Analytical evaluation of relativistic molecular integrals. II: Method of computation for molecular auxiliary functions involved

Abstract

The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The non-analyticity of these orbitals at r= 0 , however, requires analytical relations for multi-center integrals to be derived. This is nearly insurmountable. Previous papers by the present authors eliminated this difficulty. Highly accurate results can be achieved by the procedure described in these papers, which place no restrictions on quantum numbers in all ranges of orbital parameters. The purpose of this work is to investigate computational aspects of the formulae given in the previous paper. It is to present a method which helps to increase computational efficiency. In terms of the processing time, evaluation of integrals over Slater-type orbitals with non-integer principal quantum numbers is competitive with those over Slater-type orbitals with integer principal quantum numbers. © 2018, Accademia Nazionale dei Lincei.