Density Functional Theory of Polar Insulators

TL;DR

This paper investigates the density-functional theory of polar insulators, revealing differences between large-cluster and periodic boundary approaches, especially regarding the exchange-correlation potential and polarization calculations.

Contribution

It demonstrates that the two common procedures for modeling insulators are not equivalent and highlights the importance of the boundary conditions in DFT calculations for polar materials.

Findings

Large-cluster approach introduces a homogeneous electric field.

Periodic boundary conditions forbid the electric field, affecting polarization.

Kohn-Sham polarization can be incorrect even with exact functionals.

Abstract

We examine the density-functional theory of macroscopic insulators, obtained in the large-cluster limit or under periodic boundary conditions. For polar crystals, we find that the two procedures are not equivalent. In a large-cluster case, the exact exchange-correlation potential acquires a homogeneous ``electric field'' which is absent from the usual local approximations, and the Kohn-Sham electronic system becomes metallic. With periodic boundary conditions, such a field is forbidden, and the polarization deduced from Kohn-Sham wavefunctions is incorrect even if the exact functional is used.