Finite-size effects in response functions of molecular systems

TL;DR

This paper analyzes how finite computational domains affect the accuracy of response functions in molecular systems, providing error estimates for numerical approximations near ionization thresholds.

Contribution

It offers new error bounds for the numerical approximation of response functions using finite regions, accounting for regularization effects.

Findings

Error estimates for response functions near ionization thresholds

Impact of domain size and smoothing on approximation accuracy

Guidelines for choosing regularization parameters

Abstract

We consider an electron in a localized potential submitted to a weak external, timedependent field. In the linear response regime, the response function can be computed using Kubo's formula. In this paper, we consider the numerical approximation of the response function by means of a truncation to a finite region of space. This is necessarily a singular approximation because of the discreteness of the spectrum of the truncated Hamiltonian, and in practice a regularization (smoothing) has to be used. Our results provide error estimates for the response function past the ionization threshold with respect to both the smoothing parameter and the size of the computational domain.