Nonlocality of Kohn-Sham exchange-correlation fields in dielectrics

TL;DR

This paper reveals that the Kohn-Sham exchange-correlation field in dielectrics has an intrinsic nonlocal dependence on the global electrostatic configuration, challenging the assumption of purely local determination.

Contribution

It demonstrates that the macroscopic Kohn-Sham field cannot be derived solely from local properties but depends on the overall electrostatic setup.

Findings

Kohn-Sham field is nonlocal and depends on global electrostatics.

In transverse configurations, the Kohn-Sham field vanishes.

In longitudinal configurations, the Kohn-Sham field remains non-zero.

Abstract

The theory of the macroscopic field appearing in the Kohn-Sham exchange-correlation potential for dielectric materials, as introduced by Gonze, Ghosez and Godby, is reexamined. It is shown that this Kohn-Sham field cannot be determined from a knowledge of the local state of the material (local crystal potential, electric field, and polarization) alone. Instead, it has an intrinsically nonlocal dependence on the global electrostatic configuration. For example, it vanishes in simple transverse configurations of a polarized dielectric, but not in longitudinal ones.