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arXiv · 0812.2296

Exact dynamical exchange-correlation kernel of a weakly inhomogeneous electron gas

V. U. Nazarov·G. Vignale·Y. -C. Chang
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Abstract

The dynamical exchange-correlation kernel $f_{xc}$ of a non-uniform electron gas is an essential input for the time-dependent density functional theory of electronic systems. The long-wavelength behavior of this kernel is known to be of the form $f_{xc}= α/q^2$ where $q$ is the wave vector and $α$ is a frequency-dependent coefficient. We show that in the limit of weak non-uniformity the coefficient $α$ has a simple and exact expression in terms of the ground-state density and the frequency-dependent kernel of a {\it uniform} electron gas at the average density. We present an approximate evaluation of this expression for Si and discuss its implications for the theory of excitonic effects.

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V. U. Nazarov, G. Vignale, Y. -C. Chang. 2008-12-12. Exact dynamical exchange-correlation kernel of a weakly inhomogeneous electron gas. https://doi.org/10.1103/physrevlett.102.113001

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