4360 J. Phys. Chem. 1993,97, 4360-4364 Methyl Substitution in Carbenes: Lack of Steric or Hyperconjugative Stabilization Effects on the CH3CH Singlet-Triplet Splitting Shervin Khodabandeh and Emily A. Carter’ Department of Chemistry and Biochemistry, University of California, Los Angeles, 405 Hilgard Ave., Los Angeles, California 90024-1 569 Received: August 10, 1992; In Final Form: January 29, I993 Ab initio GVB-CI (generalized valence bond theory with configuration interaction) and MCSCF (multicon- figuration self-consistent-field) calculations have been carried out on methylene and ethylidene (CH3CH) to investigate the effects of methyl substitution on the singlet-triplet splitting of methylene. We predict that ethylidene has a singlet-triplet splitting of 3 f 2 kcal/mol, about 6 kcal/mol less than the value for methylene. Furthermore, our investigations show that neither steric effects nor hyperconjugative singlet stabilization effects are large enough to account for this decrease in the singlet-triplet splitting. Rather, the dominant effects of the CH3 group are to (i) decreasep character in the nonbonding u orbital of the triplet state, (ii) reduce electron donation to the methylenic carbon, and (iii) induce repulsions in the triplet state between the CH3 and the singly occupied methylenic C PA orbital. All of these effects destabilize the triplet ground state and thus decrease the singlet-triplet splitting. I. Introduction Hyperconjugationalso potentially may affect the singlet-triplet splitting. For example, valence electron pairs on the substituent The geometric and electronic structure of substituted carbenes X in CXY may donate electron density to the nonbonding a is of importance in synthetic chemistry. The diverse reactivity orbital of the central carbon. Since this u orbital in the singlet of such molecules can be understood in terms of their electronic is empty, this should stabilize the singlet state, while the triplet structure. The singlet state (u2) has both of its nonbonding state should be destabilized since its a orbital is already singly electrons in a u orbital localized on the carbenoid carbon while occupied. the triplet state (uW) has one electron in that u orbital and one Thus, the singlet state should be stabilized by substituents that in a a orbital also localized on the carbenoid carbon. As a result, are electronegativeand/or have electron pairs that can be donated the chemistry in which they participate is very different: singlet via hyperconjugation to the empty a orbital. The triplet state, carbenes undergo one-step stereospecific reactions while triplet on the other hand, should be stabilized by substituents that are carbenes participate in two-step, nonspecific reactions.’ The bulky and/or electropositive.2 trends in the reactivity of carbenes can thus be better understood It is of interest to compare the singlet-triplet splitting in upon determination of their singlet-triplet splittings. ethylidene (CHjCH) to that of the parent carbene, methylene. The singlet-triplet gap in a substituted carbene depends strongly Such a comparison will provide information regarding the effect on the hybridization of the u and a orbitals of the central carbon. of a methyl group as a substituent on the singlet-triplet splitting For both the triplet and the singlet states, the A orbital is essentially of methylene. Several previous ab initio studies have been a pure p-like orbital while the u orbital is a hybrid of s- and p-like re~rted.3-~However, the previous work does not attempt to atomicorbitals. Thus, u orbitals with increased p character favor explain the physical basis for the effect of CH3 on the A&. a triplet ground state, since both nonbonding orbitals (u and A) Thus, our goal in the present work was to obtain quantitative lie close in energy when both have high p character, favoring information on the magnitude of the singlet-triplet splitting in singly occupied u and a orbitals. On the other hand, u orbitals CH3CH and to determine the importance and contribution of with increased s character favor singlet coupling of the electrons, each of the aforementioned factors to the observed splitting. We since increased s character substantially lowers the energy of the employ a correlation-consistent CI method shown previously to u orbital relative to the r orbital, favoring a doubly occupied u provide a balanced description of both the high and low spin orbital.* states of molecules. The hybridization of the u orbital is in turn determined by the Our calculations indicate that substitution of a methyl group following factors. First, steric effects: bulky substituents favor for a hydrogen atom in CH2 reduces the singlet-triplet splitting a large bond angle. This is accomplished by increasing s character by approximately 6 kcal/mol, yielding a A& of 3 f 2 kcal/mol in the C-X bond which will result in decreased s character (and for CH3CH. Further, we find that hyperconjugation plays a a concomitantly increased p character) in the nonbonding u orbital, minimal role, while changes in hybridization are key factors in thus favoring the triplet state.2 Second, charge-transfer effects: determining the magnitude of A&. The rest of the paper is laid substituents that are more electronegative with respect to carbon out as follows. Section I1 outlines the calculations performed, form polar bonds to carbon with electrons transferred to the section I11 presents our results, section IV discusses these results substituent. Since p orbitals have a lower ionization potential in light of previous work, and section V presents concluding than s orbitals, such polar bonds exhibit increased p orbital remarks. contributions, which in turn results in decreased p character in the nonbonding carbon u orbital.2 As a result, the u orbital will 11. Calculations Details have increased s character, favoring the singlet u2 state. By the reverse reasoning, substituents that are more electropositivethan Basis Sets. The following basis sets were used: VDZp. For carbon will form C-X bonds that utilizegreater carbons character, carbon, the standard Huzinaga-Dunning valence double-zeta yielding nonbonding uorbitals with less s character, thus favoring contraction (9~5p/[3~2p])’~J~was augmented by a set of 3d the triplet ulal state. polarization functions (p= 0.64)13 with the 3s combination of 0022-3654/93/2091-436Q$04.00/0 0 1993 American Chemical Society Methyl Substitution in Carbenes The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4361 the d functions removed. For the hydrogens, the (4s/[2s]) trensCH,CH Huzinaga-Dunning valence double-zeta basis (exponents scaled by 1.2)10,11was augmented by a set of 2p polarization functions singlet triplet (sp = 1.0). TZ2p. For carbon, the Huzinaga (1 ls7p) basis12 was con- tracted to triple-zeta for both core and valence by contracting the H3 six tightest s primitives into one, leaving the other fives primitives R(H2-CZ) = 1.084 A R(H2-CZ) = 1.086 A uncontracted, and contracting the five tightest p primitives into R(H3-CZ) = 1.091 A R(H3-CZ) = 1.088 A B(H3-CZ.H4) = 106.4’ B(H3-CZ-H4) = 108.3’ one, leaving the other two p primitives uncontracted. Two sets e(Hz-a-ci)= 112.6’ B(HZ-CZ-CI) = IIO.Oo of 3d polarization functions centered at 0.64 and scaled by 2.3 e(~4-a.~~= 109.7’ BlH4-CZ-HZ) = 108.1’ (p= 0.97 1 and 0.422) were added to the carbon valence basis, c/S-CH,CH with the 3s combination of the d functions removed. For the hydrogens, the Huzinaga” unscaled (6s) basis set was contracted to triple-zeta (by contracting the four tightest primitives into one, leaving theother two primitives uncontracted) and augmented by two sets of 2p polarization functions centered at 0.91 (optimizedI3for C-H bonds) and scaled by 2.3 (p= 1.38 and 0.60). R(H2-CZ) = 1.085 A R(HZ-C2) = 1.087 A R(H3-CZ) = 1.090 A R(H3.CZ) = 1.087 A Geometries. The geometries for CH3CH were optimized via B(H3-CZ-H4) = 105.3’ B(H3-CZ-H4) = 108.0’ analytic gradient techniquesl4JSat the GVB(2/4)-PP levelI6for B(HZ-CZ-Cl) = 118.3’ B(H2-CZ-CI) = 110.5° the triplet state and the GVB(3/6)-PP level for the singlet state B(H4-CZ-HZ) = 109.9’ B(H4-CZ.H2) = lO8.Z0 with C, symmetry imposed. Lower symmetry geometries were not explored in detail, but preliminary investigations found them Geometrles for CHI to be higher in energy. The optimum values obtained are shown singlet triplet in Figure 1. The equilibrium geometries for CH2 were taken from the Harding and Goddard GVB-POL-CI calculation^.^^ MCSCF and Calculations. GVB(MI2M)-PP. A correct CI Figure 1. Equilibrium geometries for CH&H optimized at the VDZp/ prediction of the singlet-triplet splitting relies on equivalent GVB-PP level for both cis and trans isomers. Geometries for CH2 were treatment of the singlet and triplet statesa2At a first-order level, taken from ref 17 (GVB-POL-CI calculations). this is achieved by describing the singlet state (62) by a two- configuration wave function of the form u2 - X2u2,where X is CI wave function that is not denoted as “(opt)” utilizes the GVB- optimized variationally. This is the simplest form of the PP orbitals as the CI basis and only optimizes the CI expansion generalizedvalencebond (GVB) theoryl6 and is denoted by GVB- coefficients. (1 /2)-PP, which signifies the representation of one correlated electron pair by two natural orbitals. The corresponding one- electron GVB orbitals for this case are = u + Xu and f$b = In. Results u- Xu, where theseorbitals are singlet coupled [so-called “perfect pairing”, denoted by (PP)].