Variational treatment of electron-polyatomic molecule scattering calculations using adaptive overset grids

TL;DR

This paper introduces a variational method for electron-polyatomic molecule scattering using an overset grid approach, enabling efficient and accurate calculations with rapid convergence, demonstrated on methane and CF4.

Contribution

It develops a novel overset grid formulation of the Complex Kohn variational method, improving convergence and computational efficiency for scattering calculations.

Findings

Rapid convergence with respect to basis functions and partial waves.

Accurate scattering calculations for methane and CF4.

Comparison showing advantages over single-center expansions.

Abstract

The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense, atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free particle Green's function and potential, $\hat{G}^+_0\hat{V}$ on the overset grid in a "Born-Arnoldi" solution of the working equations. The theory is shown to be equivalent to a specific Pad\'e approximant to the $T$-matrix, and has rapid convergence properties, both in the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF$_4$ in the static-exchange approximation, and compared in detail with calculations performed with the numerical Schwinger variational approach based on single center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.