Exchange-correlation potential for Current Density Functional Theory of frequency dependent linear response

TL;DR

This paper derives exchange-correlation potentials for current density functional theory in a homogeneous electron gas, revealing spectral features near twice the plasma frequency and providing essential input for time-dependent current density functional calculations.

Contribution

It provides a microscopic model for exchange-correlation potentials in current density functional theory, including spectral structures relevant for inelastic scattering.

Findings

Transverse spectrum similar to longitudinal spectrum

Spectral structure near twice the plasma frequency

Results facilitate implementation of time-dependent current DFT

Abstract

The dynamical, long-wavelength longitudinal and transverse exchange-correlation potentials for a homogeneous electron gas are evaluated in a microscopic model based on an approximate decoupling of the equation of motion for the current-current response function. The transverse spectrum turns out to be very similar to the longitudinal one. We obtain evidence for a strong spectral structure near twice the plasma frequency due to a two-plasmon threshold for two-pair excitations, which may be observable in inelastic scattering experiments. Our results give the entire input needed to implement the Time-Dependent Current Density Functional Theory scheme recently developed by G. Vignale and W. Kohn [Phys. Rev. Lett. 77, 2037 (1996)] and are fitted to analytic functions to facilitate such applications.