein lies the difficulty. A hydrogen s orbital at the tran- sition state is equally suited for either bonding configuration (19) or (20); however, for methyl the bonding orbital is an sp® hybrid that can be directed either for making an M-C bond, (21) or for making a C-C bond Qs “ae 0 but not both. This is illustrated in Figures 8 and 9, which show the vari- ous orbitals for (12), (13), and (14) at a geometry near the saddle point. The CH3 radical orients itself to a position intermediate between the geometries appropriate for (21) and for (22), leading to too weak a bond for either. The consequence of these effects is that each methyl group leads to a doubling of the barrier. Clearly this methyl orientation effect can account for the observed differences in the efficacy of H-C versus C-C coupling in Pt phosphine complexes. These results are consistent with the facile H-C coupling on Pt and C-C coupling on Pd, with the apparent lack of stability of the cts- Pd(H)(CH3)(PH3)2 complex, and with the difficulty of C-C coupling from Pt dimethyl complexes. 5. Geometries The bond distances for Pd-CH, and Pt-CHs bonds are nearly identical [1.96 + 0.01 A] for all complexes. For M-H bonds there is more variation with Pd-H = 1.51 + 0.01 & and Pt-H = 1.48 + 0.01 A. On the other hand, the bond angles for the various M(H)e, M(H)(CH3), and M(CH3)zg complexes vary considerably, being 73°, 80°, and 92° for Pd and 82°, 89°, and 98° for Pt. «-26= The ideal bond angle between two bonds formed with symmetric linear combinations of a Pt s and a Pt d orbital is 90°. Thus, if the repul- sive steric interactions were solely responsible for the trend of bond angle with methyl substitution, one would expect to find R-M-R angles greater than 90°, but most of the equilibrium geometries have R-M-R angles less than 90°. Of course the actual hybridization is not exactly sd, and the calculated angles between the lobes of the metal-like GVB orbi- tals vary between 86° and 100° [86° for PtH2, 91° for Pt(H)(CH3), and 100° for Pt(CHs)s, leading to the an average of 92°] for Pt complexes and the average for Pd complexes is 88°+1°. The observed angles between the metal-like GVB orbitals for Pt track closely with the actual bond angle (80, 91, and 100 versus 82, 89, and 98, respectively); however, this does not constitute an explanation since we have not provided an a priori cri- terion for predicting the hybridization leading to these angles (other than being s)°d!° to correspond to the siqd® state). Thus, compared with the 90° expected from the sid® configuration, there must be attractive interactions between the ligands bound to the metal atom. This attrac- tive interaction can be explained by noting that the d?° resonance struc- ture has an R-R bonding interaction. The more important the d!° reso- nance structure, the more attractive the interaction between ligands and the smaller the R-M-R angle. Since the d!° resonance structure is more important in PdRg than in PtRg, there will be greater bonding character between the R groups in PdRg, providing a rationalization for the R-Pd-R bond angles being 10° smaller than the corresponding bond angles in the PtR, complexes (see Figures 4 and 5). yy 6. Changes Along Reaction Path As discussed above, there are two important resonance structures in the M(R,)(Re) complexes responsible for determining the relative amounts of s and d character. The dominant resonance structure for PdR, and PtRzg has the metal atom in an s'd® configuration, shown schematically in (19) and denoted as the s'd® resonance structure. Here the singly-occupied s and d orbitals rehybridize to form sd hybrid orbi- tals that spin-pair (or form bonds) to the singly-occupied orbitals of the R group. The second resonance structure, which dominates the wavefunc- tion at the dissociated limit, has the metal atom in a d! configuration and an R-R bond, as shown schematically in (20). This is referred to as the d!° resonance structure. As oxidative addition proceeds, the dominant resonance structure changes from the d? structure to the s‘d® struc- ture. Since Pd prefers d!° while Pt prefers s'd®, PdRz should have more of the d!° resonance structure than PtR,. This is consistent with the observation that PdRe complexes have larger d populations than PtR, complexes. The Mulliken populations as a function of reaction coordinate for reaction (12) (see Table V) show that at the dissociated limit the Pd atom is in a d!° state, and as the hydrogen molecule approaches, the Pd atom mixes in s'd® character. Finally, when two Pd-H bonds have formed, the Pd atom has 75% s'd® character (defined by the occupation of the Pd s orbital). The spherically symmetric H,, orbital allows it to form bonds in more than one direction at a time. This multi-centered bonding increases the H-H bonding character of the d!° resonance structure, causes the H atoms to have an attractive interaction in the dihydrides, and leads to =~28— smaller H-M-H bond angles. The sp®* hybrid orbital of the CHg group is more directional than the _ Hj, orbital. The shape of this orbital makes it difficult for this orbital to bond in more than one direction at a time. Consequently, there will be less bonding character in the d!9 resonance structure of the hydri- domethyl complexes than in the dihydrides. This will cause the hydri- domethyl complexes to have larger bond angles than the dihydrides. Since the sp® orbitals of the methyl groups are directed at the metal, they have trouble forming the C-C bond in the d’° structure. Conse- quently, the dimethyl complexes have the least amount of bonding char- acter in the d!° resonance structure. Therefore, the dimethyl complexes should have the largest bond angles. The increased ligand-ligand bonding in the d!° resonance structure should stabilize it relative to the s!d® resonance structure. This will cause metal d populations to be larger for dihydride complexes and smaller for the dimethyl complexes, which is consistent with the Mulliken populations in Table II. The potential curves along the reaction paths are shown in Figures 6 and 7. In each of the potential curves the R;-M—Rg bond angle (On, R,) was fixed, and all other geometric parameters were fully optimized (see Sec- tion V). In this manner, we were able to obtain the energy as a function of @g,p, from the MR, complex to the dissociated limit (On.R = 0°). The potential curves for reactions (12)-(14), (16), and (17) can be par- titioned into three regions: 1. The MRz complex region, where the metal atom has sid® character and each R group forms a covalent bond to the metal. 2. The transition state region, where the M-R bonds are breaking and the R-R bond is forming (or vice versa), with a strong mixture of both the d!° and s!d® resonance structures. 3. The dissociated limit, where the R-R bond is fully formed and the metal is in the d’° state. In region 1 the M-R bond lengths change by less than 0.02 A as the zp, is varied, indicating that the M-R bond is still intact. As the complex enters region 2, the M-R bonds begin to stretch and the methyl groups in the hydridomethyl and dimethyl complexes rotate so that their sp? orbi- tals are directed more toward the other R group. At the transition state, the ligand-ligand bond distances are generally closer to the bound complex geometry than to the dissociated limit. Pd complexes have smaller distortions (they are more reactant-like) than the corresponding Pt complexes (see Figures 4 and 5) at the transition state, as would be expected from the Hammond Postulate. The dimethyl complexes have the largest distortions. Pt + Hz > PtHg differs from the other reactions studied here in that there is no barrier to oxidative addi- tion (it is quite exothermic, 33,6 kcal/mol). Past the transition state there exists a second minimum for the Pd + Ho, Pd + CHy, and Pt + CH, cases. In this bound complex, the H-H or C-H bonds are intact and behave as Lewis bases, while the d’° configuration of the transition metal serves as a Lewis acid (empty valence s orbital). The geometries for the Lewis acid/Lewis base complex are shown in Figure 10. These geometries were not separately optimized but were interpolated from the calculations along the reaction path. [Notice the lack of sym- metry in the M(CH,) complexes.] As a result, the geometry obtained for each complex is not particularly accurate [the internal coordinates of Hg -30- and CH, in these complexes should be accurate, while the error in metal- ligand distance (+0.2 4) and in orientation (+10°) will be larger]. However, Lewis acid/Lewis base complexes in these systems are clearly stable with respect to the dissociated limit. There seems to be a small increase in the H-H bond length (0.07 A) and very little distortion in the C-H bond lengths of methane (two CH bonds of methane interact with the metal atom in this region). Our reaction path restricted the orientation of the methyl group in such a way that at most two C-H bonds could complex to the metal atom. Therefore, the Lewis acid/Lewis base complexes, with three C-H bonds complexed to the metal atom (probably the most stable), were not examined. Previous calculations found a similar bound complex for PdH)** and described it as a van der Waals complex. Since our wavefunction does not include the electronic configurations involved in the dynamic polariza- tions responsible for van der Waals forces (nor the f functions needed on the Pt for a proper description of such effects), our results cannot be explained in terms of a van der Waals complex.”? Rather, they should be thought of as weak Lewis acid/Lewis base complexes. Similar 7* bonding of Hg to a transition metal has been observed experimentally in M(CO)3(PR3)eHe (M = Mo,W; R = Cy,i-Pr) complexes studied by Kubas et at.248 and theoretically by Hay.24” The interactions responsible for these Lewis base/Lewis acid com- plexes of CH, to metal atoms are probably identical to those involved in "agostic” 25a interactions of C-H bonds and transition metals observed experimentally*"* and theoretically“ in several complexes. This type of interaction has thus far only been observed for C-H bonds of ligands that are also covalently bound to the complex. The very small binding ener- gies found in our calculations [5 kcal/mol for Pd(Hg), 2 kcal/mol for Pd(CH,), and 4 kcal/mol for Pt(CH,)] are insufficient to balance the entropic contribution to the free energy of binding at room temperature (~10 keal/mol), indicating that such bonds to alkyl groups that are not already part of the complex will in gas phase only be observed at low tem- peratures. -32- II. Comparison With Experiment The results presented in the previous section explain many of the _experimentally observed trends. Halpern et al.®2 and Michelin et ap.8> observed intramolecular reductive coupling from various hydridoalkyl- bisphosphine Pt(II) complexes. However, reductive coupling from Pt(II) dialkyls to form C-C bonds has never been reported, even though this reaction is thought to be thermodynamically favored.“© Rather, the Pt(I!) dialkyls prefer S-hydride elimination," H a [src + rcs] ——> (PR,),Pt + CH, + CH, (23) CH,—CH, CH,—CH, RIEL CH,—-CH, TK (PR,),Pt + CH,—CH,—CH,—CH, (24) despite the fact that (24) is favored thermodynamically (by AHsg9 = -22-5 keal/mol and AGgoq = -11.0 kcal/mol). These observations are con- sistent with our findings that C-H reductive coupling leads to a barrier half that for CC reductive coupling. This trend should be applicable to concerted addition/elimination reactions for other Group VII metals because it depends primarily on the relative shapes of H 1s and CHg sp° orbitals. Unlike their Pt analogs, Pd(II) dimethyl complexes do reductively eliminate ethane, a result we attribute to the strong preference (by 34 kcal/mol relative to Pt) of Pd for the d!° configuration, which leads to a greatly reduced barrier [we estimate 10 keal/mol for Pd(CH3)e(PHs)2 compared with 40 keal/mol for Pt(CHg)e(PHs)2].2" This is in agreement with observed reductive elimination of ethane from Pd(CHg)ele complexes**4 (where L = PPhg, PPhgCHg; Le = PPhgPCHzCH2PPhg) and the -33- fact that hydrogen will not oxidatively add to a Pd bisphosphine complex but does add to the corresponding Pt complex." Oxidative addition of Hz to square planar Ir(I) complexes is the most thoroughly studied system experimentally, and it is believed to involve a concerted mechanism.® In contrast to the results presented here for the addition of Hz to Pt and Pd and earlier work for Hz addition to Pt(PHs)e, the Ir(I) complexes have a relatively high barrier to oxidative addition (10-12 kcal/mol for Vaska’s complex®*>:4) and reductive elimination (25 kcal/mol). This difference probably arises from the difference in elec- tronic configurations, with Pt and Pd having a spherically symmetric a'0 shell of electrons on the metal atom, while Ir(I) leads to square planar four-coordinate complexes. Thus Pt(PHs)2,!° has a P-Pt-P angle of 180°, being determined by steric interactions between phosphines. Promoting the Pt(PHs)2 complex to a triplet state leads to a P-Pt-P bond angle of 100°, where the phosphine lone pairs maximize their overlap with the singly-occupied dy, orbital of the triplet state.!° On the other hand, Ir(1) has a strong preference for square planar geometries. Addition of Hz to such complexes should lead to a distortion of ligands toward the six- coordinate Ir(IID product.” Here a significant distortion away from square planar is required at the transition state in order to allow the d? » s!d! excitation required for formation of the new Ir-ligand covalent bonds. Thus the higher barrier in Ir(I) is attributed to the lack of a sym- metric d!° shell and the concomitant strong preference for square planar geometries. Indeed, Vaska and Werneke”> proposed a similar effect, the "reorganization or rehybridization energy,” whose magnitude was deduced from the trends observed in AH* and AH for oxidative addition of Hp to Ir(I) complexes. They equated this reorganization energy to the AH?* for reductive elimination of Hg. We find low barriers for concerted reac- tions of Hy with Pd, Pt(#S), and Pt(PHg)g; therefore, the reorganization _energy must be very small (~2 kcal/mol) for these d?° systems. It has generally been believed that oxidative addition (being oxida- tive) should be promoted by electron-rich metals.© However, C-H activa- tion of C-H bonds has been observed to occur for both electron-rich®*¢ and electrophilic Ir systems.°° Since the electronegativity'* of Ir(2.2) is the same as for Pt(2.2) and Pd(2.2), we expect it to form covalent bonds to H and CHg so that the electron density on the metal should have little effect on the energetics for oxidative addition (as observed). In every case where stable hydridoalkyl complexes have been formed by oxidative addition of M to sp® C-H bonds, a photochemically generated Cp*ML (L = CO or PMes) (M =[r844 or Rh’) (Cpt=cCsMes5) complex has been involved. The Cp* ligand can easily occupy three coordination sites of the octahedral complex for Ir({III) or Rh{III). However, Cp*” cannot occupy three coordination sites of a square planar complex. Thus, the Cp*ML complexes are distorted significantly away from the square planar preferred by Ir(I) and Rh(I), and hence have smaller reorganization energy for oxidative addition than does Vaska’s complex [they are much closer to the octahedral geometry favored by Ir(III) and Rh(IIT) complexes].3!%4 Therefore, these complexes will have lower activation barriers and greater driving forces favorable for oxidative addition. Con- straining the geometry of the ligands appears to be a more important effect than the electron richness of the metal center. Similar analyses 52 and Dedieu and have also been given by Saillard and Hoffmann,** Sevin, Strich.*9 We find that oxidative addition of Hz, CH4y, and CgHg to the Pd atom is ~35~ uphill energetically. These results suggest that the Pd atom is unreactive with respect to He, CHy, and CeHg. This is consistent with the results of Klabunde and Tanaka®*“* who found no reaction of Pd codeposited with CH, at 10°K. This lack of reactivity of Pd at low temperatures is due to the unreactive nature of the d!° state of Pd and the large excitation energy (21.9 kcal/mol) needed to promote the Pd atom to the s'q® configuration that can make two covalent bonds. In fact, no transition metal in its ground state has been found to be reactive with CH, at low temperatures.** This can be easily explained despite the diverse nature of transition metal atoms. Every transition metal except Pd has either a singly- or doubly-occupied valence s orbital in its ground state. In reactions (12), (13), and (16), the empty s orbital gave rise to attractive Lewis acid/Lewis base interactions at long M-R dis- tances, resulting in an decreased barrier for oxidative addition. For a metal where the s orbital is occupied, this orbital must become orthogo- nal to the incoming R-R bond, leading to a repulsive interaction at long M-Rz distances. Thus, one would expect every transition metal in its ground state to have an activation barrier to oxidative addition. For excited states of transition metal atoms, one can have states in which the s orbital is unoccupied and for which oxidative addition is exothermic. For example, we find that Pt('S) + Hz » PtHe(1A,;) leads to no barrier. These predictions are consistent with experiments°* that find photoexcited metal atoms reactive with methane at low temperatures. [Extended Hiickel calculations of Sevin and Chaquin®> lead to similar results. | -36~= IV. Comparison With Other Theoretical Work Several previous theoretical studies?*>*2:56.37 have addressed vari- _ous issues relevant to the oxidative addition/reductive elimination of Hg, CH,, and CgHg to transition metal complexes, although most have not examined the full reaction surfaces. Using fixed bond distances, Tatsumi et al.°© calculated activation energies at the extended Hiuckel level for reductive elimination of CeHg from Pd(CHs3)2(PHs)z and Hz from (PdH,)~* models. They found higher barriers for reductive couplings for C-C bonds (39.1 keal/mol) than for H-H bonds (4.6 keal/mol) because of the "weak- 36a ening necessitated by the rocking motion of the methyl group. Balacz et at.°® carried out muffin-tin Xa calculations at assumed geometries for various complexes and suggested, on the basis of the shapes of the molecular orbitals, that three-center bonding might be more important in the reductive elimination of Hz from HgPtlg than for CH, from H(CH3)PtLg or for CgHg from (CH3)gPtle. (They did not calculate barriers or geometries.) | Previous theoretical studies**?5 of Pd(H)z did not find the local minimum corresponding to the Pd-H bonded complex. However, these calculations did not include relativistic effects and consequently the s'd® (3D) state [important in the Pd(H)zg complex] is 15 kcal/mol too high®® relative to the d!° state. Since our calculated barrier for reductive coupling is only 1.5 kcal/mol, it is not surprising that nonrelativistic cal- culations of this minimum do not find a Pd-H bonded complex. Obara et al.'®* have recently reported a6 initio calculations on oxida- tive addition of Hz and CH, to Pt(PHs)2. Their transition state geometry for Hz addition is in reasonable aggreement with our previously published results on the sarne system. 9 The transition state geometry for CH, «3T- addition calculated by Obara ef al, 168 (C-Pt-H angle = 36°, Pt—CHg3 dis- tance = 2.27 A, and Pt-H distance = 1.59 A) is remarkably close to ours (C-Pt-H angle = 42°, Pt—CHs distance = 2.12 A, and Pt-H distance = 1.57 A), considering the lack of phosphines in our model. Their energetics, however, are difficult to compare with ours since the Pt effective core potential used by Obara ef al.°* is known to give stronger Pt-H bonds that are far too strong.*° [We used the Hay*! effective core potential which gives excellent bond energies and excitation energies.| The similarity of the transition states indicates that the PHs ligands do not significantly affect the reaction path for reductive coupling of C-H bonds. We would expect PHs ligands to lower the barrier for reductive elimination, since phosphines stablize the d’° configuration relative to s'd® and increase the driving force for reductive elimination from Pt(H)e(PHs)e,° Pt(H)(CHg)(PHs)2,2® Pt(CHs)a(PHs)z,°9 and Pd(CHg)a(PHs)2.° No other ab initio theoretical studies on oxidative addition/reductive elimination to Pd and Pt atoms have been reported; however, similar stu- dies have been reported for oxidative addition of Hz, CH,, and CgHg to the lowest singlet state of the Ni atom.*2»:372.> These results on Ni differ con- siderably from ours on Pd and Pt. For example, Siegbahn et al 22b.37a,b find oxidative addition barriers of 4.2 kcal/mol for Hg, 54.1 kcal/mol for CHy, and 42.3 kcal/mol for addition to the CC bond of CoHg. In addition, they report an unusually small equilibrium bond angle of 57° for NiHg. There are significant differences in the properties of Ni versus Pd and Pt, even though they are in the same column. For example, Ni is much more electropositive than Pd or Pt (Pauling electronegativities® of 1.8 versus 2.2 and 2.2). In addition, the ground state of Ni has nearly degenerate s@a® (3F) and s!d® (3D) triplet states, with the d’° (1S) state 40 kcal/mol ~38- higher.’* For Ni the lowest singlet state is sid® (1D) at 7.7 keal/mol.‘* On the other hand, Pd has a d!° (!S) ground state with the s'd® (9D) triplet at 22 kcal/mol,while the lowest singlet for Pt is also d'° (1S) with s'd® (3D) 11 ‘keal/mol lower.'4 Consequently, we include in Appendix A some calcula- tions performed on the Ni + Hz system for comparison purposes. Siegbahn and co-workers*“037 calculated potential surfaces at the contracted CI level for the reactions Ni + CH, ~ NiH(CHs) (26) Ni + CoHe > Ni(CHs)2 - (27) They find, in contrast to our results, higher barriers for C-H activation than for C-C activation. Since this trend parallels the trend in C-H versus C-C bond energies, it is possible that Siegbahn's calculations are model- ling nonconcerted additions of Ni to CH, and CoH,’ To estimate the AF’s for the formation of the radical intermediates (AE;,q), we used Siegbahn’s AE for Ni + H2> NiH2?74 (-9.6 kcal/mol) and Ni + CoH, > Ni(CH3)2°"? (5.3 kcal/mol) to estimate average Ni-H ( D, = 56 kcal/mol) and Ni-CHg bond energies (D; = 45 keal/mol).*” Ni(1D) + CH, > ‘Ni-H + -CHg AFveq = 50 kcal/mol (28) Ni(1D) + CgHg > -Ni-CHs + -CHsg AEraq = 43 kcal/mol (29) These AE,,q’8 are very close to the AE?'s for C-H activation (54 kcal/mol) and C-C activation (42 kcal/mol), as calculated by Siegbahn et al," sug- gesting that their calculations are not modelling the concerted processes. On the other hand, for our studies on Pd and Pt, a similar analysis leads to energies of formation for radical intermediates far higher than our calculated barriers for the concerted processes. The sole =~ 39 exception is for C-C activation of Pt where the AH-aq is 43 keal/mol, which is close to the Aut for oxidative addition of 39 kcal/mol. This suggests that radical processes are competitive with concerted processes for reac- tions (17), (26), and (27). For the organometallic systems being modeled in this paper, the metal atoms will generally have other ligands (e.g., phosphines) on them. We have shown! that the effect of phosphines is to stabilize the qi? versus sid® states in Pt(PHs)2 and expect the same effect for Pd(PHg)z and Ni(PHg)g. The lowest singlet states of Pd and Pt are d!°, like the M(PRs)z2 complexes that we are modelling, whereas the lowest singlet state of Niis s'd®. Thus, the calculations for oxidative coupling of Pd and Pt atoms are more relevant for organometallic chemistry than similar calculations?’ on Ni. Since the lowest singlet state of Ni differs so much from the lowest singlet state of Pd, Pt, and M(PRs3)2 (M = Ni, Pd, Pt), it is not surprising that Siegbahn’s results are different from ours and run counter to the observed experimental trends. 40 V. Calculational Details A. Potentials and Basis Sets We used ab initio effective core potentials (ECP) to represent the core electrons of Ni, Pd, and Pt. For Ni we used the ECP of Melius et ai.,*8 144 and the sp basis associ- with the five-gaussian d basis of Rappé ef a ated with the SHC potential of Rappé.*” The relativistic effective core potentials (RECP) and basis of Hay*! were used on Pd and Pt with a valence double zeta basis. The Dunning“® double zeta contraction of the Huzinaga (9s5p) gaussian basis was used on carbon. The active hydrogens bound directly to metal atoms were described by a triple zeta contrac- tion of the Huzinaga six-gaussian basis.*” The nonactive methyl hydrogen atoms were described by a double zeta contraction of the Huzinaga four- gaussian hydrogen basis scaled by a factor of 1.2,46:47 For highly accu- rate bond energies and geometries, f functions should be included on the metal center, d functions on the C atoms, and p functions on the H atoms. However, the present basis is expected to be adequate for extracting the important issues about these various reactions. B. Configuration Interaction Calculations For PdHz and PtH, there are 12 valence electrons with four electrons involved in M-H bonds and eight involved in four pairs of metal d orbitals. As the Hp molecule is eliminated, the four bonding electrons change dramatically, leading to two electrons describing H-H bonding and two describing a doubly-occupied d orbital on the metal, while the other eight electrons change little. [Note that the spin-allowed product M(H) + M + He involves a d?° singlet state for both Pd and Pt.| Thus, to provide a balanced description of this system, we described each of the four fairly constant pairs of electrons in terms of a standard (one orbital ~41. per electron) GVB description. This is denoted as GVB(1/2) for each pair and GVB-PP(4/8) to indicate four pairs of electrons, each with two GVB ‘orbitals for a total of eight. The PP (for perfect-pairing) indicates that the spin coupling is that of a simple valence bond wavefunction with each of these four pairs singlet-spin paired. Expanded as a configuration interaction (CI) wavefunction in terms of natural orbitals, the GVB- PP(4/8) wavefunction leads to 2* = 16 configurations. Instead, we allowed the two electrons of each pair to recouple in all three possible ways using two orbitals, leading to a total of 34 = 81 configurations, a calculation referred to as GVB-RCI(4/8). This GVB-RCI level of wavefunction allows the spin-coupling terms often important in transition metal systems and allows the interpair correlation so important for doubly-occupied d orbi- tals. The other four electrons have very different requirements for Pd(Hg) versus Pd + Hg. Thus, for Pd(H)g, a standard GVB wavefunction leads to two localized orbitals for describing each Pd-H bond pair (as shown in Fig- ure 1). In terms of symmetry orbitals, this would lead to two a, and two bg orbitals. On the other hand, for separated Hz and Pd, the standard GVB(2/4) description has two localized orbitals on the Hg (leading to one a, and one bg) and a correlated d,, orbital (leading to two bg orbitals). In order to provide an unbiased description of these reactions all along the reaction path, we used a wavefunction with three a, and three bg orbitals for the four bonding electrons. Allowing all possible occupations of the four electrons among these six.orbitals leads to a wavefunction with 48 configurations and is referred to as GVB-Cl(2/6). For all points along the reaction path we combined the GVB-RCI(4/8) and GVB-CIl(2/6) wavefunc- tions to obtain a composite containing 8568 configurations*® and denoted . -42. as GVB-RCI(4/8)xGVB-Cl(2/6). The orbitals for this wavefunction were optimized for this 8568 configuration wavefunction using the GVB3 pro- 49 . gram. For calculations involving methyl groups, the inactive C-H bonds were uncorrelated [as in Hartree-Fock (HF)], and the M-C, active C-H and C-C bonds were included in the GVB-CI space. All the other metal electrons were described in the same manner as MHp. A special virtue of this GVB approach to wavefunctions is that since the orbitals are divided into active (GVB-CI), semi-active (GVB-RCI), and inactive (HF) orbitals, the number of configurations does not increase when ligands are added, so large systems [e.g., Pt(CHs3)2(PHe)e|*" can be treated nearly as easily as small ones. Often it has been convenient to calculate the GVB-RCI wavefunction using orbitals from corresponding GVB-PP calculations. This saves con- siderable time because the GVB-PP calculation does not require transfor- mation of electron repulsion integrals to the molecular orbital basis. Indeed, such GVB-RCI calculations, using orbitals from GVB wavefunc- tions, yield atomic state splittings that are in good agreement with state splittings calculated self-consistently at the GVB-RCI level (see Table VI), However, it is necessary to optimize orbitals at the full GVB- RCI(4/8)xGVB-CI(2/6) level of wavefunction in order to self-consistently include the resonance between the d!° and s'd® configurations near the transition states for reactions (12)-(17). To indicate how well this type of wavefunction does for atomic state splittings, we show in Table VII comparisons with experiment for HF and GVB-RCI(5/ 10)18:50 state splittings. Here the GVB-RCI involves a total of ten optimized GVB orbitals for each state (d!°, s'd®, or s*d8), and we see ~43. that GVB-RCI does quite well, with errors of 1 to 3 kcal/mol in the 'S(d!°) to 8D(s'd®) excitation, and 0 to 6 kcal/mol in the energy of 'D(s'd®) rela- tive to 4(s!d®). These three states describe the dominant character of the wavefunction for the reactions studied in this paper. [Larger errors occur for the s“d® state because angular correlation of the s pair of elec- trons, which is important for this state, was not included in this wavefunction. However, the s“d® state is destabilized by addition of phos- phine ligands, and it will not play a significant role®° in the chemistry of such complexes.] In contrast, HF wavefunctions lead to errors of 20 to 60 kcal/mol in the 'S(d!°) to 3D(s!d®) excitation and 2 to 11 kcal/mol in the position of 'D(s!d®) relative to 9D(s'd°). Configurations with more than six singly-occupied orbitals in the GVB-RCI wavefunction lead to numerous spin eigenfunctions (SEF) (e.g., a triplet with ten open shells has 90 SEF’s). In order to save computer time, it is convenient to restrict the wavefunction so that there is a maximum of six open shells in any configuration. Thus the GVB-RCI for the 1S state of Pt restricted to six open shells contains 72 configurations and 328 SEF’s, whereas the full GVB-RCI contains 81 configurations with 642 SEF’s. Table VI shows the differences in state splittings of Pt atom for calcula- tions in which the number of open shells was restricted to a minimum of six compared with the case where no restrictions were made (up to ten open shells. The restriction of a maximum of six open shells leads to errors of only ~0.2 kcal/mol in the atomic state splitting relevant for this work, an error quite tolerable for our studies. We should emphasize that inclusion of at least six open shells is required in order to describe inter- pair correlations (a single excitation within one GVB pair times a single excitation within another GVB pair) for both the triplet and open- shell ~44.— singlet states of the atom. In conclusion, the use of the six-open-shell res- triction is justified for these studies, and all wavefunctions reported here are restricted to a maximun of six open shells unless otherwise noted. C. Geometry Optimization We used a distinguished coordinate method”! to follow the potential curve from reactants to products. Each geometry was calculated by holding the R-M-R angle fixed and optimizing all other geometric parame- ters for the HF wavefunction. Using this sequence of geometries, we then carried out the self-consistent GVB-RCI(4/8)xGVB-Cl(2/6) calculations. This allowed us to follow a continuous path from reactant to products for each system studied and to extract the concepts permitting us to explain the various features and to interpret the experiments. To obtain various critical points (minima and saddle points), we fitted the variations in energy and all other geometric parameters along the reaction path to cubic splines and interpolated the geometric parameters for the optimum energy. Thus, the geometries are not as accurate as they would be if separate energy optimizations had been carried out. To determine the effect of electronic correlation on geometry, we calculated (see Table VIII) the equilibrium bond angles for PdHz, PtHe, PdH(CHs), and NiH, at the HF, GVB-Ci(2/6) and GVB-RCI(4/8)xGVB- Cl(2/6) levels. For Pd and Pt complexes, the bond angle determined at the HF level is within 5° of the GVB-RCI(4/8)xGVB-Cl(2/6) level. On the other hand, the equilibrium geometry of NiHg is strongly affected by elec- tronic correlation, as discussed in Appendix A. In order to test the effects of correlation on the transition state geometries, we reoptimized the geometry of PdH, at the GVB- RCI(4/8)xGVB-CI(2/6) level. This optimized transition state has a Pd-H -~45 distance of 1.595 & and an H-Pd-H bond angle of 50.6°, with an activation energy of 0.74 kcal/mol (versus 1.547 A, 50.8°, and 1.551 kcal/mol for interpolated value based on the HF distinguished coordinate studies fol- lowed by GVB-RCI). These changes of 0.048 A in Pd-H distance, 0.2° in bond angle, and 0.81 kcal/mol in activation barrier” indicate that use of the GVB calculations along the HF reaction path provides a reasonable description for these reactions. Our calculations for reductive elimination of dimethyl and dihydride complexes assume a transition state with Ce, symmetry. It is possible that the transition state for these reactions has lower symmetry.°9 How- ever, it has been shown that the Cy, transition state is a true saddle point in recent ab initio calculations on a similar system, oxidative addition of Hz to Pt(PHs)e. 162,54 Therefore it is plausible that the Ce, transition state for H-H coupling from PdHg and C-C coupling from Pd(CHs)2 is also a true saddlepoint; however, we did not demonstrate this (by solving for the eigenvectors of the Hessian and showing there to be one negative eigen- value). Acknowledgments: This work was supported by a grant from the National Science Foundation (No. CHE83-18041). One of the authors (J. J. L.) was an Exxon Education Foundation Fellow (1983) and then an Atlantic Richfield Foundation Summer Fellow (1984) during part of the time the project was in process. Appendix A. Although not strictly required for the studies of this paper, we car- ried out some limited calculations on NiHz in order to compare with a 22b,37a,b series of studies carried out by Siegbahn and co-workers on Ni(R,)(Re) > Ni + R,-Rg processes. The calculations by Siegbahn and co-workers*’* on NiHg started with a CASSCF in which three pairs of electrons are correlated. Thus, of the 12 valence electrons, six are in doubly-occupied orbitals, while the other six are described by a full CI in which six electrons are distributed among five orbitals. All orbitals are solved for self-consistently in this wavefunc- tion [denoted as CASSCF (3/5)], which corresponds closely to our GVB- Cl(2/6) wavefunction, except that we have four doubly-occupied orbitals (rather than three) and four electrons distributed among six orbitals (rather than six electrons distributed among four orbitals), all of which are optimized self-consistently [thus our wavefunction could be denoted CASSCF(2/6)]. In addition, we also calculated the wavefunction in which all four doubly-occupied orbitals were correlated simultaneously at the GVB-RCI(4/8) level. This calculation is denoted GVB-RCI(4/8)xGVB- CI(2/6) (see Section V), where all orbitals are solved for self-consistently for the full wavefunction. We find that the GVB-RCI wavefunction gives a balanced description of the s7d®, s'd®, and d’° atomic states (see Section V), and this is the level used in the various calculations on Pd and Pt sys- tems. 37 However, Siegbahn and co-workers considered an alternative wavefunction in which several dominant configurations from the CASSCF were selected (all configurations with coefficients larger than 0.05),°74 and all single and double excitations from the dominant configurations to -47- all virtuals were allowed. Siegbahn’'s contracted CI method? was used to solve for this CI wavefunction. On top of this, the multi-reference analog 56 _ of Davidson's correction™ was used to estimate the effect of quadruple excitations. To mimic Siegbahn’s CI calculation, we carried out a CI calculation (denoted CISD) that involved all single and double excitations from the three dominant spatial configurations of the CASSCF wavefunction, accounting for about 99.0+0.1% of the CASSCF wavefunction for the geometries considered. This size-consistent CI involved 6324 spatial configurations and 19,740 spin eigenfunctions.>” We also added the multi-reference analog of Davidson's correction™ for quadruple excita- tions (denoted CISD+Q). We also carried out HF, GVB-CI(2/6), GVB- RCI(4/8)xGVB-Cl(2/6), and CASSCF calculations (without p functions on the hydrogens to be consistent with how PdHg and PtH, were calculated). CASSCF, CISD, and CISD+Q levels were also calculated with polarization functions on each hydrogen to be consistent with the basis set used by Blomberg and Siegbahn.??4 The effect of hydrogen p functions is to make the H-Ni-H angle larger by 2° at the CASSCF level. (All calculations with p functions of hydrogens will henceforth have an apostrophe after their names, e.g., CASSCF’.) These results are presented in Figure 11, where we see that the equilibrium H-Ni-H bond angle decreases as the level of correlation increases. Since the H-Ni-H angle is the same at the CISD’ and CISD+Q’ levels, this angle has probably converged to 69° with respect to electronic correlation. This bond angle is significantly different from the 57° bond angle found by Blomberg and Siegbahn®?@ and is closer to the GVB-RCI(4/8)xGVB-CI(2/6) result of 76°. We believe that the smaller bond angle found by Blomberg and 48. Siegbahn®”@ is due to the fact that their CI calculation was not a “fully variational CI calculation".3”¢ Siegbahn’s contracted CI] method has been shown to give errors of 2% of the total correlation energy in simple sys- tems such as CHg, CHs, and CH5.°° In NiH», the total correlation energy is on the order of 0.30 hartrees (HF energy minus CISD+Q energy). Thus, 2% errors in the contracted CI would lead to changes of about 6 millihartrees = 3.8 kcal/mol. Since the difference in energy between the 57° geometry and the 69° geometry (from CISD+Q) is only 0.5 millihartrees, we con- clude that the contracted CI should not be reliable for such geometric quantities. It is appropriate to examine why electron correlation has such a large effect on the bond angle in NiH2 (99° at HF, 76° at GVB-RCI, and 69° at the best CI; see Table A-I). For all three systems, NiHz, PdHe, and PtHe, the dominant resonance structure is the same, s'd®, However, the second resonance structure for NiHz is different from PdHz and PtH [see (19) and (20)],.as should be expected since the lowest singlet state for Pd and Pt is d?°, whereas it is s'd® ("D) for Ni. Thus, while the second reso- nance structure of PdHz and PtHg is d}0 it is expected to be s'd® for the Ni atom. But the s'd® open-shell singlet cannot be described by the closed-shell HF wavefunction. This bias against the sid® singlet state of the Ni atom leads to repulsive interactions between hydrogen atoms and a large H-Ni-H bond angle at the HF level. The Cl wavefunction includes a good description of s'd® singlet and hence leads to significantly smaller bond angles. Therefore, HF bond angles should be accurate for the Pd and Pt complexes but not for NiHe. ~49.. Appendix B. We report here (in Tables B.I-V1) the optimized geometries along the reaction path for the various reactions studied in this paper. All of the geometries were optimized at the HF level (described in Section V). We also report energies for HF, GVB-Cl(2/6), and GVB-RCI(4/8)xGVB-Cl(2/6) qi8 wavefunctions, all of which were foun to be consistent levels of calcula- tion for the reaction Hz + Pt(PH3)z > HgPt(PHs)z. The following trends can be observed from these results. In going from HF to GVB-CI(2/6), oxidative addition always becomes more favor- able (or reductive elimination is made less favorable). This occurs because the GVB-CI(2/6) wavefunction includes terms that provide a better description of the two M-R bonds, which have larger correlation errors than the corresponding pairs for the dissociated limit (involving a metal d pair and an H-H bond pair). In going from the GVB-CI(2/6) level to the GVB-RCI(4/8)xGVB-CI(2/6) level, we have added terms to describe the correlation effects between d electrons. These terms are needed to get accurate d!0—s'd® splittings. These correlation terms always stabilize the d!° (1S) state relative to the s!d® (9D) state and make oxidative addi- tion less favorable (and reductive elimination more favorable). Thus there is some degree of cancellation in the correlation errors for HF. Table B.VII shows the effect of electron correlation on AE?, R-M-R angle at the transition state, and AE. The trends in AE? follow the same general trend as the AE for these reactions except with smaller magni- tudes. ~50- References and Notes (1) (2) (3) (4) (5) Colman, J .P.; Hegedus, L. S. "Principles and Applications of Organotransition Metal Chemistry," University Science Books: Mill Valley, California, 1980. (a) James, B. R. "Homogeneous Hydrogenation," Wiley: New York, 1973; (b) James, B. R. Adv. Organometal. 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Soc. 1959, 705-716; (b}) Ruddick, J. D.; Shaw, B. L. J. Chem. Soc. 1969, 2801-2808. Low, J. J.; Goddard Ill, W. A. J. Am. Chem. Soc. 1984, 106, 6928- 6937. Moore, C. E. Atomic Energy Levels,'’ NBS: Washington, D.C., 1971; Vol. III. (These state splittings were averaged over j states to can- cel out spin-orbit coupling.) Pauling, L. "The Nature of the Chemical Bond,” 3rd ed.; Cornell University Press: Ithaca, 1960; pp 88-98. The vibrational frequencies used to estimate the zero point ener- gies were taken from those calculated for Pt(H)o(PH3)2 and PtH(CH3)(PH,)2. 164 (a) Obara, S.; Kitaura, K.; Morokuma, K. J. Am. Chem. Soc. 1984, 106, 7482-7492; (b) The C-Pt-C bend was calculated using the angle bending force (17) (18) (19) (20) (21) (22) constant derived from the potential of reaction (14). This gave a frequency for the H3C—Pt—CHg bend of 190 cm™!. The Dggg used in these calculations are Dggg(H-H) = 104.2 kcal/mol Daga(H—CHg) = 105.1 kcal/mol and Degg(H3C—CHs) = 90.4 kcal/mol. These bond energies were derived from spectroscopic measure- ments of H,'?? and the reported Degat® for H3C—CH3 and H—-CH3. (a) Huber, K.P; Herzberg, G. "Constants of Diatomic Molecules," Van Nostrand: New York, 1979; (b) McMillen, D. F.; Golden, D. M. Ann. Rev. Phys. Chem. 1982, 33, 493-352. The vibrational frequencies (550, 1230, and 1230 cm™') used to cal- culate the zero point energy correction of chemisorbed H are those from the EELS spectra of H on Pt(111). 288 The zero point energy correction for chemisorbed CH3 is that calculated and estimated for CH; chemisorbed on Ni(001). !8 (a) Baro, A. M.: Ibach, H.; Bruchmann, H. D. Surf. Sci. 1979, 88, 384-398. (b) Low, J. J. Ph.D. Thesis, California Institute of Technology, Pasadena, California, 1985, Chapter 4. MacDonald, A. H.; Daams, J. M.; Vosko, S. H.; Koelling, D. D. Phys. Rev. B 1981, 23, 6377-6398. Conrad, H.; Ertl, G.; Latta, E. E. Surf. Sci. 1974, 41, 435-446. Weinberg, W.H. Survey of Progress in Chemistry 1983, 10, 1-59. (a) Bagatur’yants, A.; Anikin, N.; Zhidomirov, G.; Kazanskii, V. Zh. Fiz. Khim. 1981, 55, 2035-2039; (b) Blomberg, M.; Brandemark, U.; Pettersson, L.; Siegbahn, P. Int. (23) (24) (25) (26) (27) ~54- J. Quant. Chem. 1983, 23, 855-863. Brandemark, U. B.; Blomberg, M. R. A.; Pettersson, L. G. M.; Sieg- bahn, P. E. M. J. Phys. Chem. 1984, 88, 4617-4621. In this paper, convincing proof is provided that the Pd(Hz) complex is not a van der Waals complex. (a) Kubas, R.; Ryan, R.; Swanson, B.; Vergamini, P.; Wasserman, H. J. Am. Chem. Soc. 1984, 106, 451-452: (b) Hay, P. J. Chem. Phys. Lett. 1984, 103, 466-469. (a) Brookhart, M.; Green, M. L.H. J. Organomet. Chem. 1983, 250, 395-408, and references therein; (b) Koga, N.; Obara, S.; Morokuma, K. J. 4m. Chem. Soc. 1984, 106, 4625-4626. Halpern, J. Acc. Chem. Res. 1982 15, 238-244. (a) Whitesides, G. M.; Gaasch, J. F.; Stedronsky, E. R. J. 4m. Chem. Soc. 1972, 94, 5258-5270; (b) McDermott, J. X.; White, J. F.; Whitesides, G. M. ibid. 1976, 98, 6521-6528; (c) Young, G. B.; Whitesides, G. M. ibid. 1978, 100, 5808-5815; (d) McCarthy, T. J.; Nuzzo, R. G.; Whitesides, G. M. ibid. 1981, /03, 1676-1678; (e) McCarthy, T. J.; Nuzzo, R. G.; Whitesides, G. M. rbid. 1981, 103, 3396-3403; (f) Nuzzo, R. G.; McCarthy, T. J.; Whitesides, G. M. ibid. 1981, 103, 3404-3410; (g) Komiya, S.; Morimoto, Y.; Yamamoto, A.; Yamamoto, T. Organometallics 1982, 1, 1528-1536. (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) ~55e Pt(Et)e(PEt3)e is known to decompose via f-hydride elimination to yield ethylene (AHQo9 = 12.5 kcal/mol, Sag9 = 52.4 e.u.) and ethane (AH S09 = -20.2 kcal/mol, Sag9 = 54.9 e.u.) rather than by reductive elimination to give n-butane (AH&9 = -30.2 kcal/mol, S99 = 74.1 e.u.) even though n-propane is the thermodynamically favored pro- duct (AH399 = -22.5 kcal/mol, ASsg99 = -34.2 e.u., AGggg = -11.0 keal/mol for CgH, + CgHg » n—C,Hyo). The AH&o) and S$. were taken from Benson, 8. W. ‘Thermochemical Kinetics,” 2nd ed.; J. Wiley and Sons: New York, 1976. Low, J.J. Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 1985; Chapter 3. Yoshida, T.: Otsuka, S. J. Am. Chem. Soc. 1977, 99, 2134-2140. Saillard, J.; Hoffmann, R. J. Am. Chem. Soc. 1984, 106, 2006-2028. Sevin, A. Nowv. J. Chim. 1981, 5, 233-241. Dedieu, A; Strich, A. Inorg. Chem. 1979, 10, 2940-2943. (a) Billups, W. E.; Kararski, M. M.; Hauge, R. H.; Margrave, J. L. J. Am. Chem. Soc. 1982, 102, 7394-7396; (b) Ozin, G. A.; McCaffrey, J.G. ibid. 1982, 104, 7351-7352; (c) Klabunde, K.J.; Tanaka, Y. ibid. 1983, 105, 3544-3546. Sevin, A.; Chaquin, P. Nouv. J. Chim. 1983, 7, 353-360. (a) Tatsumi, K.; Hoffmann, R.; Yamamoto, A.; Stille, J. K. Bull. Chem. Soc. Jpn. 1981, 54, 1857-1867; (b) Balaze, A. C.; Johnson, K. H.; Whitesides, G. M. Imorg. Chem. 1982, 21, 2162-2174. (a) Blomberg, M. R. A; Siegbahn, P. E.M. J. Chem. Phys. 1983, 78, 986-987; (38) (39) (40) (41) (42) (43) -56- (b) Blomberg, M. R. A; Brandemark, U.; Siegbahn, P. E. M. J. Am. Chem. Soc. 1983, 104, 5557-5563; (c) Siegbahn, P. E. M.; Blomberg, M. R. A; Bauschlicher, C. W. J. Chem. Phys. 1984, 81, 1373-1382. Martin, R. L.; Hay, P.J. J. Chem. Phys. 1981, 75, 4539-4545. Basch, H.; Topiol, S. J. Chem. Phys. 1979, 71, 802-814. Noell, J. 0.; Hay, P. J. J. Am. Chem. Soc. 1982, 104, 4578-4584. Hay, P. J. J. Am. Chem. Soc. 1981, 103, 1390-1393. It is important to point out here that the multi-reference singles and doubles CI method is not size-consistent at every section of the potential surface.2”° The number of configurations reported in ref. 3%a "varied between 30,000 and 130,000 for Ni(CH3)2 depending on the part of the potential surface." Small inconsistencies at different geometries can generate large errors in the optimum geometries if the potential surface has small curvatures. It appears that the energetics derived from these calculations are reasonable and useful in discussing the properties of Ni atom vs Pd and Pt. We have used the following D, and state splitting to calcu- late average bond energies and energetics; D,(H-H) = 109.6, D.(H3C-H) = 112.6, D.(HsC—CHg) = 95.0, and 3D—!D splitting of 7.1 kcal/mol. *“# (a) Blomberg, M. R. A.; Siegbahn, P. E. M.; Roos, B. O. Mol. Phys. 1982, 47, 127-143. Melius, C. F.; Olafson, B. D.; Goddard III, W. A. Chem. Phys. Lett. 1974, 28, 457-462. (44) (45) (46) (47) (48) (49) (50) (51) =5le- Rappé, A. K.; Smedley, T. A.; Goddard III, W. A. J. Phys. Chem. 1981, 85, 2607-2611. Rappé, A. K., unpublished results. We have tested the SHC basis sp basis by reoptimizing the H-Ni-H angle with the 5p basis associated with the one-electron MEP of Upton and Goddard [Upton, T. H.; Goddard II, W. A. "Chemistry and Physics of Solid Surfaces," Vanselow, R; England, W.; Eds.; CRC Press: Boca Raton, 1982; Vol. 3, pp 127-162]. The MEP basis yielded an H-Ni-H angle of 83.2° at the GVB-CI(2/6) level, while the SHC gave 81.0° at the same level of calculation. Dunning, Jr.; T. H.; Hay, P. J. In "Modern Theorectical Chemistry: Methods of Electronic Structure Theory,” Schaefer HI, H.F., Ed.; Plenum Press: New York, 1977; Vol. 3, Chapter 1, pp 1-27. Huzinaga, 5S. J. Chem. Phys. 1965, 42, 1293-1302. This CI level was restricted to allow only six open shells. This was found to be an adequate level for the state splittings of Ni, Pd, and Pt atoms. Yaffe, L. G.; Goddard III, W. A. Phys. Rev. A 1976, 73, 1682-1691. This level is very close to atomic wavefunctions at the dissociated limit of reactions (1)-(6). (a) Rothman, M. J.; Lohr, L. L. Chem. Phys. Lett. 1980, 70, 405; (b) Williams, I. H.; Maggiora, G. M. J. Mol. Structure, THROCHEM, 1982, 89, 365-378. Williams and Maggiora have shown that the dis- tinguished coordinate method can yield a discontinuous reaction path if multiple local minima exist for the same value of dis- tinguished coordinate. Since the M-H and M—CH, equilibrium bond (52) (53) (54) (55) (58) (57) -58~- lengths are much longer than the corresponding R-H and R-CHg3 bond lengths, it is not likely that more than one local minimum can exist for any value of R,-M—Rz bond angle in the bound com- plex to transition state region. The M-R bond lengths in this region are close to those of the bound complex. If another minimum existed, it would have an R,—Rg distance closer to those of the pro- ducts, which would force unphysically short M-R bond lengths. The typical symptom of a discontinuous reaction path would be a discontinuous change in geometric parameters, which is not evi- dent in our results (see Appendix B). A similar energy lowering would be expected for the PdHg complex if the geometry was reoptimized at the RCI(4/8)xGVB-Cl(2/6) level. (a) Metiu, H.; Ross, J.; Silbey, R.; George, T. F. J. Chem. Phys. 1974, 8, 3200-3209; (b) Stanton, R. E.; McIver, J. W. J. Am. Chem. Soc. 1975, 97, 3632- 3646; | (c) Pechukas, P. J. Chem. Phys. 1976, 64, 1516-1521. Kitaura, K.; Obara, S.: Morokuma, K. J. Am. Chem. Soc. 1981, 103, 2891-2892. Siegbahn, P. E.M. Chem. Phys. 1977, 25, 197-205. Davidson, E. R. In ‘The World of Quantum Chemistry," Daudel, R.; Pullman, B., Eds.; Reidel: Dordrecht, 1974. Unfortunately no total energies or number of configurations were 37. reported for Siegbahn’s calculations ’* on NiHz, so a comparison of how closely our calculations mimic his results is not possible. -59- Table I. Mulliken Populations for the GVB Bond Pairs of M(R;)(R2). For each bond there are two listings, the top one is the metal-like GVB orbital and the bottom one is the ligand-like orbital. Populations of System GVB Orbitals M R, Re M-H M —CHs 0-28 10.02 40.57 770.12 . Pd H H (sp)? 0.18 79-80 - 0-30.02, 0.43(-0.04740.19 0-17 poo! 0-68 (0.12 Pd H CHg ° 3 (sp)?-92q0-15¢.0-0240.81 (sp)°% 0:17 © 50.10 0.67 - 50-16 pos 0-55 (0.24 Pd CH3 CH3 . (sp)®-9 9-20 ¢ 0.28 10.52 3°29 0.02 0-83 440.07 . Pt H H (sp)? qo.18 H°-80 . 0-30 p02 0-60 470.08 50-28 p?01 0-84 c0.08 Pt H CHs (sp) 0-18 j70.60 (sp) 40-28 ¢ 50.12 10.70 - 5°27 poo? @e-82 0.10 Pt CHg CHy (sp)? 2-35 Cc g014 p°-7 -60- Table I]. Mulliken Total Populations for M(R,)(Re). Metal Total Overlap of GVB System Total Population Population Bond Orbitals M R; Re Msp Md H CHs N-H N-CHs Pd H H 0.76 9.36 0.94 0.76 Pd H CHy 0.71 9.19 1.05 9.06 0.76 0.68 Pd CHs CHs 0.60 9.15 9.13 0.72 Pt H H 1.16 9.15 0.85 0.73 Pi H CHs 1.05 §.03 0.89 9.04 0.74 0.71 Pt CH; | CH | 0.97 8.91 9.06 0.71 “Pug O-W 343 Noge UOHEIOI Gazz aALY WO}e JEJaUT aI) 0} papuog sdnosd [Ayjour yey) pauinsse aacy ay (e ¥°O- 8'I- | 6'EP 0°9F (1 °0-) Pd i + <€— "HD fe) € ge “ye . . ae fe) °s at 6 "eh 0'9F (9 *s-) Wd H 6°t- 1'e@- | zoe €°LZ (1 °t) Pd + ~<— "HD £"8- 1'e- | toe £12 ("e-) a a 4H z°SI- le | s°9 9°8 (p’st-) | pa i, a“ <— L°02~ I‘@- | €°9 9°8 (6 °0Z-) PY: a H \ S ‘bs SSI £0 8660 6’ €°8h O'Le | S‘Es € ‘SI (xt) “HD +1a — (“HONG ® 1°82) GL €0 8 2't TOE =e SLZsté«é< DSS COC GR 1°91 (91) "HO + Id — (*HO)(H)a -- zee nr a | £°9 -- 6‘ aed 9 ee (st) "H +4d — “(Hid 9°82 8°8I- €°0 6°0 6'€h £'8h O'Lb | 9°22 0'9I- (bt) “HD + pa — (*HO)pa S°6 AF Co | a A | TOS 8 8=6S'LS OBZ SSC OT 1 °0%- (et) "HO + Pd — (°HO)(H)Pd v0 0'b- £0 3=a't €‘9 2 nn ie } 9°1 9 ‘E~ (21) "H + Pd — (H)Pd “HV SSHY ph¥- HVS | A+ {HN) = “UW p2V av uopWoeay “HV OHV (e4S10ug yujog oraz, *(,,P) Ja1Suys pamoT[e-ujds ay} s} iq 10} aje7s D}wWO;e ayeredeg aL “UOHOBAT BY} AO} 97L}S UOT}{[sUeI] BazBdIpuy JadZep ayqnog ‘sopas1euq jo Areulumg ‘]Ty aqqe ~6§2- Table IV. Average M-R Bond Energies. Adiabatic _ Intrinsic Bond Energy Bond Energy M R Da D; (kcal/mol) (kcal /mol)®) Pd H 50 60 Pt H 69 62 Pd CHs 36 45 Pt CHs 53 47 ®) State splittings are those determined at the GVB-RCI level (see Section V). -6§3- Table V. Mulliken Populations and Geometries Along Reaction Path for Pd + H2 + PdHp. The transition state is at a H-Pd-H angle of 51°. H-Pd-H Mulliken Mulliken Mulliken Pd-H H-H Angle Population Population Population distance distance (deg.) Pt sp Ptd H (A) (A) 90 0.80 9.28 0.958 1.51 2.14 80 0.79 9.31 0.949 1.51 1.94 70 0.76 9.36 0.940 1.51 1.73 60 0.71 9.41 0.839 1.52 1.52 50 0.62 9.49 0.948 1.55 1.31 40 0.50 9.59 0.957 1.60 1.10 30 0.36 9.71 0.963 1.71 0.89 20 0.14 9.88 0.989 2.12 0.74 0 0 10.0 1.00 ad 0.73 (@64- [949] JH ay} ye ‘Afaatjoadsa ‘2g 190G'22- ‘6B2EI 11 62- ‘EGB2ST 6E- are 1q pue ‘pq ‘IN Jo sazeis Ug 24} 10} Saansey Ul saldiaua [eyo] (2 “Alaarjoadsa ‘gL61SG'L2- ‘1 10ST 62- ‘L868E26E- are ‘Iq pue ‘Pd ‘IN JO Sa7@1S (jy aly Joy saasysey ut salSiaua [e107 (O1/S)IDN-GAD (q ‘pl aoUata]aY og v8 eel 4 Vt |G bG 4S9 09S | EST- ET! 40 dg gP2S 0'L2e 6'S2e Vee | eet ett vtt | ver 62 Lh dy eP,S vie Let Ol | det 0'6T- 6 12- | S66 9°0F OOF; SS, oP 00 00 00 | 00 0°0 oo |0'0 00 00 dg eP 1S (aH | (qlON-AA9 | (09% | (oH | qlDU-GA9 | (oH | (oH | qlOU-GAD | @dxa | way, | ‘Byu09 Id Pd IN ‘PRL IN 10} (JOuL/Teoyx) sFurjyWds a7e1g OTWIOTY “IA aIQUL Table VII. The Effect of Maximum Number of Open Shells and Level of Optimization on GVB-RCI(5/10) State Splittings in Pt Atom. State Splittings (kcal/mol) six open shells ten open shells GVB-PP | GVB-RCI GVB-RCI State Orbitals | Orbitals Orbitals 3p ( d¥s 1) 02) o>) oo) 1§(d?9) 12.3 12.7 12.5 1D(d®s!) 26.1 25.9 25.9 SF(d8s?) |. 18.5 18.8 18.9 ®) Total energy in hartrees for the °D state of Pt is -27.551297 for GVB- RCI(5/10) with GVB-PP orbitals and restricted to six open shells. >) Total energy in hartrees for the °D state of Pt is -27.551978 for GVB- RCI(5/10) with optimized orbitals and restricted to six open shells. ©) Total energy in hartrees for the °D state of Pt is -27.552461 for GVB- RCI(5/10) with optimized orbitals. -66~ Table VII. The Effect of Electron Correlation on R,-M—R2 Equilibrium Bond Angles. System Bond Angle (deg.) GVB-RCI(4/8) M R; Re HF GVBCI(2/6) xGVBCI(2/6) Pd H H 68 73 73 Pt H H 84 81 84 Pd H CH, 83 83 80 Ni H H gg®) a1") 76°) *) Bond length frozen at geometry of Blomberg and Siegbahn.378 67 ‘uloze H ay} UO s.d papnjout suotounjaaem asayy (q “2y Jo suoleyasaidas ajqionpait 07 Fulsuo[aq sTeytqJo pasn SUOT}OUNJaAeM BS3Y] JO [IV (yg - -- - 0°69 4SSOSE OF- (q-5+asI9 1S9'09S'8 OFL‘6T bee's 0°69 OOPEEE OF- (q:GSI9 Z1L‘60r g9S‘8 oge'e £94 G62aTE'Ob- (9/2)ID-AADx(8/ PION 482 82 Se I 4 | O86 T9T OF- (q .(G/£)49SS¥9 £82 82 Se €°e8 612eST OF- (S/€)d9SSvo gto't 4g av o'1e QIESST O- (9/2)ID-€A9 I I T v'68 LE9CL0 0F- 4H sjuaula[y S,AAS Jo ‘s#yuoy) (saaidap) (saamjzey) lorjounjaaem xllyeW ID Jaquiny jo alduy UNUITUTU o.1aZU0N Jaqumy umnuindg +e jo Jaquiny Adiaugq [eyO], ‘@HIN JOj S}[Nsay ‘]-y aqqeL -68. Table B-I. Geometries and Energies Along Reaction Path for Pd + He ~ PdHpo. Geometric Parameters” Energy?) PdHo2 Pd-H H-H HF GVB-RCI(4/8) GVBCI(2/6) angle distance distance xGVBCI(2/6) (deg.) A A (kcal/mol) (kcal/mol) (kcal/mo)) 90 1.510 2.136 21.0 2.13 6.33 80 1.508 1.939 18.4 0.0 4.04 70 1.512 1.734 17.6 -0.31 3.55 60 1.524 1.524 17.8 1.15 4.44 50 1.550 1.310 17.5 3.47 5.09 40 1.601 1.095 13.1 3.55 2.44 30 1.714 0.887 3.8 0.66 -4.61 20 2.124 0.738 0.0 “2.13 “4.42 0 so 0.734 0.0 0.0 0.0 @) Each geometry optimized at the HF leve] with H-Pd-H angle held fixed. b) Total energies (in hartrees) at the dissociated limit are -30.237961 at the HF level, -30.265687 at the GVB-CI(2/6) level, and -30.336364 at the GVB-RCI(4/8)xGVB-CI(2/6) level. “aUoVOsd [AYJaUs ay) JO SEeAI Jo 2a;Uad ayy 0q 0} Poutjep a} aAy (a *(/8NIAADs(8/d)1DU 205 COLLEGE “69- PUR (9/2)IDGAD 20] BOLIC '69- “AH 40} COLz6Z ‘e9- a2e JIU Pae|souRTP ay) Je SaaI,IEY UT BE PBI8UA JeEIOL, a “PAX PI94 SHO-Pd-H 84) WNIe 1249] ZH 94) 98 peayurpdo Lajem0as WUd ¢@ bd H—6, “a ‘ H 0 0 0 ov 601 601 801 -- - 60°) 80°) ost iad @0°1 @ @ 0 giie 6€ ‘O- ba'o ou 601 601 ou zh s"es 80% 80.3 08) veel 80°} 90's U4 oz 6b'b eso oz ‘ol eo1 601 2401 At} oat 9°l9 60°) 60°) OLi 9"LEL tt ii 4 so'e oc t c.'et Tm 4 b°6z 601 601 20% O21 bz) S*eL 60°) 60°1 sor Ct 4 2} ec’ +) 4 ou') OF 3 6z"oc onic 68°2> au TE} c6 seh on Loe 80°1 ot os} ops) ss‘l 66°) ss*l os ‘ 06 "sz 96 "pz se'lp ou our 6 6cl Li 6°16 80°) 60°! isk o'lol ze" 10°% ts‘h oo thee Oc ‘61 L0°e¢ the Oo 6e Stl eth 2°00) 90°) oul Shi 2041 ¥0'2 ee") es‘) OL 30°08 ev'ol 99 9C 601 Wa 8e 9b) 33) z*h0) 00 "1 60°1 4 2 OL) 92°¢ 96 “1 es't oa 20°18 io so'o¢ oul ol 26 is 2) zal bas 80°1 80°) 6h ae 2 ace 56°) is) 98 (9/8)19-@AD x aiaue apue aytue araue oydue ajgue = aaueys{p «= aoueyeyp @ ame @ aus 81p 1191p 3181p aie e/eou-aad (9/eaaD aH | ho HO HO CHD Pd pg 5.dy 35% 3d Wy My “HO pd “Hepa HO “lH - -H -H -H (eABtaug (qitaiauesed aytpautoasy “JOw/[edy UY Gasaua [ye ‘swosjedue uy waouEs IP We ‘saas3ap uy sayaue [py (SHO) Pd ~ "HOt Pd 40} Yitd LoQaeeYy Juoyy sayd1aug pue sajzjau0an “H-g a198L “(9/2NIGA De(8/PDU 40) BOLSOP “9OT- PUE (9/Z)IDGAD 40; SZbPCE “BOL- “AH 40) 226216 “G01 axe (9 = aydueD t Pd. d / Ny3e H#—)' y Te Vou day ‘suojoad [Ayjou ayy jo seew 40 10,Ua2 ay} aq 0} paugap a} oAy ry “Pd~D) WT] Paye}D0geTP ay) y¥ sea.NseY Uy sayBsaue yeV0, ta “paxtupido Aqiny gem yojys ‘spFue .¢°1¢ ay) 0} \daoxa paxy play afsue O-Pd-3 OY) Ye [909] ZH 94) 38 PezpWAdS Lz,;aW0ND (e 0 (') 0 90} 801 WI wu -- 7 oat 06 60° 60" ost o t) i es vt Lol ol zu a C4 154 oe) 001 60") 90°! vel ced oz 9008 ity Ces Lol ou ott 901 oF 4) Va GLI 60°) 80° set OL’s av t v6 "ve aly sor 401 Vt SzI oh i) 92 cor eel 90°) w'l L6°1 Lat 4 os L 6y'os o’te 200 ol 901 col S6 ca tral 1st ov 60% 60's or's oz'e os i] S6 "bE mid Ly Ww 801 LSi ve z01 cit oct 691 90°1 6o'l veg wo's OL tout gsi 6's¢ Ou 601 ssh va sor aut Set sul 90's 60'1 es’s 10°g oe S6"St im) O’es 601 601 ost rh) (23) 901 ov Out 80°1 601 co's 96") 6'l6 Gruen (9/2IGAD =H 3H on 34 30H nano a Pa. 3H oe Coa3 y5 - 4ye3 9 ° pa “ - AL S (qf tteea (e242 eure eg dpajawoay “Jour [eazy Uy sapBsaua Tye ‘swosjedue Uy Seoueyslp [ye ‘waer3ap uy saydue piv“ "HO)pa °H*D + Pd JO} yyed UORIBeY Auoly BOReS1euq pue BajqjauoaD “1N-g 191 -T1le Table B-IV. Geometries and Energetics Along Reaction Path for Pt + He ad PtH2. Geometric Parameters” Energies” PtH, Pt-H H-H HF GVB-RCI(4/8) GVBCI(2/6) angie distance distance xGBCI(2/6) (deg.) A A (kcal/mol) (kcal/mol) (kcal/mol) 90 1.47 2.07 -25.8 -30.6 -33.1 82.5 1.46 1.93 -26.2 -33.8 -33.6 70 1.47 1.68 -23.6 “31.2 “31.3 60 1.48 1.48 -18.7 -25.6 -26.5 50 1.50 1.27 -12.7 “16.9 “14.4 40 1.55 1.06 -8.1 -10.2 -7.7 20 2.12 0.74 “3.2 -3.7 -3.9 0 20 0.734 0 0 0 ®) Geometry optimized at the HF level with the H-Pt-H angle held fixed except for the 82.5° H-Pt-H angle that was the result of a full geometry optmization. >) Total energies (in hartrees) at the dissociated limit are -27.584343 for HF, -27.619193 for GVB-Cl(2/6), and -27.693296 for GVB-RCI(4/8)xGVB- C1(2/6). d HL Ad, Hy f AY Yn shay ‘suojoud [Aya samy] ayy 10; seew JO 1aqUad ay aq 0] Peuyap a} aWy res “0 /EIGADe(8/$)1DH JO} ZeOdbL “LO- PUE ‘(9/Z)LIMAD 40] 6ZG0L0°L9- “ZH JO} CSR1¥O “LO- 2c YUN] PayepoGeTp ay) ye MOON IEY UT ea]DZOUE [EVOL a ‘woNezwAdo £Nawoad yng e Jo yNeaT By) GEM YDIYR ‘a[Zue puog D-id-H of 6B A) JO) daoxe paxy prey aydue D-7g-H 2) Ye [aaa] AH 04) 1# pezjwAdO L2VamI0aD ( 00 0 t') 601 6o1 601 601 -- -- 901 90°} oet 7 90'% o ® 0 G's- e"o- SI- } 601 ou 601 om Gel +s oo" 60°) oet ita! 601 we 00's 0z o's 9'¢ e's Gol 601 vol 61 vet 89 80° 60° OLt ect wt 16° ors os i) vst mt 4 601 aul 66 ter 43 te 80°} 60°} 093 est eel 6st s'z ov 9'a L's bor 601 zu 16 Vl st 6 00°) 60°T ost ver us‘ art wo'e os ' L’e- O'L- wu 6ol 1303 ue 6ri mt sol 80°41 60°! abl 7A) te‘l one 20 °8 oo x S*s- L‘vI- ve oul Mi Le ost oul 101 6071 60° ov eLI te 4 sol eo'k OL a o'vl- $'6l- e't- on Om 18 6ri 601 801 80°T 60°T wi OL ve'2 Lb'} u6 "1 oe vate U*hg- L't- oun On 98 obi 603 601 80°1 60°1 ev 081 vere Ci a 96°1 ¢ 68 (9/2O-GAD x aviue uve oraue asus = ajJue apzue aounyeip SOUEIIP (,213ue (gtldue Souris sounisip R ore @/ylou-aap 9/DEAD au 4-3 4-9 H-9 89 l ya-0-n 3 a-0-49 -3-°H o-“n Ho ed H-9 Heid o-id “4 HO -H -Ho-H cH tu (qi®eua (oP eulesed apajawoas) “Jou 1894 Uy BapBJaUE je ‘suOIySBuE Uy saauE;sTP [Te ‘saaadap uy sapdue iy “(‘HOMH)d — "HOD + Id 20} ed UOWIeaH MOLY eopjassaug pus sajsjawoay ‘A-d aiquL -T3- “8/8)1D8A.De(8/¥)LIe 205 ceozeL “901- PUE “(9/z)IDGAD 405 zeezeo “901- “OUOp aba UOREZ}W Ido Kaj;awW0ad TINY & YDTys 40j Bue puog 96 ay) 10; ydaoxa Pexy play ayue puog 3 “suojord |Ayjaw ay) Jo BER JO saqUas ayy aq O4 pauyap oy My re “AH 20} 222299 “901- ase yyw payeloousyp ON 18 602,40y Uy BayFs0U0 }e}01 (a “id =D 9U) Ye Janay AH 04) 7e pezjuAdo Lnaui0ed yaeg (e [) 0 0 90) Or Wi Thy -- Saad 60°} 60°h oer - bs‘) @ 0 eu i a | 1’e Lol wt Zu ail tw ze 60°) 80°1 oal ool sc‘t id 0% i's a 39 801 10} in elt c21 ee 90°} 60'I Py Ay 1 va‘) 00's oc Cty 4 gle 1 ‘eg ol 601 sol 6tl sel 6r 00 °T 60°1 Sol Sti 86°] 60°2 ov z’ss L°u6 t "ep on on iol As 34] oe 80°} 60°1 obi ocl o's se"s os »'6} 641 s"6c ou 60r 48 est bul £6 80°1 60'1 stl 001 c's Lae 4 09 Lb te o‘sl th L401 ye es] vil £0} 90 °I oll scl OL} ie 4 coe OL s‘L- 8'L- 6") ol 80) se us eu LOL 00°} 60°} och sil BL‘? 00°2 oe 6°ul- €‘2I- 0'b- onl Oo +8 Si 603 601 80°) 60°) Tei 6LI 16°% i6°) 06 €‘@i- € ‘o2- I's- OU 601 16 osl Ol 601 80°) 60°) Osh OL) ees 16") ] (q@2ueug (ef 8auleseg ayayauosn “POur/{eay UY Sasaua Je ‘gwojs4ue uy gaouEysIp Te ‘saaagap uj soydue Tv “(SHO)d — “HD + 1d 40; Wied UOHWsEaY Buoy soyaZzaUg Bue gajsjauoay “lA-g aig -~74- *978}8 UO} ISU} ye a[due sa}0UEp pu-W-u (e € ‘SI 86h Tes | Lz 86h 86869 | L's O°%S = 8 ‘ay "HD +1d — (HO) a) 47 0°62 | 2°Iz Sob s'9e | 4's fbb = «18 "HO +44 — (SHO)(H)a 9 "ce -- -- 8°E£ - -- 2°92 -- -- ‘H+ 4d — “aha O'9I- = ggg 9% | 8'EI- ses 6oe | o'se- oO'8S g'2z *H'D + pd — ("HO)pa T'0z- ‘Ig 501 £°OI- = L6H G°9E- SES a'k "HD + Pd — ("HO)(H)Pa 9't- 9°0S- 9'T ¥'0 S‘bb Og 'b 9°LI- = 8cs—g‘0 ‘H+ pd — “(H)pa av ay3ue 4V dV = ajgue rd av = aygue yV pw-u pu-w-u pu-W-a uopjseey (9/2)1ID-GAD x(8/p)1IDU (9/2)1I0-GAD 490q -339.24.18H *JOUL/[eoy Uy sayZiaua Te *80a1Zap uy saqdue [Iv APPL (e *AayaUIOSH a7e1g UOHIsuer], uo pur sopasiaug™ uoyoeay uo uoyepas05 jo PIA ‘WA-d ajquy =~15— ‘uoTyeMNdod vay [NW @ jo suis, Ul pazéfeue st [wyIqio gay yoRg ‘cQ‘O st SMojU0d Uaamjaq Futoeds ayy ‘saysep Guo] ase saul] fepou pue ‘payjop aie sunoju0s aaljedau ‘plfos are SINOYUOS aalyisod ‘Sy¥sliayse Aq payeorpurl aie auejd ay} UT lafony ‘[suon “enofed dd-(v/2)aAD wWory] AHYq pue 2ypq soy speyquo GAN ayy “| amIy 40H 69 PS x9 9942 4g 08'H 6: Sy qj 6910 ar'Hyg PP 29959, 8S Pd 00 Mg) PSpq 99,9 $9Pd Vo ad NS \ )) 3NO e ¢ 9 410g PUOG H- td 1427 (P) 40d PUOG H-Pd 4497 (4) ~~ Ov " Hg: PS 69 Wyo 91d y 40°H py PG aq 9942 *9i _ an 141 P0349 27H 6 PP 2915 9 8GPd 00H g, PSc999,5 598d ~ ) ¢ / ( | (\ Xp Po we? %, 410g PUCG H- Pg 14biy (0) ‘suOTYBMaTBO (#/2) GAD YO paseq (HD)Hid Pus (fHD)HPd JO] sjeyqso gay ayy, "gz amdyy 3 10 Ng PScq F329 8904 @v og PS eg Guy, S8ts te H go Fy? Sur BP 24 Uy SGhu ™ ay ‘ ano} ¢ ert 90. 4059, 02595 25 Shed 4D PUOG H-4d (P) ~76~ 40g PUG H-Pg (9) 820-83 99 P19 49g 7 5914 3NO} ¢ INO ANO 6140-89 gg P49 9S,,55Pa 3NO 40g Puog J-id (9) 40d Pu0g J-Ad (0) -17~- “‘suoryEMoyres (b/2) GAD YO paseq 2(fH9)1q pure 2(Sy9)pq s0J speqiquo GAH ayL “gE amsy o 21429 $229 9%)9.99,2 8910 02 4y58'Ig, PS29 99 2g SOK 1 7 . 26 %ez “22? P 2995) 35Pd 19,9" 65 P00 95 9, $5Pd PuUog J-id 4497 (P) 40g PU0_ D-Pd 97 (9) GEE) aNO 049918" 6152099 20'-89d aNO sy 8*D 6g PQS 9, SSP 40g PUuog J- Pd wbly (0) ~-78= “suore[Nda[e@ (9/2) INGA Dx(B/F) ION “AAD uo paseq *(fH9)pd + *H29 + Pd pue ‘(fHD)HPd+ "HO + Pd ‘tHpd + *Y + Pd 40} sarjadiaua pue satijauload jo Areurums ‘pf amdry 06S =H [Ayjou 0G 'b = Hb Aya ¢ "HO "HON ms yos! | +Pd Wi], t96(Pd yee 2z6(Pd jow fH9 jOuw HO-Ysz'2 ‘ 9“ Y96' /\WGESI- = 3V ANPWIS2=,3V JOus/|D9} Q ¢ oSc = Hilt Ayjou 082 = HH yaw - HO FHOY66 | HO. v6"! yao | + Pd WLS" ets{Pd yee"? oth jow iH H ySs'l H“ Yes | N94 |'OZ- = 3V JOW/|024 p'O}=,5V [Ow/(094 O H H YeL0o | + Pd yee ire VEL he Lea}Pd jouw H H-Yss't bYis AOUGG'e- ="3V lOuy|oHGGI=,3aV° [OW jO9y O SJONPOJ B}DIS SJUDJIDaY UOIPISUDA| “suoTyana[ea (9/Z)INGADx(9/ PON “GAD uo paseq 4(fHO)id « H%29 + Yd PUe ‘(fHO)HIide "HD + Id ‘id « 4H + 3d 40} soljadieua pue satijauioa’d Jo Areurums -g ams olG =H Aujou o& = 44 Mypous E19 fH 2 =H4 Ut fH9 yes! | + td yore ae yeze bid jouw ; HO jouw HO-Yoe'? fH9/yz6'! /1094 €°81= “3V /ODNG'ES = 43V jow/}034 O oS =H (Ayjou oO= Hit yjou HO FHA yer'2 ®HO. y96"I ' yao! | + Id Yoo tlid yor? soba e jw low H“yzs'l Hyer 1094 1°91 = 73aV /094 O'62=,3V JOw/109} © H H Yreso | + Id yee el jou H t /\094 9°¢e = “39 jOw/ 1094 O H“yse" sjonposd 9{DIS SjUuD|IDAaY UO!jISUDI | “SuotzB[NI[@9 (9/2)IDGADx(B/ b)IDY-AAD UO paseq 2(£y9)pg + 925 + pd pure ‘(fHO)HPd + "HO + Pd “@HPd © 7H + Pd 10} saama jeruajog “g amsty (saaabap) ajbuy Yy— Pd ym e) S| O£ Gb O09 GL GG’¢ - ae £H9-H+Pd =~ H(®HO)Pd \ 70 ' HOD-9°H+Pd ("HO)Pd 922 G2 ({OW7|D9y) ABsauy ‘suOT} -BIN9[29 [OY-GAD (9/2)IDGADx(8/P)IOU-BAD UO paseq 2(fY9)1q + 9Y29 + Id pue ‘(°H9)Hid © "HO + Id “@Hid + 2H + Iq JO} Saaina [enuajog “4 amaty (saasbap) ajbuy Wi bd 0 Ge OS G2 ere) { { CH td — “Hid SS PHO + id —HEHO)Id \ \ : \ JS soot 9H20 + 4d —2FHO)I 0 Si Mm a rq?) —< WO < oc x Qo 3 Go 09 Carbon sp> hybrid orbital ~82— 9 ONE \ ONE 205, Oly 54 cis p'5 c2¢ ahd Pds Hydrogen {s orbital 4, oO Paliadium sd hybrid orbital ONE -Of 024.18 4,79 ,02 Pd §0! pg! 79 He ONE (7 Pd 528 02 4.56 A2 4.0 p H, H3 Figure 8. The GVB orbitals for PdHz and Pd(CHg)z near the transition state for reductive elimination based on GVB(2/4)-PP calculations. ~83- Pd-C Bond Pair ONE ONE Pd 5 5p Src gl2,50 Pd Ss 5p aghh g0 Pd-H Bond Pair ONE {/ | JONE \ ad- \ Pads apg pi YE Pa 58°57 ae? ¢ New Figure 9. GVB orbitals for PdH(CH3) near the transition state for reduc- tive elimination based on GVB(2/4)-PP calculations. Figure 10. Geometries of Lewis acid /Lewis base complexes of Pd + Hp, Pd + CHy, and Pt + CHy. The bond energy with respect to dissociation is 5, 2, and 4 kcal/mol, respectively. Energy (Hartrees) 8 5e ~ 40,02 —40,04- -40,06+ 40,081 ~ Hor tree - Fock T a ee + GVBCI(2/6) -40.16H +——_# + CASSCF al + CASSCF’ AL ee - 40.28 —*- = RC1(4/8)*GVBC1(2/6) ~ 40,30 — 40.32 ,— ~-% + #\<-CISD’ 40.34 . —ik —# ae CISD+Q’ 40,36 1 4 1 4 _j l 55 60 65 70 % & 85 9 H a Ni=—-H Angle (degrees) Figure 11. Total energy versus H-Ni-H angle for the lowest singlet state (7A,) of NiHz. The asterisks mark the minimum of each curve. The HF minimum is at 99° (off the scale plotted here). ~86- CHAPTER 3 Theoretical Studies of Oxidative Addition and Reductive Elimination: Il. C-H and C-C Reductive Coupling from Pd and Pt Bisphosphine Complexes The following chapter has been submitted for publication to the Journal of the American Chemical Society. 87= I. Introduction In spite of the importance of oxidative addition and reductive elmina- _ tion in organometallic chemistry,} a fundamental understanding of the electronic structure of these reactions is only just emerging.” Focusing only on Pd and Pt complexes, some of the experimental observations are: (i) C-C coupling from Pd dialkylbisphosphines® Pd(CHg)o(PRa)2 > Pd(PRs)o + CHg—CHg (1) and from dimethyl, trimethyl and tetramethyl Pt(Iv)* complexes, e.g., Pt(CHs)a(Cl)a(PRs)2 + Pt(Cl)2(PRs)g + CH3—CHs (2) is intramolecular and consistent with a concerted process. Con- versely, (ii) Pt dialkyls tend to decompose through f-hydride elimination? if this pathway is available, even though direct C-C reductive coupling is thermodynamically favored (by 11 kcal/mol):? H (PR,),Pt + H,C=CH,| ——» (PR,),Pt + C,H, + C,H, a \cu,—-cH, CH,—CH, (PRPC (3) CH,—CHs TK (PR,),Pt + CH,—CH,—CH,—CH, (iii) Pt(CH3)2(PR3)2 complexes are thus very stable and have never been observed to undergo reductive elimination, 1° while ~88- (iv) Pt(II) biphenyls, on the other hand, reductively couple to form C-C bonds.!! -(v) In contrast, reductive H-C coupling occurs readily from Pt({II) com- plexes, 12,13 Pt(H)(CH3)(PRg)z + Pt(PRs)g + CHy (4) and presumably would also occur from analogous Pd(II) and Pt(IV) complexes should they be formed. (vi) On the other hand, the reverse (oxidative addition) reaction to (1), (2), and (4) has not been observed and oxidative addition has been observed !4 only for Pt(PRs)z2 + Hg > Pt(H)e(PRs)2 (5) {and not for the analogous Pd(II) species]. In order to elucidate the general trends about reductive elimination/oxidative addition, we have carried out ab initio calculations for the species Pt(CH, )a(PHs )s Pd(CH,),(PH,), - Pt(Cl), (CH,),(PH,), i 2 3 Pt(Cl),(PH,), Pt(H)(CH,) (PH,); Pt(H),(PH,), 4 5 8 and for the reductive coupling products Pt(PH, ), Pd(PH; ), 7 8 These data plus the results from previous studies* on the transition states and barriers for reductive coupling from Mt(H)pg, Mt(H)(CHs), and Mt(CH3)z complexes (where Mt = Pd,Pt) are used to estimate the energet- ics and barriers for various reductive coupling processes in Pd and Pt bisphosphine complexes. I. A. -90- Summary of Results Nature of the Chemical Bonds As a basis for understanding the differences in energetics for C-C, C- H, and H-H reductive coupling from Pt(II), Pd(II), and Pt(IV) complexes, we first develop a qualitative picture for the bonding in these systems. 1. MU(II) Systems The Mt—CHg bond orbitals (from GVB calculations) of 1, 2, 3, and 5 are shown in Figures 1-4, the Pt-Cl orbitals of 3 and 4 are shown in F igures 5 and 6, and the Pt-H orbital of 5 is shown in figure 4. The GVB orbitals are analyzed in terms of Mulliken populations in Table I and in Figures 1-6; total populations are given in Table Il. The overall qualitative description is as follows: (1) (2) (3) (4) The Mt—CHgs bonds are covalent, with one electron in an sp® hybrid orbital on the CHg and one electron in an spd hybrid orbital (60% to 75% d) mainly on the metal, The Mt-H bonds are covalent, with one electron in an H 1s orbital and one electron in an spd hybrid orbital on the metal, The Mt-Cl bonds are partially ionic, with one electron in a Cl pz orbi- tal and the other electron in an orbital that is partly on the Cl and partly on the metal (spd hybrid with 30% to 50% d character), There are generally about ten electrons on the metal with character corresponding to either (i) the atomic d’ configuration for 7 and 8 [generally denoted as Mt(0)], . (ii) the atomic s'd® configuration for 1, 2, 4, 5, and 6 [generally denoted as Mt(II)], or (iii) the atomic s*d®° configuration for 3 [generally denoted as Mt(IV)]. This focus on the ten-electron atomic configuration on the metal arises naturally from the generalized valence bond description, and we find that it provides a means for quantitative comparison of the various reaction energetics. A more quantitative analysis of the character in the GVB orbitals is as follows (see Tables I and II). For the Pt-CH3 bond of 1, the metal orbital is 82% on the Pt and 17% on the C. The metal part of this orbital is 60% d, 28% s and 12% p character, very similar to other Mt-C and Mt-H bonds.!° The methyl orbital of the Pt-CHs bond pair is 89% on the C atom (18% s and 71% p or s'p*). The HCH bond angles (108°, 108° and 110°) are very close to the tetrahedral bond angles expected for sp? carbon. These orbi- tals are similar to the bond orbitals of Pt(CHg3)2, where the metal orbital has 90% Pt character (69% d, 30% s and 1% p). The carbon in the methyl group in this complex is also sp*-like (18% s and 71% p or s!p*), with H-C-H bond angles of 109°, 109° and 110°.7° The preference for ~60% d character in covalent metal-carbon and metal-hydrogen bonds was also observed in Ti(H)2(Cl)2 [74%] and Zr(H)o(Cl)e [58%] and has been rationalized in terms of maximal lowering of kinetic energy.!® The major effect of the phasphines here is to decrease the Pt d char- acter (69% to 60%) and Pt s character (30% to 28%), to increase the Pt p character (1% to 12%), and to increase the charge transfer to the methyl (0.06 e~ to 0.13 e”). These changes arise because each phosphine lone pair forms a Lewis base/Lewis acid bond to the Pt by overlapping the -92- empty valence s and p space of the metal atom. Thus the Mt(PH3)2 com- plex favors the d!° configuration. However, with five doubly-occupied d orbitals, the d!° configuration cannot form covalent bonds to CH or H” ligands. Thus, in order to add to H-H, H-C, or C-C bonds, the metal must be promoted from d?° to s'd°. With two singly-occupied orbitals (one s and one d that may be hybridized to form two sd hybrids pointing at 90° to each other), the s'd® state can form the requisite pair of covalent bonds. The singly-occupied sd bonding orbitals must become orthogonal to phosphine lone pairs [not required for Mt(CH3)2], which they do by mix- ing in p character. This destabilization by the phosphines of the metal bonding orbitals makes them easier to ionize and thereby increases the ionic character of the M-C bonds. Although Mulliken populations are always somewhat ambiguous in identifying the absolute location of charges [e.g., the dipole moment for PtH indicates that Pt is positively charged (Pt*H7) by an amount corresponding to a transfer of 0.26 e~ to H, whereas the Mulliken popula- tion indicates a positive charge on H of 0.1 e7],74 we find these popula- tions useful for comparisons with related systems. From Table II the total populations indicate that each phosphine in 1 is essentially neutral (-0.06 e~ total charge). The total populations on the Pt for 1 lead to (sp)°75(d)®-5®, reasonably consistent with the characterization as s'd° The description of the two M-C bonds as covalent is in reasonable agree- ment with the Pauling electronegativities!® (2.2 for Pt and 2.5 for car- bon). Changing the metal atom from Pt in 1 to Pd in 2 leads to a small increase in charge transfer to CHg (0.13 e~ versus 0.20 e~) and to PHs (0.06 e~ versus 0.10 e), to decreased sp population (0.73 e~ versus 0.33 ~-93- e~), and to a slight increase in d population (8.89 e~ versus 9.09 e7). These differences indicate that Pd has essentially the same electronegi- tivity as Pt (the Pauling scale assigns both as 2.2) and that Pd is biased toward d” relative to s'd®. (This is expected since the ground state of Pd atom is d’°, while that of Pt is s!4d®.) The character of the GVB orbitals reflects these differences. Thus, comparing 1 (Pt) and 2 (Pd), the metal part of the Mt-CHs bond orbital has 0.17 e~ versus 0.24 e~ on the C, while the M sp character decreases by 0.09 e~ and the percentage d character on the metal part of the orbital increases from 60% to 67%. Comparison of 1 and 4 allows us to analyse the differences between Pt-CH3 and Pt-Cl bonds. The net effect of replacing both CHg by Cl is to decrease the charge on each PHs by 0.14 e~ and to decrease the charge on Pt by 0.07 e~. Comparing the GVB orbitals, we see that the metal orbi- tal is 27% on the Cl (versus 17% on the CHg) and that the percent d char- acter of the metal part decreases from 60% to 51%. As would be expected, the Cl-like GVB orbital is nearly pure p character (95%) with very little metal character (3%), Summarizing, all complexes that would be described as Mt(II) in the normal oxidation state formalism are unoxidized and have s!d®° character on the metal. Thus oridative addition of these metals to H-H, H-C, and C-C bonds is not oxidative! In the GVB description, we think of the two singly-occupied orbitals (s and d) as combined into sd hybrids (pointing at 90° from each other) and covalently paired with the singly-occupied ligand orbital (H, CHg, or Cl) to form a covalent bond pair. The presence of phosphines leads to destabilization of the M s orbital, with a concomi- tant increase in p character and increased charge transfer to the ligand. Thus we use the notation Mt(II) to indicate the configuration (s'd®) capa- ble of forming two covalent bonds. 2. Mt(IV) Systems Before considering the Pt(IV) complex 3, it is appropriate to examine the GVB description of the s*d®° state of Pt (and Ni and Pd). In the d!0 state of Pt, the Hartree-Fock (HF) description has five doubly-occupied valence orbitals, while the GVB description leads to five pairs of orbitals, each of which involves two overlapping orbitals of the same character (e.g., d,,) orthogonal to the other four pairs. In each pair, one of these orbitals is more compact and the other is more diffuse (reflecting the tendency of the electrons to correlate their motions so as to reduce electron-electron interaction while keeping the electrons close to the nucleus). Thus GVB describes d!° in terms of ten orbitals for the ten electrons, while HF uses five orbitals. However, since the GVB orbitals within each pair have a high overlap (S = 0.91) and similar shape, the GVB description leads to the same qualitative description as HF, and we dis- cuss the d?° state as if there were five doubly-occupied orbitals. For the s!d® configuration, the ground state is 5D, which in HF is described with four doubly-occupied d orbitals, a singly-occupied d orbi- tal, and a singly-occupied s orbital (a total of six). In the GVB descrip- tion, each of the four doubly-occupied HF orbitals leads to a pair of highly overlapping GVB orbitals so that GVB again has ten orbitals for the ten electrons. Although the shapes of the singly-occupied orbitals change slightly between HF and GVB, there is again no qualitative difference in the description of the s'd° state. However, for s*d8 there is a qualitative difference between HF and GVB. Here the ground state is 3F, leading in HF theory to three doubly- occupied d orbitals, a doubly-accupied s orbital, and two singly-occupied ~95- d orbitals, for a total of six. In the GVB description there are once again ten orbitals with three pairs of highly overlapping d orbitals (correspond- ing to the HF pairs), two singly-occupied d orbitals, and a pair of orbitals corresponding to the HF s pair. However, this last pair of GVB orbitals differs remarkably from HF, leading to sp hybrids as shown in Figure 7. The overlap for this pair is 0.75, but most significantly these sp hybrids point to opposite sides of the atom so that they can each participate in separate covalent bonds. This is quite analogous to the situation in Zn, Cd, and Hg, where the valence s pair can make two covalent bonds (say to CH3’s), leading to a 180° bond angle. Indeed, the triplet state of PtHg, Pt(CHg)2, and PtClz should be linear, being formed by bonding to these sp hybrids, leaving a d® configuration (probably 3A). [For Ni there should also be similar strongly bound triplet states; however, for Pd the very high energy of the s*d® state may lead to unstable triplet states.] Of course the two singly-occupied d orbitals can also be used for bonding, leading to a total of four possible covalent bonds for Pt s*d®. Electrone- gative ligands favor bonding to the sp hybrid orbital!” since the ionization potential of the s orbital is 2.79 eV lower (leading to Ptt s'd5) than the d orbital (leading to Pt*s*d”). Thus in 3 we expect the Pt-Cl bonding to favor Pt sp, while Pt-CHg should favor Pt d. In addition, bonding both Cl to sp orbitals should favor trans Cl ligands. Indeed, the geometry of 3 is essentially octahedral (vide infra). (We have assumed the Cl as trans and the CHg groups as cis.) Comparing the Mt-Cl bonds in 4 and 3 we see an increase in ionic character for 3 (for the metal-like orbital the number of electrons on the Cl increases from 0.27 e~ to 0.37 e7). Concomitantly, the d character on the metal part of the metal orbital decreases from 52% to 32%, while the ratio of p tos =~96= increases from 2/3 to 4/3. Comparing the Mulliken populations in 1 and 3, we see a slight change in polarity from Pt*C~ to Pt~C*, while remaining essentially covalent (the Pt component of the metal orbital increases from 0.82 to 0.93 e”, while the component of C character of the methyl orbital decreases from 0.89 to 0.78 e~). Simultaneously, the d character in the metal part of the bond pair increases dramatically (60% to 74%), as expected. To simplify the description we will refer to the Pt-C bond in 3 asa covalent bond to a Pt 5d orbital and the Pt-Cl bond as a partially ionic bond to a Pt 6sp hybrid orbital. In this simplified picture we visually represent the Pt(IV) complexes as having the Pt atom promoted to the s*d5 configuration, having two sp hybrid pairs as in Mg, Al, and Si, This state is the only one that can allow Pt atom to form four covalent bonds, two bonds to singly-occupied d orbitals and two bonds to the pair of sp lobe orbitals. 8 The Mulliken populations for 3 are ambiguous in assigning the elec- tronic configuration of Pt atom. Significant amounts of charge transfer from the Pt sp orbitals to the chlorines (0.56 e~) and from the methyl groups to the Pt d orbitals (0.28 e~) make Pt atom appear intermediate between s*d® and s!d® (8.33 e~ in d orbitals and 1.12 e~ in s and p orbi- tals). Adjusting the Mulliken populations by assigning the excess charge on the chlorines as Pt sp and replacing the charge deficiency on the methyl groups with charge from the Pt dm orbitals, we obtain a charge of 1.68 for sp and 8.05 for d, reasonably close to s?d§. The bonding in this Pt(IV) complex is essentially covalent, which should not be too surprising since the Pauling electronegativity® for Pt is _ 2.2 versus 3.0 for Cl and 2.5 for carbon. 3. Mt(0) Systems The ground state of Pd(0) is d!°, with the (triplet) s!d®° configuration 21.9 keal/mol higher!® (calculated value 19.6 kcal/mol). The ground state of Pt is s!d® with the d!° state 11.0 kcal/mol higher!® (calculated value 12.3 kcal/mol). For both Pd and Pt, reductive coupling involves s'd® for the reactant and d!° for the product, and hence reductive cou- pling should be more exothermic for Pd than for Pt by 19.6 + 12.3 = 31.9 kcal/mol (experimental value 32.9 kcal). The lowest singlet state of Pt(0) is d!° so that the spin-allowed pro- duct of is d!° in both cases. Adding two phosphines stabilizes d!° with respect to s'd® so that the ground state of Mt(PHs)s is the linear d!° singlet for both Mt = Pd and Pt. This stabilization of d!° arises from overlap between the phosphine lone pair and the metal valence s orbital. If the Mt s orbital is empty (d!°), the phosphine lone pair can donate into this orbital (Lewis base-Lewis acid interaction), leading to extra bonding. If the metal s orbital is occupied, it must be orthogonalized to the phosphine lone pair, increasing the energy. The result is that reductive coupling from Mt(Phg)g is about 20-25 kcal/mol more exothermic for both Mt = Pd and Pt. 4. Summary Our conclusion is that the oxidation state formalism for Pt and Pd =98~— complexes should be interpreted in terms of maximum covalency rather than degree of oxidation. Thus, Pt(II) and Pd(II) should be considered as neutral atoms with a s'd® configuration forming two covalent bonds, while Pt(IV) should be described as a neutral platinum atom in an s*d8 configuration forming four covalent bonds. We will find this view to be quite useful in rationalizing the relative reaction energetics of Pt/(II) versus Pd(II) and of Pt(II) versus Pt(IV) (Section II.C), where appropriate atomic excitation energies provide excellent predictions. B. Energetics The energetics for various reactions were obtained by calculating GVB correlated wavefunctions (which give accurate s'd®—d!° state split- tings) at geometries optimized for HF wavefunctions (see Section IV for calculational details). The results are summarized in Table III. 1. Calculated Energetics for C-C Reductive Coupling Considering C-C coupling processes, we find Pt(CHs3)o(PHs)e > Pt(PHs)2 + CoH (8) with AHg = —11.3 kcal/mol which can be compared to Pt(CHs)e > Pt + CeHe (9) with AHg = 15.5 kcal/ mol. Thus, the presence of two phosphines favors reductive coupling by an extra 26.8 kcal/mol. The reason for this is that the Pt has a s'd?® configuration for the reactant side of (8) and (9) but a d'° configuration for the product side. As discussed in Section II.A.3, phosphines stabilize d? relative to s!d®, leading to a more exothermic reaction. Consider next the analogous reactions with Pd, Pd(CHg)2(PH3)2 > Pd(PHg)e + C2He (10) with All, 9 = ~45.8 keal/ mol, _which can be compared to Pd(CHs)z » Pd + CoH, (11) with AHzg = —18.8 kcal/ mol. The reaction enthalpies differ dramatically from those of Pt; however, these differences are easily explained. All four reactions involve convert- ing the metal from s!d® to d!°, but using d?° as the reference Pt favors s'd® by 12.3 keal/mol, whereas Pd disfavors s'd® by 19.6 kcal/mol. Thus, relative to Pt, Pd has a bias against s!q® of 31.9 kcal/mol. Consequently, the driving force for Pd reductive coupling should be exothermic by 31.9 kcal/mol more than for Pt. Indeed, we calculate a difference of 34.5 kcal/mol for the bisphosphine and 34.3 kcal/mol for the unsubstituted metal. These results for Mt(II) can be compared to the Mt(IV) reaction, Pt(CHs)a(Cl)a(PHg)2 ~ Pt(Cl)e(PHs)e + CeHe (12) with AH,2 = —27.0 kcal/ mol. Here the metal changes from s*d® to s'd®, which for the free atom is exothermic by 17.2 kcal/mol. Comparing to reaction (8) involving s'd° to d’° which is endothermic in the atom by 12.3 kcal/mol, we would expect from atomic considerations that (12) should be 29.5 kcal/mol more exothermic than (8). Of course the four-coordinate Pt(II) and six- coordinate Pt(IV) also differ in other respects; however, we find that (12) is 16 kcal/mol more exothermic than (8), so that the atomic change of configuration effects dominate. Based on differential atomic excitation energies, the Pd analog of (12) should be exothermic by an extra 45 kcal/mol, leading to a total =-100- exothermicity (AE) of about 70 kcal/mol. We estimate that there is no barrier for this decomposition and hence that this species is unstable. Summarizing, we find that reductive CC coupling is exothermic by 45.8 keal/mol for Pd(II), by 27.0 kcal/mol for Pt(IV), and by 11.3 keal/mol for Pt(II), differences that can be understood in terms of the relative atomic energies of s!d°, d!°, and s*d® configurations. 2. Calculated Energetics for C-H Reductive Coupling We calculate that Pt(H)(CH3)(PHs)e > Pt(PHsje + CHy (13) with AH,3; = -—5.8 kcal/ mol, whereas Pt(H)(CH3) > Pt + CH, (14) Thus two phosphines promote H-C reductive coupling by 24.8 kcal/mol, which can be compared witha promotion of 26.8 kcal/mol for C-C reduc- tive coupling on Pt and 27.0 for C-C reductive coupling on Pd. For Pd we studied reductive coupling for the free atoms, finding Pd(H)(CH3)~Pd+CH, (15) with AH, = —17.2 kcal/ mol but did not calculate the H-C coupling from the bisphosphine. However, the above resulls suggest that for Pd the bisphosphine would promote I- C reductive coupling by ~25.0 kcal/mol, leading to with AH, © —42.2 kcal/ mol. We did not calculate the energetics for H-C coupling from Pt(IV) or Pd(IV) complexes; however, comparisons with the C-C coupling cases sug- -101- gest that Pt(H)(CHs)(Cl)2(PHs)2 > Pt(Cl)2(PHs)2 + CHy (17) with AH,, ® -—19.5 kcal/ mol, ° while the analogous Pd complex would not be stable. 3. Calculated Energetics for H-H Reductive Coupling We calculate that Pt(H)2(PHs)e > Pt(PHs)2 + He (18) with AHig = 12.3 kcal/ mol, whereas Pt(H)}2 > Pt + He (19) with AHig = 33.2 kcal/ mol. Thus the phosphines promote H-H reductive coupling by 20.9 kcal/mol, which can be compared with 24.8 kcal/mol for H-C and 26.8 kcal/mol for C-C. For Pd we studied reductive coupling from the free atom, finding Pd(H)z + Pd + He (20) with AHzg = —4.0 kcalY mol but did not calculate the reductive H-H coupling from the bisphosphine. However, the above results suggest that the phosphines would promote H-H coupling on Pd by about 21.1 kcal/mol, leading to Pd(H)g(PHg)z » Pd(PHs3)zg + He (21) with AHz, * —25 kcal/ mol. We did not calculate the energetics of H-H coupling from Pt(IV) or Pd(IV) complexes; however, we estimate that Pt(H)a(C2(PHs)g 2 Pt(Cl)a(PHs)2 + He (22) with AHge ® 2.5 kcal/ mol and that the analogous Pd complex is unstable. ~102- 4. Adiabatic Bond Energies Since the C-C bond energy in ethane is 90.4 kcal/mol, !? the exother- -micity of 11.3 kcal/mol for (8) leads to an average Pt-C bond energy of Dagel(PH3)2Pt-CH3] = 38.6 kcal/mol. (23) Similarly, since the H-H bond energy is 104.2 keal/mol,!™ the energetics in (18) correspond to an average Pt-H bond energy of As a check upon the utility of such average bond energies, we can use (23) and (24) plus the C-H bond energy in CH, (105.1 kcal/mol)!® to predict AHi3 = 39.6 + 58.3 — 105.1 = ~7.2 kcal/mol, in reasonable agreement with the calculated valuc of -5.8 keal/mol. The average bond energies for the bare metal are obtained from (9) and (19) as Dogg(Pt-H) = 68.7 kcal/ mol, (26) which leads to a prediction of AH,, = 53.0 + 68.9 — 105.2 = +16.5 kcal/mol, in reasonable agreement with the calculated value of AH,, = 19.0 keal/mol. The average bond energies for Pd complexes are calculated to be about 18 kcal/mol lower (see Table TV) because of the propensity for Pd to form d!° configurations. -103- Averaging the results for Pd and Pt, we find that M-H bonds are 18 kcal/mol stronger than M-CHs bonds for the bisphosphine and 15 _ keal/mol stronger for the bare metal. Thus, the phosphines lead to’a relative weakening of M-CHgs versus M-H bonds. This could be simply a steric effect. If so, the bulky phosphines endemic to experiments might have even a greater bias against M-CHg bonds. The Pt(IV) system leads to weaker Pt-CH3 bonds, As discussed above, this 8 kcal/mol decrease from the value for Pt({I) is dominated by the preference of Pt to convert from s*d8 to d®s!. 5. Intrinsic Bond Energies It is often useful to define an intrinsic bond strength as the energy to break a bond A-B without allowing the fragments to relax. This intrinsic bond strength is then reduced by various relaxation effects that occur in the fragments A and B after the bond is broken. These relaxation effects can involve geometric relazation and electronic relazation The final bond energy including all these effects is the adiabatic bond energy Dogg. Thus, for example, the C-H bond energy of cyclopropane is 11 kcal/mol stronger”° than for H~CH(CHs)2 partly because geometric constraints prevent most of the geometry relaxation in cyclopropane. A good example for the role of electronic relaxation upon bond energy is in the difference in carbon-carbon double bond strengths in C2H, and CoF4."! The double bond requires a singly-occupied o and 7 orbital on each carbon corresponding to the 5B, state of free CHg or CFe. For CHg, the triplet state is the ground state and hence the observed (adiabatic) bond energy of 172.2 keal/mol™ is electronically diabatic (it -104. involves a small amount of geometric relaxation). However, for CF, the 3B, state is 56.6 kcal/mol*® above the ground state ('A,). Thus, if the dia- .batic C-C double bond energy is assumed unchanged (172.2 kcal/mol), we would expect the adiabatic bond energy in C2F,4 to be 172.2 - 2(56.6) = 09.0 kcal/mol. This is in good agreement with the observed bond energy of 69.0 + 2.7 keal/mol,”* demonstrating the power in using the concept of electronic relaxation in estimating bond energies. The adiabatic bond energies calculated in the previous section included both geometrical and electronic relaxation effects. In order to correct the average bond energies for these relaxation effects, we must add the atomic excitation energy (d!9+d%s! or s!d9+s*d5) in the complex to the driving force for reductive elimination. We calculate the energy of the triplet at the geometry of the Mt(PHs3)2 [or MtClg(PH3)a] fragment in the MtR2(PH3)2 [or MtR2Cle(PH3)2| complex. Of course the energy of the Mt(PH3)e [or MtCle(PH3)2] singlet was calculated at the equilibrium geometry. The singlet-triplet splittings calculated with these reference states include all differential relaxation effects which occur during reduc- tive elimination from these complexes. Thus the intrinsic bond energy is defined as D, = ¥[AH(MR2 > M + Re) + 6E(M > M) + Doga(R—-R)], (28) where 6E(M > M) is the singlet-triplet excitation energy described above, M is the singlet metal complex product in its ground state geometry, and M is the triplet state of the same complex frozen at the geometry it had in the reactant complex. Average bond energies and the relevant state splittings are presented in Table IV. The corrected bond energies show that the intrin- sic strengths of Pt-C and Pd-C bonds are very similar and that the -105- relative stability toward reductive coupling is dominated by the relative energies of the s'd® and d?° states and of bent versus linear phosphines. Comparing the intrinsic Mt-R bond strengths of bisphosphine complexes leg. 56 kcal/mol for Pt(CHs)e(PHs3)2] and the corresponding MtR, complexes”° (e.g., 47 kcal/mol for PtMeg), indicates that the presence of phosphines strengthens the intrinsic Mt-R bonds by 6-12 kcal/mol. This is because the metal spd hybrid orbitals used to form the M-R bonds must be orthogonalized to the phosphines, leading to an increase in the p character of the metal hybrid. This in turn increases the overlap of the M-R bond,?° increasing the intrinsic bond strength. On the other hand, the phosphines lead to a decrease in the adiabatic bond energies [from 53 kcal/mol for Pt(CHg3)z to 40 kcal/mol for Pt(CH3)e(PHs3)2]. This is prob- ably because the phosphines greatly favor the d!° form of the product. The intrinsic Pt(IV)-C bond is 5 kcal/mol weaker than the Pt(II)-C bond in bisphosphine complexes. This is probably because the Pt 6s char- acter of the Pt(IV)-C bonds is used up in the Pt-Cl bonds. Consequently, the methyl group in Pt(IV) is forced to bond to metal orbitals that have mainly d character rather than the optimal hybridization’® (~60% d and 40 % sp) that is available in the Pt(II) bisphospine complex. Few bond strengths are known experimentally for Pt-C or Pd-C. From studies of the decomposition of PtMesCp,** an experimental Pt-CH3 bond energy of 39+5 kcal/mol has been determined. This is an adiabatic bond energy, PtMe3Cp > -Me + -PtMesCp, (29) but the Pt atom no doubt retains s°d5-character. Thus the exothermicity of (29) should be less than the intrinsic bond energy (51 kcal/mol) but probably larger than our estimated adiabatic bond strength of 32 -106- keal/mol, which involves relaxation to s!d®°. Thus the theory and experi- ment are in reasonably agreement. -C. Barriers and Rates In previous studies of? Mt —> Mt + | (30) where Mt = Pd,Pt and R,,Re = H and CHs, we showed that the intrinsic barrier (i.e., the barrier exceeding the endothermicity) is (i) large for CC coupling (e.g., 23 kcal/mol for Pd, 54 kcal/mol for Pt), (ii) intermediate for CH coupling (e.g., 10 kcal/mol for Pd, 29 kcal/mol for Pt), and (iii) small for HH coupling (e.g., 2 kcal/mol for Pd). The origin for such dramatic differences for H-H, H-C, and C-C coupling is found in the shapes of the H 1s and C sp® orbitals. At the transition state, the wavefunction involes a mixture of the sid® resonance structure (31) for the reactant (31) s'd® Resonance Configuration and the d’° resonance structure (32) of the product -107- UN SY ; xX (32) d}° Resonance Configuration Since the H ts orbital is spherical, it can simultaneously overlap either the Mt sd hybrid orbital in (31) or the valence orbital of the other R group in (32). The result is that these two resonance structures have a high overlap for R, = Rg = H, leading to a large resonance stabilization and a low barrier. If R; = H and Rg = CHs, then the directed form of the valence orbital for CH3 is such that one CHs orientation favors (31) (33) while a diferent CHs orientation favors (32) H H We, (34) ONY Consequently, at the transition state the CHs group has an intermediate -108- orientation which is less favorable for both (31) and (32), leading to a significant barrier. If R; = Re = CH3, then there is a similar problem for both ligands, leading to a barrier that is roughly twice as large. Adding two phosphines to the metal stabilizes the d!° state over sid? making reductive coupling about 23 kcal/mol more exothermic (27 kcal/mol] for H-H, 23 keal/mol for H-C, and 21 keal/mol for C-C) and should similarly decrease the activation barrier. Assuring that the tran- sition state involves about equal parts of the d!° and s'd® configurations, it is plausible that the barrier will be decreased by about half as much as is the reactive enthalpy. This leads to the estimated activation energies in Table III and Figure 8. Particularly clean experiments have been carried out for H-C cou- pling from Pt(11),1*!5 (13), for which we estimate AH}, = 15.7 kcal/ mol. This can be compared to cis—Pt(H)(CHgCF3)(PPh3)2 » Pt(PPhs)g + CH3CF3, (35) where in benzene solvents AHt = 24.6 + 0.6 and Ast =49+2., and to cis—Pt(H)(CH3)(PPh3)2 > Pt(PPhslo + CH,, (36) where (in toluene at -25°C) AG? = 18.2.1? Assuming AS? © 5, this latter value leads to AH? = 17.0 kcal/mol, in good agreement with our predic- tions. Other relevant activation energies have been measured by Moravskiy and Stille®° for reductive elimination of ethane from cis- Pd(CHs)o(PPhe(CHs3)2. They find activation energies (E,) of 6-11 kcal/mol in polar-coordinating solvents (MegSO—dg, MegCO—dg, and CD3CN) and 25- -109- 28 kcal/mol in aromatic solvents (CgDsCDs and CgDg). It is uncertain how to compare these numbers with our calculations since it is likely that reductive elimination does not proceed directly from the bisphosphire complex (see Section III.A). However, we estimate AH#, = 10.4 kcal/mol (at 300°K), and hence the estimated barrier (at 300°K) is E, = AH} + RT = 10.7 kcal/mol, surprisingly close to the E, measured in coordinating sol- vent. On the other hand, our estimates Icad to AHf = 41 keal/ mol for C-C coupling on Pt(II), certainly consistent with the lack of observa- tion of this reaction. The calculated endothermicity (AH,g = 12.3 kcal/mol) and barrier (AH#, = 14.0 kcal/mol) for H-H coupling from Pt(II) are consistent with the equilibrium observed in such systems by Trogler. 4 On the other hand, our calculations suggest that cis-Pd(H)o(PH3)z and cis- Pd(H)(CHs3)(PH3)2 would have no barrier for decomposition and hence should not be stable. The estimated barriers for Mt(IV) complexes are much more uncer- tain since barriers were not calculated even for complexes without phos- phines. In this case we have assumed that half of the addition exothermi- city relative to Mt(II) goes into the transition state. Brown et al.’> have measured E, for reductive elimination of ethane from various Pt(IV) trimethyl complexes. They find E, = 27.7 4 1.2 for reductive elimination from PtCl(CHs3)3(PMesPh)e at 353°K. Our estimate is E, = 34.9 kcal/mol (AHfg = 34.2 kcal/mol) for elimination from -110- PtCle(CH3)o(PHs)2. The good agreement between experiment and theory may be fortuitous since it appears experimentally that the reductive elimination takes place from a five-coordinate intermediate formed by loss of phosphine. Similar estimates for H-H and H-C coupling from Pt(IV) lead to AH* = 9 kcal/mol for both reactions, indicating rather unstable species. The analogous Pd(IV) complexes are predicted to be unstable. Experimentally it is known that Pt(II) dimethyl complexes are much more stable than Pd(II) dimethyl complexes, with C-C coupling facile for Pd(11)® and unobserved for Pt(1t).!° In addition, it is known that Pt(IV) dimethyl, trimethyl, and tetramethyl complexes will reductively elim- inate ethane,’ while Pt(II) dimethyl complexes do not. 10 Our results are consistent with these experimental observations. As indicated, the theoretical results are consistent with current experimental knowledge concerning reductive coupling and oxidative addition of Pt(II), Pd(II), and Pt(IV) complexes. These experiments can be understood on the basis of the changes in the electronic configuration of the metal plus simple ideas on the relative barriers for C-C versus C-H versus H-H coupling. Given results for one metal, these ideas may be used to predict the results on other metals using only atomic data. D. Geometries The geometries for all molecules studied in this work have been optimized for the HF wavefunctions using analytic gradient techniques. The fully optimized HF geometries of 1 Pt(Me)o(PH3)2, 2 Pd(Me)o(PHs)z, and 3 Pt(Me)e(Cl)2(PHs)z are shown in Figures 9 and 10, and the calcula- tional details are described in Section [V. The internal coordinates around the metal atom for the complexes studied in this work are presented in Table V. Cartesian coordinates for each molecule are given -i1l- in the Appendix. We find very good agreement between our calculated geometries and x-ray structures on related molecules, as described below. . The calculated Pt-C bond distance (2.06 A) in 1 is very close to the sum of covalent radii!® (Pt-Csp%) 2.09 A and is in the range observed in x- ray structures of Pt(II) dialkyl complexes:”" {an average of 2.05 A in PtgMe, (u—dppm)2"°° [dppm = PhgPCH2PPh,]; 2.18 A and 2.15 A in PtMe, (tripod) [tripod = 1,1,1-tris(diphenylphosphinomethyl)ethane] 258 and 2.05 A and 2.12 4 in Pt(CyHg(PPhg) 2°}. The calculated C-Pt-C bond angle in 1 of 89° is ~10° larger than the C-Pt-C angles observed in the x-ray structure of PtgMe,(yu-dppm) (81.6°) and Pt(C,Hg)(PPhg)2 (80.9°).*° This difference is most likely due to the PHs ligands having less steric bulk than substituted phosphines. The calculated Pt-Cl bond distance in 4 of 2.35 A and the Cl-Pt-Cl bond angle of 91° match very well with the observed Pt-Cl distances (2.368 A and 2.377 A) observed in the x-ray structure of cis- Pt(PMes)oClo.76 The calculated Pt-P bond distances are 0.1-0.2 A longer than experi- ment [Pt-P = 2.23 and 2.24 A in PtClo(PMe3)2°° versus 2.44 A calculated for (4); 2.279 and 2.285 & in Pt(C,H,)(PPhs)2"°> versus 2.46 & calculated in (1)]. This is systematic for Pt-P bonds at this level of calculation” and may be partially due to the effect of substituted phosphines versus PHg. The P-Pt-P bond angle is apparently less sensitive, and good matches to the experimentally observed P-Pt-P angles are found [101° in (1) versus 98.9° in Pt(C,I1,)(PPhz)2 and 102° in (6) versus 96.2° in PtCl,(PMes)2}."6 Noell and Hay*? were the first to show that HF wavefunctions yield geometries of Pt and Pd complexes which compare well with x-ray structures, indicating that HF is a reasonable level of wavefunction with which to optimize geometries. Il. -113- Discussion The Effect of Added Phosphine on the Rate of Reductive Elimina- tion One of the unresolved questions in the experimental literature is the effect of added phosphines on the rate of C-C coupling. There are three classes of systems: (A) (B) (C) For PdMegL 2° and AuMe3L9-*” experiment shows that reductive elimination of ethane is retarded by added phosphine. This led Hoffman et al.2%> to propose a mechanism by which reductive elimination proceeds through a three-coordinate intermediate, an interpretation supported by Extended Hiickel (EH) calculations. Contrasted with these results are Pd(CH3)(CH=CHPh)(PPhs)2 » CH3CH=CHPh + Pd(PPhs)2 (37) Ni(CH3)2(DIPHOS) > Ni(DIPHOS) + CoH, (38) [DIPHOS = PhgP(CHg)gPPhg] where the addition of phosphine has no affect on the rate of C-C coupling.7828 These systems apparently can reductively eliminate directly from the original four-coordinate complex. There are also Ni(II) and Pt(II) complexes such as cis—NiPh(CH3)(DPE) (39) and where reductive coupling of C-C bonds is promoted by the addition of phosphines. !1*8 This led Braterman and Cross” to propose a mechanism by which reductive elimination proceeds through a five-coordinate intermediate, a mechanism that was also sup- ported by EH calculations of Tatsumi ef al,34 Our calculations on reductive elimination of ethane from PdR,g and PtRg show that reductive elimination is favored energetically from PdRg because Pd prefers the d!° configuration.”° It is interesting to note that the difference in AH for elimination of CzHg from Pd(CH3)z and Pt(CH3)2 (30.9 kcal/mol) is very close to the difference in the driving force for each reaction (34.3 kcal/mol). This suggests that the barrier to reduc- tive coupling of C-C bonds is strongly coupled to the driving force. Since phosphines stablize d’° relative to s'd®, we would expect the three coordi- nate complexes to have a larger barrier for reductive elimination than the four-coordinate complex, which should in turn have a larger barrier than the five-coordinate complex. The consideration of only the three-coordinate intermediate for sys- tems of class A may be an oversimplification of the real system. /nfer- molecular paths clearly are important for the decompostion of AuMes3L in some solvents [e.g., benzene, decalin, PhCl, n—BugO, and Tetrahydrofuran (THF y}.8 More strongly coordinating solvents [MegSO (DMSO) and dimethylformamide (DMF)]| appear to block intermolecular paths, result- ing in very little crossover.2” For reductive elimination of ethane from Pd(CH3)aL2, crossover experiments show that reductive elimination of ethane is intramolecular only in DMSO or noncoordinating solvents con- taining dimethylmaleate (DMM).® It has been assumed that DMM serves to trap the Pdlg product before it can decompose (and thereby affect the decompostion pathway); however, Ozawa et al.®4 have shown that varia- tion in concentration of DMM does not affect the rate of decomposition. (They did not report the rate with no added DMM.) This only proves that @115- DMM is not involved in the rate determining step of reductive elimination (which appears to be loss of a phosphine). The loss of phosphine could also be the rate-determining step in the formation of a four-coordinate ‘intermediate in which one of the phosphines is replaced by DMSO, DMF, or DMM. If reductive elimination is facile from these intermediates then loss of phosphine would be the slow step which would be inhibited by added ligand. Palladium might be expected to prefer pathways involving loss of phosphine, while other metals of the nickel triad reductively eliminate through four- and five-coordinate pathways since Pd forms weaker bonds to phosphines than Ni and Pt.*! Apparently reductive elimination of CH3CH=CHPh from Pd(CH=CHPh)(CHs)(PPhg). is not affected by added phosphine because the AG# for elimination from the four coordinate start- ing complex is lower than the AG; of the three coordinate intermediate. Unfortunately it has not been possible to observe directly the three- or five-coordinate intermediates proposed for class A and C systems. Although EH calculations do support lower barriers for three and five coordinate complexes than four coordinate complexes, these predicted trends in activation energies do not correlate with our observed correla- tion of AE* and AE. EH calculations are well known” not to give accurate geometries and energetics and should not be considered as proof for the proposed mechanisms. What is needed are ab initio calculations of the relative barriers of reductive elimination from three, four and five coordi- nate intermediates. -116- B. Reactivity of Metal ~Carbon Bonds Involving sp® Hybrids Versus sp Hybrids Another trend which has been observed but not explained is the lower stability of cis—methylphenyl and cis —biphenyl complexes relative to dimethyl complexes. Reductive elimination from cis —Ni(CH3)(CgHs)Le is faster than from cis —Ni(CHg)gl.25 complexes.”8 The reaction of PhLi with PdCla(DIPHOS) yields biphenyl directly, whereas MeLi reacts with PdCl(DIPHOS) to give PdMe,(DIPHOS) which eliminates ethane slowly.6# Platinum diphenyl bisphosphine complexes can eliminate biphenyl}! while Pt dimethyl bisphosphine complexes are very stable.!° This trend can be explained by noting that the phenyl group uses a C sp® hybrid orbital to form bonds while the methyl group uses a C sp® hybrid orbital. The increased s character of the sp® hybrids causes this orbital to be less directional than the sp* hybrids. Therefore the sp? hybrid can have more multicentered bonding at the transition state, leading to lower activation energies for CHs-CH=CHPh, CHs—Ph and Ph-Ph coupling. It should be noted the Ph—-CHs and Ph-Ph bond energies are 11.4 keal/mol!®© and 26 kcal/mol stronger®° than the H3C—CHg bond energy (90.4 keal/mol).!9> Thus, tf the Mt—CHg3 and Mt-Ph bond energies were approximately the same, this would lead to a larger driving force for reductive elimination of sp® species. Evans ef al. have made a thermo- chemical estimate for the Pt-Ph bond energy of 63.155 that is 7 kcal/mol stronger than our calculated Pt—CH, intrinsic bond energy. This value for the bond energy is, however, strongly dependent on their estimated Pt-Cl bond energy in PtClp(PPhg)p [which was assummed to be the same as the Pt-Cl bond energy in PtCle], which could easily cause errors of ~10 kcal/mol. Therefore, there currently are insufficient data to determine -117- whether the diphenyl and methylphenyl Pt complexes are less stable thermodynamically than the dimethyl complex. Thermochemical data™* from ThR,(Cp*)z complexes demonstrate that Th-Ph bond energies are 13 kcal/mol stronger than Th-CHg bond energies. Therefore it does appear that diphenyl and methylphenyl complexes have approximately the same enthalpy for reductive elimination as dimethyl complexes. Either of the above interpretations for the increased lability of sp* versus sp® carbons would suggest that alkynyl groups will reductively eliminate faster than phenyl or vinyl groups. Indeed, Ph-C=C-—C=C-—Ph has been indentified in the decompostion products. of cis -Pt(C=C—Ph)ely.* A more careful analysis of the decompostion of dialkynyl complexes should help establish the trend of sp hybridization versus rate of reductive elimination. C. Heat of Formation Of Pt(II) and Pd(Ii) salts We have found that the difference in enthaplies [A(AH)] for reductive elimination from the corresponding Pt(Il) and Pd(Il) compounds is always within 5 kcal/mol of the difference in the s'd® + d!° splittings for these metals (33 keal /mol). 18 Unfortunately, there are no reliable AH?’s for Pt and Pd complexes available in the literature to provide a test of this theoretical trend. However AH? for various Pt(II) and Pd(II) salts are available.°® Since Pt and Pd have the same covalent radii and electrone- 16 we can assume that the lattice energies for the correspond- gativities, ing PtX, and PdXg salts are the same. Therefore the A(AH) for the reac- tion Mt(4S)(,) + Xz) > MtXag) should also be approximatly equal to 33 keal/mol. Indeed, as indicated in Table VI, the experimental A(AH) are 33 + 3 kcal/mol, in excellent agreement with our prediction. ~118- The alternative interpretation based on an ionic model for Mt-C bonds would suggest that the A(AH) is equal to the difference in the sums of the first and second ionization potentials for Pt and Pd.1® This would predict a A(AH) of 15 kcal/mol instead of 33 kcal/mol. Therefore, our covalent bonding model is far more consistent with the experimentally observed AHf for these salts. D. Comparison With Other Theoretical Studies Hoffmann et al.2@ analyzed Extended Hiickel (EH) calculations on reductive elimination from complexes of the Ni triad to obtain five con- clusions concerning these reactions. The first three of which are relevant to this work since they concern reductive elimination from dimethyl bisphosphine complexes.*” 1. "The better the o-donating capability of the leaving groups, the more readily the elimination reaction proceeds. 2. "Stronger donor ligands that are trans to the leaving groups give a higher barrier for the elimination reaction. 3. “Increased stability of the MAp bg orbital [where A indicates modified hydrogens used to model phosphines] facilitates the reductive elimination of Dz [where D is a modified hydrogen used to model CHz groups]. A lower MA be energy will be given by a lower metal d orbital energy."2 Since we find essentially covalent bonding in Pt and Pd complexes, a better o-donor leaving group is equivalent to a leaving group with lower electronegativity. Leaving groups (R) with higher electronegativities would help stabilize the s orbital of the metal atom by increasing the amount of s character in the metal sd hybrid orbital used in the M-R bond. This will stabilize the s'd® configuration of the metal atom and reduce the driving force for reductive elimination. This is in agreement with Hoffmann’s first conclusion. We have not made systematic variations in the ligands; however, the trends in going from no ligands (a very weak donor!) to two PH3 groups are quite suggestive. We find that (due to the overlap between the phos- phine lone pairs and the metal s orbital) the sd hybrid orbital used in the M-R bond has to build in p character to stay orthogonal to phosphine lone pairs. This increased p character makes the inirinsic M-R bond strengths slightly stronger, as expected from simple valence bond calcu- lations.!° The o-donating ability of substituted phosphine ligands is directly related to the overlap between the ligand lone pair and metals orbital. The stronger the donor, the larger the overlap. The larger over- lap will lead to stronger M-R bonds which may cause the barriers for reductive elimination to be higher. Therefore, our results are also con- sistent with the second conclusion of Hoffmann. However, we believe that Hoffmann’s third conclusion, although rea- sonable, does not present the complete picture. We find that the impor- tant issue here is the relative energy of the s'd® and d!° configurations (VB language) or in MO language the relative energy of the valence s and d orbitals of the metal atom and not just the d orbital energy. The d?° configuration is stabilized relative to s'd® by destabilizing the the s orbi- tal relative to the d orbital. Stabilization of the d!° configuration leads to larger driving forces and lower barriers for reductive elimination. We have shown in an earlier paper that reductive coupling of C-C bonds from PdMeg is favored over PtMez, both kinetically and energetically. This dramatic difference arises because relative to Pt, Pd has a 33 kcal/mol ~120= bias for the d!° state. This effect is much more dramatic than the other two and should dominate the stability of the these complexes. Related trends were also observed in the CNDO calculations of Gritsenko et al.*) where the stability of MH2(PHa)2 complexes (Mt = Pd,Pt) was correlated with the Mt s character of the wavefunction. Other ab initio theoretical calculations involving square planar com- plexes of the Ni triad include studies of NiMeg(H20)2 by Akermark et al.*° and PdH,(H20)zg by Siegbahn ef al.°© In both of these studies, H,O was used as a model ligand. Akermark et al.*® found little change in the d orbital occupations upon addition of H20 ligands, and Siegbahn actually found a small stabilization (~5 keal/mol)® of the s'd® singlet versus the d!° singlet of Pd(Hz20)z relative to the atomic state splittings of Pd. The differences between these previous studies and ours probably results from their use of H20 ligands rather than PH. The lone pairs of HzO are much smaller than the lone pair of PHs. The overlap between the lone pairs of HzO and the Pd 5s orbital is probably much smaller than for phosphine lone pairs. This would lead to a smaller destabilization of the s orbital, favoring the s'd® configuration over d!° (Pd and Pt prefer "softer" ligands such as PRg over Hg0). The relevant experiments all involve com- plexes with phosphine ligands, and hence our studies using phosphines are more pertinent for understanding the observed trends in C-C cou- pling. IV. Calculational Details A. Basis Sets and Effective Potentials The basis sets and relativistic effective potentials used in this study for Pd and Pt are those of Hay et al.*> The basis on carbon is the Dunning double zeta contraction of the Huzinaga (9s5p) basis.°” The effective potential for phosphorus is the SHC potential of Rappé et at.*° The SHC 40 was contracted to a minimum basis set basis for phosphorus atom using atomic calculations. Three different basis sets were used on the hydrogen atoms depending on their chemical environment. For hydrogen atoms bound to phosphorus, we used a minimum basis set contraction of the Huzinaga four-gaussian hydrogen basis (no scaling).41 Methyl protons were described using a double zeta contraction of the Huzinaga four- gaussian basis scaled by a factor of 1.2.59 The active hydrogen bound to the metal atoms in the Pt(H)(Me)(PH3)2 and Pt(H)2(PH3)2 complexes was treated with a triple zeta contraction of the Huzinaga six-gaussian basis.*! This was necessary to allow the hydrogen to adjust for optimum bonding to the metal atom in the reactant and optimum bonding to the methyl group or H atom in the products. The chlorine potential was the SHC potential of Rappé et al, 4° and the double zeta contraction of the SHC basis*? was used. The effective potentials for P, Cl, Pt, and Pd are expected to provide ab initio quality descriptions for these atoms. Good measures for the quality of description for Pd and Pt are the atomic state splittings as indicated in figure 11. For highly accurate calculations, polarization functions (p’s on H, d's on C, P and Cl, f’s on Pt or Pd) are needed. This will lead to stronger intrinsic bond energies but will probably have little effect on the AE for oxidative addition/reductive elimination reactions -122~ (since bonds of reactant and product are affected similarly). The major factor in understanding these reactions is that the s'd°—d!° splitting of the metal atoms be accurately described.” Although the level of basig ‘ean certainly be improved, it should be quite adequate for the purposes here, namely, the conceptual description of the differences between Pt(II), Pt(IV), and Pd(II) complexes. B. Geometries All geometries of the various complexes were fully optimized at the HF level using analytic energy gradients and the Newton-Raphson pro- cedure.** For the calculations on the triplet states of Mle and MClele, the geometries were frozen at the geometry of the fragment in the corresponding MRgle or MRpgClglg complex. This was done so that geometric relaxation energy would not be included in calculating intrinsic bond energies. C. Wavefunctions All energetics reported here involve the GVB description of electron correlation for the important valence electrons. For an electron pair that would be described as doubly-occupied in HF theory, the GVB description would allow two orbitals each optimized self-consistently with all other orbitals of the molecules, $7F(1,2) = y(1)¢(2)(aB - Ba) > (41) V3 (1,2) = [ga(1)on(2) + vo(1)¢(2) (a8 — Ba). When there are additional electron pairs, each may be correlated as in (41), so that the doubly-occupied orbitals ¢;,¢2,--- of an HF wavefune- tion become singly-occupied orbitals [as in (41)], dia, Yip, Pon Yep Of the GVB wavefunction. Although for HF wavefunctions the doubly-occupied -123- orbitals can generally be taken as either delocalized (canonical) or local- ized, the GVB orbitals are uniquely determined and are generally local- ized (reminiscent of simple valence bond theory). The general form of a GVB wavefunction is Dl (eraPePeaPon >: +x]. (42) where x is an appropriate optimized spin function for N electrons. How- ever, in calculaling Lhe GVB orbitals, il is generally convenient to choose x as the simple valence bond function (perfect pairing) VB ~ _ ee xX” = (a8 — Ba)(aB — fa) (43) In this case the orbitals for different electron pairs are taken as orthogo- nal, and the resulting orbitals are denoted as GVB-PP to indicate the res- tricted form of the wavefunction. If five pairs of electrons are so corre- lated (using ten orbitals), the wavefunction is denoted as GVB-PP(5/10); however, other orbitals of the wavefunction are understood to be calcu- lated self-consistently. (This wavefunction would involve 2° = 32 different orbital configurations.) Such wavefunctions quite accurately describe systems where one valence bond structure is adequate (no resonance); however, for transition metal systems, spin couplings other than (43) are often important. These spin coupling effects are usually accurately described using the GVB-PP orbitals but allowing the two electrons of each orbital pair to be either in different orbitals [as in (41})] or in the same orbital [e.g., g,(1)¢,(2)]. Allowing a similar description for all correlated pairs leads to the GVB-RCI wavefunction. Since there are three orbital products for each pair of electrons, the GVB-RCI(5/10) wavefunction has 3° = 243 orbital products. In addition to an optimized spin coupling, the RCI wavefunction includes important electron correla- 124. tion effects in which two electrons in one bond pair can respond instan- taneously to the motions of two electrons in another bond pair (interpair correlation). The orbitals of the GVB-RCI wavefunction can be solved ‘self-consistently; however, it is generally adequate to use the orbitals of the GVB-PP wavefunction, and we have found this to be the case for com- plexes of the type studied in this paper. For cases where resonance of simple valence bond structures would be important, it is often essential to allow readjustments in those bond pairs that would change in the reso- nance. Thus, for reductive C-C coupling, the two localized M-C pairs change into a C-C bond pair and a metal d pair as the bond is broken, and resonance between these configurations is important. In this case we refine the GVB-RCI(2/4) description of these two pairs by using the GVB- Cl(2/4) description, where all four electrons are allowed to occupy all four orbitals in any way (leading to 19 orbital products). We find (see Figure 11) for Ni, Pd, and Pt that the GVB description (which uses ten optimized orbital for all states) leads to a rather accu- rate description of the relative energies for the d!°, s'd®, and s*a® ® versus d!° the states configurations and is particularly accurate for s'd relevant for this paper. For the s*d® states the s* pair was polarized in the +Z directions and d,2 and the d,, were singly occupied. For the various M(Re)(Rz) complexes, it is necessary to correlate not only the ten metal valence electrons but also the additional electrons involved in the covalent M-R, and M-Re bonds. Thus, a total of 12 elec- trons or six electron pairs must be correlated. Consequently, we first carried out GVB-PP(6/12) calculations using 12 orbitals to correlate the motions of these six pairs (12 electrons). (All other orbitals are doubly- occupied but are solved self-consistently.) In order to include the spin- “125+ 2a,c coupling, interpair correlation, and resonance effects, the energetics reported here were determined at the GVB-Cl(2/4)xRCI(4/8) level. In previous studies of the reaction path for reductive coupling, the “necessity for simultaneous description of both the reactant (s'd®) and the product (d!°) resonance structures in the transition state region required use of three orbitals (rather than two) for each of the two bond pairs that change during the reaction”. Thus, rather than GVB-PP(2/4), these two electron pairs were described with GVB-PP(2/6). In order to allow a full description of resonance effects in the transition state, all occupations of these six orbitals were allowed for all four electrons, denoted as GVB- CI(2/6). The other four pairs of electrons were correlated as usual, lead- ing to a composite wavefunction of the form GVB-Cl(2/6)xRCI(4/8). We also optimized the orbitals at this level. In the current study, the main interest is in overall energy differences between products and reactants, where this resonance is not so important. Consequently, we use only two orbitals for these bond pairs, and the orbitals were optimized at the GVB-PP level. However, as in the previous studies, we carry out a full Cl among the (four) orbitals involving those two bond pairs [ClI(2/4)]. Thus the wavefunction used in these studies is GVB-C1(2/4)xRCI(4/8). Acknowledgments: This work was supported in part by a grant fron the National Science Foundation (No. CHE83-18041). One of the authors (J.J.L.) wishes to acknowledge financial support in the form of fellowships from Exxon and ARCO. -126-~ References and Notes (1) (2) (3) (4) Collman, J. P.; Hegedus, L. 8. 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M.; Sieg- bahn, P.E.M. J. Phys. Chem. 1984, &&, 4617-4621. (a) Gillie, A.; Stille, J. K. J. Am. Chem. Soc. 1980, 102, 4933-4941; (b) Loar, M. K.; Stille, J. K. ibid. 1981, 103, 4174-4181; (c) Moravskiy, A.; Stille, J. K. ibid, 1981, 103, 4182-4186; (d) Ozawa, F.; Ito, T.; Nakamura, Y.; Yamamoto, A. Bull. Chem. Soc. Jpn. 1981, 54, 1868-1880. (a) Ruddick, J. D.; Shaw, B. L. J. Chem. Soc. (A) 1969, 2969-2970; (b) Brown, M. P.; Puddephat, R. J.; Upton, C. E. E. J. Chem. Soc., Dalton Trans. 1974, 2457-2465; (c) Appleton, T. G.; Clark, H. C.; Manzer, L. E. J. Organomet. Chem. 1974, 65, 275-287. | (8) (9) (10) (11) ~128- (a) Whitesides, G. M.; Gaasch, J. F.; Stedronsky, E. R. J. Am. Chem. Soc. 1972, 94, 5258-5270; (b} McDermott, J. X.; White, J. F.; Whitesides, G. M. ibid. 1984, 98, 6521-6528; (c) Young, G. B.; Whitesides, G. M. ibid. 1978, 100, 5808-5815; (d) McCarthy, T. J.; Nuzzo, R. G.; Whitesides, G. M. ibid. 1981, 103, 1676-1678; {e) wid. 1981, 103, 3396-3403; (f) Nuzzo, R. G.; McCarthy, T. J.; Whitesides, G. M. ibid. 1981, 103, 3404-3410; (g) Komiya, 3.; Morimoto, Y.; Yamamoto, A.; Yamamoto, T. Organometallics 1981, 7, 1528-1536. (a) PtEte(PEts)2 is known to f-hydride eliminate to give ethylene (AH 2 o9 = 12.5 kcal/mol, Sgo9 = 52.4 e.u.) and ethane (AH& 9 = -20.2 keal/mol, Sag9 = 54.9 e.u.) rather than to reductively eliminate to give n-butane (AHS) = -30.2 kcal/mol, S99 = 74.1 e.u.) even though n-propane is the thermodynamically favored product (AHsq9 = -22.5 keal/mol, ASsg99 = -33.2 e.u., AGsog = -12.5 kcal/mol for CoH, + CoHg > n-C4Hy9). The AH& oq and S&o were taken from ref 9b. (b) Benson, S. W. "Thermochemical Kinetics," J. Wiley and Sons: New York; 1976, Second Edition, p 295. Chatt, J.; Shaw, B. L. J. Chem. Sec. 1959, 705-716. (a) Braterman, P. §8.; Cross, R. J.; Young, G. B. J. Chem. Soc., Dal- ton Trans. 1976, 1306-1309; (b) ibid. 1976, 1310-1314; (c) wid. 1977, 1892-1897. (12) (19) (14) (15) (16) (17) (18) (19) -129- (a) Abis, L; Sen, A.; Halpern, J. J. Am. Chem. Soc. 1978, 100, 2915-2916; (b) Halpern, J. Acc. Chem. Res. 1982, 15, 332-338. Michelin, R.A; Faglia, S.; Uguagliati, P. Mmorg. Chem. 1983, 22, 1831-1834. Paonessa, R. S.; Trogler, W. C. J. Am. Chem. Soc. 1982, 104, 1138- 1140. Steigerwald, M. L. Ph.D. Thesis, California Institute of Technology Pasadena, CA, 1984. Pauling, L. The Nature of the Chemical Bond," 3rd ed.; Cornell University Press: Ithaca, 1960. A similar preference for p versus s character is found in carbon- halogen bonds. Goddard III, W. A.; Harding, L. B. Ann. Rev. Phys. Chem. 1979, 29, 363-396. Moore, C. E. “Atomic Energy Levels," National Bureau of Standards: Washington, DC, 1971; Vol. Ill. (These state splittings were aver- aged over j states to cancel out spin-orbit coupling.) The Dogg used in these calculations are Dogg(H-H) = 104.2 kcal/mol Degg(H—CH3) = 105.1 kcal/mol and Dagg(H3C—-CH3) = 90.4 kcal/mol. These bond energies were derived from spectroscopic measure- ments of Hg!®* and the reported Degg!® for HgC-CHg and H—CHs. (a) Huber, K.P.; Herzberg, G. Constants of Diatomic Molecules,” Van Nostrand: New York. 1979; (b) McMillen, D. F.; Golden, D. M. Ann. Rev. Phys. Chem. 1982, 33, 493-352. (20) (21) (22) (23) (24) (25) -130- Dzga [cyclopropyl-H] = 106.3 kcal/mol;!® Dogg [H-CH(CHs3)e] = 95.1 kcal/mol). 65 Simons, J. P. Nature 1965, 205, 1308-1309. Deg [HeC=CH2] = 172.2 + 2.07 kcal/mol and Dogg [F2C=CF2] = 69.3 + 2.7 were derived from the following enthalpies: AH-(C2F,) = -157.7 + 0.7 keal/mol and AH;(CgH,) = 12.54 + 0.07 keal/mol [see Stull, D. R.; Prophet, H. "JANAF Thermochemical Tables,” 2nd ed.; National Bureau of Standards: Washington, DC, June 1971; NSRDS-NBS 37]. AH;(CHg) = 92.35 + 1.0 kcal/mol [Chase, M. W.; Curnett, J. L.; Pro- phet, H.; McDonald, R. A.; Syverd, A. N. J. Phys. Chem. Ref. Data 1975, 4, 1-175]. AH:(CF2) = -44.2 + 1.0 kcal/mol [Berman, D. W.; Bomse, D. S.; Beau- champ. J. L. Int. J. Mass Spectrom. Jon Phys. 1981, 39, 263-271]. (a) Koda, 5. Chem. Phys. Lett. 1978, 55, 353-357; Chem. Phys. 1982, 66, 383-390; (b) A theoretical calculation leads to 51.4 kcal/mol; Feller, D.: Bor- den, W. T.; Davidson, E.R. Chem. Phys. Lett. 1980, 71, 22-26. Egger, K. W. J. Organomet. Chem. 1970, 24, 501-506. (a) Kirchner, R. M.; Little, R. G.; Tau, K. D.; Meek, D. W. J. Organomet. Chem. 1978, 149, C15-C18; (b) Biefeld, C. G.; Eick, H. A.; Grubbs, R. H. Inorg. Chem. 1973, 12, 2166-2170; (c} Puddephatt, R. J.; Thomson, M. A.; Manojlovi¢é-Muir, L.; Muir, K. W.; Frew, A. A.; Brown, M. P. J. Chem. Soc., Chem. Commun. 1981, 805-806. (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) -131- Del Pra, A.; Zanotti, G. Cryst. Struct. Comm. 1979, &, 737-742. Tamaki, A.; Magennis, S.A.; Kochi, J.K. J. Am. Chem. Soc. 1974, 96, 6140-6148. Komiya, S.; Abe, Y.; Yamamoto, A.; Yamamoto, T. Organometallics 1983, 2, 1466-1468. Kohara, T.; Yamamoto, T.; Yamamoto, A. J. Organomet. Chem. 1980, 192, 265-274. Braterman, P.S.; Cross, R.J. Chem. Soc. Rev. 1973, 2, 271-294. Basolo, F. 7rans. N.Y. Acad. Sct. 1969, 3, 676-685. Levine, I. N. “Quantum Chemistry,” 2nd ed.; Allyn and Bacon: Bos- ton, 1974; pp 450-452. (a) Evans, A.; Mortimer, C.T.; Puddephat, R.J. J. Organomet. Chem. 1975, 96, C58-C60; (b) Ashcroft, 5.J.; Mortimer, C.T. J. Chem. Soc. (A) 1967, 930-931. Bruno, J. W.; Marks, T. J.; Morss, L. R. J. Am. Chem. Soc. 1983, 105, 6824-6832. Collamati, I.; Furlani, A. J. Organomet. Chem. 1969, 17, 457-461. Hartley, F. R. "The Chemistry of Platinum and Palladium,” John Wiley & Sons: New York, 1973; Chapter 2. The last two conclusions concern the three-coordinate intermedi- ates resulting from loss of phosphine from the square planar com- plexes. This stabilization energy was derived from the results of Siegbahn et al.°© by summing the energy needed to bend the O-Pd-0 angle in Pd(OHe)e from its equilibrium value of 180° to 90° (15 kcal/mol) and the diabatic d!° + s'd® singlet splitting for Pd(OH2)2 (20 (38) (40) (41) (42) -132- kcal/mol), at a 90° O-Pd-O angle to give an adiabatic splitting of 35 keal/mol. This splitting is 5 kcal/mol smaller than their calcu- lated d!° » s!d® splitting for Pd atom of 40 kcal/mol. Dunning, Jr., T. H.; Hay, P. J. In "Modern Theoretical Chemistry: Methods of Electronic Structure Theory," Schaefer II, H. F., Ed; Plenum Press: New York, 1977; Vol. 3, Chapter 4, pp 79-127. Rappé, A. K.; Smedley, T. A; Goddard Ill, W. A. J. Phys. Chem. 1981, 85, 1662-1666. Huzinaga, S. J. Chem. Phys. 1965, 42, 1293-1302. All of the geometry optimizations were obtained by using an ana- lytic gradient program (GVBGRAD). This program was based on subroutines from (a) the GVB2P5 program [Bobrowicz, F. W.; God- dard III, W. A. In "Modern Theoretical Chemistry: Methods of Elec- tronic Structure Theory," Schaefer III, H. F., Ed.; Plenum Press: New York, 1977; Vol. 3, Chapter 4, pp 79-127} to evaluate density matrices for restricted HF and GVB-PP wavefunctions, (b) the HONDO program [Dupuis, M.; King, H. F. J. Chem. Phys. 1978, 68, 3998-4004] to calculate derivatives of the ab initio terms in the energy expression, and (c) routines from the GAUSS 80 program [Binkely, J. W., Whitesides, R. A.; Krishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol, 5., Kahn, L. R.; Pople, J. A. "Gauss 80," Department of Chemistry, Carnegie-Mellon University: Pittsburgh, PA, 1980] to calculate the effective potential terms of the deriva- tive. To determine the step size taken each iteration, we used a relatively simple Newton-Raphson technique in which the second derivative matrix is updated after every gradient calculation (except for the starting geometry) [Low, J. J.; Goddard III, W. A,, ~133- manuscript in preparation]. -134- Table I. Mulliken Populations for the GVB Bond Pairs of M(R,)(Re). For each bond there are two listings, the top one is the metal-like GVB orbital and the bottom one is the ligand-like orbital. Populations in GVB Bond Orbitals M-CHy M-H or M-Cl 39-23) 0. 10,40.48.0. 17 1 Pt(CH3)2(PHs)2 (sp)70.08q0.13¢ 0.18,0.71 9017,0.07 g0.48¢0.24 2 Pd(CHs)2(PHs)z (sp)-%2g0-15¢ .0.18,,0.58 no.tch,PE 30.17,,0.07 g0.60(-0.08 g0-10,,0.5g0.21¢]0.57 3 Pt(CHs)e(Cl)o(PHs)2 (sp)°%q°-28¢ 50.1107 (sp)70-°8g0.07¢] 50.05,0.83 0-21) 0. 14q0.370}0.27 4 Pt(Clo(PHs)e (sp) “0-98 q0.96] 0.01,,0.95 30-245,0.11 4040015 30-27 p0.15.g0.51540.08 5 Pt(H)(CH3)(PHs)2 (sp)70-4g0-28¢ 60.18,,0.72 (sp)~2-52q0-18¢0.01440.85 2) 90-20), 0.02 40.63; 70.07 PL) 2 (sp)0-2q0-19}0.80 0.26_0.01,70.64,-0.00 0.30 0.02,40.60;70.08 PUH)(CH e) g0-26),0.01 40.64 spe dh YH 3 (sp)°01g9-18¢.50.12,0.70 (sp)°01 g0.18}30.80 §0-2750.0140.63¢0.10 Pt(CHg)2” (sp)-0g0-15¢50.14,,0.70 0 16,0.05 40.50.24 Pd(CH,)22) (sp)? d2-20(0.28,,0.52 ®) Reference 2c. -135- Table If. Mulliken Populations for Pt and Pd bisphosphine complexes. Complex Populations Msp Ma CHg H PHs Cl i Pt(CHs)o(PHs)e 0.73 8.89 9.13 8.08 2 Pd(CH,)o(PHs)2 0.33 9.09 9.20 8.10 3 Pt(CHg)o(Cl)o(PHs)e 1.12 8.57 8.86 8.02 7.28 4 Pt(Cl)o(PHa)e 0.80 8.83 7.92 7.25 5 Pt(H)(CHs)(PHs)2 0.85 8.99 9.12 0.93 8.05") 6 Pt(H)o(PHs)e 0.96 9.10 0.98 7 Pt(PHs)e - 0.38 9.51 8.07 8 Pd(PHs)e 0.19 9.63 8.09 Pt(H),») 1.16 9.15 0.85 Pt(H)(CHs)») 1.05 9.03 9.04 0.89 Pt(CH)o” 0.97 8.91 9.06 Pd(CH,)2”) 0.60 9.15 9.13 8) This is the average occupation of the PH, groups in this complex. The PHs group trans to CHs has 8.04 e~ and the PHg group trans to H has 8.06 e~. b) Reference 2c. 07e}2 LOPsueT) a 07 KR *[low/qeoy 9 Z9 = (0.7 ~ ,8,P)pd pue jour/qeay g “Ly = (8p — ,8. pid] joU/Eoy "gp = AY Buyen avea “"Ha)*ID)id = W 94) 9UNI0I209 uo pose e 2P ~ 8,1 Qa 4, zoo dz “a- latin - (aul 405 9 ayy 8 (JONPoId ayy 07 aANETes) AB19Ua payeUySa ay) ayed[puT BanteA GAEZau eyL, “Buydnos aaponpes 30}; punoj 9} 49]118qQ ON (a “UOR PPE GASP AKO JO} Puno; 8} A9]11eq ON (e (8-81) (e°a2) (6 *18)) ((8°e2)) (18) ((e‘ot)} BoNEZTae SIP 1D ale") falh'0L-) {q(e"st- porno) (alts “s1°))) goles) | “CBayUo)pa = WP {e"1) sa) L°St 6'o1 ((6 “9)) (6'9)) (a "et) (9s) (6 "4)) (ry) (86) (za) voHyeZTIGUIseP 1D &b (eee) (ets) ‘Lt o’se- } (e's) (bod) = ts "8 t~). (o-zz-) | «r'6)) (ory) = (s“e) (ut) “Sua)"ond =n oD ner (o's) st) = Ok 9 ‘9g (lg°22)) (te"11) (o’sz) (se) (901) ((0"6)) (1 tz) (6°21) foneatqeeep “Hd ‘ ('ot) (ce) @'Sb- Db | gilt igile1-)) (2"2b-) force) | fl@Ot-)) gil 'L-)) (t*se-) (s"32-) ‘CHa)pd = W oes ot @"at- 0'OI- $6 vO aul 1"02- ¥-0 9't he 9"s- Pd= AW (bet) fsa '9z ¥'9R (v'zn) (L*11) B°ve ay 60z Lut [eoneziqeyap ‘Ha G*iv) (cov) oT 1'8- (s °s1) (6 "41) a"s- Zt 0‘b 181 e'el 6's! ‘CHdhd = « S"¥s s'ss s‘s) cer Veg 06% o'6L 191 (7 7” a 9 occ WN (8 yv Vv iy av HV cu uy av guy 7 “uv av ‘HO + Ww “CHOW ‘O+w — (HO)G)W tw “HW “poul/Teoy g F JO AuPEpIeIIM [eUuOH PPE UE sppe Atqeqord syaeuuered yo yeaa} YORA ‘onjua poyeuyse ue Zuyuyezqgo uf uopyeuprordde jo [asa] ayy ayeorpuy savayjueze d “H.g6Z 18 Jayl1eq vOQeAyoE pajoypaad ayy st 89 pue Sugydnoa aagamped soy 19f 112 A210ua payeqnaqed ay) et Vv *eU0}}I9II09 ainjeradwiay pue AB1aua yujod 0397 payeusa Uy Butppe Mq (AY) auadazpip AZrsua payepasyes ay wor psuy By Yous ‘SM .e6e 1e Adjeyqua vo}oEas ayy sy B6%qy -jour/quoy uy are sOYIENO [Ty ‘eagsao0ad Auydnos eaponpaes 10; saWaFzeua payoyperd pus payeqnayed “HI AIAVL -137- Table IV. Average bond energies for M(R)z complexes (kcal/mol). Difference in M-H and M-CHg Excitation M-H M-CH3 Bond Energies Molecule Energy Dogg D; Doos D; Dogg and D, M=Pt -12.3 68.7 62.6 530 46.9 15.7 M = Pd +19.6 50.1 59.9 358 45.7 14.2 M = Pt(PHs)2 +32.12) 58.3 (74.4) 39.6 55.7 18.7 M = Pd(PHs)e 457.29) (39.6) (68.2) 223 509 (17.3) M = Pt(Cl)o(PHs)2 36.6”) (53.4) (72.7) «31.75 1.0 (21.7) M=Pd(Cl).(PHs)2 (84.0)) = ((33.3)) ((75.3)) (10.0) (52.0) ((23.3)) ®) Based on the geometry of the M(CHs)z complex. >) Based on AE = 38.6 kcal for Pt complex plus the differential d®s! to d8s? energy (45.4 kcal). -138- Table V. Geometric parameters around metal atom in Pt and Pd complexes (all dis- tances are in & and all angles are in degrees). M-P M-C misc. P-M-P C-M-C misc. Molecule distance distance distance angle angle angle 1 Pt(CHs)e(PHs)e 2.46 2.06 - 101 89 i- 2 Pd(CHs)2(PHs)2 2.50 2.02 - 98 Al - 3 PtClo(CHs)e(PHs)2 2.44 2.03 M-CK(2.38) 95 90 CI-M-Cl(177) 4 PtCl(PH,)2 2.44 - M-C1(2.35) 102 - CLM-C1(97) 5 Pt(H)(CHs)(PHs)s™ 2.46 2.06 M-H(1.50) 101 - —_-H-Pt-C(84) 6 PtH2(PHs)2?) 2.45 - M-H(1.50) 100 - _-H-Pt-H(79) 7 Pt(PHs)e 2.32 - - 180 - - 8 Pd(PHs)2 2.41 - - 180 - - Pt(CHs)2™ - 197 - - 98 - Pt(H)(CH3)” - 1.96 | M-H(1.48) - - — _H-Pt-C(98) Pt(H)2” - - M-H(1.51) - a3.Cié« Pd(CHs)2” - 196 - - 92. - ®) This geometry was not optimized but was estimated from the geometries (1) and (6). The geometries of the Pt(CH3)(PHs) fragment were taken frozen at the geometry of (1), and the C-Pt-H angle was chosen to be the average of the C-Pt-C angle of (1) and the H- Pt-H angle of (6). b) Reference 2a. °) Reference 2c. ‘I,)*ealdav = (pa) sav ‘osoyoroyy ‘S, 81 Pd JO 97438 punos8 ayy, gg TOU/TEOH 96 “26 = (Pa) HY (, ‘Tow /Teo¥ 9°ZET = O11 + 9"T2t = has, AV ‘Ayjuanbasu oo eI TOUL/TeOy QT] = (s, ~d,)av 9¢ ‘9 .G% 18 TOW /TEay g “T@1 = Qa)? ay (q "LE SAN-SGUSN ‘(1L61 eunp ‘Od ‘uojZuTyseM “spaepueyg Jo neang TeuoyeN) yoydorg Hue TMs “U “d ‘Uontpa puosag ‘sopqeL TeoTWOyDOULIONL AVNVE “lou /qeoy eg "ze- = ("0°H) 86g | ry 1 8hI- GZ SI- "103 - SB ve zer~ 991- - 68> ee- 7103 re " 9¢ 8bI- (e ¥81- 88- ¥8- (e (HOW (HY)¥ (1 )*xpa ~ x + ig) palny [)yxaq - (3)2y +(5,),a]n0 [S!xpakuv [()*%a}Juy punoduos *pajou se qydaoxe ‘9€ 304 woay are FHY Ty ‘sites (I1)Pd pue (II)1d 203 (I, g6z 38 Toul/Teoy) satdjeyug” “TA atqe. Suplementary Material. ~140- . The following seven tables contain the cartesian coordinates of the optimized geometries for the molecules studing in this paper. The eigth table contains the internal coordinates of the phosphine and methyl groups for the geometries tabulated in tables SI-SVII. Table S.I. Cartesian Coordinates for Pt(CHs)2(PHs)2 (A) -141- Atom x Y Z Pt 0.000000 0.000000 0.030594 C(1) 0.000000 -1.378597 1.528559 HC(1) 0.000000 -2.406768 1.173832 HC(2) -0.883506 -1.241806 2.145267 HC(3) 0.883506 -1.241806 2.145267 C(2) 0.000000 1.378597 1.528559 HC(4) 0.000000 2.406768 1.173832 HC(5) 0.883506 1.241806 2.145267 HC(6) -0.883506 1.241806 2.145267 P(1) 0.000000 -1.896819 -1.490378 HP(1) 0.000000 “3.237424 -0.779494 HP(2) -1.147403 “2.175522 ~2.452186 HP(3) 1.147403 -2.175522 “2.452186 P(2) 0.000000 1.896819 -1.480378 HP(4) 0.000000 3.237424 -0.779494 HP(5) 1.147403 2.175522 “2.452186 HP(6) -1.147403 2.175522 -2.452186 Level of Total Energies at | Total Energies at AE Wavefunction This Geometry | Dissociated Limit (kcal/mol) (hartrees) (hartrees) Hartree-Fock -791.3B02 -791.4082 -19.0 GVB-CI(2/4) -791.4183 -791.4290 -6.7 GVB-RCI(4/8)xGVB-CI(2/4) -791.4851 -791.4980 -8.1 ~142. Table S.II. Cartesian Coordinates for Pd(CHs)2(PHs)2 (A) Atom Xx Y Z Pd 0.000000 0.000000 0.055150 C(1) 0.000000 -1.305608 1.592483 HC(1) 0.000000 ~2.343222 1.269129 HC(2) -0.880756 -1.121416 2.196919 HC(3) 0.880756 -1.121416 2.196919 c(2) 0.000000 1.305608 1.592483 HC(4) 0.000000 2.343222 1.269129 HC(5) 0.880756 1.121416 2.196919 HC(6) -0.880756 1.121416 2.196919 P(1) 0.000000 -1.885864 -1.581444 HP(1) 0.000000 -3.171799 -0.786064 HP(2) -1.138148 -2.226994 -2.540769 HP(3) 1.138148 “2.226994 -2.540769 P(2) 0.000000 1.885864 -1.581444 HP(4) 0.000000 3.171799 -0.786064 HP(5) 1.198148 2.226994 -2.540769 HP(6) -1.138146 2.226994 “2.540769 Level of Total Energies at | Total Energies at AE Wavefunction This Geometry Dissociated Limit (kcal/mol) (hartrees) (hartrees) Hartree-Fock -792.9620 -793.0295 42.4 GVB-Cl(2/4) -793.0066 -793.0498 ~27.1 GVB-RCI(4/8)xGVB-Cl(2 /4) -793.0639 -793.1318 -42.6 Table S.III. Cartesian Coordinates for PtCle(CHg)2(PHs)2 (A) -143- Atom Xx Y Z Pt 0.000000 0.000000 0.136317 C(1) 0.000000 -1.438951 1.574711 HC(t) 0.000000 -2.448813 1.169736 -HC(2) -0.902419 -1.902946 2.157062 HC(3) 0.902419 -1.302946 2.157062 C(2) 0.000000 1.438951 1.574711 HC(4) 0.000000 2.448813 1.169736 HC(5) 0.902419 1.302946 2.157062 HC(8) -0.902419 1.302946 2.157062 Cl(1) -2.982457 0.000000 0.066219 Ci(2) 2.382457 0.000000 0.066219 P(1) 0.000000 1.797415 -1.509749 HP(1) 0.000000 3.055002 -0.692679 HP(2) 1.187320 2.017055 -2.424796 HP(3) -1.187320 2.017055 -2.424796 P(2) 0.000000 ~1.797415 -1.509749 HP(4) 0.000000 -3.055002 -0.692679 HP(5) ~1.187320 -2.017055 “2.424796 HP(6) 1.187320 -2.017055 ~2.424796 Level of Total Energies at | Total Energies at AE Wavefunction This Geometry | Dissociated Limit (kcal/mol) (hartrees) (hartrees) Hartree-Fock -1710.3463 -1710.4079 -38.7 | GVB-RCI(2/4)xGVB-Cl(2/4) -1710.4272 -1710.4554 “17.7 GVB-RCI(5/10)xGVB-CI(2/4) -1710.4718 -1710.5116 -25.0 | ~144. Table S.IV. Cartesian Coordinates for PtCl2(PH3)2 (A) Atom Xx Y Zz Pt 0.000000 0.000000 0.066550 Ci(1)} 0.000000 1.683502 1.712871 ci(2) 0.000000 -1.683502 1.712871 P(t) 0.000000 -1.905718 -1.463152 HP(1) 0.000000 -3.257738 -0.758184 HP(2) -1.153527 -2.147114 -2.437360 HP(3) 1.153527 -2.147114 -2.437360 P(2) 0.000000 1.905718 -1.463152 HP(4) 0.000000 3.257738 -0.758184 HP(5) 1.153527 2.147114 -2.437360 HP(6) -1.153527 2.147114 -2.437360 Level of Total Energies at Wavefunction This Geometry (hartrees) Hartree-Fock -1631.2019 RCI(2/4) -1631.2343 GVB-RCI(6/12) -1631.2906 -145. Table S.V. Cartesian Coordinates for Pt(H)(CH3)(PHs)z2 (A) Atom X Y Z PT 0.000000 0.000000 0.030594 C(1) 0.000000 -1.378597 1.528559 CH(1) 0.000000 -2.406768 1.173832 CH(2) -0.883506 -1.241806 2.145267 CH(3) 0.883506 -1.241806 2.145267 H(1) 0.000000 0.960402 1.187922 P(1) 0.000000 -1.896819 -1.490378 HP(1)} 0.000000 ~3.2937424 -0.779494 HP(2) ~1.147403 -2.175522 -2.452186 HP(3) 1.147403 -2.175522 -2.452186 P(2) 0.000000 1.896819 -1.490378 HP(4) 0.000000 3.237424 -0.779494 HP(5) 1.147403 2.175522 -2.452186 HP(6) -1.147403 2.175522 -2.452186 Level of Total Energies at } Total Energies at AE Wavefunction This Geometry | Dissociated Limit (keal/mol) (hartrees) (hartrees) Hartree-Fock -791.3671 -791.3880 -13.2 GVB-C1(2/4) ~791.4085 -791.4095 -0.6 GVB-RCI(4/8)xGVB-Cl(2/4) -791.4670 -791.4785 -7.2 -146- Table 5.VI. Cartesian Coordinates for Pt(PHs)z (A) Atom 4 Y Z Pt 0.000000 0.000000 0.000000 P(1) 0.000000 -2.318176 0.000000 HP(1) 0.000000 -3.097940 1.312807 HP(2) -1.196924 -3.097940 -0.656404 HP(3) 1.136924 ~3,097940 -0.656404 P(2) 0.000000 2.318176 0.000000 HP(4) 0.000000 3.097940 1.312807 HP(5) 1.196924 3.097940 ~0.656404 HP(6) -1.136924 3.097940 -0.656404 Level of Total Energies at is G t Wavefunction This Geometry (hartrees) Hartree-Fock -712.2023 GVB-CI(1/2) -712.20B80 GVB-RCI(5/10) -712.2770 Table S.VII. Cartesian Coordinates for Pd(PH3)2 (A) -147~ Atom Xx Y Z Pd 0.000000 0.000000 0.000000 P(1) 0.000000 ~2.405422 0.000000 HP(1) 0.000000 -3.210795 1.301985 HP(2) -1.127552 -3.210795 ~0.650993 HP(3) 1.127552 -3.210795 -0.650993 P(2) 0.000000 2.405422 0.000000 HP(4) 0.000000 3.210795 1.301985 ~HP(5) 1.127552 3.210795 -0.650993 HP(6) -1.127552 3.210795 ~0.650993 Level of Total Energies at . This Geometry Wavefunction (hartrees) Hartree-Fock -713.8235 GVB-CI(1/2) -713.8288 GVB-RCI(5/ 10) -713.9107 ~-148- 66 96 86 £01 96 86 ol (€)dH~(1)d-(z)adH]@ G6 96 66 86 86 86 ol(2)dH-(1)d-(1)dH] 9 es" gS" eS‘ 2s ‘I eo‘ 2s ‘I y [(z)aH-(1)a]s £¢o'T eo ‘T ea ‘I os ‘1 £9'T ST y ((DaH-(a)2 -- -- -- elt 601 601 ol(8)OH-(1)9=(2)0H] 6 -- -- -- 801 60T 801 ol(2)OH=(1)9-(1)9H] @ -- -- -- 80 "I 80 "I 60 ‘1 y [(2)0H-(1)9] 4 -- -- :- 60 ‘I 80 ‘I 60 ‘T y [(on-(1)0] 4 *("Hd)Pd “fuayd “CHd) 103d *PHa)*CHD) 101d *PHa)*FHO)Pa *('Ha)*(CHO)d *sauTydsoyd pue spTAyZaI JO sayeuTps0OD TeUdaqUy] “THA ‘S S142 Right Pt-C Bond Pair -149- H oH H H v7 \e H-G, C2—H en $e i; t Pp H,P PH, ONE Pt 6s7°3 6p? 54:5 Cos8p'7! Left Pt-C Bond Pair ONE ~ Pt 5s Ep 5q-5 Cys"'® p" _ @, | ONE $4 Pt 652 6p !%q-49 Cys° ot Figure 1. The CVB orbitals for 1 [from the CVB(5/10)-PP wavefunction]. Nuclei in the plane are indicated by asterisks. Positive contours are solid, ncgative contours are dotted, and nodal lines arc long dashes. The spacing between contours is 0.05 a.u. Analysis of each GVB orbital in terms of a Mulliken population is shown. Right Pd-C Bond -150- ONE Pd 57-02 5p° 4a''$ Cps'8 ps Left Pd-C Bond ONE “ Pd 55/7 5p°" 4a°*%c, 3°? pi Figure 2. The GVB orbitals for the Pt-C bonds of 2. -151- Ht # até cl $, FH H—-G=<— —" / $471 bp H,P—_____ PH 3 CI 3 Right Pt-C Bond ONE Pt 657-05 6p°3 59 Cas"! po? Pr 6s:'7 6p°” 5-69 Ces po” Left Pt-C Bond ONE ONE 4 , a7) \ RED \ / — Y Pt 65-93 6p 93 54/3 Cg: p-67- Pt 6s-7 6p 97 548? Cys" p07 Figure 3. The GVB orbitals for the Pt-C bonds of 3. Pt-C Bond Pair H—C H * ot. apr ° H p’ ‘pH, ONE 7 Pt 65:24 6p! 1 5q49 C 50! pie ~~ — Pts Gp U5 gI3¢ 518,72 , / / Pt-H Bond Pair ONE ONE ~~, Ng / Nae m m —N PAIRED|- \ y \ \ / Pr 63-2? 6p!35q5!}.09 / Pt 65793 6p'5a:'6 C01 ,4-85 Figure 4. The GVB orbitals for the Pt-H and Pt-C bonds of 5. Upper Pt-C! Bond -153- ONE er Pt 637-02 6p: 5d .07 cis o> ONE Pt 6s"? 6p2* 5?! Cis"? p? Lower Pt-Ci Bond ONE ————a VA a ») NX | 4 $c \ | - ] ONE be — a < ~se ~N -~\ i — ED Pt 657-92 6 p04 507), g°93,-93 Figure 5. The GVB orbitals for the Pt-Cl bond of 3. Left Pt-Cl Bond Pair -154- ONE \ ) Pt 6s-2! 6p" 5q°57 Cle 37 02 p?? ONE Pt 6792 Gp! 5g: C) 5p 95 Right Pt-Cl Bond Pair . 4 Pt 6s'2! 6p" 54-37 Cl, 57-02 p29 ~_/ Pt 657 02 6p" Ot 5g 0 Cl, gO p= Figure 6. The GVB orbitals for the Pt-Cl bond of 4. -155- ‘Id JO 87218 ,SyP at]} Jo red ,s ay} JOJ STeNTQIO AAD aL “2 ama 2199 ggS9 Id Vd 5) jaz ANO “p 2199 g9$9 td ANO p S|D}IG4Q PlUUqAH ds9Q {qd ~156- 14.02 aHt 25.1" DHagg vt P 2] (PHs)» Pt —— > (PHs), Pt +H, (PHy), Pd + (Pry), Pa + He “Sa “a T BHagg &-42.2 15.77 AHt v -5.8* AHagg a4 4 (PH). Pt —~—> (PHs)o Pt + CHe (Pry) Pa a> (PHs)2 Pd + CHe CHy “crs ry 4 t 10.32 AHt 25 AH 41.02 OH! -45.8= AHag, sera + W1L3* AHogg -27.0* AHaeg wv v + 7s ws a“ (PH), on —_ (PHs), PT +CaHg (PH), PON —> (PHs)Pd+ CoH, Cig (PH), rN Cl, (PH,), Pt + CH, 3 3 Figure 8. Estimated energetics for R,—Rg reductive coupling of (PH3)2Mt(R,)(Rz) complexes. All quantities are enthalpies at 298°K. -157- HP (5) HP (2) HP(5) HP(2) | HC (2) _ Figure 9. ORTEP plot of 1 and 2. -158- "e Jo 101d GALYO (1) 19 ‘OT andy (9)dH (1)dH ‘OurL/[eoyx Ul SatyiyueNb [Ty ‘Iq pue ‘pd ‘IN JO} salsiaua uotjeyoxe ommow “11 amadg --" 6'le- ai? - /vee — ~02 ! ¢'Si-' i \ i \ / \ -- -- d-- a _\. — rely 0°0 xe) OO Ie? [00 | 00 00 156? [OO \ OO TO 28 oP b's “s -———— ol? } \ / /ee Oil s.o2 el ———” Pan a py ake? 2b é 4 é —~ \ vie Ob ra ‘pop. Ovo? - ’ t i i mn G'vS *. CT pipP ! “SN ae 0 9S 2 8 H +09 9°29 ; i t ; ! —08 i tf I H 4H IOYN-@AD = ‘dxg JH I0Y-8AD “4Ox9} 4H IOYN-GAD = ‘dxQ Pd iN Id (JOw/|D9y) SBulyj]dS e404 -160- CHAPTER 4 Theoretical Studies of CH, and NH, Species Chemisorbed on Ni Clusters -161- I. Introduction The chemisorption of small molecules on metal surfaces has been the subject of many experimental! and theoretical” studies. The low index surfaces of metals have been used to model many catalytic reactions including methanation® and ammonia decomposition on metal surfaces.* The problem with experimental studies is that critical intermediates are often very unstable and cannot be observed under typical experimental conditions. The advantage theory has is that a theorist can perform cal- culations on the various proposed intermediates and compare their rela- tive energetics to see whether the proposed mechanism is reasonable or not.° The problem that a theorist has is that the system to be modelled is very large, which forces him to make various approximations in his calcu- lations. These approximations affect the results in various ways that should be accounted for when attempting to relate theory to experiment. In this paper we examine theoretically cluster models for the various intermediates important for methanation and ammonia decomposition on Ni surfaces. We have used the one-electron modified effective potential (MEP) of Upton and Goddard (UG)§ to simulate the Ni atoms of the clus- ter. This approximation involves replacing the Ar core and 3d° shell of Ni by the MEP. Only the Ni 4s electrons are treated explicitly. This method allows the use of large clusters (13-20 atoms) to model the metal surface for chemisorption. The method has been used with considerable success in modelling chemisorption of H, 0, 8, c1§ and CO” on Ni surfaces. We have used the four-coordinate site of the Nij3 cluster (see Figure 1) to model chemisorption of small molecules on the Ni(100) surface. This site allows the singly-occupied orbitals of the radical to have the largest overlap with the conduction band orbitals. This should lead to radical -162- species forming the strongest bonds on high coordination sites. Carbon has been observed to bond to a similiar site in various carbidocarbonyl clusters® (ie., FesC(CO)i5). Akylidynes have been observed to be coordi- nated to three metal atoms in various metal cluster compounds.® Since such a site is not available on the Ni(100) cluster, methylidyne and car- bon should both prefer the four-coordinate site. Methylene, on the other hand, has only been observed to bind to metal clusters at two-coordinate bridge sites.!° In this work we intend a first pass at the relative energet- ics for these chemisorbed intermediates. For these purposes the four- coordinate site of Ni,g is quite adequate. We have used the Ni,, (see figure 2) cluster to model chemisorption of closed shell molecules (i.e., NHs and CO) where the bonding is dominated by lewis acid/base interactions. More quantitative results would require larger clusters and perhaps higher levels of theory. This work is intended to provide a qualitative understanding of the nature of the surface chemical bond and to help organize further theoretical study in this area. -163-— Il. Results A. Qualitative Description of Bonding The “Tj, (1a7,th,t3,e2) excited state of the Nis cluster was chosen to model the bulk for the four-coordinate site of Ni(100). This state is 5.6 kcal/mol above the *T 1, (1aZth,ts,) ground state. This state was chosen because it had orbitals available for forming o and 7 bonds to the various intermediates studied here. The Tip ground state only had a singly- occupied orbital of m symmetry available for forming bonds. In the ground state of all the CH, and NH, complexes studied here, the Ni,3 clus- ter was in its “Tig electronic state. (For more details about the low lying states of the Ni,3 cluster see Appendix A.) The "Arg ground state of Nii, cluster’ was chosen to model the bulk for the one-coordinate site of Ni(100). The calculated geometries, vibrational frequencies and energet- ics are shown in Table I. The GVB orbitals for methylidyne (CH), methylene (CHg), and methyl (CHs) are shown in Figures 3-5. In general, the bonding of these species can be characterized as forming a high-overlap ionic o-bond and low- overlap covalent m bonds. The surface bonds for methylidyne, methylene, and methyl are best described as triple (10 and 27), double (10 and 17), and single (10) bonds, respectively. The carbon-surface 7m bonds in these systems are quite strong. This causes the decomposition of chemisorbed CH, to chemisorbed CH,_, and chemisorbed H to be about 14 kcal/mol downhill for x=(2 and 3). CHya) > CHa) + Hay) AH? = -12.7 kcal/ mol CHara) > CHiay + Ha) AH? = —15.0 kcal’ mol ~164- By assuming a C-H bond strength of 98 keal/mol!! and a surface-H bond strength of 63 kcal/mol,” we estimate a surface-carbon 7m bond strength of 49 kcal/mol. This is only 5 kcal/mol stronger than our calcu- lated surface-carbon o bond strength of 43.6 kcal/mol for chemisorbed methyl. The surface-carbon 7 bond strength is close to the difference in the C-H bond strength (98 kcal/mol) and half of the H-H bond strength (52.1 keal/mol)!8 which causes the dehydrogenation of chemisorbed methyl or methylene to give dihydrogen and chemisorbed methylene or methylidyne to be essentially isoenergetic processes. CHsca) > CHasia) + BHarg) AH? = —1.2 kcal/ mol CHaa) > CHyy + 4Haz) AHP = —3.5 keal/ mol Carbon atom bonds to the surface in a very different manner (see the GVB orbitals in Figure 6). The chemisorbed carbon atom is best described as a C’, which has formed two covalent 7 bonds to the surface. An electron from the cluster has moved to the C 2p, orbital. This implies that the maximum number of bonds that a CH, species can form to the surface is three. When the last C-H bond is broken in chemisorbed methylidyne to yield chemisorbed carbon, the carbon electron involved in the C-H bond is not able to form another bond to the surface. Thus the chemisorbed carbon ends up having significant radical character. There- fore it is uphill energetically to dissociate methylidyne to carbon and hydrogen atoms on our clusters. This will have a significant impact on the surface chemistry of carbon, which will be discussed in the next section. -165~ CHa) > Cia) + Hay 9H? = 25.7 kcal/ mol CHa) > Cra) + WHp AH? = 37.2 kcal/ mol The GVB orbitals for imidogen (NH), amidogen (NH), and ammonia (NH3) are shown in Figures 7-9. In general, these species make o bonds that can be characterized as donor-acceptor bonds and covalent 7m bonds. The bonds that imidogen, amidogen, and ammonia make to the surface are triple, double, and single bonds, respectively. Nitrogen atom (see GVB orbitals in Figure 10) forms a triple bond to the surface. The three bonds consist of an ionic o bond and two covalent m7 bonds to the surface that are similar to the methylidyne surface bonds. Just like the CH, species, the NH, species also makes fairly strong 7 bonds to the surface. This causes the decomposition of NHy(4) to NH,-1(4) and H(,) to be downhill by about 18 kcal/mol for x=(2 and 3). Assuming a N-H bond strength of 106 kcal/mol, 4 we can estimate a surface-N 7 bond energy of 61 kcal/mol. NHga) * NHg(aytHeey AHP = -17.1 kcal/mol NHa¢e) ad NH a) +Hay AH? = —18.7 keal/ mol When chemisorbed imidogen decomposes to chemisorbed nitrogen and hydrogen, the lewis acid/base surface-N bond and N-H bond are replaced by a surface-N ionic bond and surface-H bond. The difference between these two bond energies is apparently very close to difference in energy between a N-H (106 kcal/mol) and a surface-hydrogen bond (63 ~166- keal/mol) which causes the decompostion of chemisorbed imidogen to chemisorbed nitrogen and hydrogen to be essentially isoenergetic. NH) > Nea) + Hea) AH? = —0.9 kcal/ mol The bond that ammonia makes to the four-coordinate site of Nijs is very weak (2.04 keal/mol). In fact, when the zero point energy is added, it is unbound by 1.6 kcal/mol. Ammonia is bound by 10 keal/mol to the one-coordinate site of the Ni,, cluster. This shows that the donor/acceptor bond of ammonia is stronger when bound to the one- coordinate site than to higher coordination sites. The lone pair of ammonia favors the on-top site because it can form a lewis acid/base bond to the metal center, without disrupting metal-metal bonding in the cluster. Even though the lone pair of ammonia would be stablized by more metal centers at a higher coordination site through lewis acid/base interactons, it would also have higher overlap with the occuppied orbitals of the conduction band (4s) electrons. We therefore believe that ammonia prefers sites where it is coordinated to only a single metal center. We find that the surface-carbon and surface-nitrogen m bonds are very important in the nature of the surface chemical bond. In general, we find that these 7 bonds are slightly stronger than the corresponding o bonds for CH, species. This is also true for NH, species, because we have found that these species prefer to bind oriented perpendicular to the surface where it can make a 7 bond and a lewis acid/base o bond -167- \ rather than to bend over where it can only make a o bond. We find that oxygen atom binds to the surface by making an ionic o bond and a covalent 7 bond (see figures 11 and 12). This state is very similiar to the oxide state found on Nigg by uG.é B. Quantitative Discussion The parameters calculated for chemisorbed species discussed above are shown in Table I. In general, in going from single to double to triple bonds, the bond energy increases. The calculated bond energies for the multiple surface bonds appear to be systematically high. The worst case is for the surface oxygen bond of 157 kcal/mol, which is much higher than the experimental estimates of 94-135 kcal/mol.!° The calculated bond energy for H on Ni, (66 kcal/mol) is fortuitously close to the exper- imental value for hydrogen bound to Ni surfaces (63 keal/mol).!? If we examine the process -168- Nijg-H + H ~ Niyg + Ho, we calculate a AHf for this reaction of -23.3 kcal/mol compared to exper- imental AH? of -40.1 kcal/mol. This means that the calculated Dg for the chemisorbed hydrogen is 16.8 kcal/mol too strong, assuming that the correlation error is the same for the surface H bond as it is for the H-H bond. This error can arise from either the small cluster size or the ten- dency of the MEP to have systematically large bond energies. 6 In order to account for this bias toward stronger bond strengths, we have used the error in the Ni-H bond to account for the errors made in carbon-surface and nitrogen-surface bonds. The procedure we have used is essentially an equibondedness approach, !” in which the total number of bonds and the number of bonds to the surface were held fixed (see Calcu- lational Details). All of the bonds made through donor-acceptor bonds to the surface have been assumed to have no correlation error. This appears to be reasonable in light of the bond strength (10.9 kcal/mol) of NHg to Ni,4, which compares well to the experimental chemisorption energy of NH; to nickel surfaces (~12 kcal/mol)*. The reactions used to calculate enthalpies of formation at 0°K are shown in Table Il. The enthal- pies for any particular intermediate are predicted from the change in the calculated energies and from enthalpies known either from experiment (see Table III) or previous equibondedness reactions. We have used the experimental enthalpies of methane, ammonia, chemisorbed H and chemisorbed CO!8 as references. The AH? calculated in this manner along with experimental AH? (see table III and IV) can then be used to cal- culate the corrected Dp shown in Table I and to compare the relative enthalpies of various intermediates. -169- A good test of these energetics is to compare them to two simple reactions which are known to proceed on Ni surfaces.’? Our calculated enthalpy for the disproportionation reaction of CO (the Boudouard Reaction)! eCO > Cray + CO2 AH; = —14.8 kcal/ mol indicates that our carbon-surface bond strength is reasonable, but we calculate the reduction of chemisorbed oxygen! Hz + Om) > H20 AH®; = 35.2 kcal/ mol to be uphill energetically, indicating that our corrected oxygen-surface bond strength is still too high. The enthalpies of formation at 0° K for NH, intermediates are shown in Figure 13. The enthalpy changes for the steps shown in figure 13 are tabulated in table V. Chemisorbed imidogen is calculated to be the most stable NH, intermediate. Decomposition of ammonia has been observed to occur at low temperature (200° K) in an electron beam on Ni(111) sur- 20 and the decomposition product was tentatively assigned to chem- faces isorbed imidogen by ultraviolet photoelectron spectroscopy. Ammonia also decomposes on Ni(110) at temperatures above 150° K to some unidentified NH, intermediate.7!;#4 Huttinger and Kiippers”3 have per- formed thermal desorption spectroscopy (TDS) experiments suggesting that chemisorbed amidogen is formed by exposing ammonia to Ni(110) at temperatures below 350° K. This species decomposes at 410° K to give He and chemisorbed nitrogen atom. Exposure of ammonia to Ni(110) at 400° K yields chemisorbed imidogen which decomposes at ‘~800° K to give No and Hg. Ammonia gas also been observed to decompose when exposed to 24 Ni(100) at room temperature.“* The intermediates were assigned to a -170- imidogen and amidogen intermediates by X-ray Photoelectron Spectros- copy. Unfortunately, all of the experimental work for ammonia decompo- sition only really shows that chemisorbed amidogen and imidogen are kinetically stable and not necessarily energetically stable. The experi- mental work does indicate that it is energetically favorable to dissociate ammonia on Ni surfaces, which is in agreement with our results, but the activation energy for dissociative chemisorption is higher than that for desorption of NHs molecules. The relative enthalpies at 0° K for the various intermediates relevant for methanation are shown in Figure 14. The enthalpy changes for the steps shown in figure 14 are tabulated in table VI. These enthalpies imply that methylidyne is the most stable CH, intermediate on Ni. Experimen- tally it is known that both acetylene and ethylene will decompose to chemisorbed methylidyne on Ni(100)° and Ni(111),?” suggesting that methylidyne is the most stable CH, intermediate on Ni. Kinetic experi- ments”8 suggest that the most abundant species on supported Ni catalysts during methanation is chemisorbed carbon and chemisorbed methylidyne. Both of these experiments are consistent with our calcu- lated energetics and proposal that methylidyne is the most stable CH, intermediate on Ni surfaces. The first step in dissociation of CO to chemisorbed carbon and oxygen is calculated to be downhill by 10.3 kcal/mol. Experimentally it is known that the dissociative chemisorption of CO does not occur for the low index faces of Ni[(111) and (100)]*%-8° tor temperatures below 450° K, at this temperature CO will have desorbed under ultra high vacuum conditions. This implies that the activation barrier for CO decomposition is larger than for molecular desorption. Dissociative chemisorption of CO takes -171- place at low temperatures (180° K) on Ni(110) surfaces’! and on stepped 30 This is most probably caused by a lower activation surfaces of Ni. energy at steps on these surfaces. This experimental evidence supports favorable energetics for CO dissociation. Unfortunately the removal of chemisorbed oxygen by hydrogen molecule or chemisorbed hydrogen (reactions 3 and 9 in figure 14) is cal- culated to be extremely endothermic (35.1 kcal/mol and 58.1 kcal/mol). These enthalpies do not appear to be reasonable in light of kinetic experi- ments which give an activation barrier of 24.7 kcal/mol for the methana- tion reaction.? Water was a principle product under the conditions under which these experiments were carried out. Although the observations of the chemistry of chemisorbed oxygen do not agree with our estimates, the relative energetics of the various chemisorbed CH, and NH, inter- mediates appear to be resonable and consistent with experimental results. There has been considerable controversy regarding the geometry of O on Ni(100). UG have carried out calculations on Nigo9 to model this sys- 6 tem and found two low lying electronic states:” an “oxide” state with a surface-oxygen distance of 0.55 A and vibrational frequency of 218 cm} and a "radical" state with a surface-oxygen distance of 0.88 A and vibra- tional frequency of 371 cm™!. In order to model higher coverages ucé® carried out calculations on Nig90* and obtained a R,=0.26 A and a vibra- tional frequency of 266 cm™}. These results provided an explanation for why the metal-oxygen stretching frequency (310 cm™) in the c(2x2) O overlayer was lower than in the p(2x2) O overlayer (430 em7!)** on Ni(100). Parameters derived from these calculations were used in detailed calculations of the low frequency phonon spectrum which agreed -172- well with experiment.*3 This led to the conclusion that the c(2x2) O over- layer had chemisorbed oxygen atoms in the "oxide" state with an R,=0.26 A and the p(2x2) 0 overlayer contained chemisorbed oxygen atoms in the "radical" with an R, = 0.88 A state. However, many experiments have been performed since then which find a longer surface-oxygen distance of 0.8 to 0.9 A for the c(2x2) overlayer,°* although some experiments do support the shorter Ni-O bond distance.34¢-4.35 Bauschlicher et al.*® have performed calculations on the Ni;0 cluster in which they found that the meclusion of Ni 4p functions to the double-¢ basis of uG® increased the surface-oxygen distance from 0.57 A to 0.68 A for the oxide state at the HF level. Their final surface-oxygen distance of 0.74 A and vibrational fre- 1 was calculated at the singles and doubles CI level. In quency of 320 cm™ our GVB-CI calculations we have used a basis of the same quality as Bauschlicher et al. (see appendix) and find a surface-oxygen distance of 0.712 A and vibrational frequency of 380 cm™! for Ni,30. We have also car- ried out calculations on Nigg) with the same cluster basis and found an R; of 0.647 A and a vibrational frequency of 358 cm7 at the GVB-CI level. The results are in good agreement with the Ni,;O calculations and fair agreement with the experimental geometries of 0.8-0.9 A. Our calculated geometry for H chemisorbed at the four fold site of Niig (R,=0.74A) is also substantially longer than that calculated by UG® at the same site (R,=0.304). A recent experimental determination of geometry for deuterium on Ni(100) by transmission tunneling gives a value of Rj = 05 + O.1 AS’. Helium diffraction experiments”® gave: a geometry for chemisorbed hydrogen on Ni(100) with an R, of 0.9-1.0 A. Our calculated value of 0.74 A lies in between the two experimental results, which does support the longer R; we are finding with a more com- -1t73- plete cluster basis. However, our calculated vibrational frequency of 845 em! for the surface-hydrogen stretch does not agree as well with the experimental” frequency of 596 cm! as that calculated by uc§ (589 em). The experimental determination of the geometry of carbon on Ni(100) has been hampered by significant reconstruction of the sub- strate.*° The LEED data has been shown to be consistent with two struc- tures. In one structure the carbon atoms are 0.9 A from the surface and in the other structure the carbon atoms are 0.1 A from the surface. The best fit was found for the second structure and helium diffraction experi- ments” also support the shorter R,. However, we calculate a surface- carbon distance of 0.858 A which is in better aggreement with the R,=0.9 A structure. Since we have held the Ni atoms in our cluster fixed we can- not rule out the shorter surface-C distance, which could be favored if the Ni atoms were allowed to relax. -174- Ii. Calculational details In all of the calculations presented here the Ni atoms were described by the MEP of uG® The double-¢ basis of uc§ plus bond functions (DZB) at octahedral and tetrahedral interstitials with exponents of 0.208 and 0.310 respectively was used to describe the Ni cluster. In the appendix we compare the DZB basis with a cluster basis in which the double-¢ basis is augmented by a single-~ Ni 4p function with an exponent of 0.14. The exponents for the bond functions and single-¢ Ni 4p function were optim- ized for an averaged field wavefunction of Nij3, in which one-third of an electron was placed in the Raj, and le, orbitals, four-thirds of an electron was placed in the 1tg, orbitals, and the laj, and 1t;,, orbitals were doubly occupied. This wavefunction corresponds to an average of all electronic states in which one electron occupies a le, or aj, orbital and four elec- trons with triplet spin occupy the tg, set of orbitals. This average field wavefunction includes many of the low lying states of the Nijg cluster and should give a basis which is unbiased toward any particular state of the cluster. Dunning’s valence double-¢ contraction (9S5P|3S2P) augmented by polarization functions (D exponents 0.75, 0.80, 0.85) was used for car- bon, nitrogen, and oxygen.*? Hunzinaga’s four gaussian*” basis con- 2*! was used for hydro- tracted double zeta and scaled by a factor of 1. gens bound to nitrogen, carbon and oxygen. Hydrogen bound directly to the cluster was described by a double zeta contraction of Hunzinaga’s 42 four gaussian basis” unscaled. The internal coordinates and orientation relative to the surface of each chemisorbed species were optimized with the Nijs cluster described by the double zeta basis (DZ) without bond functions at the Hartree-Fock level. Every CH, and NH, intermediate was found to have its axis of sym- -175~- metry oriented perpendicular to the surface. The calculated internal coordinates of each chemisorbed molecule is listed in table VII. The dis- tance of each molecule from the surface (R,) was reoptimized with the double zeta plus bond functions basis at the GVB-CI level, while holding the internal coordinates fixed. The nearest neighbor distance between Ni atoms in the clusters was fixed at 2.487 KS The GVB-CI wavefunction is a full configuration interaction (CI) caleu- lation in which the orbitals were optimized at the GVB perfect-pairing (GVBPP) level.*9 For every complex studied here, except Ni,3C, we have used a GVBPP wavefunction where only the electrons in absorbate valence orbitals and metal-surface bonds were correlated. This generally corresponded to wavefunctions which contained four GVB pairs described by two orbitals each [GVB(4/8)]. The GVB-CI wavefunction for nitrogen on Nis, which has zero spin, contains 331 configurations and 492 spin eigen- functions. The chemisorbed carbon atom is an exception in that only seven electrons were localized on the carbon and in surface-carbon bonds. The wavefunction used to described this complex was a full CI in the orbitals described by three GVB pairs and the singly occupied Con, orbital. In appendix A we show results from RCI wavefunctions. This Cl wavefunction involves single and double excitations within each pair times single and double excitations in all other pairs. Excitations between pairs are not allowed. This calculation was felt to be a good test of basis set effects. The RCI wavefunction for nitrogen on Ni, contains 81 configurations and 150 spin eigenfunctions. The equibondedness reactions used to cancel correlation errors are shown in Table II. The total energies, zero point energies and enthalpies ~176- used to calculated the enthalpies of Table I are tabulated in Table I, II and Ill. The AHP for these reactions represent the difference in total energies from our calculations and estimated zero point energies. In each of this reactions the number of bonds to the surface and the total number of H- H, C-H and N-H bonds were held constant. Chemisorbed carbon did not fit well into this scheme because it appears to make between two and three bonds to the surface (two metal-carbon 7 bonds and a one-electron ionic o bond). Two reactions are shown to predict the AH? of chemisorbed car- bon. The second reaction (NijsCH + Ni,sH + NijgsC + He + Ni,s3) was not considered a fair cancellation of errors because in order for this reaction to be considered an equibondedness reaction chemisorbed carbon would have to make four bonds to the surface, which it is not able to do. We felt that using singlet methylene in the first reaction (2Ni;3H + (7A,)CHe > NiysC + 2@He + Nijg3) to cancel correlation errors was better because methylene is divalent and has a doubly occupied 2s orbital, like chem- isorbed carbon atom which has two surface m bonds and a doubly occu- pied 2s orbital. Unfortunately carbon has also picked up an extra elec- tron from the cluster, which we have not accounted for in our equibond- edness scheme. This will cause larger errors in our corrected surface- carbon enthalpy estimate. As a test of the accuracy of the equibondedness schemes we have cal- culated the enthalpy change for hydrogen abstraction from various gas phase CH, and NH, species. The results of these calculations are tabu- jated in Table VIII and give C-H and N-H bonds energies which agree with the experimental enthalpies to within + 6 kcal/mol, which justifies its use in these cluster calculations. Our calculated surface-O bond energy (157.2 kcal/mol) in Ni,30 is -177- disturbingly large. This is much larger than the experimental values (94- 134 kcal/mol) 19 but the experimental estimates are very uncertain since chemisorbed oxygen will tend to form oxides at higher temperatures. The fact that we calculate the reduction of oxygen to be uphill is disturb- ing and means that we must be overestimating the surface-oxygen bond strength by as much as 30 kcal/mol. This is most likely due to the small size of the cluster. We have calculated a surface-oxygen bond energy of 142.6 kcal/mol in NiggO at the same level of electronic correlation and basis set.** We can use this difference in bond energies to estimate a “cluster effect" of 15 kcal/mol. This correction applied to the Ni,,0 results derived from the equibondedness analysis gives a bond energy of 136 kcal/mol for oxygen chemisorption on Ni. This is in the range of bond energies found for oxygen on Ni polycrystalline films which range from 94 to 134 kcal/mol. !4 -178~ IV. Conclusions These results are at best qualitative estimates of the heat of forma- tion for various chemisorbed intermediates on Ni(100). Each step of the equibondedness procedure gives errors of approximately +7 kcal/mol. The Nig cluster appears to give bond strengths which are too large; an attempt to correct this bias yields reasonable energetics for NH, (x = 0-3) and CH, (x = 1-3). The energetics for carbon and oxygen chemisorption appear to have larger errors which are most likely due to cluster effects. Our results do indicate that it is energetically favorable to decompose NHg on Ni, that imidogen is the most stable NH, intermediate, and that methylidyne is the most stable CH, intermediate on Ni, all of which are consistent with experiment. We find that nitrogen-surface and carbon-surface 7 bonds are slightly stronger than the corresponding 9 bonds. This causes both CH, and NH, species to be oriented perpendicular to the surface and favors species which are multiply bonded to the surface. We feel that this is a general trend and can be extrapolated to the surface of bulk metals. -17T9- Appendix A. A. Introduction Upton and Goddard (UG)® have developed the basic approximations used in this work and applied them to large clusters of Ni atoms (up to 87 atoms).*° The heart of this method involves simulating the Ni atoms by a modified effective potential® (MEP) in which the Ar core and d® shell of electrons are included in the MEP. Only the 4s electrons of the Ni atoms are treated explicitly. UG made several tests of the frozen d® shell approximation, both for the electronic structure of the Nijs cluster“ and for chemisorption of hydrogen on Nigg.&46 These tests showed that the frozen d® shell was a good approximation for large clusters of Ni atoms and for chemisorption on them. uG*® felt that large clusters of atoms (20-87 atoms) were needed to simulate the bulk for chemisorption. This was only made feasible by using an unpolarized basis that contained a double zeta (DZ) 4s function for each Ni atom. In spite of the relatively large differences in the ioniza- tion potential (IP) (1.42, 2.46, and 1.63 eV for 13-, 19-, and 20-atom clus- ters), electron affinity (EA) (1.34, 1.89, and 1.47 eV), and cohesive energy (0.62 and 0.48 eV/atom) for the 13- and 19-atom clusters between the polarized and unpolarized basis sets,4> 4" UG felt that in order to mimic the bulk for chemisorption, it was more important to use large clusters approximately than to do highly accurate calculations on small clusters. This approximation appeared to be justified in that the IP and EA of large clusters approached those of the bulk metal as the clusters grew larger.” This result implied that the effect of polarization functions was less important for large clusters than small ones. -180- Siegbahn ef al.*® have also done tests on the effects of including Ni 3d electrons explicitly in cluster models of hydrogen chemisorption. These results basically confirm the conclusions of UG in that the replace- ment of d electrons by the MEP did not significantly affect the equili- brium properties of chemisorbed hydrogen atom. However, Siegbahn ef al.“® did find that the addition of polarization functions significantly altered the energetics (~10 kcal/mol per H atom) calculated for hydro- gen chemisorption. Siegbahn ef at.*® found that freezing the Ni d orbitals significantly affected their calculated barriers for the dissociative chemisorption of Hg. They found a barrier of 4.4 kcal/mol in calculations which include d orbitals, while they find a barrier of 48 kcal/mol for calculations in which the d orbitals were included in the MEP. These results indicate that the d orbitals played an important role in the barrier for activation of dihydro- gen but not for the equilibrium structure of hydrogen chemisorption. Upton*® has presented arguments based on the orbital phase continuity princple®® that suggest that low barriers for Hz dissociation on Ni can be obtained by just considering the s and p bands of the bulk. Although he did not completely optimize the transition state Hy dissociation, the lowest barrier he finds is 10 kcal/mol. This result directly contradicts the results of Siegbahn et al. We believe that Upton’s barrier is more reli- able since the wavefunction he used allowed the electrons in the conduc- tion band of the cluster to have the optimun spin coupling at the transi- tion state. Since dissociative chemisorption of Hz on Ni surface is known to be an unactivated process, the barrier height calculated by various methods should be a good test of their validity. Upton’s results show that the frozen d® shell approximation is valid for this process as well. ~181- Bauschlicher et al.°® have carried out calculations on chemisorption of oxygen ators on a small Ni cluster (five atoms) to test the effect of Ni polarization functions on the calculated parameters for oxygen chem- isorption. They found that polarization functions caused an increase in the distance of the oxygen atom from the surface (0.11 A) and a small increase in the vibrational frequencies (39 ecm™! out of 290 cm7}), Bauschlicher and co-workers have also tested the importance of d elec- trons for oxygen chemisorption on Ni(100)°! and for CO chemisorption on Ni(100).5* In both cases MEP Ni atoms were replaced by all-electron Ni atoms at the Hartree-Fock level (AEHF). The differences in these calcula- tions are not surprising in light of the fact that AEHF Ni atoms have a 28.7 kcal/mol bias”? favoring the °F (s*d®) versus 3D (s!d®) state of Ni atom, while the 10 e~ MEP was constructed to match the experimental state splitting (0.07 kcal/mol).™”. It is very likely that the Ni atoms in these studies have a significant amount of d® character that would have increased the 4s population of their wavefunction. This could very likely explain the long oxygen-surface distance (1.05 A AE versus 0.68 A MEP) for Nis50. It is well known that errors in the state splittings for Ni atom at the AEHF level can cause significant errors in description of the elec- tronic structure of molecules containing Ni. For example, AEHF predicts the ground state for NiCO to be 3A while good quality CI calculations predict the ground state to be 15.58 Thus all tests of the d® frozen shell approximation carried out with the 10 e~ MEP have shown that this approximation is valid. The AEHF tests conducted so far have given different results because of their bias towards the s*d° configuration and are therefore not fair tests. Until it becomes possible to do all electron CI calculations for Ni clusters in which the 5F-5D state splitting is well ~182- described, the MEP is a necessary and reasonable approximation for describing Ni clusters. In this appendix we demonstrate that for a large number of cases, the double-¢ cluster basis is not an adequate basis set for modelling chemisorption. Clusters described at the double-¢ level have basis set deficencies which cause errors in geometries, vibration frequencies and bond energies. It is shown that augmenting the double-¢ cluster basis with s gaussians placed at the tetrahedral and octahedral interstitials of the cluster (bond functions) give results as good as those in the basis set included p polarization functions. ~183- B. Results and Discussion The results of Siegbahn et al. ,48 Bauschlicher et al. 36:51 and the results presented in this appendix show that polarization functions are necessary for accurate cluster chemisorption studies. Test calculations for hydrogen (see Table AI) and nitrogen (see Table AII) chemisorption on Ni,3 show that clusters described by the DZ basis of UG are basis set deficient. In chemisorption studies, this basis set deficiency causes the cluster to compensate by using the basis set of the adsorbate, leading to bond energies that are too large and bond distances that are too short. Polarization functions also affect the ordering of electronic states in the cluster (see Table AIII). Basically, the lack of polarization functions favors high spin states because of weaker bonds between Ni atoms in the cluster. The major disadvantage of using p functions to polarize the basis set is that the size of the polarized basis is factor 3.5 times that of the DZ basis. For Ni,s3, the DZ basis contains 26 basis functions, while the DZ plus single-¢ p functions basis (DZP) contains 65 basis functions. The larger basis set will increase the computational effort by a factor of approxi- mately 39 (= 2.5%). The high computational cost of the DZP basis will make the study of the chemisorption of polyatomic molecules (i.e., CH, or NH) unpractical with the technology currently available to quantum chemists. An intermediate basis that corrects the basis set deficiency of clusters described with the DZ basis is one that uses bond functions at the octahedral and tetrahedral interstitials of the metal cluster. This basis set was found to mimic quite well the DZP results for hydrogen and nitrogen chemisorption (see Tables AI and AII) and the ordering of elec- tronic states for the Ni,5 cluster (see Table AIII). The advantage of bond functions is that the improvement in the basis set is concentrated where -184-— it is most needed, inside the cluster. This improvement is accomplished with smaller basis sets and considerable savings in cost. For Nij3, the DZ plus bond functions (DZB) basis, which contains 40 functions (26 Ni 4s functions plus one bond function each at six octahedral and eight tetrahedral intersitial sites), yielded a savings of 25 functions and 85% [1 - (40/ 65)*] of the computation effort over the DZP basis. The DZB basis should not be as flexible as the DZP basis in calculating geometries or cohesive energies of the clusters themselves. However, since we are hold- ing the geometry of the cluster fixed in these studies, the use of bond functions is an appropriate way to correct the artifacts due to the basis set deficiencies of clusters described by the DZ basis. A comparison of the results for various CH, and NH, species is shown in Table AIV for clus- ters described by the DZ and DZB basis sets. In general, the DZ basis results have shorter surface adsorbate dis- tances (R,) and larger dissociation energies than the DZB results. For larger R,, this basis set error gets smaller. This is consistent with the cluster using adsorbate basis functions at the DZ level, in that the effect appears to get smaller as the adsorbate moves farther away from the cluster. It is strongly recommended that all future calculations are per- formed either with the DZB or DZP basis sets. Although the other approx- imations made in this work may affect the accuracy of these calculations, correcting the basis set deficiency makes the method self-consistent in that larger basis sets should not affect the results toa significant extent. Because of the large number of atoms and the complicated nature of transition metals, a highly accurate method that would include all of the valence electrons and the differential electronic correlation effects of -185- large clusters is not yet feasible. -186- References (1) (2) (3) (4) (5) (6) (7) (9) (10) (11) For a recent review, see "The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis,” King, D. A; Woodruff, D. P., Eds., Elsevier: New York, 1982; Vol. 4. For a recent review, see Grimley, T. B. In “The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis," King, D. A.; Woodruff, D. P., Eds., Elsevier: New York, 1983; Vol. 2, Chapter 5. Kelly, R. D.; Goodman, D. W. In "The Chemical Physics of Solid Sur- _ faces and Heterogeneous Catalysis," King, D. A.: Woodruff, D. P., Eds., Elsevier: New York, 1982; Vol. 4, Chapter 10. Grunze, M. In "The Chemical Physics of Solid Surfaces and Hetero- geneous Catalysis,” King, D. A.; Woodruff, D. 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"Electronic Spectra of Polyatomic Molecules," Van Nostrand-Reinhold: New York, 1966; Huber, K. D.; Herzberg, G., “Constants of Diatomic Molecules," Van Nostrand-Reinhold: New York, 1979. The N-H bond strength was assumed to be the same as that in NH3, which was derived from the experimental enthalpies in Tables V and VIL. Toyoshima, I.; Somorjai, G. A. Catal. Rev. - Sci. Eng. 1979, 19, 105. Bauschlicher, Jr., C. W.; Cox, B.N. Surf. Sci. 1981, 108, 483-502. Rappé, A. K., Goddard III, W. A. In ‘Potential Energy Surfaces and Dynamics Calculations,” Truhlar, D.G., Ed., Plenum Press: New York, 1981; pp. 661-684. Bertolini, J. C.; Tardy, B. Surf. Sci. 1981, 102, 131-150. (a) Goodman, D.W.; Kelly, R.D.; Madey, T.E.; White, J.M. J. Catal. 1980, 64, 479-481; (b) Dadayan, K.A.;; Boreskov, G.K.; Savchencko, V.I.; Bulgakov, N.N. Kinet. Catal. (Engl. Trans.) 1977, 18, 480-481; Kinet. Katal. 1977, 974-575; Dadayan, K.A.; Boreskov, G.K.; Savchencko, V.I.; Bulgakov, N.N.; Smolikov, M.D. Dokl. Acad. 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In “Vibrations at Surfaces,'’ Caudano, R.; Guilles, J.-M.; Lucas, A.A., Eds., Plenum Press: New York, 1982. Rahman, T.; Black, J.E.; Mills, D.L. Phys. Rev. Lett. 1981, 46, 1469- 1472. (a} Norman, D; Stohr, J.; Jaeger, R.; Durham, PJ.; Pendry, J.B. Phys. Rev. Lett. 1983, 5/, 2052-2055; (b) Stohr, J.; Jaeger, R.; Kendelewicz, T. Phys. Rev. Lett. 1982, 49, 142-146; (c) Demuth, J.E.; Dinardo, N.J.; Cargill II], G.S. Phys. Rev. Lett. 1983, 50, 1373-1376. In this paper the authors propose a structure for the c(2x2) O overlayer in which the oxygen atom has moved 0.3 A along the <110> direction. This results in two shorter Ni-O (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) -189- distances of 1.74 A and two longer distances of 2.14 A. The shorter distance is in agreement with the Ni-O distance calculated by uG8 of 1.78 A, (d) Tong, S.Y.; Lau, K.H. Phys. Rev. B 1982, 25, 7382-7387. The analysis of the LEED data in this paper was shown to be consistent with a surface-oxygen distance of either less than 0.1 A or 0.9 A. Petersson, L.G.; Kono, 3.; Hall, N.F.T; Goldberg, S.; Lloyd, J.T.; Fad- ley, C.S.; Pendry, J.B. Mater. Sci. Eng. 1980, 42, 111-119. Bauschlicher, Jr., C. W.; Walch, S. P.; Bagus, P. S.; Brundle, C. R. Phys. Rev. Lett. 1983, 50, 864. stensgaard, I.; Jakobsen, F. Phys. Rev. Lett. 1985, 54, 711-713. Reider, K.H.; Wilsch, H. Surf. Sci. 1983, 131, 245-257. Andersson, 5. Chem. Phys. Lett. 1978, 55, 185-188. Onuferko, J.H.; Woodruff, D.P.; Holland, B.W. Surf. Sci. 1979, 8&7, 357-374. Dunning, T. H.; Hay, D. J. In “Modern Theoretical Chemistry," Schaefer II], H. F., Ed.; Plenum Press: New York, 1977; Vol. 3, Chapter 1, pp 1 - 27. Huzinaga, 5. J. Chem. Phys. 1965, 42, 1293-1302. Bobrowicz, F. W.; Goddard III, W. A. In ‘Modern Theoretical Chemis- try: Methods of Electronic Structure Theory," Schaefer III, H. F., Ed.; Plenum Press: New York, 1977; Vol. 3, Chapter 4, pp 79-127. The same Nigg cluster was used by UG® to model the bulk for chem- isorption. (45) (46) (47) (48) (49) (50) (51) (52) (53) (54) (55) (36) -190- — Melius, C. F.; Upton, T. H.; Goddard III, W. A. Solid State Commun. 1978, 28, 501-504. Upton, T. H., Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 1980. Upton, T. H.; Goddard HI, W. A. J. Vac. Sct. Technol, 1979, 16, 531- 035. Siegbahn, P. E. M.; Blomberg, M. R. A.; Bauschlicher, Jr., C. W. J. Chem. Phys. 1984, 81, 2103-2111. Upton, T.H. J. Am. Chem. Soc. 1984, 106, 1561-1571. Goddard III, W.A. J. Am. Chem. Soc, 1972, 94, 793-807. Bauschlicher, Jr., C. W.; Bagus, P. S. Phys. Rev. Lett. 1984, 52, 200-203. . Bagus, P.S.; Bauschlicher, Jr., C. W.; Nelin, N. J.; Laskowski, B. C.; Seel, B.C. J. Chem. Phys. 1984, 81, 3594-3602. Martin, R. L.; Hay, P. J. J. Chem. Phys. 1981, 75, 4539-4545. Sollenberger M., M.S. Thesis, California Institute of Technology, Pasadena, CA, 1977. Moore, C. E. "Atomic Energy Levels,’ National Bureau of Standards: Washington, DC, 1971; Vol. II. (These state splittings were averaged over j states to cancei out spin-orbit coupling.) (a) Rives, A. B.; Fenske, R. F. J. Chem. Phys. 1981, 75, 1293-1302; (b) Ha, T.; Nguyen. M. T. J. Mol. Struct. (Theochem) 1984, 109, 331- 338. -191-— Table I. GVB-CI Parameters for Chemisorption on Four-Coordinate (100) Site of Ni;5. Chemisorbed/R(Ni-X)} Ry w,°) D, Total |Corrected|CorrectedjGround| Zero Species (A) | (A) (em™}\(xcel/mol)) Energy Do AHP | State | Point (a.u.) | (kcal/mol) | (kcal/mol) lEnergy (kcal /maol) c 1.957 0.858 390 142.1 -42.1654 144.8 24.8 "A, 1.7 CH 1.991 0.934 457 175.5° ~42.6130 153.6 “12.4 1A 6.5 CH, 2.051 1.056 490 111.8 -~43.3735 101.1 6.9 2B. 15.6 CH,” 2.223 1.360 341 53.4 43.9983 43.6 -7.7 3a” 22.9 N 1.848 0.569 347 141.3 -58.8561 154.6 -22.1 ta, 1.5 NH 1.960 0.910 482 129.4 -59.4426 117.0 -32.7 1A, 9.2 NH2 2.102 1.152 424 6813 -58.9987 70.6 -25.5 3B, 17.2 NH,” 2.702 2.052 129 2.04 -60.5369 -1.6 “7.7 4a" 24.8 NHs*) 2.092 2.092 354 15.0 -61.0079 100 -193 1a’ 26.0 co) 2.017 2.017 330 17.5 -117.6932 30.09 +572 ta, +) ) 1.897 0.712 380 157.2 -79.3197 151.3 -923 29 1.6 H 1.908 0.740 645 656 -4.6904 631" -115) 3, 3.6 ®) The reduced mass used to calculate vibrational frequencies was the same as a die- tomic in which one atom had a mass equal to the mass of four Ni atoms and the other atom had the mass of the chemisorbed species. >) The zero point energies were based on w,, frequencies from calculations with the DZ cluster basis and estimated frequencies. ©) Relative to 42- methylidyne dissociated limit (Total energy of ‘£~ methylidyne is -38.2876 hartrees.) 4) Geometry optimized at the GVB-perfect pairing level. ° Chemisorption on one-coordinate site of Ni,,. Experimental value for Dp (M-CO). (see ref. 18) ®) Not evaluated since not used in equibondedness reactions (see table II). ») Experimental value for Do (M-H) (see ref. 11) ~192- Table II. Equibondedness Reactions Used to Calculate AH? for Chemisorbed Species Shown in Table I. (All energies are kcal/mol.) Reaction AH? Calculated Quantity CH, + NijgH + Ni,gCHs + He 19.6 AHP(Ni,gCH3) = -7.7 Ni,sCH3 + NijgsH > NijgCHy + He + Nijg 10.5 AH?(Ni,3;CHg) = -8.9 Ni,gCHe + NijgH ~» Ni,sCH + He + Nijs 8.0 AH~(Ni,3CH) = -12.4 2[NijsH] + ('A\)CHg > NijgC + 2He+Nijyg -53.5 AHP(NiygC) = 24.8 Ni,sC—H + Nijs-H > Ni,gC + He + Nijg 62.9 AHP(Ni,,C) = 39.0 Ni,gNH3 + NijgH > NijgNHe + He -6.3. AH/(NijgNHe) = -25.5 Ni,gNHz + Ni,;sH > Ni,gNH + He 4.3. AHP(Ni,3NH) = -32.7 Ni,gNH + NijsH > Ni,sN + He 22.1 AHP(NijsN) = -22.1 2[Ni;sH] + HzO > Ni,gO0 + 2He + Nijg -12.2 AHP(Ny30) = -92.3 -193- Table IT. Total Energies, Zero Point Energies, and AH? for Molecules Used in Table II. Total Energy Zero Point) Nt) Molecule GVB-CI (hartrees) Energy (kcal/mol) (kcal/mol) Hp “1.1445 6.3 0.0 CH, 40.2771 27.1 -16.0 NHg -56.2979 21.0 -9.3 H,0 ~76.1495 12.9 -57.1 Co -112.9192 3.1 “27.2 (7A,) CHe -38.9396 15.6 101.39 (4T1.) Nis” -4.2357 - 0.0 (Are) Niza”? -4,6861 - 0.0 ®) Calculated at experimental geometry; (ref. 13) >) Calculated with experimental vibrational frequencies (ref. 13). ©) D. R. Stull and H. Prophet, JANAF Thermochemical Tables, National Standard Reference Data Series (National Bureau of Standards, Washing- ton, DC, 1971), NSRDS-NBS 37. 4) aH,[(5B,)(CHg] + AE(5B, > 1A,), state splitting (9.1 kcal/mol), from L. B. Harding and W. A. Goddard III, Chem. Phys. Lett., 55, 217-220 (1978). ©) We have assumed that the heat of formation of the Ni cluster is the same as the bulk and that the zero point energy of the cluster is essen- tially constant during the reactions studied here. The geometries of the Ni;3 and Ni,, clusters are described in the text. ~194~ Table IV. Calculated Total Energies, Zero Point Energies and Experimental Enthalpies at 0°K for Various Radicals Used in This Paper.) Total Energy Zero Point AH? Molecule GVB-Cl(hartrees) energy (kcal/mol) (kcal/mol) H -0.4993 0.0 51.6 C -37.7033 0.0 169.6 CH -38.3100 41 141.2 CHe -38.9597 10.4 92.2») CHg -39.6176 18.2 35.9°) N -54.3972 0.0 112.5 NH -55.0008 4.7 84.3%) NHe -55.6335 11.2 45.1°) 9) ~74.8274 0.0 59.0 ®) Values are from JANAF [footnote (c), Table V] unless otherwise specified. Geometries and vibrational frequencies are those of reference 13. ) McMillen, D. F.; Golden,D. M., Ann. Rev. Phys. Chem., 33, 493-532 (1982). This value was extrapolated to 0° K from AH og = 35.1 kcal/mol. ©) Chase, M.W.; Curnutt, J.L.; Prophey, H.; McDonald, R.A.; Syverud, A.N., J. Phys. Chem. Ref. Data, 1975, 4, 1-175. 4) Foner, S.N.; Hudson, R.L., J. Chem. Phys., 1981, 74, 5017-5021. e) Bohme, D.K.; Hemsworth, R.S.; Rundle, H.W., J. Chem. Phys., 1973, 59, 77-81. -195- Table V. Reactions for Ammonia Decompositon. (see figure 13) AH? (kcal/mol) ovr oOo on fF Hw NW NH) ~ NHafa) NH) * NHawe) + 4 Hayy NHge) * NH) + 4 Heyy NH) > Nea) + 2 Ha) No > RNa) Nga) * NHawa + He) NHaa) > NH) + Ha) NH) * Ney + He) -10.0 ~6.2 “7.2 10.6 22.1 -17.7 -18.7 -0.9 -196- Table VI. Reactions for Methanation. (see figure 14) AH? (kcal/mol) 1 COg) + CO(e) -30.0 2 CO) + Cray + Oe) -10.3 3 Of) + Hag) + He) 35.2 4 Cray + ’Horg) » CHe) -37.2 5 CHa, + ’Hegy + CHa) 3.5 6 CHaay + ’Hag + CHyray 1.2 7 CHsay + ’Haey > CHa) -8.3 8 sameas 1 9 OQ) + 2H) > He0¢) 58.2 10 Cray + Hye > CHa) “25.7 11 CH, + Hay + CHaray 15.0 12 CHa) + Hay > CHaay 12.7 13 CHgay + Hay > CHagy 3.2 -197- Table VII. Internal coordinates of AH, (where A = N or C) used in this study. Chemisorbed Internal Coordinate of Fragment Species A-H distance (A) H-A-H angle (degrees) NH 1.013 NH» 1.017 97.7 NH3 1.003 105.1 CH 1.095 CHo 1.107 100.4 CHs 1.094 104.1 ~198. Table VIL. Test of Equibondedness Reactions (in keal / mol). Reaction AH? (exp) AHP (GVB-CI) Error C+H, >CH+H 23.2 21.9 -1.3 CH+H, ~ CHg+H 2.6 -2.8 -5.4 CHp + Hz > CH3 +H -5.0 -6.5 1.5 CH3 + Hg > CHy+H -0.3 -6.4 “6.1 N+H, > NH+H 23.4 24.5 1.2 NH +H, > NH2 +H 12.4 7.6 -4.8 NH2 + He > NH3 + H -2.8 -8.5 -5.7 -199- Table Al. Hydrogen C Ch ochenetien on Ni,3™ Leve) of Basis R, o>) Bond Energy Total Energy Calculation Set (4) (em7?) (kcal/mol) (hartrees) HF DZ 0.355 | 637 60.0 -4.6190 GVB(1/2) | DZ 0.385 | 659 67.1 -4.6301 RCI(1/2) DZ 0.368 | 661 67.3 ~4.6304 HF DZP 0.680 828 58.6 4.9125 GVB(1/2) DZFP 0.726 614 66.7 -4,9254 RCI(1/2) DZP 0.724 804 66.9 4.9256 HF DZB 0.730 B91 57.2 -4.B266 GVB(1/2) pzB | 0.764 | 871 65.4 -4.8393 RCI(1/2) DZB 0.740 845 65.6 -4.8394 ®) The bond lengths (R,), vibrational (w,), bond energies, and total ener- gies are extrapolated from spline fits to calculated values. >) The vibrational frequencies were calculated using the reduced mass for a hydrogen atom and a particle four times the mass of a nickel atom; uz = 1.0035 atomic mass units. -200- Table All. Basis Set Effects on Nitrogen Chemisorption on Ni,3.™ Level of Basis R w >) Bond Energy | Total Energy Calculation Set (A) (em7?) (kcal/mol) (hartrees) HF DZ 0.157 410 71.5 -58.4584 GVB(4/8) DZ 0.205 | 387 106.6 -58.5173 RCI(4/8) DZ 0.232 352 146.2 -58.5804 HF DZP 0.442 325 52.7 -58.7239 GVB(4/8) DZP 0.550 308 93.4 -58.7917 RCI(4/8) DZP | 0.511 332 133.5 -58.8556 HF DZB 0.487 325 50.7 -58.6370 GVB(4/8) DZB | 0.612 320 91.8 -58.7055 RCI(4/8) DZB | 0.550 320 130.7 -58.7675 ®) The bond lengths (R,), vibrational (w,), bond energies, and total ener- gies are extrapolated from spline fits to calculated values. The Nitrogen basis used for these calculations was a double-¢ contraction of Rappé’s "fours" basis (see table AV). >) The vibrational frequencies were calculated using the reduced mass for a nitrogen atom four times the mass of a nickel atom; yw = 13.2084. -201- ‘syas sISeq GZ PUe dZC at} UI Joj paajos sem aze}s "Ty, AB19u9 ysamoy ayy ATU (2 Y G29Pbe P- SI SIseq AZq OY} Ut SIN Joy AdLaUA [e107 AY], (p Y PEEP SI SISeq {ZC 94) Ul SHIN Joy ABrauA [210 SUL, (, "Y 90ZO'P- ST Stseq 7 a4} Ut FIN Joy ABTaua [2107 GUL (q “UMOYS you are saye1s asayy Jo [Te 10] patdnoso Ajqnop ase Yona syeqyiqse "4, pue "ey ayy (e 611 get 22 i t I I t cry Te £01 i 1 I I i ity, Ve- i i i 2 | ily 9g 28 vel t 1 1 2 L, Z01 gel SAT 1 1 1 2 1, (p0 (20 (q0 1] 2|2) ez wa va | tee (el—228) | (gh—gx) | (24) | (2x) | (4x) amg aza a en i a (joul/{eay) s#uryYds ayeis aloryeinsyuo) “Sty Jo s#un dg eye}g Uo sayy 78g siseg ‘THY F199, ‘(AV 9198} 388) siseq ,Smo, s,pddey JO WoTpOeI}UOD )-a[qnop e@ SBM SUOT}EIMITeD 7 JO] siseq ussoIzU at] (a ‘TaadT (8/P)IOY 94172 paeullojiad [fe a1aM SUOT}ETNI[eO asa], (e OCG EP- eee. ep- res 488 WE | SLE} GET | eget ®H9 Wg zeoeep- | cezter OTIt | t1et| oer | Top | Aso'l | seao _ *HO "a, TL0B '2F- Ogeo'et- = SEAT 9°06T LoP7 bor | VEG'O | 220 HO V, E0gT er- QL96'Th- 6 BET Berl | Elh | CEB | EERO | SCEO #) We ’ 61ES"09- ese 09 ee 802 6el | ge | SOS) 2ST fHN Wy 8 266 '6S- 2be.'6s- 608 9°66 ger | cor | ST | e90T *HN *a5 ' P9EP'6S- E641 '6S-| A Le G6el | Per | 94% | 8060 | 4080 HN We 29¢9'8S- bORS'BS-| 1 PET oovl| GE | ese | ISG’O | see°0 N Wy, azd (qzd aza yACi azqd | 2d | azd vACI saloadg 3721S (searjaey) AB1aUg 1e1O]) (jour/Te0q) °G (,-W9) Teo (y) Ty Peqiosiulayy) | punory co 'IN J0 811s ayeUTps00j Noy aq} Uo () JO N = ¥ Aaya) "HY UO suOTOUNY puog Jo sayy “AV FIGVBL ~203- Table AV. The (7s4p[3s2p) Contraction of Rappé’s "Fours" Nitrogen basis set”) Component Type Exponent Coefficient i 5 588.790042 0.0207721952 2 5 88.7013675 0.142129065 3 iS) 19.8226575 0.479025723 4 S 5.26862757 0.500943653 1 5 7.003173828 -0.195396724 2 5 0.767161436 1.07488965 1 iS) 0.231739294 1.00000000 1 P 13.5561742 0.0589506223 2 Pp 2.92431073 0.320281888 3 Pp 0.799357604 0.753138039 1 Pp 0.219198754 1.00000000 ®) Rappé, A.K.; Goddard, W.A., III, unpublished results ‘ayIS ayeUIps00d- 8U0 otf} SYIVUI MOIIe al], “Iaysnjo *TN aul, “eg andy -205~ -206- Carbon- Surface o Bond bia {001} [oid] {O10} Carbon - Surface 7 Bond One / | ~ One | ds « \e / NG] ee / [001] so rT a ee | | | {010} [010] Carbon-Hydrogen Bond fool] {010} [010] Figure 3. ‘he GVB orbitals for Ni,sCH [from the GVB(4/8)-PP wavefunc- tion]. Nuclei in the plane are indicated by asterisks. Positive contours are solid, negative contours are dotted, and nodal lines are long dashes. The spacing between contours is 0.02 a.u. -207- Carbon- Surface o Bond One ¢o] {Ome db SS / [001] SS [PA ee aT OM WTF FONT © TOI0] (O10) Carbon- Surface 7r Bond One/ | ‘ge One | +s ann | [ool] faio) foio] Carbon-Hydrogen Bond / \ { \ [oo] S~ [o10] Figure 4. The GVB orbitals for the Ni,sCH2 cluster. [001] -208-— Hee yn a. Carbon- Hydrogen Bond Pair zs One \ $o One dp Mak A \\ “ / \ a / \ . XN W4 \ \L ee \ Nee NS [PAIRED] \— | \ | \ | | [ ! [110] [110] Carbon- Surface Bond Pair (ore One {110} [110] Figure 5. The GVB orbitals for the Ni,3CHg cluster. -209- Carbon Lone Pair One fo \ aq] {One / Nb \ / \ / \ / \ }/ ' J foo] [PAIRED] \ x ae PONE Ww Ne foro] {010} Carbon- Surface m7 Bond {o10] Figure 6. The GVB orbitals for the NijsC cluster. -210- Nitrogen-Hydrogen o Bond ONE {001} a a a mm * {o10] [O10] Nitrogen-Surface m7 Bond ONE 7 | \ & | [ONE | ¢, NL : — x | & | | {o10] Nitrogen- Surface o Bond ONE ¢,| [ONE $, [ool] aa [PAIRED Sa — “co SN —_— =a “To —_——! Te a WW WW [010] {010} Figure 7. The GVB orbitals for the Ni,3NH cluster. -211- Nitrogen- Hydrogen o Bond ONE “¢, ONE / [001] ~ x \ x ™ | * | / | id [100] [100] Nitrogen-Surface o Bond ONE | |ONE oe %, [oo] Figure 8. The GVB orbitals for the Ni,3NHp cluster. {001} [100] [100] Nitrogen- Surface o Bond ONE rg a i { \ \ } \ = / (001) SSO" PAIR & % L_ _ . —— - [!00} [100] ~ Figure 9. The GVB orbitals for the Ni,3NH3 cluster. @213- Nitrogen- Surface o Bond One ¢g| | One dp [ool] [O10] (010) Nitrogen-Surfoce 7 Bond ~ ) | mee 4 ¢,| {One | da / | / . \ ¥ {oor} So a | | | [oi] Nitrogen-Lone Pair One de} |One ot [oo] foe ON ~~ ee” x x g R [o10) {010} Figure 10. The GVB orbitals for the Ni,,N cluster. ~214- One $| {One $p [001] [100] [100] Oxygen sp Lone Pair One dc One oa [ool] / {100} [100] Figure 11. The GVB orbitals for the o orbitals of the Ni,30 cluster. ~215~ Oxygen Py Lone Pair [ool] Oxygen 7 Bond Pair One. eo dg One | x “ NN a | ol ——1PA oF | | x | x | | [100] Figure 12. The GVB orbitals for the 7 orbitals of the Ni,30 cluster. ‘uor}Isoduiosaq eiuoury 10} Waavjay Sazywipauazyy] Jo} (jow,|vox) saidjeyjuy “Fy anda TT TT T_ Tr H €+N ~216- [OW jDOy -21T- aL -40- y +H +H20 aL CHs +4 Hg +20 i kcal /mol ~t00 “OF -i20 a -126.2 C+6H it “130 71365 OL o+eH deh L Figure 14. Enthalpies (kcal/mol) for Intermediates Relavent for Metha- nation.