Exact Dynamical Exchange-Correlation Kernel of a Weakly Inhomogeneous Electron Gas
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The dynamical exchange-correlation kernel fxc of a nonuniform 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 fxc=α/q2 where q is the wave vector and α is a frequency-dependent coefficient. We show that in the limit of weak nonuniformity the coefficient α has a simple and exact expression in terms of the ground-state density and the frequency-dependent kernel of a 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.
Phys. Rev. Lett. 102, 113001 (2009) [4 pages]