Matrix elements of z/r³ and (3z²-r ²)/r⁵ in a slater basis for linear systems

Abstract

Methods are given, which are adequate for computation of all matrix elements of the operators z/r3 and (3z2-r 2)/r5 in a Slater basis set for linear systems with an arbitrary number of nuclei. The one-center integrals are evaluated analytically. The remainder are evaluated using a two-dimensional numerical quadrature after having modified the integrand to remove any infinities in those cases where they occur. With reasonable grids, these procedures are adequate for the evaluation of the force on, and the electric field gradient at, the nuclei in linear systems with an accuracy of four to five decimal places (in atomic units). This is all that is, in general, justified by the accuracy of the wavefunction.