First-principles approach to electric polarization and dielectric constant calculations using generalized Wannier functions

TL;DR

This paper introduces a first-principles method using generalized Wannier functions to accurately compute electric polarization and dielectric constants in insulators under electric fields, improving localization and reducing errors.

Contribution

It extends previous Wannier-based methods by employing non-orthogonal functions, enhancing localization and accuracy in polarization and dielectric calculations.

Findings

Non-orthogonal Wannier functions are more localized than orthogonal ones.

The method reduces errors caused by localization constraints.

Improved accuracy in calculating electric polarization and dielectric constants.

Abstract

We describe a method to calculate the electronic properties of an insulator under an applied electric field. It is based on the minimization of an electric enthalpy functional with respect to the orbitals, which behave as Wannier functions under crystal translations, but are not necessarily orthogonal. This paper extends the approach of Nunes and Vanderbilt (NV) [Phys. Rev. Lett. 73, 712 (1994)], who demonstrated that a Wannier function representation can be used to study insulating crystals in the presence of a finite electric field. According to a study by Fern\'{a}ndez et al. [Phys. Rev. B. 58, R7480 (1998)], first-principles implementations of the NV approach suffer from the impact of the localization constraint on the orthogonal wave functions, what affects the accuracy of the physical results. We show that because non-orthogonal generalized Wannier functions can be more localized than their orthogonal counterparts, the error due to localization constraints is reduced, thus improving the accuracy of the calculated physical quantities.