J . Phys. Chem. 1987, 91, 4651-4652
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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 contribute 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 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.
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 difficulties with the interpretations used in this field in general: (1) As we pointed out p r e v i o ~ s l y 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-
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 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-consistentcalculations [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, nonstereospecific chemistry., , Carter and Goddard3 recently suggested a means of extracting the sin- Etriplet) in halogenated glet-triplet splittings (AEsT = Esinglet 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 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 C I result (involving -220 000 spin eigenfunctions) for the singlettriplet splitting in m e t h ~ l e n e . ~ ‘Contribution No. 7592 from the Arthur Amos Noyes Laboratory of Chemical Physics.
0022-3654/87/2091-4651$01.50/0
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 p a 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, 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. J . Am. Chem. SOC.1986, 108, 270. (6) Scuseria. 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.
0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
Letters
TABLE I: Singlet-Triplet Splittings (AEW = EShle,- EMPlet) in CXY" theory (this work) thermochem CXY HF G V B ( 3 / 6 b P P RCI*IICI(PP) RCI*IICI(oDt) CCCIb exDt est' CH2 26.1 9.1 11.1 11.6 9.0 9.09 f 0.2Id CHSiH, -2
CCI, CHF CHCl
34.7
18.3
19.7
20.4
18.4
-32.5 0.1 4.5
-47.2 -16.5 -11.7
-5 1.9 -21.1 -14.0
-59.8 -23.2 -20.2
-57.5 -25.9 -17.7
12.3
-3.9
-5.8
-6.7
-9.3
-56.6'
--I9
other theorv 12.0 (full CI),g 13.5 (CI-SD)," 16.8 (MP4)' 20.3 (CEPA);' 25.7 (MP4),k 27.2 (CI-SD)' -50.0 f 10.8 -46.5 [GVB(1/2)lm -31.0 f 10.7 -13.5 [GVB(1/2)lm -22.4 f 6.6 -9.2 [GVB(1/2)],'" -12.7 (MP4),k -12.9 (CI-SD)" -1.6 [GVB(1/2)],"'-3.7 (CI-SD)n -16.7 f 8.2
OSee ref 7 for more details. bRCI*[IICI + SD,,](PP). lBased on the theoretical relationship between D(C=C) and AEsT(CXY) (ref 3 and IO). dReferences 11-13, eReference 1. 'Reference 14. XReference 15. "Reference 16. 'Reference 17. 'Reference 18. kReference 5. 'Reference 19. Reference 4. "Reference 6.
and CH, (both within 3 kcal/mol of experiment). Even for CF,, this self-consistent method involves only a small number of configurations [63 for CF, ('Al)], making the method tractable for large substituents. Since such multiconfiguration self-consistent field (MCSCF) calculations require integral transformations every iteration, we have also developed an alternate C I method, which makes use of the GVB-PP orbitals as the basis for the CI calculation (and hence requires only one integral transformation). Since the process of interest involves an electronic excitation between the two carbene nonbonding orbitals (one u, one T ) , we include full correlation of the two nonbonding electrons on carbon. Thus, in addition to the RCI*nCI configurations, we include (from all RCI reference states) all single and double excitations from the nonbonding carbon orbitals to all virtual orbitals. This level of CI is referred to as correlation-cowistent CZ (CCCI), since the same correlation and spin-coupling descriptions are used for both singlet and triplet carbenes. The CCCI method yields another set of predictions for U s T , comparing favorably to the RCI*IICI described above and to experiment (within 1 kcal/mol). CCCI still leads to simple wave functions [e.g., 1174, 1219, and 4180 configurations for the singlet states of CH,, CF,, and CH(SiH3), respectively]. In contrast, singles and doubles CI from a H F wave function leads to 415, 2633, and 9261 configurations within the same bases for CH,, CF2, and CH(SiH3), but results in errors in AEST of 4.5 and 8.8 kcal/mol for CH2and CH(SiH3), even for more extensive bases (CI-SD results for CF2 have not been reported). Table I reports for the RCI*IICI (both within the PP basis and the self-consistently optimized basis) and the CCCI wave functions for CH,, CH(SiH3), CF,, CCI,, CHF, and CHC1.' Hartree-Fock (HF) and GVB-PP values are included for comparison, along with thermochemical estimates from ref 3,1° experimental and previous theoretical prediction^.^^^^-'^ We see immediately (IO) The estimates for A E ~ Tshown in Table I differ from those derived in ref 3, since we have now utilized additional values for AHfolSs(CXY). The large uncertainties associated with the thermochemical estimates (Table I) are due in large part to the uncertainties associated with these experimental heats of formation. (1 1) McKellar, A. R. W.; Bunker, P. R.; Sears, T. J.; Evenson, K. M.; Saykally, R. J.; Langhoff, S . R. J . Chem. Phys. 1983, 79, 5251. (12) (a) Leopold, D. G.;Murray, K. K.; Lineberger, W. C . J. Chem. Phys. 1984, 81, 1048. (b) Leopold, D. G . ;Murray, K. K.; Miller, A. E. S.; Lineberger, W. C . J . Chem. Phys. 1985, 83, 4849. (13) (a) Bunker, P. R.; Sears, T. J. J . Chem. Phys. 1985, 83, 4866. (b) Bunker, P. R.; Jensen, P.; Kraemer, W. P.; Beardsworth, R. J . Chem. Phys. 1986.85, 3724. (14) Leopold, D. G.; Murray, K. K.; Lineberger, W. C., private communication. (15) Bauschiicher, Jr., C. W.; Taylor, P. R. J. Chem. Phys. 1986,85, 5936. (16) Lucchese, R. R.: Schaefer 111, H. F. J . Am. Chem. SOC.1977, 99, 6165. (17) Luke, B. T.; Pople, J. A.; Krogh-Jespersen, M.-B.; Apeloig, Y . ; Chandrasekhar, J.; Schleyer, P. v. R. J . Am. Chem. SOC.1986, 108, 260.
that the CCCI method gives values in excellent agreement with experiment and within the uncertainties of the thermochemical estimates, but leads to differences of up to 12 kcal/mol when compared to previous theoretical predictions. We see that the HF method fails miserably in all cases (yielding the wrong ground states for half of the carbenes examined) with an average error of 21.4 kcal/mol (against singlet). For CH, and CH(SiH3), the GVB(3/6)-PP results are nearly identical with CCCI. However, for CF,, CC12, CHF, and CHC1, the AEST's are too small by 5-10 kcal/mol. This is because the GVB(3/6)-PP wave function does not allow the simultaneous u and T charge-transfer configurations important in the singlet state. Since GVB( 1/2) accounts for neither u or T charge transfer, those AEST'sengender larger errors than GVB(3/6)-PP. The CI-SD approach [starting from either H F or GVB( 1/2)] treats the singlet and triplet states inequivalently, both in terms of correlation [less correlation error for the triplet at the GVB( 1/2) level] and in terms of spin coupling [the triplet can have up to six open shell electrons (nine spin couplings) whereas the singlet has a maximum of four open shells (two spin couplings)]. Both of these biases favor the triplet, leading to AEsT's too high (by 4-9 kcal/mol) for CH, and CH(SiH,) (ground state triplets) and too low (by 5-6 kcal/mol) for C H F and CHCl (ground-state singlets). In constrast, both the CCCI and RCI*IICI methods allow the same maximum number of open shell electrons (six) and include the same correlations for each state. The MP4 method (Merller-Plesset perturbation theory through fourth order) begins with a U H F (unrestricted HF) reference state and hence is also biased toward the triplet. Thus MP4 is high by 7.8 kcal/mol for CH2and by 7.3 kcal/mol for CH(SiH3),and low by 5.0 kcal/mol for CHF. The CEPA method (coupled electron pair approximation) is similar to GVB and yields similar results for the one case reported [high by 2 kcal/mol for CH(SiH3)]. In summary, only the CCCI and RCI*IICI methods provide accurate assessments of the singlet-triplet splittings in all six carbenes examined. New experimental methods are being de~ e l o p e d which '~ should be able to test these new predictions. Acknowledgment. This work was supported by the National Science Foundation (Grant No. CHE83-18041) and the Shell Companies Foundation. E.A.C. acknowledges a National Science Foundation predoctoral fellowship (1 982-1 985), a research grant award from the International Precious Metals Institute and Gemini Industries (1985-1986), and a S O H 1 0 fellowship in Catalysis (1987). (18) Kohler, H. J.; Lischka, H. J . Am. Chem. SOC.1982, 104, 5884. (19) Goddard, J. D.; Yoshioka, Y.; Schaefer 111, H. F. J . Am. Chem. SOC. 1980, 102, 1644.
