Exact time-dependent exchange-correlation potential in electron scattering processes

TL;DR

This paper reveals the importance of peak and valley structures in the exact exchange-correlation potential for accurately modeling time-resolved electron scattering, highlighting limitations of adiabatic approximations and improvements with non-adiabatic methods.

Contribution

It identifies critical features in the exact potential and evaluates the performance of non-adiabatic approximations in electron scattering simulations.

Findings

Adiabatic approximations miss key potential structures

Non-adiabatic approximation captures electron approach better

Reflection is still not accurately modeled

Abstract

We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations which consequently significantly underestimate the scattering probability. A recently-proposed non-adiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and is more accurate than standard adiabatic functionals, but it ultimately fails to accurately capture reflection. These results may explain the underestimate of scattering probabilities in some recent studies on molecules and surfaces.