Modified effective potentials for transition metal atoms Citation Sollenberger, Michael J. (1975) Modified effective potentials for transition metal atoms. Master's thesis, California Institute of Technology. doi:10.7907/HC7N-TD51. https://resolver.caltech.edu/CaltechTHESIS:03292010-083257156 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: Chemistry Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 6 June 1975 Record Number: CaltechTHESIS:03292010-083257156 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:03292010-083257156 DOI: 10.7907/HC7N-TD51 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 5638 Collection: CaltechTHESIS Deposited By: Tony Diaz Deposited On: 15 Apr 2010 19:08 Last Modified: 21 Dec 2019 02:33 Thesis Files Preview PDF - Final Version See Usage Policy. 724kB Repository Staff Only: item control page

Modified Effective Potentials for Transition Metal Atoms Thesis by MICHAEL J. SOLLENBERGER In Partial Fulfillment of the Requirements TA nw. Ln Wha wn Hf PUL US woyeys. ce ul Master of Science California Institute of Technology Pasadena, California 1975 (Submitted June 6, 1975) I. Introduction Melius, Olafson and Goddard! have developed techniques for obtaining ab initio effective potentials to replace the core electrons of transition metals and still obtain ab initio quality descriptions of the valence electrons (4s, 4p and 3d). Using these ab initio effective potentials (AI-EP) in calculations of various electronic states of atoms and molecules leads to good agreement with the results of full-electron ab initio calculations. However, for transition metals such as Ni and Fe, even extensive ab initio calculations agree poorly with experi- mental results. For example, for Ni the separation of the °D (s'd’) and *F (s"d°) states should be 0.03 eV, whereas ab initio calculations using a large basis Set yield a separation Of -2.29 eV. The ailficuity nere seems to involve correlations among the d orbitals. To include such effects would require f basis functions (very expensive for molecules) and extensive configuration interaction. In this paper, we propose an alternate approach in which the effective potential is modified to include in an average way these var- ious correlation effects. The form of the modification is based on simple ideas concerning the role of such correlation effects and the magnitude of the modifications are determined so as to yield correct excitation energies and ionization potentials for the atom. In this paper we obtain modified effective potentials (MEP) for Ni and Fe, and they are tested by solving for the potential curves of several states of NiH and FeH. Ii. Modified Effective Potential As mentioned above, the °F (s?d°) state of Ni should be 0.03 ev? above the °D(s'd°) state, whereas ab initio Hartree-Fock calculations* place the °F state 2.29 eV below the °D state. We believe that this is a result of the extra correlation error in the “D state due to the additional doubly-occupied d orbital. Including these correlation effects will lead to a slight contraction of the d orbitals and a sub- stantial decrease in the total energies of both states, but an appropriately larger decrease in favor of the °D state. We include these correlation effects by adding an additional term, V @? to the d effective potential. In doing so we apply two restrictions: | (a) Orbitals centered on atoms far from the Ni-or Fe atom being considered should not be affected by the correlations in the d orbitals. Thus we require that we) [ Vgolr)r° dr = 0 0 for p = constant and for p = lr]. (ob) The new orbitals obtained using V d should be concentrated in the same region as the original ab initio orbitals (since the correla- tions lead to only a slight contraction of the d orbitals with little change in electron density). Similar considerations apply to the 4s orbital. Even for the sa? states there are considerable correlation corrections involving the 4s orbitals. A simple way to think about this is to consider that an elec- tron in the 4s orbital will polarize the core and thus decrease its | -energy. These effects are included in correlation terms such as 4s — 4p simultaneous with 3p — 3d and 4s — 4p simultaneous with 3d — 4f, but are excluded from Hartree-Fock calculations. We expect these correlation terms to result in only a small change in the shape of the 4s orbital and hence have applied restrictions (a) and (b) above to a modified s potential Ve- g and a modified p potential Vp- a Each correction term Vy is given by -a,r° -B r’ xT 1 g £ which is of the same form as the AI-EP: Applying condition (a) above leads to Yg = 4p5/ay for p = constant 2 or equivalently to ay = By /4 ¥ = 4By Condition (b) above was satisfied through the following pro- cedure: a typical s or d orbital? (yr) was plotted against Ve. q OF Va over a range of 8. As a Starting point, we used the values of Beg and Bag for which the minimum of Vy occurred at the maximum amplitude of the corresponding orbital. An SCF calculation was necessary to determine the final values, as the shapes of the orbitals proved to be very Sensitive functions of 8. We chose By. d to equal Bz_g- The final results are shown in Table I. The AI-EP and MEP orbitals are compared in Figures 1-4. The values of C g were then varied to yield the correct sepa- rations for the following key states of Ni and Fe, respectively: the lowest-lving e* CF and "D), ¢ (Gn and °F) and stn’ CD and "D) states of the atom and the lowest-lying ionic state ("D(s°d) and °D(s‘d°)). The optimum values are listed in Table I. The MEP's are tabulated in Table I, and Vy is shown in relation to V, (AI-MEP) and V, (MEP) in Figures 5-10, A guiding principle in this approach to modifying effective potentials is to obtain potentials that lead to orbital shapes consistent with those that would be obtained from accurate ab initio calculations, In this way we may expect that orbitals on different centers will over- lap and interact correctly and hence lead to accurate bond energies, bond lengths.and potential curves. Note that no molecular information is used in determining the effective potential. Tl. Basis Set Information The basis sets are from those optimized by Wachters® for the ground states of the neutral atoms. We use all five d primitives, but the four tightest functions are contracted together with relative coef- ficients from Wachters' Hartree-Fock calculations, As discussed elsewhere, 1 only the outer four of Wachters' 4s functions are required for describing the coreless Hartree-Fock orbital of the AI-EP. The tightest two of these functions were contracted using relative coef- ficients from a Hartree-Fock calculation on the high spin state (s*a® for Ni and sd’ for Fe). We used four p basis functions with orbital exponents of 0.85 times the value of the corresponding s function. The tightest three p basis functions were contracted together based on the p orbital from the Ni s'pd’ and Fe s'p'd’ high spin state. For the calculations on NiH and FeH, the H basis consisted of four s functions (based on 6 = 1.0) contracted to two, plus a PB, basis function with orbital exponent 0.230. These basis sets are summarized in Table ITI. IV. Results A. Nickel The nickel MEP was tested on various states of Ni, Ni* and Ni**. The highest spin state of the basic configurations (s'd°, s’*d° d’° and s'p'd> for Ni; d°’ ands d° for Ni* ; d° for Ni**) were solved for at the Hartree-Fock level. The resulting s and d orbitals were then used as a basis for a complete (denoted hereinafter as | GVB-CI) CI to obtain the higher states. These results are summar- . ized in Table IV. The key states mentioned in Section II (*F, °D, "D, and 7D) are all within 0.04 eV of the experimental excitation energy. In every case, the CI calculations give correct orderings and reason- abie separations for the excited states. The results are poorest ior the *S(d*°) state, the excitation energy being over 3 eV too high (this is, however, about 4.5 eV better than the AI-EP results). B. Iron Table V was prepared in a similar fashion for iron. The con- figurations used for Hartree-Fock calculations were sd’, s'd’, s'p'd® and d@ for Fe, s'd° and d? for Fe’, and d® for Fe'*. The key states (D, °F, "D and “D) are fit within 0.03 eV. The *F (d’) state of Fe* was used as an additional test when determining Coq andC,: this state was 0. 93 eV too high, as it was not possible to fit both the °D (s'd’) and *F (d”) states of the ion. This is probably due to the large differences at the AI-EP level (the ’D state is 2.04 eV too low whereas the °F state is high by only 0.45 eV). These states required greatly different degrees of modification to obtain an accurate description. The CI calculation lowered the *F state by 0.15 eV. As with nickel, the Ss’ state of the atom is almost 4 eV too high using the MEP, but about 3.5 eV better than with the AI-EP. The | CI results are generally good, but there are some incorrect orderings of states for Fe’ and Fe'*. These are, though, small and occur in Cis of lower spin than that of the corresponding Hartree-Fock calcu- lation (the nickel CIs were of the same spin). C. Ni We carried out calculations on NiH to determine the accuracy of the MEP in describing the interaction of Ni with another atom. In order to correctly describe dissociation of the maclecule, we correlated the orbitals forming the NiH bond (a GVB(1) calculation). 6 The energies for various internuclear distances are listed in Table VI. These points were fit with a cubic spline curve (Figure 11) and the results are summarized in Table VII. The agreement is quite good: for the “A state, the experimental values’ are R, = 2.79 b and w ~ 2000 cm™*, whereas we obtain 2.74 b and 1911. cm™. The bond energy of this state is not well known, but Gaydon® gives 2,640.3 eV and we obtained 2.88 eV. The GVB orbitals are plotted in Figure 12. D. FeH We calculated potential curves for the *A and “TL states of Fed, each of which involve basically an Fe sd’ configuration for small R. At large R, there are difficulties in solving for these states since the Fe s*d° state is 0.87 eV lower at R = © and also leads to “A and “II states. Thus for R> 4.0b, we solved for the °A states using an Fe sd’ configuration. 9 The potential curves are based on GVB-CI's using the s and d orbitals from the SCF calculation [GVB(1) quartet for R = 4.0b and Hartree-Fock sextet for R>4.0b]. The points used for the cubic spline fit (Figure 13) are given in Table VII. The spectroscopic data are summarized in Table IX, and the GVB orbitals are shown in Figure 14. Table I, The parameters of the correlation term, Vos for the MEP @ yr" B r a 1 ““s£ “Pg Ni Fe Bog 0.15 0.12 By-g 0.15 0.12 By 2.0 1.5 Coq 1.50 2.05 Coed 0.50 0.60 Cc 0.85 0.87 Table I. The total MEP for Ni and Fe (V)= z C,. r k n -t.r? Ke oer Ni Fe n i Cc ¢ Cc -2 0.959 7,465 0.980 7.968 0 0.504 0.848 0.499 1.290 0 8.87 -28.67 9.44 -51.14 Vs-d -2 0.0375 1.50 0.03 2.05 0 0.15 - 0.90 0.12 - 9.84 -2 0.50 - 0.85 0.375 - 0.87 0 2.00 6.80 1.50 5.22 -2 0.465 4,807 0.388 4,457 0 5. 02 23.61 5.97 31.98 Vv -2 0.0375 0.50 0.03 0.60 p-d 0 0.15 - 0.30 0.12 - 2.88 -2 0.50 - 0.85 0.375 - 0.87 0 2.0 6.80 1.50 5,22 ~-1 21.66 - 9,827 19.88 - 9,925 -1 0.659 - 1.247 0.591 - 1.380 Va 0 5.02 -12.84 4.52 -12.66 -2 0.50 0.85 0.375 0.87 0 2.00 - 6.80 1.50 - 5.22 Table II. Basis set summary. Ni Fe H C Cc " g C e Cc 2.39417 | -0.01060 | 2.01847 | -0.01462 | 13.362 | 0.01906 0.918169 | -0.12519 | 0.779935 | -0.13323 | 2.013 | 0.13424 S | 0.130176 | --- 0.114220 | --- 0.454 | 0.47449 0.046392 | --- 0.041889 | --- 0.123 --- 2.03504 | -0.02586 | 1.71570 | -0.03653 | 0.2307] -- - 0.780444 | 0.03847 | 0.662945 | 0.07605 | -- - --- P | 0.110650 | 0.62107 | 0.097087 | 0.69593 | --- -.=- 0.039433 | --- 0.035606 | - - - ~ a _..- 48, 9403 0.02706 | 41,4526 0.02511 | --- _-- 13.7169 0.14598 | 11,5403 0.13626 | -- - _..- d | 4,63951 0.36418 | 3.88543 0.35323 | --- -.- 1.57433 0.46438 | 1.32380 0.46867 | --- _.- 0.486409 | - - - 0.416680 | - - - ee -..- “p, only Table IV. Energy comparisons for various states of Ni, Ni* and Nit* {all energies are in eV). Modified Effective Potential GvB- cr AI-EP State Experi- |Hartree-| Hartree-| *D(s'a°) *F(s’a") 's(a!°)? *p(s'p'a)® *pia®)f *E(s'a®) *F(a°)8 ment Fock Fock 5 (s'a°) 0 2.29 0? 0 0 0 0 0 0 0 S¥(57d°) 0.03 0 0.03 0.03 *p(s'd) 0.33 0.31 *pis’a®) | 1.59 1.66 *g (a*°) 1.74 9.58 5.14 4,99 Sp(s?a°) 1.86 2.52 *G(s?a°) 2.65 3.23 5p(s'p'd’) | 3.22 1,93 3.18 3.05 5G(s'p'd’) | 3.37 3.14 *F(s'p'd®) | 3.55 3.31 *s(s?d°) -- 7.84 *p(s‘p'a’) | - - 5.36 *p(s'p'd*)} = - 5.74 5g(s'p'd®) | - - 6.19 *p(a’) 7.62 8.26 7.60 7.53 *F(s'd®) | 8.70 | 6.70 .| 8.46 8.46 *p(s'a’) | 10.63 10. 94 NF@) 18.20 | 22.86 | 26.45 26.41 Spd’) | 20.16 28.80 4p = -39.1170 h. Be = 40,4943 h. rhe Hartree-Fock orbitals from the state at the head of a column are used in a GVB-CI to obtain all the states of that column. The energies are relative to the *D(sd*) CI energy of -40. 4943 h. 45 orbital from °D(s'd*) Hartree-Fock calculation, p orbitals from °D(s‘p'd’) Hartree-Fock calculation, ©The configuration used at the Hartree-Fock level Gerny2ty hey dentin) was not of pure D symmetry, and hence there is a CI energy lowering due to contributions from similar configurations. fg orbital from *D(s'd’) Hartree-Fock calculation &s orbital from *F(¢ @) Hartree-Fock calculation. Table Vo. Fnerey comparisons for various states of Fe, Feo, Feo" (all energies are in eV). Modified Effective Potential GvB-cIe AI-EP . ‘ State | Experi- | Hartree-| Hartreo- |“Dis‘d') *Fistd®) *F(@’)4 "nistp'a’) “Dis'a’) *F(a7)® Spia’t ment Fock Fock ®p(s*d°) 0 0° ob 0 0 0 0 0 0 0 *F(s'd7) 0.87 2.72 0.90 0.90 SFis'd’) | 1.49 1.86 ’p(sd’) 2.14 2.92 *p(s*d°) 2.30 2.70 "D(s'p'd’); 2.38 1.04 2.38 -- 8 SH(s"a°) 2.38 2.74 3¥(s"0°) 2.53 2.90 5G(s'd”) 2.67 3.06 5G(s’a°) 2.93 3.39 5p(s'p'd®)| 3.19 3.52 °F(s*p'd’)} 3.32 - 3.57 SF(a*) 4,07 11.40 7,96 6.70 *pis'a =| 7.90 5.86 7.87 7,87 *F(a’) 8.15 8.59 8.68 8.53 ‘pis'a’) | 8.88 9.64 *p(q’) 9.54 12.27 *G(a") 9.84 10.43 *p(d’) 10.15 10.99 *H(d’) 10.40 V 11.23 *p(d") 10.43 11.04 *p(s'a) [10.50 |. 10.73 *H(s'd*) | 10.51 11.00 *pa’) | 24. 08 21.44 25.37 25.37 Spa’) 26,51 28.46 SH(d°) 26.54 28.17 SF(a*) 26.71 28.55 Saca’) 27.11 28.84 4m = -21,5558 h. Be = -22.2480 h. “The Hartree-Fock orbitals from the state of the head of a column are used in a GVB-CI to obtain all the states of that column. The energies are relative to the D(sd} CI energy of -22. 2480 h. a, orbital from *D(s’d") Hartree-Fock calculation. &s orbital from °D(s'd*) Hartree-Fock calculation. fg orbital from *D(s?d") Hartree-Fock calculation. Bc] program does not calculate septet states. / Table VI. Energies for NiH from GVB(1) (energies are in Hartrees). calculations using the MEP Internuclear Distance 7A "II a (Bohr) 1.25 -40. 4168 -40.3315 -40. 3903 2.00 -41, 0286 -40. 9892 -40. 9756 2.29 -41,0742 -41, 0457 ~41. 0363 2.50 -41, 0942 ~41.0742 -41, 0675 2.75 -41. 0993 ~41, 0854 -41, 0808 3.00 -41. 0957 -41, 0859 -41. 0828 4.00 -41,0515 -41, 0486 -41, 0478 2.00 -41, 0146 -41,0133 -41,0129 6.00 -40. 9974 ~40. 9966 -40,9970 oo -40, 9936 -40. 9936 -40. 9936 ‘AGL°S=Uy £689 °0 OFSz "0 Sh? 6ELI PP '0 os'o | tego'rb-]| e6°2 | 3, 8078 ‘0 OILT "0 g5°Z LOST GeO ge‘0 | 99g0'tp-| se‘e | U, (§°0 #9°Z) | (0002) (6L °2) ZL¥6 ‘0 ZITO 88°Z 1161 0 0 €660'Ib-| bL°2 | VY, eTetaso spin jo | BHO} | (q0) ASaoug nom dieas, uonSndar 9 3 voREIndog wexTTIN| “SS re45- puog |4-")?! oneqepy!| eons, | (Da | (2)°H| oes Ppepnpoul axe Sanyea TeyUsUlTIedx™ “HIN JO} szoyeweased oidoososzjoeds ay} jo Areuruing *sasoyjuared ut “TIA ST4BL "ID 94} Oj STsBy sy} SB pasn araM sTezIGQIO (T)GAD JoWenb oy q "ID OU} LOZ STSvq OY} Se pasn atOM STL}IGQIO ¥90,{-aaA}IU]] 19}X9sS OY e CTOL‘@2- | gptu'ee- | Lete‘ez- | og onon"ee- | tgte-ee- | pete-ze- | 00's CTOL'@@- | sotn'ee- | zete-zz- | og°9 coru"ce- | Leta‘ee- | ezte‘ze- | 00°9 crug"@@- | teenee- | getu‘ez- | og's 1969°%e- | soen‘ee- | Ltte‘ee- | 00's eyen'ee- | atpeee- | gote‘zz- | os" POLL'@e- | FELL “ee~ 00°F roe"ee- | oon'ee- | toos’ee- | cuenee- 0s" egos'ez- | esun‘ee- | 6os'zz- | E908‘ze- gue artg‘ez- | o6eu'ee- | ests‘ee- | ser8-ee- 00's cpis‘ce- | ryen'ee- | tors‘ee- | sttB-ee- gu°e suos‘ze- | Lesu‘ee- | egos-ee- | otos-ee- 0g°Z teeL"e2- | geou'ee- | neue ‘ze- | ebun‘ee- 92°2 coen"ee- | uezn'ee- | Lyeb‘ee- | sozn'ee- 00°2 gzee"12- | 698e"12- -- L9Ze “12- 00°T (Garo 1) | (pans Garo ¥,) | (taan Bax v5) ood | |aoteiste gl0-aA9 glO-AAD Jo-aaD | -sonrey Powis Vv Vv -Jd}U] t 9 da ey} Zuysn suopyemMoteo *(Seaa}IBY Ul are seTs.19ua) ID pus “(T)GAD ‘Yoog-e0aj18H Woay Hoy 107 SayFouy ‘IA olga, ‘AGL‘Z=Uy 980€ ‘T 6€S0°0 EL°S voor 40°0 600 _SPI8 "Ge LL‘G -O, ¥6G0 ‘T 9960 °0 6L °C TPLT 0 0 69T8 °3o~ 98°C V; gltHiato Sf ad =e HO} (A2) (A2) (A) 3 3 Jo uoljyeindog daoajsuery, Asrzeuq (m9) M UOL}ISUBIT, UOTISUBL], (q) “a (q) HU ayers UsTIMIA adreyoD puod oTyeqeipy yeolytoA ‘Haq roy sasqyawesed ordoossoajpads jo Areuumng ‘XT elqeL References 1. a on e . 10. C. F. Melius, B. D. Olafson, and W. A. Goddard TI, Chem. Phys. Lett., 28, 457 (1974); see also C. F, Melius and W. A. Goddard Il, Phys. Rev. A, 10, 1528 (1974). C. E. Moore, Atomic Energy Levels, Vol. II, National Bureau of Standards (1952). All experimental excitation energies referred to in this paper are a weighted average over the J levels of the state of spectral L and S (we do not include spin-orbit interation in our calculations). The values are from C. Moore. 2 For these states, it suffices to do only a Hartree-Fock calculation since they are pure states; thus a CI using the Hartree-Fock S and d orbitals would yield the same energy. A. J. H. Wachters, J. Chem. Phys., 52, 1033 (1970). W. A. Goddard I, T. H. Dunning, Jr., W. J. Hunt, and P. J. Hay, Accts. Chem. Res., 6, 368 (1973). B. Rosen, Spectroscopic Data Relative to Diatomic Molecules, Pergamon Press (1970). ~~ A. G. Gaydon, Dissociation Energies and Spectra of Diatomic Molecules, Chapman and Hall (1968). The lowest °A is also an s*d° configuration, but the trial orbitals used in the Hartree-Fock calculation were from the s'd’ atomic states. The 4s~3d_2 rotations were not allowed and thus we obtained a good energy for the s'd’ °a state. The *A curve between 4.5 and 5.5 b is hand-drawn. AMPLITUDE (A.U.) 1. The 4s orbitals of Ni using the ab initio effective potential (AI-EP) and the modified effective potential (MEP) for the °F(s7d*) and *p(s'd ) states. 0.20 Ni4s 0.16 t—- i a =~S 0.12 | i / 3D (Al- EP) IT 3F (MEP) iy 3F (AI- EP) 0.08+ ; FY) a ry, 2 y 0.04 h | | | O80 1.0 2.0 3,0 4.0 5.0 6.0 DISTANCE (BOHR) AMPLITUDE (A.U.) 2. The 4s orbitals of Fe using the AI-EP and the MEP for the *D(s?d°) and °F(s’d”) states. 0.20 Fe4s = Wen O12 °D (Al- EP) i SF (MEP) ~ oy SF (AI- EP) a» iy 5p (MEP) AN 0.08; sf SOD i/ NSD f 0.04- } l l | | | o20 1.0 2.0 3.0 4.0 5.0 6.0 DISTANCE (BOHR) 3. The 3d orbitals of Ni using the AI-EP and the MEP for the S¥(s’d°) and *D(s'd*) states. The AI-EP and MEP orbitals are barely distinguishable. 0.6 0.5 j— AMPLITUCE (A.U,) fe) fe) WG aay | o Nm | 3D (AI- EP and MEP) Ni 3d 0.5 1.0 5 2.0 DISTANCE (BOHR) 3.0 AMPLITUDE (A.U,) 4. The 3d orbitals of Fe using the AT-FP and the MEP 5D(s7d°) and °F(s7d’) states. far tha 0.6 0.5 -- o eS O w o nm 0.1 | | | Fe 3d 1,0 5 2.0 DISTANCE (BOHR) 3.0 5. The s-d effective potential of Ni. V s-q i8 the modification which is added to the AI-EP, but note that V._4 + Vg_q (AI-EP) # Ve q (MEP). This is because the term added to the d potential’ (V4) must also be subtracted from the s-d potential: Vend + Vgug (AI-EP) - Vy = Vs_g (MEP). - Ni Vs-q | || 20- | || I | - | Fo | oO { <_ ‘ q = 1.OF | > i] © fe \ \ Vs-q (AI-EP) \ Vs-a (MEP) Ve-¢—7% “O85 0 36 3.0 4.0 DISTANCE (BOHR) (HARTREE) ENERGY added to the AI-EP, but again note that Vo- at Vp.q(Al-EP) # Vv . The p-d effective potential of Ni. V p-d (MEP). The explanation is analogous to that of Figure 5. p-d 2.5 : 20 | | | | ISK \ \ \ ost \ Vp-q (MEP) \ —Vp-g (Al- EP) 0.0 SS ~O.5 ! | L 0.0 1.0 2.0 3.0 4.0 DISTANCE (BOHR) is the modification which is ENERGY (HARTREE) t A) © | 7. The d effective potential of Ni. Vv d is the modification which is added to the AI-EP: V4 + Vy (AI-EP) = V4 (MEP). \ Ni Vg 0.0 -4.0/- ‘0.0 0.3 0.6 09 1.2 1.5 DISTANCE (BOHR) 8. The s-d effective potential of Fe. See Figure 5 for explanation. 2.5 oO | ENERGY (HARTREE) ) 0.0 -~O. | ! | 5.0 1.0 2.0 ' 3.0 4.0 DISTANCE (BOHR) 9. The p-d effective potential of Fe. See Figure 6 for explanation. 2.5 i bok | | Gist | wm 1 a Xiok | > | i \ 2 0.5- Vp-d (AI-EP) \ Vp-d (MEP) 0.0 S. . <= | Gyo “9.595 0 50 3.0 4.0 DISTANCE (BOHR) 10. The d effective potential of Fe. See Figure 7 for explanation. 0.0 -2.0b Vq (Al- EP) ENERGY (HARTREE) -4.0+- DISTANCE (BOHR) ENERGY (HART REE) 11. Potential curves of NiH from GVB(1) calculations using the MEP. The arrow on the right indicates the energy for R = «, INTERNUCLEAR DISTANCE (A?) 1.0 1.5 2.0 2.5 3.0 1 ] i bo | | Ni H -41.00b \ \ 2.5 -41.02F 2.0 -41.04}- | ~41.06-- LO -41.08F 05 -41.10- 0.0 | | | | 1.5 2.5 3.5 4.5 5.5 6.5 INTERNUCLEAR DISTANCE (BOHR) ENERGY (eV) ~ 4 ve — C Vd) { + “4GL°¢ = W ye HIN JO STRVUGI0 GAD “ZT 13, Potential curves of FeH from GVB-CI calculations using the MEP. 10 ~22.70 -— -22.72 — -22.7 — -22.76 — -22.78 — ENERGY CHARTREE ? ~22.80 -— ~22 62 — [ [ [ I [ I 2.0 3.0 y.0 5.0 6.0 7.0 RC BOHR 2 14. GVB orbitals of FeH at R = 2.75. fo 4.00 ~2.00 z Y.7 bp oo il EE” \