1606
J . Phys. Chem. 1992,96, 1606-1610
Ground-State Geometry, Electronic Structure, and Bonding of the Titanium-Vanadium and Vanadium-Nickel Dimers by Local-Spin-Density LCAO Techniques Saba M. Mattar* and William D. Hamilton Department of Chemistry, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 6E2 (Received: May 31, 1991)
The electronic structures of the TiV and VNi dimers are computed b the LSD-LCAO method and are found to have 42ground states. Their electronic configurations are 5r4 12d 1 6 ~ - 916,~ and 5r4 13at 2 6 ~ 26,f, 9 ~ respectively. These results are in agreement with existing experimental matrix-isolated EPR studies. The dimers are predicted to have stable bound ground states with a titanium-vanadium distance of 1.77 A and a vanadium-nickel distance of 2.00 A. The dissociation energies, corrected for basis set superposition errors (BSSE),are found to be 5.88 eV for TiV and 4.48 eV for VNi. The corresponding uncorrected values are 6.88 and 4.65 eV, respectively.
Y
Introduction Homogeneous and heterogeneous metal dimers are easily isolated and studied in inert gas matrices. These studies have been reviewed by Weltner and Van Zee.' Many of the homogeneous dimers, including Cr2,2V2,3Cu2? and M O ~have , ~ been studied in the gas phase. The lack of experimental data for mixed-metal dimers is due to the difficulty of their preparation coupled with their high reactivity. However, a few heterogeneous transition metal dimers containing first-row atoms have been matrix-isolated and characterized by electron paramagnetic resonance (EPR) spectroscopy."1° In most cases, an electronic ground state for these molecules has been proposed. In the past 15 years, the number of theoretical studies and electronic structure computations of homogeneous metal dimers has increased dramatically. These computations have been reviewed by Salahub," Shim,'* and Walch et In contrast, few computations have been performed for mixed-metal dimers. HF-CI results for NiCu14 and NiFe15 have been reported. The (1) Weltner, W., Jr.; Van Zee, R. J. Annu. Reu. Phys. Chem. 1984,35, 291-327. (2) (a) Efremov, Y . M.; Samoilova, A. N.; Kozhukhovsky, V. B.; Gurvich, L. V. J . Mol. Specrrosc. 1978, 73, 430. (b) Michalopoulos, D. L.; Geusic, M. E.; Hansen, S. G.; Powers, D. E.; Smalley, R. E. J . Phys. Chem. 1982, 86, 3914. (c) Bondybey, V. E.; English, J. Chem. Phys. Leu. 1983,94,443. (d) Riley, S. J.; Parks, E. K.; Pobo, L. G.; Wexler, S. J . Chem. Phys. 1983, 79, 2577. (3) Langridge-Smith, P. R. R.; Morse, M. D.; Hansen, S. G.; Smalley, R. E.; Merer, A. J. J . Chem. Phys. 1984, 80, 593. (4) (a) Aslund, N.; Barrow, R. F.; Richards, W. G.; Travis, D. N. Ark. Fys. 1965, 30, 171. (b) Lochet, J. J . Phys. B 1978, 11, L55. (c) Preuss, D. R.; Pace, S. A.; Gole, J. L. J . Chem. Phys. 1979, 71, 3553. (d) Gole, J. L.; English, J. H.; Bondybey, V. E. J . Phys. Chem. 1982,86, 2560. (e) Powers, D. E.; Hansen, S. G.; Geusic, M. E.; Michalopoulos, D. L.; Smalley, R. E. J . Chem. Phys. 1983, 78, 2866. (5) (a) Efremov, Y. M.; Samoilova, A. N.; Kozhukhovsky, V. B.; Gurvich, L. V. J . Mol. Spectrosc. 1978, 73,430. (b) Hopkins, J. B.; Langridge-Smith, P. R. R.; Morse, M. D.; Smalley, R. E. J . Chem. Phys. 1983, 78, 1627. (6) Baumann, C. A,; Van Zee, R. J.; Weltner, W., Jr. J . Phys. Chem. 1983, 79, 5272. (7) Van Zee, R. J.; Weltner, W., Jr. Chem. Phys. Lett. 1984, 107, 173-1 77. . - .
(8) Cheeseman, M.; Van Zee, R. J.; Weltner, W., Jr. High Temp. Sci. 1988, 25, 143-52.
(9) Van Zee, R. J.; Weltner, W., Jr. Chem. Phys. Lett. 1988, 150, 329-333. (IO) Cheeseman, M.; Van Zee, R. J.; Flanagan, H. L.; Weltner, W., Jr. J . Chem. Phys. 1990, 92, 1553-1559. (11) Salahub, D. R. Adu. Chem. Phys. 1987,69 (Ab Initio Methods in Quantum Chemistry Part II), 447-520. Salahub, D. R. In Applied Quantum Chemistry; Smith, V. H., Jr., Schaefer, H. F., 111, Morokuma, K., Jr., Eds.; Reidel: Dordrecht, 1986; pp 185-212. Salahub, D. R. Contribution of Clusrer Physics to Material Science and Technology;Davenas, J., Rabette, P., Eds.; Nijhoff The Hague, 1986; pp 143-194. (12) Shim, I. Ten Papers in rhe Exact Sciences and Geology; Royal Danish Academy of Sciences and Letters: Copenhagen, 1985; pp 147-208. (13) Walch, S. P.; Bauschlicher, C. W. In Comparison of Ab-fnitio Quantum Chemistry With Experiment For Small Molecules; Bartlett, R. J . Ed.; Reidel: Dordrecht, 1985; pp 17-53.
iron dimers FeMn, FeCo, FeNi, and FeCu were investigated using the DVM-Xa methodI6 and HF-SCF techniques." FeCr has been investigated using SCF-Xa-SW and compared with matrix isolation results.'* Van Zee and Weltner' have studied the matrix-isolated dimers TiV and VNi using X-band EPR spectroscopy. From the spectra of TiSIVand V N i , they concluded that both molecules had 48 ground states. Valence shell orbital configurations of su%1d#d62 for TiV and s ~ ~ d $ d . l r ~ d 6 ~ s u *for ~ dVNi 6 * ~ were proposed. These molecules were chosen as the first contains the minimum number of electrons for a heterogeneous transition metal dimer while the second combines atoms from opposite ends of the transition metal series. The purpose of this paper is to confirm the ground states and molecular orbital bonding picture of these dimers as proposed by Van Zee and Weltner.' LSD-LCAO computations complement the experimental work by predicting equilibrium distances and binding energies for these molecules. These properties are not obtainable by matrix-isolated EPR spectroscopy. The LSD-LCAO method has proven successful in the investigation of homogeneous metal dimers while corresponding HF-SCF and HF-CI methods have encountered difficulties." A model potential version of this method has also been tested on heterogeneous palladium diatomic~.~~ MiedemaZ0has published theoretical dissociation energies for homo- and heterogeneous metal dimers. Predicted dissociation energy values for dimers composed of the 3d, 4d, and 5d metals were reported. The dissociation energy for VNi was determined to be 272 kJ/mol (2.8 eV) and 183 kJ/mol (1.9 eV) for TiV. It is important to understand the electronic structure, bonding, and properties of these dimers as they have naked hemispheres to which the addition of other metal atoms or stabilizing ligands (CO, CS, NO, C6H6,etc.) is possible. Consequently, they are potentially important intermediates for the synthesis of organometallic complexes and clusters.
Computational Details Bond optimization and computation of the electronic structure of the ground and three low-lying excited states of the TiV and VNi are performed using the local-spin-density linear combination of atomic orbitals (LSD-LCAO) method that gives reliable total energies.2' The effects of electron-electron exchange and cor(14) Shim, I. Theor. Chim. Acta 1980, 54, 113-122. (15) Shim, I . Theor. Chim. Acta 1981, 59, 413-421. (16) Guenzburger, D.; Baggio Saitovitch, E. M. Phys. Reu. B 1981, 24, 2368-2379. (17) Goldstein, E.; Flores, C.; Hsia, Y . P. J . Mol. Struct. (THEOCHEM) 1985, 124, 191-200. (18) Nagarathna, H. M.; Montano, P. A,; Naik, V. M. J . Am. Chem. SOC. 1983, 105. 2938-2943. (19) Russo, N.; Andzelm, J.; Salahub, D. R. Chem. Phys. 1987, 114, 331-338. (20) Miedema, A. R. Faraday Symp. Chem. SOC.1980, 14, 136-48.
0022-3654 19212096- 1606S03.00/0 , 0 1992 American Chemical Society I
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The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1607
Structures of Ti-V and V-Ni Dimers TABLE I: Mulliken Population Analysis for the TiV and VNi Dimers
orbital analysis vanadium molecule VNi
orbital
1,' lld 120' 12d 13u' 57r' 5r' 16' 161
26t TiV
lla'
11u1 12a' 5r' 5r4 16'
overlap 0.06
0.02 0.27 0.28 -0.21 0.17 0.09 0.07 0.02 -0.08 0.28 0.29 0.10 0.26 0.26 0.24
other
S
P
d
S
0.06 0.02 0.49 0.31 0.16
0.00 0.00 0.00 0.01 0.00
0.30 0.16 0.02 0.01 0.50 0.56 0.19 0.28 0.02 1.72 0.21 0.16 0.32 1.13 1.01 1.32
0.10 0.07 0.34 0.55 0.08
0.00 0.00
0.32 0.30 0.19
0.01 0.01 0.03 0.02 0.03
relation are introduced using the interpolation formulas of Perdew and Zunger22that parametrizes the exchange-correlation potentials and energy densities of an electron gas as computed by Ceperly and Alder.23 The 13s/8p/5d [4333/431*/311+] basis sets of Andzelm et al. are used.24 This basis set is specifically designed for LSDLCAO computations. The exponents of the p-type polarization functions for Ti, V, and Ni are 0.0951, 0.1051, and 0.1531 while the diffuse d-type functions have exponents of 0.0700, 0.08600, and 0.14800, r a p e c t i ~ e l y The . ~ ~ auxiliary basis sets for the charge density and exchange-correlation potential are constructed according to the method of Dunlap.z' Due to the size of the basis sets, basis set superposition error (BSSE) corrections are performed. The counterpoise method of Boys and Bemardi is u~ed.2~ This method requires the total energy of the atoms be computed ~ e p a r a t e l y . The ~ ~ same C,, symmetry adapted basis sets used for the dimer are also used for the Ti, V, and Ni fragments. The S C F iterations are performed until the relative change in the charge density and exchange-correlation potential is less than Mulliken population analyses were camed out for the molecules. This method, although deficient in some aspects, can be used in conjunction with contour diagrams for the wave functions to provide a qualitative or semiquantitative picture of the structure and bonding. Results and Discussion TiV. Titanium-vanadium is found to have a 4Z- ground state with a 57r4 1 2 1 1~ ~~ 3 113, ~ ~~ electronic ~ 2 ~ configuration. The potential energy curves for the ground and three low-lying excited states are given in Figure 1. These configurations all display energy minima and their computed binding energies indicate that all four states are stable. For the ground state De is calculated to be 6.88 eV, the equilibrium bond distance 1.77 A, and the dipole moment 0.63 D in the direction of the titanium. The exchange-correlation method of computation generally predicts excellent equilibrium distances for dimers but tends to overestimate their binding energie~."*~',*~ Hence the bond dissociation energy
-7.0
no. I
d
0.54 0.75 0.15 0.12 0.25 1.42 1.80 1.72 1.98 0.28 0.14 0.14 0.24 0.85 0.95 0.68
0.00 0.00 0.00
-0.01 0.03 0.01
0.01 0.01 0.02 0.00 0.01
0.30 0.38 0.20
-1O.O .o
occupn
P 0.10
I 1 1 1
2 2 2 2 2 1 1 1
2 2 2
l-7---+93 1, 1.5
-
,
2.5
2.0
R Ti-V / A Figure 1. The relative energy of TiV states as a function of the titanium-vanadium distance, R. (a) 42-ground state (12at5r416ft); (b) *A (12~~5r~16~); (c) 2A ( 1 1 ~ ~ 5 r ~ 1 (d) 6 ~ 22+ ~ ~ )(;1 3 ~ ~ 5 ~ ~ 1Basis 6 ~ ) .set from ref 24. The atomic limit shown on the right-hand side, represents the sum of the ground state energies of Ti(3F) and V(4F).
0.0
>
$ a, r
-
7% 6%
-1.0
26
- 6% 26 __I
-130
- 16
-2.0
1
-3.0
~
16
120
LL
110
5% Spin (I
Spin D
TiV (21)(a) Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R. J . Chem. Phys. 1979, 71,4993. (b) Lamson, S.H.; Messmer, R. P. Chem. Phys. Lett. 1983, 98, 72.
(22)Perdew, J. P.;Zunger, A. Phys. Rev. B 1981, 23, 5048. (23)Ceperly, D.M.; Alder, B. J. Phys. Reu. Lett. 1980, 45, 566. (24)Andzelm, J.; Radzio, E.; Salahub, D. R. J . Comput. Chem. 1985, 6, 520-532. (25)(a) Radzio, E.;Andzelm, J.; Salahub, D. R. J . Comput. Chem. 1985, 6, 533-537. (b) Tatewaki, H.;Miyoshi, E.; Nakamura, T. J . Chem. Phys. 1982, 76,5073. (c) Andzelm, J.; Klobukowski, M.; Radzio-Andzelm, E. J. Comput. Chem. 1984, 5, 146. (26)Boys, S . F.;Bernardi, F. Mol. Phys. 1970, 19, 553-566. (27) Baykara, N . A.; McMaster, B. N.; Salahub, D. R. Mol. Phys. 1984, 52, 891.
Figure 2. Spin-unrestricted molecular orbital diagram for the ground state configuration of titanium-vanadium. Core electrons occupy the l o to 4r orbitals.
for this molecule may be lower than predicted. Figure 2 contains the valence molecular orbitals for TiV. The orbitals containing the unpaired electrons are all lower in energy than their empty counterparts. This illustrates, at the one-electron orbital level, that the ground state is indeed a quartet. The results (28)Salahub, D.R.;Baykara, N. A. SurJ Sci. 1985, 156, 605.
1608 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
Figure 3. Titanium-vanadium contour diagrams of the u valence orbitals. (a, top) 120; (b, bottom) 1 lu. Contour values are 0.04, 0.08,0.12,0.16 for contours 1-4 and -0.04, -0.08, -0.12, -0.16 for contours 5-8. The / ~ . 120 zero contour is denoted by a 0. Units are ( e l e ~ t r o n s / a , ~ ) ~ The orbital has no contour 4.
of the Mulliken population analysis for the 42-ground state are given in Table I. The gross atomic charges for this state show that approximately 0.075 of an electron is transferred from the titanium to the vanadium. By examination of the population and distribution of the component atomic orbitals, the extent of bonding or antibonding within a molecular orbital may be determined. Figure 3 contains contour diagrams for the 11u and 120 spin-up orbitals. The 126 orbital is a hybrid of s and d,l atomic orbitals with the d t forming the larger component. The contour of Figure 3a shows that all s and d components are in-phase and bonding in nature. In contrast, the 1l u orbital has a larger s component. Figure 3b indicates that both the 4s(Ti)-4s(V) and 3d?(Ti)3d,Z(V) interactions are bonding. However, the s and d components are out of phase with one another. The 5~ orbital is predominantly 3d in character, and Figure 4a shows typical d x bonding between the two centers. This orbital displays relatively equal contributions from the Ti and V. This is confirmed in Table I where the V population is 2.2 while that of Ti is 1.8. The overlap of 0.52 indicates a largely covalent bond. Figure 4b contains the 16 orbital. Its contours indicate that it is largely V in character. Table I shows a vanadium population of 1.32 and only 0.68 for titanium. An overlap value of 0.24 and the wave function contour diagram show that there is appreciable delocalization in the internuclear region, indicating a strong 6 bond. Table I indicates that vanadium has a valence population of d4,15s0.81 while the titanium has a d3%0.88 valence orbital occupation. One may qualitatively conclude that the d4s1and d3s1states of V and Ti participate in the bonding of the ground-state molecule.
Mattar and Hamilton
II x1Figure 4. Titanium-vanadium contour diagrams of the n and 6 valence orbitals. (a, top) 57c; (b, bottom) 16. The planes denoted are 1 the molecular axis. Contour values are listed in Figure 3.
4
1
-1.0
=
$e
a
-5.0
1.7 1.8
A above
1.9
2.0 2.1
2.2 2.3 2.4
atomic
R V-Ni Figure 5. The relative energy of VNi states as a function of the vanadium-nickel distance, R. (a) 42- ground state ( 1 3 0 ~ 5 ~ ~ 2 (b) 6 ~ 411 ~); ( 1 2 ~ ~ 6 7 c ~ 2 (c) 6 ~ ~2A ) ;( 1 2 ~ ~ 6 ~ ~ (d) 2 6211 ~ ~( )1; 2 ~ ~ 6 ~ ~ ~Basis ~ 1 set 6~). from ref 24. The atomic limit is shown on the right-hand side and represents the sum of ground state energies of V(4F) and NiOF).
From the EPR hyperfine splittings, Van Zee and Weltner’ found that the unpaired electrons contain 8% s character on the vanadium and 7% on the titanium. Our results are in good agreement with these values. The computed charge distribution indicates values of approximately 6% for V and 7% for Ti. They also proposed an electron configuration of s ~ ~ d u ~ d The ~~d6~. one-electron MO diagram of Figure 2 closely supports this con-
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1609
Structures of Ti-V and V-Ni Dimers
-1.01
'=
-
- 26
Ill0
I
-7.0
Spin a
Spin 0
VN i Figure 6. Spin-unrestricted molecular orbital diagram for the 42-ground state of vanadium-nickel. Only the valence orbitals are shown.
figuration. The only difference is that the computation shows that the u orbitals are actual hybrids of the s and d,2 and cannot be classified as pure s or d in character. Figure 2 also illustrates that the TiV molecule resembles the V, dimer when one electron is removed.28 It is interesting to note that the lost electron is not removed from the 6 but rather the u orbital. VNi. The vanadium-nickel dimer is also determined to have a 42-ground state, with a 5a4 13ut 2 6 ~ ~2t6,~ 2 felectronic configuration. Potential energy curves for the ground and three low-lying states are given in Figure 5 . The ground state has an equilibrium bond length of 2.01 A, and the dissociation energy is determined to be 4.65 eV. The dipole moment, in the direction of the vanadium, is computed to be 1.99 D. The one-electron valence molecular orbital diagram for VNi is given in Figure 6. This valence region contains 15 electrons, 10 from nickel and 5 from vanadium. The 1lu, 57~,126, and 16 orbitals are filled and the 26 and 136 orbitals are partially filled. The contour diagrams for the a orbitals are given in Figure 7. Table I indicates that the l l u t and 1 1 d have 84 and 91% d character, respectively. The 1lut orbital in Figure 7a shows strong d A , z bonding. The 12u orbitals are largely 4s-4s in character. Table I shows that both the spin-up and spin-down components have the largest overlap in the molecule. This overlap is positive, indicating a bonding situation as shown in Figure 7b. Finally, the 13ut orbital shown in Figure 7c is distinctly antibonding. This is confirmed by the overlap value of -0.21 found in Table I. Figure 8 and Table I show that the 5a orbital is mainly Ni in character. The spin-up and spin-down orbitals have 3d(Ni) populations of 1.42 and 1.8, respectively. The positive overlap of these orbitals is second only to the 12a orbitals and indicates a relatively strong bond. The larger overlap value for the spin-up orbital arises from the greater 3d(V) contribution. Figure 9 contains the contour plots for the occupied 6 orbitals. The 16 is bonding with larger nickel character while the 26 is antibonding and mainly vanadium in character. Overlap values are small due to the localization of charge on the 3d,2-$ and 3d, nickel and vanadium orbitals. These small values also indicate that the bonding and antibonding character is weak. The proposed electron configuration' of su2du2da4d64sa*'d6*2 is essentially the same as determined in the current study. From the EPR results,' it was determined that the high-spin wave function contains about 10% vanadium s character. The population results presented in Table I give just over 5% vanadium s character for the unpaired electrons. The smaller percentages of s character computed for both TiV and VNi will increase slightly if core-polarization effects are taken into consideration. Therefore, the experimental and computed results seem to be in good agreement. Inspection of the gross atomic populations show that 0.31 of
Figure 7. Vanadium-nickel contour diagrams of the u valence orbitals. (a, top) 1la; (b, middle) 12u; (c, bottom) 13u. Contour values are listed in Figure 3.
an electron is transferred from the vanadium to the nickel. This is reasonable as vanadium will lose an electron more readily than nickel. Table I indicates that the nickel valence shell population is d9.01s'.'4and the vanadium is d3.76s1.04.One may assume that the d9s1and d4s' states of Ni and V are involved in the bonding of the molecular ground state. The only available data on the binding energies of TiV and VNi are those of Miedema.20 They are obtained from the surface and interfacial energies of the constituent bulk metals at zero temperature. In this method the microscopic dimer binding energies are derived from macroscopic parameters such as differences in work functions and bulk cell boundary electron densities between
1610 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
Mattar and Hamilton
1
I
1
Figure 8. Vanadium-nickel contour diagram of the 5ri valence orbital. The plane denoted is 1 A above the molecular axis. Contour values are listed in Figure 3. TABLE 11: Equilibrium Distances and Binding Energies for the TiV and VNi Dimers" V-Ni Ti-V
R,. A 2.005 (2.000) 1.767 (1.762)
D.. eV 4.65 (4.48) 6.88 (5.88)
"Basis set superposition error corrected values are noted in parentheses.
two pure metalsSz0This method is very different from the one used here, where the binding energies are computed from the total energies as a function of the internuclear distances. Consequently, one must exercise some care when comparing the binding energies computed by these two different methods. The binding energies given in Table I1 are somewhat larger than those computed by Miedema.20 Overestimation of the binding energies is a wellknown consequence of the LSD method.11*27-28 Post-SCF nonlocal corrections may help reduce these values. However, to determine how good the computed De values are they must be ultimately compared with those obtained experimentally. Finally, the larger binding energy of TiV as compared to VNi cannot be rationalized in terms of their bond orders alone. If the one-electron orbitals are classified simply as bonding and antibonding then both molecules have a formal bond order of 4.5. The reason for the larger binding energy of TiV becomes apparent when both the magnitude and sign of the overlap integrals between the atoms are taken into consideration. Table I shows that for T N the 5n,11u, and 16 orbitals have large positive overlap values leading to four strong bonds. On the other hand the VNi overlap and occupations in Table I show that only the 12u orbital forms a strong bond. The VNi Sn, 110, and 16 have much smaller overlaps leading to much weaker bonds when compared with those of TiV. In addition, the large negative overlap of VNi 13u renders it strongly antibonding which further reduces this dimer's binding energy. Conclusions In conclusion, the LSD-LCAO results predict that TiV and V N i have bound ground states similar to the experimentally observed
I
X
Figure 9. Vanadium-nickel contour diagrams of the 6 valence orbitals. (a, top) 16; (b, bottom) 26. The planes denoted are 1 A above the molecular axis. Contour values are listed in Figure 3.
dimers. The bond dissociation energies computed for these two atoms seem reasonable but larger than expected. This is due to the local density functional approximation and compact basis sets in the computations. Basis set superposition error corrections reduce this overestimation somewhat. There are very few computations for heterogeneous metal dimers that predict their ground states and bond and total energies accurately. In order to determine if the LSD-LCAO method can generally predict these properties, more computations on a whole series of metal dimer compounds must be performed and compared with accurate experimental data.
Acknowledgment. S.M.M. acknowledges the financial assistance from the Natural Sciences and Engineering Research Council of Canada and the University of New Bnmwick Research Fund and the allocation of computer time from the Computer Center of the University of New Brunswick. Registry No. TiV, 90955-52-5; NiV, 65453-97-6.
