Basis sets in correlated effective potential calculations

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Abstract
Due to the behavior of the pseudo-orbitals near nuclei, basis set selection in shape-consistent effective potential calculations can be problematic in studies using correlation techniques based on virtual orbital expansions (configuration interaction, etc.). In this paper we quantify the magnitude of the problem and give simple rules for the selection of correlating functions in a manner that parallels the use of simple diffuse primitives in all-electron work. Our calculations show the problem to be substantial for s and p basis sets, and to involve both one- and two-center effects, but is negligible for higher l. We also show that the problems can be avoided by the inclusion of one additional high exponent s primitive in the basis set and by augmenting p primitives with a higher exponent function so as to give zero first derivatives at the nucleus. By this recipe, computed s and p shell correlation energies in single and double promotion configuration interaction calculations can be increased by 3%–7%, as compared to basis sets using simple diffuse primitives for correlation.