Analytical evaluation of the electrostatic potential for diatomic molecules

Abstract

The technique of expanding Lowdin alpha-functions in a Taylor series has been further developed and applied to the problem of the electrostatic potential due to H{sub 2} with given 1s, 2s, 2p Slater-type orbitals. In contrast to other methods, the approach is completely analytic, and capable of arbitrary precision. The ultimate accuracy of our method is dependent upon the number of partial waves used; here by use of only 13 harmonics excellent results are achieved. The methods are readily generalized to larger molecules. The electron-molecule static interaction potentials is of central importance to calculations of cross sections for electron-molecule collisions. In this paper, using the diatomic hydrogen molecule of Fraga and Ransil, the authors introduce a fully analytic method and make a few comparisons with computer runs using the codes of Morrison and Schmid et al. They, as well as others, need numerical integrals for the potential. The authors analytical methods avoid cancellation errors and singularities by expanding the exponentials in the Lowdin alpha-functions, which are used to represent displaced orbitals in a spherical harmonic series.