Non-empirical versus empirical choices for overlapping-sphere radii ratios in SCF-Xα-SW calculations on ClO₄^- and SO₂

Abstract

Two non-empirical schemes for establishing ratios of atomic sphere radii for Xα-SW calculations are proposed and compared with known methods of partitioning molecules into atomic fragments along paths of maximum change in electrostatic potential or charge density. In the initial Xα-SW molecular charge distribution, the radius of a sphere around each atom containing the atomic number of electrons is shown to be constant within a few per cent no matter what atomic charges are assumed in constructing the charge distribution. This contrasts with the radius of a sphere containing the number of electrons put in for the atom in calculating its atomic charge density, which shows a significant inverse variation with the assumed charge. Ionization energies for ClO₄ ^- and SO₂ are calculated using ratios of sphere radii established both from the atomic number sphere sizes and from Slater's empirical atomic radii. The results are compared with experiment and with HF-LCAO calculations. The Xα-SW calculations using atomic number radii ratios are in the best overall agreement with experiment.