A complex Gaussian representation of continuum wavefunctions respectful of their asymptotic behaviour

TL;DR

This paper introduces a novel complex Gaussian basis set method for accurately representing continuum wavefunctions, preserving their asymptotic behaviour, and improving the analytical properties of transition integrals in molecular ionization.

Contribution

It presents an indirect fitting approach that maintains the oscillatory asymptotic behaviour of continuum functions using Gaussian basis sets, enhancing accuracy and analytical structure.

Findings

Improved Gaussian basis sets for continuum wavefunctions

Method preserves asymptotic oscillatory behaviour

Maintains analytical structure of transition integrals

Abstract

Complex Gaussian basis sets are optimized to accurately represent continuum radial wavefunctions over the whole space. First, attention is put on the technical ability of the optimization method to get more flexible series of Gaussian exponents, in order to improve the accuracy of the fitting approach. Second, an indirect fitting method is proposed, allowing for the oscillatory behaviour of continuum functions to be conserved up to infinity as a factorized asymptotic function, while the Gaussian representation is applied to some appropriately defined distortion factor with limited spatial extension. As an illustration, the method is applied to radial Coulomb functions with realistic energy parameters. We also show that the indirect fitting approach keeps the advantageous analytical structure of typical one-electron transition integrals occurring in molecular ionization applications.