1209.1258 (Krzysztof Pachucki)

On the correlated exponential functions in high precision calculations
for diatomic molecules    [PDF]

Krzysztof Pachucki

Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional integral representation is found, which is suited for the direct numerical evaluation. Together with recurrences in powers of electron distances, it makes possible the use of exponentially correlated basis in the molecular calculations. Alternative approach via the Taylor series in the internuclear distance is also investigated. Although numerically slower, it can be used in cases when recurrences lose stability. Separate analysis is devoted to molecular integrals with integer powers of interelectronic distances $r_{12}$ and the vanishing corresponding nonlinear parameter. Several ways of their evaluation is proposed.

View original: http://arxiv.org/abs/1209.1258