Asymptotic form of molecular continuum wave function for system of non-overlapping atomic potentials

TL;DR

This paper analyzes the asymptotic behavior of molecular continuum wave functions for non-overlapping atomic potentials, showing that multiple spherical waves are necessary for accurate descriptions, which impacts scattering cross section calculations.

Contribution

It demonstrates that the common single spherical wave approximation is inadequate for multicenter molecules, proposing a more accurate multiple spherical wave approach.

Findings

Single spherical wave approximation leads to significant errors in cross sections.

Multiple spherical waves are essential for correct asymptotic wave function representation.

Comparison shows improved accuracy with the proposed method.

Abstract

The asymptotic behavior of the molecular continuum wave function has been analyzed within a model of non-overlapping atomic potentials. It is been shown that the representation of the wave function far from a molecule as a plane wave and single spherical wave emitted by the molecular center cannot be corrected. Because of the multicenter character of the problem, the asymptotic form of the wave function must contain N spherical waves with centers at the nuclei of the N atoms that form the molecule. A method of partial waves for a spherically non-symmetrical target is considered for the simplest multicenter target formed by two non-overlapping potentials. The results are compared with those obtained within the single spherical wave approximation. It has been shown that the use of this approximation results in significant mistakes in differential and total cross sections of electron elastic scattering by a target.