Implementation of the exact semi-classical light-matter interaction - the easy way

TL;DR

This paper introduces an analytical and numerical approach for calculating transition moments in semi-classical light-matter interactions using Gaussian basis functions, offering improved stability and physical interpretation over traditional multipole expansions.

Contribution

The authors develop a new method for exact semi-classical light-matter interaction calculations that simplifies implementation and enhances numerical stability compared to multipole expansion methods.

Findings

Numerical examples demonstrate the method's ability to distinguish symmetries.

The approach shows better numerical stability with respect to basis set choice.

Origin independence is confirmed for the exact operator.

Abstract

We present an analytical and numerical solution of the calculation of the transition moments for the exact semi-classical light-matter interaction for wavefunctions expanded in a Gaussian basis. By a simple manipulation we show that the exact semi-classical light-matter interaction of a plane wave can be compared to a Fourier transformation of a Gaussian where analytical recursive formulas are well known and hence making the difficulty in the implementation of the exact semi-classical light-matter interaction comparable to the transition dipole. Since the evaluation of the analytical expression involves a new Gaussian we instead have chosen to evaluate the integrals using a standard Gau{\ss}-Hermite quadrature since this is faster. A brief discussion of the numerical advantages of the exact semi-classical light-matter interaction in comparison to the multipole expansion along with the unphysical interpretation of the multipole expansion is discussed. Numerical examples on [CuCl$_4$]$^{2-}$ to show that the usual features of the multipole expansion is immediately visible also for the exact semi-classical light-matter interaction and that this can be used to distinguish between symmetries. Calculation on [FeCl$_4$]$^{1-}$ is presented to demonstrate the better numerical stability with respect to the choice of basis set in comparison to the multipole expansion and finally Fe-O-Fe to show origin independence is a given for the exact operator. The implementation is freely available in OpenMolcas.