Exact exchange-correlation potential for a time-dependent two electron system

TL;DR

This paper derives an exact time-dependent exchange-correlation potential for a two-electron system in a plane, providing a benchmark for approximations and analyzing the dynamical component.

Contribution

It presents the first exact solution for the time-dependent exchange-correlation potential in a two-electron system, serving as a benchmark for density functional approximations.

Findings

Exact v_xc computed for a two-electron system

Dynamical part of v_xc is negligible in this case

Provides a benchmark for approximate v_xc forms

Abstract

We obtain an exact solution of the time-dependent Schroedinger equation for a two-electron system confined to a plane by an isotropic parabolic potential whose curvature is periodically modulated in time. From this solution we compute the exact time-dependent exchange correlation potential v_xc which enters the Kohn-Sham equation of time-dependent density functional theory. Our exact result provides a benchmark against which various approximate forms for v_xc can be compared. Finally v_xc is separated in an adiabatic and a pure dynamical part and it is shown that, for the particular system studied, the dynamical part is negligible.