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

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

doi:10.1103/PhysRevB.56.12811

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

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

Physics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	12811-12817
Number of pages	6
Journal	Physical Review B
Volume	56
Issue number	20
DOIs	https://doi.org/10.1103/PhysRevB.56.12811
Publication status	Published - 15 Nov 1997

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

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.",

author = "R.W. Godby and P. Ghosez and X. Gonze",

note = "{\textcopyright} 1997 American Physical Society. Published in Physical Review B and uploaded in accordance with the publisher's self archiving policy.",

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AU - Ghosez, P.

AU - Gonze, X.

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N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevB.56.12811

DO - 10.1103/PhysRevB.56.12811

M3 - Article

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