Time-dependent exchange-correlation hole and potential of the electron gas

TL;DR

This paper investigates the time-dependent exchange-correlation hole and potential in the homogeneous electron gas using the random-phase approximation, revealing cancellation effects and providing insights for improved density functional models.

Contribution

It introduces a detailed analysis of the time and angular dependence of the exchange-correlation hole within RPA, highlighting the advantages of using a non-interacting Green function for response calculations.

Findings

Substantial cancellation between exchange and correlation potentials in space and time.

Explanation of why non-interacting Green functions are preferable in RPA calculations.

Provides a foundation for more accurate exchange-correlation models in density functional theory.

Abstract

The exchange-correlation hole and potential of the homogeneous electron gas have been investigated within the random-phase approximation, employing the plasmon-pole approximation for the linear density response function. The angular dependence as well as the time dependence of the exchange-correlation hole are illustrated for a Wigner-Seitz radius $r_s=4$ (atomic unit). It is found that there is a substantial cancellation between exchange and correlation potentials in space and time, analogous to the cancellation of exchange and correlation self-energies. Analysis of the sum rule explains why it is more advantageous to use a non-interacting Green function than a renormalized one when calculating the response function within the random-phase approximation and consequently the self-energy within the well-established $GW$ approximation. The present study provides a starting point for more accurate and comprehensive calculations of the exchange-correlation hole and potential of the electron gas with the aim of constructing a model based on the local density approximation as in density functional theory.