Calculation of hyperfine splitting constants with Slater-type cusp basis by the symmetry adapted cluster-configuration interaction theory

A method of calculating hyperfine splitting constants (hfsc) of open-shell radicals is reported. Since the hfsc reflects a very local property of the wave function at the position of the nuclei, we use Slater-type orbitals (STOs) which have cusps at the centers. Spin correlation (spin polarization) and electron correlation are taken into account with the use of the SAC-CI (symmetry adapted cluster-configuration interaction) theory. Configuration selection is not done since energy and spin density are very different properties. The dimensions of the matrices involved in the SAC-CI method are small enough to permit such a procedure. The integrals necessary for the SCF and SAC-CI methods are calculated by the STO-6G method with the use of the available Gaussian program, and the hfsc’s and the cusp values are calculated from the original STOs. Several STOs are examined for H+2 and H2O+. The resultant standard method is applied to the organic π and σ radicals CH3, CH3CH2, CH3NH, CH3O, CH3OCH+3, H2CO+, CH2CH, and HCO. The present results of hfsc’s show generally better agreement with experiment than the previous calculations based on the Gaussian-type orbitals (GTOs). In particular, the present results are free from the theoretical dilemma seen for the GTO calculations that a variationally better wave function does not necessarily give a better hfsc. This is important in developing a reliable theory for calculating hfsc’s.