Analytical quadrature method using recurrence formulas for two-electron integrals of frequency-dependent Breit interaction.

A recursive scheme was proposed to calculate two-electron integrals of frequency-dependent Breit interactions in electronic structure calculations using Gaussian basis functions. As shown in a previous study [R. Ahlrichs, Phys. Chem. Chem. Phys. 8 (2006) 3072-3077], the vertical recurrence relation for the two-electron integrals of the general two-body potential is valid. In addition, the authors have shown that the horizontal case is also valid. Explicit expressions for generalized molecular incomplete gamma function corresponding to the frequency-dependent Gaunt and gauge potentials were then derived, along with their asymptotic formulas. In addition, an implementation for computing the generalized molecular incomplete gamma function was proposed. Through numerical calculations, the shape of the curves of the generalized molecular incomplete gamma functions were found to vary significantly from that of the zero-energy case with the increase in the energy variable.