5580 J. Am. Chem. zyxwvut SOC. zyxwvu 1987, 109, zyxwvu 5580-5583 or ionic bonding. This allows all spin couplings (different VB structures), a particularly important effect for atoms with partially filled d configurations. For a wave function with N GVB pairs, this leads to 3'" configurations and hence three configurations for (1/2) and 81 configurations for (4/8). These calculations are dissociation-consistent: GVB-RCI( 1 /2) dissociates to a Har- tree-Fock (HF) description of both M+ and CH,; GVB-RCI(4/8) dissociates to an H F description of M+ and a GVB-RCI(3/6) description of CH,. For the metal hydrides the GVB-RCI( 1/2) calculations dissociate to H F fragments. (3) RCI(1/2)XD0. From the three RCI configurations all single and double excitations are allowed out of the metal-ligand zyxwvut u bond to all virtual orbitals. This calculation allows for all correlation between the two electrons of the bond pair. It dis- sociates to an HFXS, description for both the metal ion and the CH, fragments (the single excitation is from the s or d,z orbital on the metal, depending on which is used for bonding, and from the pz orbital on CH3). Metal hydrides dissociate to an HFXS, description of M+ and an H F H atom. (4) RCI(1/2)X[D, zyxwvutsrqp + S,+]. To the configurations of (3) we add all those formed by starting with the RCI configurations and allowing single excitations from the metal nonbonding valence orbitals (to all occupied and virtual orbitals). This calculation dissociates to an H F calculation on the ligand and an all singles CI for the metal valence orbitals. (5) RCI(1/2)X[D0 + zyxwvutsr SM+,val]. This calculation is similar to (4) except that the single excitations are allowed out of all valence orbitals, not just those of the metal ion. For the metal hydrides the two calculations are the same. The metal methyls dissociate to an HFXSvaI description on both fragments. This leads to an overcorrelation of the fragments in some cases (if single excitations on the metal lead to an energy lowering, e.g., ZnCH3+,PdCH,', and CdCH3+)and hence to a calculated dissociation energy that may be slightly too low. This effect is not large and calculations by Carter and GoddardZ2 on RuCH2 involving a similar disso- ciation error show that the bond energy is underestimated by -0.2 kcal/mol. We expect a similar error in our cases. As a test of the adequacy of this level of electron correlation, Carter and Goddard26 performed a similar calculation breaking the C-H bond in CH,. The theoretical bond dissociation energy was calculated at 110.5 kcal/mol in comparison to an experimental De of 112.2 * 0.5 kcal/mol. The calculated bond dissociation energy is thus only 1.7 kcal/mol lower than the experimental value, suggesting that our comparable calculations on MCH3+ species should be quite adequate. Acknowledgment. We thank the National Science Foundation (Grants CHE83-18041 and CHE84-07857) for partial support of this work. Registry No. ScH', 83018-00-2; ScCH,+, 93349-1 1-2; CrH', 75641- 98-4; CrCH,*, 89612-53-3; MnH', 75641-96-2; MnCH,', 8961 2-54-4; ZnH+, 41336-21-4; ZnCHp+,47936-33-4; YH', 101200-09-3; YCH3', 109585-23-1; MoH', 101200-12-8; MoCH,', 109585-24-2; TcH', 106520-06-3; TcCH~', 106500-86-1; PdH', 85625-94-1; PdCHj', 90624-40-1; CdH', 4141 1-12-5; CdCH3+, 106520-07-4; SC', 14336-93-7; Cr', 14067-03-9; Mn+, 14127-69-6; Zn', 15176-26-8; Y', 14782-34-4; Mo', 16727-12-1; Tc', 20205-77-0; Pd+, 20561-55-1; Cd', 14445-53-5; CH,', 2229-07-4. Bond Energy and Other Properties of the Re-Re Quadruple Bond David C. Smith and William A. Goddard III* Contribution No. 7558 from the Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91 125. Received February 18, 1987 Abstract: Using generalized valence bond (GVB) methods designed for obtaining accurate bond energies, we predict an Re-Re quadruple bond strength of 85 zyxwvutsr f 5 kcal/mol for This is much less than early estimates of 370 kcal/mol and somewhat lower than estimates (1 24 to 150 kcal/mol) based on Birge-Sponer extrapolation but is in reasonable agreement with a recent thermochemical study (97 f 12 kcal/mol). We obtain a rotational barrier of 3.0 kcal/mol and a singlet-triplet excitation energy of 3100 cm-I, and we conclude that the intrinsic strength of the 6 bond is 6 f 3 kcal/mol. Since their discovery in 1965, quadruply bonded metal dimers have provoked numerous theoretical and experimental studies. A particularly controversial issue has been the strength of the quadruple bond and, in particular, the contribution of the 6 bond to the observed structure of the unbridged dimers.'-4 We here report the results of ab initio calculations of Re2C182- designed to provide accurate bond energies and torsion barriers as well as accurate shapes for the potential curves. These studies use the generalized valence bond (GVB) approach in which electron correlations are included for all eight electrons available for the quadruple bond, while solving self-consistently for all orbital^.^*^ We use the modified-GVB (M-GVB) approach of Goodgame and G~ddard.~ They pointed out that ab initio descriptions of multiple bonds in transition metals lead to substantial errors in the bond energy due to an inadequate treatment of the electron correlations in the ionic part of the wave function describing the bond. +cov + Wionic = [4,(1)4A2) + 4,(1)4,(2)1 + N41(1)41(2) + 4r(1)4r(2)1 +GVB = In GVB, electron correlation in the covalent part of the wave (1) Cotton, F. A.; Walton, R. A. Multiple Bonds Between Metal Atoms; (2) Cotton, F. A.; Walton, R. A. Strucr. Bonding 1985, 62, 1-49. (3) Mathisen, K. B.; Wahlgren, U.; Pettersson, L. G. M. Chem. Phys. Lett. (4) Hay, P. J. J. Am. Chem. SOC. 1982, zyxwvutsrqpo 104, 7007-7017 and references Wiley: New York, 1982; and references therein. (5) Goddard, W. A,, 111; Ladner, R. C. J. Am. Chem. SOC. 1971, 93, 6750-6756. (6) Bobrowicz, F. W.; Goddard, W. A,, I11 In Modern Theoretical Chemistry: Methods ofEIectronic Structure Theory; Schaefer, H. F., 111, Plenum: New York, 1977; Vol. 3, Chapter 4, pp 79-127. 1984, 104, 336-342 and references therein. therein. 0002-7863/87/1509-5580$01.50/0 0 1987 American Chemical Society