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

R.W. Godby, P. Ghosez, X. Gonze

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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.
Original languageEnglish
Pages (from-to)12811-12817
Number of pages6
JournalPhysical Review B
Issue number20
Publication statusPublished - 15 Nov 1997

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© 1997 American Physical Society. Published in Physical Review B and uploaded in accordance with the publisher's self archiving policy.

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