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arXiv · 2301.05590

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

K. Karlsson·F. Aryasetiawan
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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.

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K. Karlsson, F. Aryasetiawan. 2023-01-13. Time-dependent exchange-correlation hole and potential of the electron gas. https://doi.org/10.1103/physrevb.107.115172

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