Analytical calculations of molecular integrals for multielectron R-matrix methods

Abstract

Closed-form analytical expressions for one- and two-electron integrals between Cartesian Gaussians over a finite spherical region of space are developed for use in ab initio molecular scattering calculations. In contrast with some previous approaches, the necessary integrals are formulated solely in terms of finite summations involving standard functions. The molecular integrals evaluated over the finite region of space are computed by subtracting the contributions outside the region from the integrals over all space. The latter integrals can be efficiently and accurately obtained from existing bound-state algorithms. Our approach incorporates molecular scattering calculations into current quantum chemistry programs and facilitates the unification of bound- and continuum-state calculations for both diatomic and polyatomic molecules. Multidimensional Monte Carlo numerical integrations validate the high accuracy of our closed form results for the two-electron integrals.

Electron induced chemistry of disilane

“…They have calculated the Rydberg and Continuum electronic states of calcium monouoride (CaF), which has a highly polar ion core 24 The ab initio calculations depend mostly on the evaluation of accurate and reliable molecular integrals or matrix elements. Wong et al 25 have given closed-form analytic expressions for one-and two-electron integrals of Cartesian Gaussian orbitals outside the R-matrix sphere which can be used in ab initio molecular scattering calculations. The molecular integral expressions for multielectron R-matrix methods are also presented in a closed form in their approach.…”

Electron impact scattering by SF6 molecule over an extensive energy range

“…This method mostly takes care of all the polarization effects, considers both polar and nonpolar ion cores in a unied fashion, and is equally valid for both short-and long-range potentials. The closed-form analytic expressions for one-and two-electron integrals of Cartesian Gaussian orbitals outside the R-matrix sphere is given by Wong et al, 48 which can be used in ab-initio molecular scattering calculations. The R-matrix method is the most widely used of the ab initio methods.…”