ABINITIO QUADRATIC CONFIGURATION-INTERACTION CALCULATION OF THE ISOTROPIC HYPERFINE COUPLING-CONSTANTS IN THE ETHYL RADICAL

The isotropic hyperfine coupling constants in the electronic ground state of the ethyl radical have been determined by means of ab initio molecular orbital theory. Extensive inclusion of electron correlation in a single-determinant unrestricted Hartree-Fock (UHF) description is coupled with finite (Fermi contact) field perturbation theory to derive the required spin density distribution. Results obtained with a modest polarized double-zeta basis set are already in quantitative accord with experiment. Augmentation of this basis set improves the level of agreement still further. An analysis is made of the correlation contributions to the magnetic coupling at each nucleus. At the radical center, C-13-alpha, a large (approximately 245 MHz) positive spin polarization estimated by the UHF method to be developed in the valence shell is seen to be sharply reduced (to approximately 155 MHz) by the inclusion of electron correlation. Taken together with the computed core polarization (approximately -75 MHz), the direct spin density (approximately 20 MHz) from the highest occupied alpha molecular orbital, and a vibrational correction (approximately 15 MHz) due to zero-point out-of-plane wagging of the methylenic hydrogens, the predicted carbon-13 splitting is within 1% of observation. At the adjoining methylenic hydrogens almost the entire coupling constant derives from spin polarization which is overestimated at the UHF level and which again is moderated by the inclusion of electron correlation. A small (< 2 MHz) vibrational correction brings the computed value into essentially exact agreement with the observed splitting. At the adjacent carbon, C-13-beta, an analysis of the UHF wave function reveals that the observed negative coupling constant is developed almost entirely from spin polarization in the valence shell, again overestimated in the UHF model. A large positive contribution from double excitations reduces the computed value to produce a result close to experiment. The hyperconjugative contribution to the spin density at the beta-hydrogens is the most difficult to describe. Correlation effects are entirely negligible for the beta-hydrogen which bisects the methylenic pair. At the out-of-plane beta-hydrogens, the most extensive calculations reveal only a 6-MHz drop (approximately 15%) in the UHF estimate upon the inclusion of electron correlation. Straightforward motional averaging, assuming free rotation, leaves the result of the most complete calculation still about 10% below the experimentally observed splitting.