Huygens-Fresnel principle for molecular continuum wave function

TL;DR

This paper analyzes the asymptotic behavior of molecular continuum wave functions, demonstrating that a multicenter approach based on the Huygens-Fresnel principle is necessary, and critiques the single spherical wave approximation.

Contribution

It introduces a multicenter asymptotic model for molecular wave functions based on the Huygens-Fresnel principle, highlighting limitations of the single spherical wave approximation.

Findings

Multicenter wave functions require N spherical waves at atomic nuclei.

Single spherical wave approximation conflicts with Huygens-Fresnel principle.

Multicenter approach provides a more accurate description of molecular scattering.

Abstract

The asymptotic behavior of the molecular continuum wave function has been analyzed within a model of non-overlapping atomic potentials. It has 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 according to the Huygens-Fresnel principle 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 is intrinsically conflicting, which is a direct consequence of refusal from the Huygens-Fresnel picture of the wave scattering process.