Theory of the Hyperfine Splittings of Pi-Electron Free Radicals. III. Methyl Radical in a Pyramidal Configuration: Temperature Dependence of the Hyperfine Splittings

Nonempirical calculations for methyl radical (CH₃·) in a pyramidal configuration ${\mathrm{(C}}_{\text{3υ}})$ were performed using two minimum basis sets of Slater‐type orbitals, one in which orbital exponents were chosen according to Slater's rules (unoptimized) and the other in which they were optimized by minimization of the SCF energy. The spin‐restricted SCF plus configuration‐interaction method, including all spin‐adapted configurations with single and double excitations of space orbitals, was employed. The temperature dependence of the contact hyperfine splittings was computed assuming that the variation with temperature arises from the out‐of‐plane bending motion. Agreement with experiment at various temperatures is good. The optimized‐basis values of the temperature coefficient of the proton splitting, ${\mathrm{da}}^H\mathrm{\hspace{0.17em}/\hspace{0.17em}dT}$ , are about 20%–50% too large and the unoptimized‐basis results are about 10%–25% too small. Temperature coefficients of the carbon‐13 splitting calculated using the optimized and unoptimized basis sets also bracket the experimental values, from which they deviate by less than 10%, which is within the experimental uncertainty. The variation of the spin densities at the magnetic nuclei with the out‐of‐plane angle is analyzed in detail. Other results of the calculation are discussed, namely, the equilibrium molecular geometry, an approximate frequency for the bending motion, and the incomplete orbital following.