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

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

1997-06-27

arxiv.org/abs/cond-mat/9706279v1

Physics

Condensed Matter

Materials Science

7 pages, 1 figure

Scientific paper

10.1103/PhysRevB.56.12811

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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