Alternative basis functions for L2 calculations on the molecular continuum. II. Integrals with higher-order functions.

Abstract

By differentiation of the expressions for the basic s-type integrals previously presented, analytic expressions are here derived for integrals, relevant for quantum-chemistry calculations, involving oscillating Hermite Gaussian functions (OHGF's) and many-center Hermite Gaussian functions (HGF's) of any order. The OHGF is the product of a HGF and a radial trigonometric factor cos(kr), and has been proposed for describing the continuum orbitals in ${\mathit{L}}^{2}$ calculations on molecules. The resulting expressions are compact and particularly suitable for numerical implementation on a computer, while the increase in the computational effort of the integral evaluation with respect to the s-type functions is estimated to be of the same order as that found in the standard case of simple Gaussian functions. Applications of the OHGF basis to the calculation of continuum states are presented and compared to the exact results for test cases: the hydrogen atom and the ${\mathrm{H}}_{2}^{+}$ molecule, in order to discuss advantages and limitations of the proposed approach.