Three-center Gaussian-type-orbital integral evaluation using solid spherical harmonics

Abstract

An analysis of various approaches to evaluating overlap and Coulomb matrix elements involving Gaussian-type-orbital primitive functions whose angular parts are solid spherical harmonics is given. Direct (angular momentum) coupled, direct uncoupled, and recursive evaluations are considered. The direct uncoupled evaluation involves some remarkably simple and transparent expressions. Using n-j symbols on a computer requires enough intermediate summations that uncoupled methods are best, particularly for higher angular momentum. Recursive methods may be competitive for low angular momenta.