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The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems

Ph. Ghosez·X. Gonze·R. W. Godby
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Abstract

The polarization-dependence of the exchange-correlation (XC) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a ${\cal O} (1/q^2)$ divergence in the XC kernel for small vectors q. This behaviour, exemplified for a one-dimensional model semiconductor, is also observed when an insulator happens to be described as a KS metal, or vice-versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semi-local or even non-local approximations to KS theory. We also show that the test-charge and electronic definitions of the macroscopic dielectric constant differ from one another in exact KS theory, but are equivalent in the above-mentioned approximations.

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Ph. Ghosez, X. Gonze, R. W. Godby. 1997-06-27. The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems. https://doi.org/10.1103/physrevb.56.12811

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