Automatic Generation of Maximally Localized Wannier Functions via Optimized Projection Functions and Self-projections

TL;DR

This paper introduces an automated method for generating maximally localized Wannier functions applicable to both occupied and unoccupied states, improving upon existing methods by providing an exact gradient expression and enhancing localization through self-projections.

Contribution

It offers an exact gradient calculation for the optimized projection function method and incorporates self-projections to further improve Wannier function localization.

Findings

Exact gradient expression for Wannier spread functional

Enhanced localization via self-projections

Applicable to both occupied and unoccupied states

Abstract

We present an automatized approach towards maximally localized Wannier functions (MLWFs) applicable to both occupied and unoccupied states. We overcome limitations of the standard optimized projection function (OPF) method and its approximations by providing an exact expression for the gradient of the Wannier spread functional with respect to a single semi-unitary OPF matrix. Moreover, we demonstrate that the localization of the resulting Wannier functions (WFs) can be further improved by including projections on reasonably localized WFs, so-called self-projections.