Alternative basis functions for L2 calculations on the molecular continuum. I. The basic prototype integrals.

Abstract

Alternative square-integrable (${\mathit{L}}^{2}$) basis functions, the oscillating Hermite Gaussian functions (OHGF's), are proposed for describing the continuum orbitals in ${\mathit{L}}^{2}$ calculations on molecules. Each function is the product of a Hermite Gaussian function (HGF), which gives the proper dumping and angular factor, and a radial trigonometric function, cos(kr), which describes the oscillating asymptotic behavior of a continuum orbital. Analytic expressions for the one- and two-electron integrals involving s-type OHGF's and many-center s-type HGF's are derived and their numerical implementation is discussed in detail. The present proposal of adopting a mixed basis set of OHGF's and many-center HGF's for the ${\mathit{L}}^{2}$ description of bound and continuum molecular states is compared with the other types of basis functions currently employed. With respect to these, it requires a greater computational effort in the integral evaluation, but it also allows an accurate description of the electronic continuum in general polyatomic systems.