Eur. Phys. J. B (2018) 91: 153
https://doi.org/10.1140/epjb/e2018-90063-3

Regular Article

Exchange and correlation in finite-temperature TDDFT^★

Dept. of Physics, BOX 351560, Univ. of Washington, Seattle, WA 98195-1560, USA

^a e-mail: jjr@uw.edu

Received: 8 February 2018
Received in final form: 11 May 2018
Published online: 4 July 2018

Abstract

We discuss the finite-temperature generalization of time-dependent density functional theory (TDDFT). The theory is directly analogous to that at temperature T = 0. For example, the finite-T TDDFT exchange-correlation kernel f_xc(T, n) in the local density approximation can again be expressed as a density derivative of the exchange correlation potential f_xc(T, n) = [∂v_xc(T, n)∕∂n]δ(r − r′), where n = N∕V is the electron number density. An approximation for the kernel f_xc(T, n) is obtained from the finite-T generalization of the retarded cumulant expansion applied to the homogeneous electron gas. Results for f_xc and the loss function are presented for a wide range of temperatures and densities including the warm dense matter regime, where T ≈ T_F, the electron degeneracy temperature. The theory also permits a physical interpretation of the exchange and correlation contributions to the theory.