Theory of the Hyperfine Splittings of Pi-Electron Free Radicals. II. Nonempirical Calculations of Methyl Radical (Planar)

Nonempirical calculations of the ground‐state electronic wavefunction, energy, and proton and carbon‐13 contact hyperfine splittings of methyl radical in its planar configuration are performed using the spin‐restricted SCF method and configuration interaction including all spin configurations involving up to double replacement of space orbitals. Two minimum basis sets of Slater‐type orbitals are employed, one in which orbital exponents are chosen according to Slater's rules (unoptimized) and the other in which they are optimized through minimization of the SCF energy. Some calculations are made which involve double‐zeta basis sets. Considerable progress toward the goal of accurate ab initio calculations of hyperfine splittings is reported [S. Y. Chang, E. R. Davidson, and G. Vincow, J. Chem. Phys. 49, 529 (1968), paper I in this series]. The proton splittings computed using the unoptimized (unopt.) (1) and optimized (opt.) (2) minimum basis sets and a double‐zeta set (3) (free atom exponents on carbon and ${\zeta }_h\text{\hspace{0.17em}=\hspace{0.17em}1.00, 1.26)}$ are − 33.1, − 43.8, and − 38.2 G, respectively (− 23 G exptl.). A “hybrid” minimum‐basis calculation using the optimized exponents on carbon and ${\zeta }_h\text{\hspace{0.17em}=\hspace{0.17em}1.0}$ yields − 27.5 G. Carbon‐13 hyperfine splittings computed with the minimum basis sets are + 142.4 (unopt.) and + 140.5 G (opt.) (+ 38 G exptl). Spin polarization of the valence shell dominates the splitting. Much better agreement with experiment is obtained using the double‐zeta set, i.e., + 25.7 G. In this case the contributions arising from inner‐ and valence‐shell excitations are comparable in magnitude and opposite in sign. Other features of this work include (1) calculation of SCF energies and contributions to the correlation energy for the three basis sets identified above, namely − 39.415 (1), − 39.487 (2), and − 39.547 a.u. (3) (− 39.60 ± 0.02 a.u. estimated HF limit), and − 0.054 (1), − 0.061 (2), and − 0.106 a.u. (3) (− 0.2 a.u. estimated correlation energy), (2) a population analysis of the minimum basis wavefunctions, and (3) transformation of the minimum basis canonical SCF–MO yielding equivalent sigma bonding ${\mathrm{(B}}_i)$ and antibonding ${\mathrm{(A}}_i)$ orbitals. $B_i$ hybridizations deviate significantly from ${\mathrm{sp}}^2$ , namely ${\mathrm{sp}}^{\text{1.36}}$ (unopt.), and ${\mathrm{sp}}^{\text{1.45}}$ (opt.). A detailed analysis of the contributions of the various configurations to the hyperfine splittings is presented. This analysis leads to the conclusion that a good approximation in computing the proton splitting can be obtained from the SCF results for $B_i$ and $A_i$ and a first‐order perturbation theory calculation of the mixing coefficient for the configuration representing the $B_i{\mathrm{\to A}}_i$ excitation. Calculations of the electron‐nuclear coalescence cusps for the SCF–MO's and spin and charge densities are reported. The spin‐density cusp at the proton is correlated with the proton hyperfine splitting. Comparison is made with previous calculations of CH₃· and with our approximate calculation of the proton splitting of CH· fragment (paper I). The results of I are found to be in very good agreement with those of the ab initio calculations of CH₃·.