We employ natural steric analysis (introduced in a previous paper) to evaluate a set of effective ab initio van der Waals radii for free and covalently bonded atoms and ions of H-Ar (Z=1-18) determined using a helium atom probe. We critically examine the degree of anisotropy, dependence charge state, and other intrinsic limitations of a simple atomic van der Waals hard sphere representation of the accurate steric surface. We also evaluate the ab initio steric force (gradient of steric energy at van der Waals contact) as a measure of ''hardness'' of the atomic van der Waals spheres. Comparison with empirical van der Waals radii shows reasonable agreement (within the acknowledged uncertainties of the latter values in the most important cases), but suggest a wider range of variability and anisotropy than could be adequately represented by any fixed constant radius. Simple expressions for incorporating the dependence on natural atomic charge or correcting for other types of intermolecular contact are given, extending the accuracy and usefulness of the atomic van der Waals sphere concept. (C) 1997 American Institute of Physics.