Evaluation of Molecular Integrals in a Mixed Gaussian and Plane-Wave Basis by Means of the Faddeeva Function and Its Derivatives

Abstract

We present formulas for two-electron free-free exchange integrals and integrals with three Gaussians and one plane-wave function that are required in calculations of electron scattering by polyatomic molecules. The formulas of integrals with p- and d-type Gaussians were obtained by differentiation of the fundamental integrals (sk'|sk) and (ss|sk) that contain s-type Gaussians only and that may be evaluated by means of the Faddeeva function w. Explicit formulas are given for the two types of integrals in the spd Gaussian basis.