Electron Affinity of the Methyl Radical: Structures of CH3 and CH3- (Anions/Molecular Orbitals/Configuration Interaction) DENNIS S

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 calculation 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. 1, the energy for the bending mode is 325 cm-1 with a corresponding methyl radical is planar. The optimized C-H bond length in inversion splitting of 27 cm-1. The adiabatic electron affinity (computed at the equilibrium Table 2. Geometries and total energies of CH3 geometries without corrections for zero point vibrational energy) is calculated to be -8.3 kcal/mole. We would expect the Symmetry r* o Et

D3h 1.086 120 -39.72414 I , I I I , I I 1.079 120 -39.72424t 1.077 120 -39.72423 16.0K CH3 CH3 1.068 120 -39.72398 C3v 1.086 120 -39.72371 W4OF 1.079 120 -39.72381 12.0[- 1.081 118 -39.72266

1.084 115 -39.72009 0 E 1.097 § 110 -39.71342 I- 8.0 1.092 106 -39.70641 6. EAt EA1 * Angstroms. w 4.0 t Atomic units: 1 atomic unit = 627.5 kcal/mole = 2625.46 kJ/mole = 219.468 cm-1 = 27.21 eV. 2.0 The computed SCF energy at the minimum is -39.57277 atomic units. The Koopmanns theorem ionization potential is 10.08 eV. The symmetric stretch vibrational frequency is 3177 cm-1 calculated -30 0 30 -30 0 30 from small displacements assuming a harmonic potential. § This bond length was used in order to directly compare the relative BENDING ANGLE energies of CH3 and CH3- near the equilibrium geometry of FIG. 1. Potential surfaces for the v2 modes of CH3 and CH3-. The CH3-. out-of-plane angle is in degrees. Downloaded by guest on September 24, 2021 412 Chemistry: Marynick and Dixon Proc. Natl. Acad. Sci. USA 74 (1977) Table 4. Estimated errors for CH3 Table 6. Comparison of (r2) for CH3, CH3-, and NH3 Energy component Estimated error* rH2 rc2 SCF error -0.004 CH3D3h 66.803 29.382 Inner shell correlation -0.055t CH3C~* 66.342 30.012 Relativistic correction -0.013* OHC3C3 92.671 51.616 Quadruple excitations -0.012§ NH3 tOC3V 60.074 26.497 Total -0.084 SCF-CI energy -39.724¶ * At the CHj- equilibrium geometry. Estimated total energy -39.80811 t Ref. 15. Experimental energy -39.824** Difference -0.016 (10.0 kcal/mole) affinity is -2.7 kcal/mole. However, the effect of triple exci- * Atomic units. tations, which we have not estimated, will favor CH3 over the t Similar to the value estimated in ref. 2. closed shell CH3- (22). This reinforces our basic conclusion that t Ref. 19. CR3- is energetically unstable with respect-to the limit of CH3 § The effect of quadruple excitations on CH3- was estimated as de- plus an electron. Our results are, of course, strictly relevant only scribed in ref. 20. The quadruple excitation energy in CH3 was as- in the gas phase. In solution, it is probable that CH3- is stabilized sumed to be proportional to the relative number of excitations in CH3, and CH3-. by a metal gegenion or by solvent. ¶ 99.75% of the experimental energy. In Table 5, we present expectation values of selected one- 11 99.96% of the experimental energy. electron operators for CH3. The direct comparison of the value ** Ref. 21. of (r2) for CH3, CH3-, and NH3 that is presented in Table 6 is especially interesting. The-very large values of (r2) for CH3- difference in zero point vibrational energy for these two mol- relative to CH3 and NH3 is a direct measure of the diffuseness ecules to be dominated by the difference in the v2 bending of the CH3- electron distribution. The much larger extent of mode, but this correction is only 0.1 kcal/mole, favoring CR3. the electron density in CH3- as compared to NH3 shows that The vertical electron affinity (computed at the equilibrium the two molecules are quite different, even though they are geometry of CR3) is -10.3 kcal/mole. Our CI correction to the isoelectronic. Such a difference can also be seen in the factor electron affinity is very large (+23 kcal/mole), and it seems of three decrease in inversion barrier height for CH3-'as clear that accurate calculations of molecular electron affinities compared to NH3 (15). must explicitly consider correlation energy changes, especially The possibility that the adiabatic electron affinity of CH3 when one is trying to obtain the electron affinity of an open shell could be in the range -2 to -6 kcal/mole suggests that the molecule. potentials for the V2 modes of these molecules may cross be- In Table 4, we estimate errors in the CR3 calculation, for tween the two equilibrium geometries. Thus, motion along the which the total energy is known experimentally (21). By in- v2 mode in CH3- could lead to autodetachment. However, cuding reasonable estimates for SCF basis set inadequacy, exploration of this possibility must await an even more extensive quadruple excitations, inner shell correlation effects, and rel- treatment of correlation energy. ativistic effects, we can account for all but 0.016 ± 0.01 atomic Since CH3-(lA,) is unstable with respect to CH3, electron unit of the experimental energy. This difference almost cer- scattering experiments from CH3 should exhibit a shape reso- tainly arises from incompleteness of the basis set at the CI level nance between 2 and 10 kcal/mole due to the existence of this and the lack of inclusion of triple excitations. Actually, the 'Al state of the negative ion. Since the lifetime of the state may absolute errors are much less important than the relative errors be long due to the curve crossing possibility, it is possible that in the CH3 and CH3 calculations. The relative error for neglect very sharp resonances may be observed (23, 24). of inner shell correlation has been estimated as +0.002 atomic The Milton Fund of Harvard University is gratefully acknowledged unit (2), and we estimate the relative error of quadruple exci- for computing support. D.A.D. thanks for the Society of Fellows, tations as +0.007 atomic unit (22) (Table 4). If no other effects Harvard University for a Junior Fellowship. We thank Dr. R. M. Ste- are important, our estimated value of the adiabatic electron vens for the use of his programs and helpful discussions. 1. Brauman, J. I., Eyler, J. R., Blair, L. K., White, M. J., Comisarow, Table 5. One-electron operator expectation M. B. & Smyth, K. C. (1971) J. Am. Chem. Soc. 93, 6360- values for CH3 6362. 2. Driessler, F., Ahlrichs, R., Staemmler, V. & Kutzelnigg, W. (1973) Expecitation value* Theor. Chim. Acta 30,315-326. 3. Ishikawa, Y. & Binning, R. C. (1976) Chem. Phys. Lett. 40, Operator SCF SCF-CI 342-346. 4. Morokuma, K., Pedersen, L. & Karplus, M. (1968) J. Chem. Phys. i/rH 4.6211 4.6167 48,4801-4802. l/rC 16.2171 16.2281 5. Millie, P. & Berthier, G. (1968) Int. J. Quantum Chem. 2S, rH2 66.8029 66.9032 67-73. rc2 29.3822 29.4825 6. McDowell, K. (1972) Ph.D. Dissertation, Harvard University, Pi rH -18.352 -18.352 Cambridge, Mass. P,/rH2 -1.5837 -1.5676 7. Herzberg, G. (1967) Electronic Spectra of Polyatomic Molecules P2r 2 112.6197 112.2620 (Van Nostrand, Princeton, N.J.), p. 609. P2 /rH 6.2934 6.3024 8. Andrews, L. & Pimentel, G. C. (1965) J. Chem. Phys. 47, P2/rH 3 1.6903 1.6856 3637-3644. 9. Ogilvie, J. F. (1976) Spectrosc. Lett. 9,203-210. * Atomic units. The carbon is at the origin and the hydrogen is at x 10. Koenig, T., Balle, T. & Snell, W. (1975) J. Am. Chem. Soc. 97, = 2.0390808, y = z = 0. 662-663. Downloaded by guest on September 24, 2021 Chemistry: Marynick and Dixon Proc. Nati. Acad. Sci. USA 74 (1977) 413

11. Blustin, P. H. & Linnett, J. W. (1975) J. Chem. Soc. Faraday 18. Marynick, D. S. & Dixon, D. A. (1976) Discuss. Faraday Soc., in Trans. 2 71,1058-1070. press. 12. Bischof, P. (1976) J. Am. Chem. Soc. 98, 6844-6849. 19. Karl, R. E. & Csizmadia, I. G. (1967) J. Chem. Phys. 46, 13. Duke, A. J. (1973) Chem. Phys. Lett. 21, 275-282. 4585-4590. 14. Jungen, M. & Ahlrichs, R. (1970) Theor. Chim. Acta 17,339- 20. Langhoff, S. R. & Davidson, E. R. (1974) Int. J. Quantum Chem. 347. 8,61-72. 21. Ritter, J. D. S. (1966) Ph.D. Dissertation, Illinois Institute of 15. Stevens, R. M. (1974) J. Chem. Phys. 61, 2086-2090. Technology, Chicago, Ill. 16. Nesbet, R. K. (1955) Proc. R. Soc. London Ser. A 230, 312- 22. Bunge, C. F. (1968) Phys. Rev. 168,92-103. 321. 23. Schulz, G. J. (1973) Rev. Mod. Phys. 45,378422. 17. Stevens, R. M. (1971) J. Chem. Phys. 55, 1725-1729. 24. Schulz, G. J. (1973) Rev. Mod. Phys. 45,423-486. Downloaded by guest on September 24, 2021