Proc. Nati. Acad. Set. USA Vol. 74, No. 2, pp. 410-413, February 1977 Chemistry Electron affinity of the methyl radical: Structures of CH3 and CH3- (anions/molecular orbitals/configuration interaction) DENNIS S. MARYNICK AND DAVID A. DIXON Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138 Communicated by William N. Lipscomb, November 22,1976 ABShACI' Ab initio self-consistent field and configuration We also present calculated potential curves for the out-of-plane interaction calculations are presented for the methyl radical and bending motions of these molecules, vibrational frequencies anion. The methyl radical is shown to be planar (Db), while the anion is pyramidal (C3v). The methyl anion is unstable with re- for the out-of-planb bending and symmetric stretch of CH8, and spect to the limit of CH3 plus an electron by 2-8 kcal/mole. expectation values for several one electron operators over the Potential curves for the out-of-plane bending motions of both full CI wavefunction. molecules are presented. Radicals and anions are considered to be extremely important CALCULATIONS as intermediates in many reaction mechanisms. Perhaps the All calculations were performed with computer programs most elementary examples of these species in organic chemistry previously described (15). For CH3, the Slater orbital basis set are the methyl radical (CH3) and the methyl anion (CH3-). chosen was: C(lsls'2s2s'3s2p2p'2p"3d), and H(ls2s~p). The However, in spite of their apparent simplicity, there have been exponents of the valence shell s and p orbitals were partially no fully reliable experimental or theoretical determinations of optimized at the SCF level without including polarization the relative stability of these two molecules. In fact, CH3- has functions, and the exponents for the parization functions were not even been observed in the gas phase (1). taken from optimied values for diatomic 0-H at the experi- Although the relative stabilities of these two simple molecules mental CH3 bond distance (R. M. Stevens, personal commu- have not yet been obtained, a number of studies on the struc- nication). The CI calculations included all single and double tures of these molecules have been carried out. Both theoretical excitations from the valence shell except tbose involving the five (2-6) and experimental (7-9) approaches have predicted CH3 orbitals with SCF eigenvalues greater than 8.0 atomic units. toUbe planar, although a' few studies have suggested the possi- Previous calculations on ammonia suggest that exclusion of bility of nonplanarity (10-12). Two recent self-consistent field these orbitals should have very little effect on the calculated CI (SCF) calculations have indicated that CHs- is nonplanar, with energy (15). For planar OHs(Dh), 2026 determinants were a bond angle of about 1100 (2, 13). included in each CI calculation. Degeneracy was not explicitly The diffe rence in energy between CH3 and CH3- is the included. The bond length for the D3h molecule was optimized electron affinity, EA by quadratic interpolation at the full SCF-CI level; however, for nonplanar geometries the bond length was obtained as a EA = E(CH3) E(CH&-) [1] function of bond angle from an optimization using the same A positive value shows that CH3- is stable with respect to the basis set without polarization functions but incluciig CI. The radical plus a free electron. The adiabatic electron affinity is resulting bond lengths for the nonplanar geometries were then the energy difference between the ground states of CH3 and scaled by a factor of 0.991, which brings the computed value CH3-, while the vertical electron affinity is the energy differ- for the bond length in the planar form into agreement with the ence between CH3- and CH3 calculated at the equilibrium optimized value for the large scale calculation including po- geometry of CH3. In order to calculate the electron affinity of larization functions. CH3, the change in correlation energy must be adequately The nonplanar CH3(C3) calculations includedall single and accounted for. However, the only attempt to calculate corre- double excitations from the valence shell except tho described lation energy changes for this reaction starting from a near above. A total of 3569 determinants were included. Degeneracy Hartree-Fock limit wavefunction used the independent elec- was again not explicitly included, but all wavefunctionsfor CH3 tron pair approximation (14), in which the full eigenvalue display the correct molecular symmetry. Because the SCF problem is not explicitly solved. This method yielded a calcu- program used here employs Nesbet's method of symmetry and lated electron affinity of +2.6 kcal/mole (2), indicating that equivalence restrictions (16), the C3v SCF orbitals are in prin- CHs- is energetically stable with respect to the limit CH3 plus ciple not eigenfunctions of the exact Fock operator; however, an electron. in practice this is not a serious problem as long as a large scale In this paper we present fully ab initio SCF and configura- C1 is included. Computation of SCF-CI wavefunctions for tion interaction (01) calculations for these molecules using a planar CH3 using C3, symmetry yielded a wavefunction with very large basis set and nearly all single and double excitations a total energy only 0.3 kcal/mole higher than the wavefunction from the valence shell. We show that CH3 is indeed planar, that calculated using the full D3h symmetry. The final basis set for CH3- is pyramidalJ and that the 'Al state of CH3- dominated CH3 is presented in Table 1, while the calculated energies at by the electron configuration various geometries are given in Table 2. The basis set for CH3- was obtained by first augmenting the lal22al21e43a,2 [2] CH3 basis with one diffuse p function. Diffuse functions are is 2-8 koal/mole less stable than the 2A2"groundstate ofCH3. knownto be necessary for a proper molecular orbtaldescription of the lone pair in this molecule (18). Thes andp orbital valence Abbreviations: SCF, self-consistent field; CI, configuration interac- shell exponents were then extensively optimized without po- tion. larization functions, the polarization functions were added, and 410 Downloaded by guest on September 24, 2021 Chemistry:L Marynick and Dixon Proc. Natl. Acad. Sci. USA 74 (1977) 411 Table 1. Basis sets Table 3. Geometries and total energies of CH3- CH3 CH3- r* 0 Et Atom Orbital exponent exponent 1.09 120 -39.70772 C is 9.055 9.055 1.08 120 -39.70787* is 5.025 5.025 1.07 120 -39.70762 2s 1.406 1.310 1.10 114 -39.71036 2s 1.910 1.994 1.10 111 -39.71094 3s 6.067 6.067 1.10 108 -39.71081 2p 4.796 5.546 1.10 110.0 -39.71098§¶ 2p 1.989 1.976 1.11 110.0 -39.71079 2p 1.122 1.067 1.09 110.0 -39.71081 2p 0.750 1.087 118.5 -39.70868 2p - 0.310 1.107 104.6 -39.70988 3d 1.720 1.80 1.112 97.2 -39.70443 H is 1.494 1.643 2s 1.530 1.423 * Angstroms. 2p 1.740 1.740 t Atomic units. The computed minimum of planar CH3- is 1.081 A, but the calcu- lation at r = 1.080 A was considered to be adequate. The SCF energy was is -39.52005 atomic units. the d orbital exponent optimized at a geometry interme- § The SCF energy at the minimum is -39.52289 atomic units. diate between the C3, minimum and the planar form. All ex- ¶ Variation ofthe exponent ofthe most diffuse p orbital at the SCF-CI ponent optimizations were performed at the SCF level of ap- level was performed to demonstrate that this orbital was sufficiently proximation. Addition of a diffuse s function lowered the en- diffuse. Lowering of the exponent raised the energy. ergy of the C3, molecule only 0.2 kcal/mole, and this function was not considered necessary. Finally, the most diffuse p CH3 is 1.079 A, in exact agreement with experiment (7). The function was split to give a "double zeta" representation of the vibrational frequency for the out-of-plane bend (computed by diffuse part of the wavefunction. This did not result in any numerical integration of the vibrational Schr6dinger equation lowering of the SCF energy, but did provide diffuse virtual using the potential of Fig. 1) is 612 cm-1, compared to the ex- orbitals which will be important in providing a proper de- perimental value of about 580 cm-' (7). The zero point energy scription of the correlation energy when the CI technique is for this mode is 281 cm-1. Thus, this mode is significantly an- used. Excitations into the four highest SCF orbitals, all with harmonic. eigenvalues greater than 9.0 atomic units, were excluded. After The calculated equilibrium geometry for CHIC is in excellent accounting for symmetry, a total of 1435 determinants were agreement with previous estimates (2, 13). The bond length at included in the CI. The geometries of the C3, inimum and the minimum is 1.100 A, which shortens to 1.081 A in the planar the D3h transition state were optimized at the SCF-CI level. The form. A degree of shortening of this bond length in the planar basis set for CH3- is given in Table 1, and the calculated molecule is expected (15). The barrier to inversion is 1.95 energies are presented in Table 3. kcal/mole including CI, and 1.78 kcal/mole without CI. This small CI correction is totally consistent with previous results for RESULTS AND DISCUSSION ammonia (17) and phosphine (18). For CH3- the zero point As indicated by the potential curve presented in Fig.