TY - JOUR

T1 - Long-wavelength behavior of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems

AU - Ghosez, Ph

AU - Gonze, X.

AU - Godby, R.

PY - 1997

Y1 - 1997

N2 - The polarization dependence of the exchange-correlation (xc) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a (Formula presented) divergence in the xc kernel for small vectors q. This behavior, 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, semilocal, or even nonlocal 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 (Formula presented) divergence in the xc kernel for small vectors q. This behavior, 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, semilocal, or even nonlocal 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.

UR - http://www.scopus.com/inward/record.url?scp=0001507708&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.56.12811

DO - 10.1103/PhysRevB.56.12811

M3 - Article

AN - SCOPUS:0001507708

VL - 56

SP - 12811

EP - 12817

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

SN - 1098-0121

IS - 20

ER -