J. Phys. Chem. zyxwvut 1987, 91, zyxwvut 4651-4652 4651 of niobium clusters with cyclohexene and 1,3-~yclohexadiene makes both the energy and the entropy contribution to the free energy even more favorable for the dehydrogenation reaction. These two factors, the lack of aromatic stability and the increased entropy change, appear to lessen the effect of the relative stability of the Nbs and Nb,,, structures on their reactivity with cyclohexene and 1,3-~yclohexadiene. There is no distinct minimum reactivity for these cluster sizes with cyclohexene and 1,3-~yclohexadiene as was observed for benzene. Before closing, we would like to point out some obvious dif- ficulties with the interpretations used in this field in general: (1) As we pointed out previo~sly,~~~ it is difficult to differentiate between neutral thermal reactions (which is generally assumed) in the reactor and a one-photon photochemical reaction induced during the detection process (or a combination). (2) The internal temperature of these clusters before, during, or after the reaction is not known. (3) The ions formed in the plasma by the vapor- ization laser are not completely neutralized prior to their arrival at the reactor. Due to the large ion-molecule reaction cross section, small amounts of unneutralized ions could greatly con- tribute to the neutral distribution of the organometallic species, which upon ionization with the excimer laser can be detected. (4) Finally, the name “cluster” probably does not apply to these compounds, in particular when the number of atoms in a cluster is as small as it zyxwv is in our system. All these compounds have relatively strong chemical bonds so they are actually molecules; for the pure metal clusters they are homonuclear polyatomics, and for their reaction products with organic compounds they are organometallic compounds. However, the word cluster here is useful in differentiating this type of work from other kinds in the field of chemical reactivity. Acknowledgment. The authors thank the support of the Office of Naval Research. New Predictions for Singlet-Trlplet Gaps of Substituted Carbenes Emily A. Carter and William A. Goddard III* Arthur Amos Noyes Laboratory zyxwvuts of Chemical Physics,+ California Institute of Technology, Pasadena, California 91 125 (Received: June 24, 1987) Recent thermodynamic analysis by Carter and Goddard suggested the best previous ab initio predictions of substituted carbene singlet-triplet splittingswere in error by 3 to 17 kcal/mol. Herein we report a new approach for correlation-consistent calculations [based on generalized valence bond with configuration interaction] which yields accurate but simple wave functions. Applying the method to the singlet-triplet splittings of CH,, CH(SiH3), CF,, CC12,CHF, and CHCI leads to good agreement (within 3 kcal/mol) with available experimental results. Considerable uncertainty exists in the values of singlet-triplet energy splittings in substituted carbenes, with CF2 being the only heterocarbene for which an experimental AEST has been reported.’ These values are crucial for understanding the chemistry expected for such carbenes, since singlet carbenes are known to undergo concerted, stereospecific reactions, while triplet carbenes are typically involved in stepwise, nonstereospecificchemistry., zyxwvuts , Carter and Goddard3 recently suggested a means of extracting the sin- glet-triplet splittings (AEsT = Esinglet - Etriplet) in halogenated carbenes, from a thermochemical analysis of bond strength trends in substituted olefins and methanes. However, the estimates obtained from this analysis were in serious disagreement (up to 17 kcal/mol) with the best previous ab initio theoretical predictions of AEST.4-6 In order to test the reliability of these empirical predictions’ and to assess the accuracy of previous theoretical results, we developed a new theoretical approach practical for large substituents on carbenes (X and Y on CXY). Herein we report the first results from this new ab initio technique.’ Elements of the method include generalized valence bond correlations for the bonds to carbon (C-X and C-Y bonds) and the nonbonding zyxwvutsrqp u orbital in singlet carbene [thus, GVB(3/6) for describing these three electron pairs with six orbitals and perfect singlet pairing].* The perfect pairing restriction is relaxed by performing a restricted configuration interaction (RCI) calculation which allows all three occupations of two electrons in two orbitals for each correlated pair (leading to 27 configurations for singlet carbene, before accounting for symmetry). This self-consistent RCI wave function (using only 20-25 spin eigenfunctions) provides an excellent approximation (within 0.5 kcal/mol) to the full CI result (involving -220 000 spin eigenfunctions) for the singlet- triplet splitting in meth~lene.~ ‘Contribution No. 7592 from the Arthur Amos Noyes Laboratory of Chemical Physics. For electronegative substituents with lone pairs (e.g. F, Cl), it is critical to allow charge-transfer (CT) configurations, in which 7r donation from the ligand lone pairs to the partially empty p7r orbital on carbon is allowed simultaneous with u CT from carbon to the ligand. Thus, to the RCI wave function above (which allows u CT), we include simultaneous excitations from the p7r lone pairs on X and Y to the C pa orbital. When optimized self-consistently, this RCI*nCI(opt) wave function yields excellent results for CF2 (1) (a) Koda, S. Chem. Phys. Lett. 1978,55, 353. (b) Chem. Phys. 1982, 66, 383. (2) (a) Kirmse, W. Carbene Chemistry; Academic: New York, 1971. (b) Gaspar, P. P.; Hammond, zyxwv G. S. In Carbenes, Vol. 2, Moss, R. A,, Jones, M., Eds.; Wiley: New York, 1975. (c) Moss, R. A,; Jones, M. In Reactive Intermediates, Vol. 2, Jones, M., Moss, R. A,, Eds.; Wiley: New York, 1981. (d) Ibid. 1985, Vol. 3. (e) Davidson, E. R. In Diradicals, Borden, W. T., Ed.; Wiley: New York, 1982. (3) Carter. E. A.: Goddard 111. W. A. J. Phvs. Chem. 1986. 90. 998. (4j Bauschlicher,’Jr., C. W.; Schaefer 111, H: F.; Bagus, P. 8. J: Am. Chem. SOC. 1977, 99, 7106. (5) Luke, B. T.; Pople, J. A.; Krogh-Jespersen, M.-B.; Apeloig, Y.; Karni, M.; Chandrasekhar, J.; Schleyer, P. v. R. zyxwv J. Am. Chem. SOC. 1986, 108, 270. (6) Scuseria. zyxwvu G. E.: DurLn. M.; Maclaean. R. G. A. R.: Schaefer 111. H. F. J. Am. Chem. SOC. 1986, 108, 3248. - (7) The halogens were described with a valence doubler basis, while valence double-{ plus polarization bases were used for all other atoms. For CI and Si, the core electrons were replaced by effective core potentials (Rap*, A. K.; Smedley, T. A.; Goddard 111, W. A. J. Phys. Chem. 1981.85, 1662). Singlet total energies at the CCCI level of theory (hartrees): -38.967 06 (CH,); -329.042 60 [CH(SiH,)]; -236.801 27 (CF,); -956.776 28 (CCI,); -137.875 60 (CHF); and -497.874 15 (CHCI). (8) (a) Hunt, W. J.; Dunning, Jr., T. H.; Goddard 111, W. A. Chem. Phys. Lett. 1969, 3, 606. Goddard 111, W. A,; Dunning, Jr., T. H.; Hunt, W. J. Chem. Phys. Let?. 1969, 4, 231. Hunt, W. J.; Goddard 111, W. A,; Dunning, Jr., T. H. Chem. Phys. Lett. 1970, 6, 147. Hunt, W. J.; Hay, P. J.; Goddard 111, W. A. J. Chem. Phys. 1972, 57, 738. Bobrowicz, F. W.; Goddard 111, W. A. In Methods of Electronic Structure Theory, Schaefer, H. F., Ed.; Plenum: New York, 1977; pp 79-127. (b) Yaffe, L. G.; Goddard 111, W. A. Phys. Rev. A 1976, 13, 1682. (9) Carter, E. A,; Goddard 111, W. A. J. Chem. Phys. 1987, 86, 862. 0022-3654/87/2091-4651$01.50/0 0 1987 American Chemical Society