Coordinate scaling in time-dependent current density functional theory

TL;DR

This paper derives the coupling constant dependence in time-dependent current density functional theory, providing a scaling relation useful for testing functionals and calculating ground-state energies.

Contribution

It introduces a new scaling relation in time-dependent current density functional theory and applies it to the uniform gas with the Vignale-Kohn approximation.

Findings

Derived the coupling constant dependence in TD-CDFT.

Established a scaling relation for approximate functionals.

Applied the relation to the uniform gas with Vignale-Kohn approximation.

Abstract

The coupling constant dependence is derived in time-dependent {\em current} density functional theory. The scaling relation can be used to check approximate functionals and in conjunction with the adiabatic connection formula to obtain the ground-state energy from the exchange-correlation kernel. The result for the uniform gas using the Vignale-Kohn approximation is deduced.