Collect. Czech. Chem. Commun. 1998, 63, 1264-1284

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

Petr Čársky and Tomáš Reschel

J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, 182 23 Prague 8, Czech Republic


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.

Keywords: Electron scattering; Two-electron integrals; Exchange free-free integrals; Hybrid integrals; Ab initio methods; Quantum chemistry.