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

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 rs = 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 noninteracting 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.

Automated summary

This study investigates the exchange-correlation hole and potential of the homogeneous electron gas using the random-phase approximation and the plasmon-pole approximation. It shows the angular and time dependence of the exchange-correlation hole for a Wigner-Seitz radius rs = 4. The study reveals a substantial cancellation between exchange and correlation potentials in space and time, similar to the cancellation of exchange and correlation self-energies. Analysis of the sum rule explains the advantage of using a noninteracting Green function in calculating the response function and self-energy within the random-phase approximation and the GW approximation. This research provides a starting point for more accurate calculations of the exchange-correlation hole and potential, aiming to construct a model based on the local density approximation in density functional theory.