Quantum-mechanical interpretation of time-dependent density-functional theory

Abstract

In this paper we derive the differential virial theorem for both time-dependent (TD) Schrödinger theory and Kohn-Sham (KS) density-functional theory. As such we obtain an exact integral expression for the TD electron-interaction potential of KS theory that is independent of the choice of action. The expression, valid for general TD phenomena other than the ionization or scattering process, is afforded the physical interpretation at each instant of time as being the work done to move an electron in a conservative field. The field is a sum of four component fields representative of Pauli and Coulomb correlations, correlation-kinetic effects, and as discovered here, correlations due to the difference in current densities of the KS and Schrödinger systems. The interpretation further reduces to that for the corresponding electron-interaction potential of stationary-state KS theory for time-independent external potentials.