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

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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.