Analytical evaluation of three-center one-electron integrals of rNYML (θ,ϕ) with slater-type atomic orbitals

Abstract

Theoretical prediction of molecular properties, such as quadrupole coupling tensor, electron-proton hyperfine interaction, chemical shift, and spin-orbit coupling, requires computation of matrix elements of rNYML, where YML is a spherical harmonic. Formulas for two- and three-center one-electron integrals of rNYML with Slater-type atomic orbitals are derived. Use is made of Fourier-transforms, generalized-function theory, and complex variable theory. The final formulas involve spherical harmonics and functions related to exp (x) and to the exponential integral, but nothing more complicated. Two alternative sets of formulas are given, but only one is valid when N–L is an even, negative integer.