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

Abstract

We obtain a solution of the time-dependent Schrödinger 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 vxc, which enters the Kohn-Sham equation of time-dependent density functional theory. Our “exact” result provides a benchmark against which various approximate forms for vxc can be compared. Finally, vxc 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.