A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations

TL;DR

This paper introduces a modified approach to directly compute Wannier functions from Hartree-Fock and Kohn-Sham equations, avoiding post-processing transformations and providing a new route to localized functions with comparable computational effort.

Contribution

It presents a novel derivation of a priori Wannier functions using modified Hartree-Fock and Kohn-Sham equations, offering an efficient alternative to traditional methods.

Findings

A priori Wannier functions can be obtained directly from modified equations.

The computational effort is comparable to conventional methods.

The approach provides a new route to maximally localized Wannier functions.

Abstract

The Hartree-Fock equations are modified to directly yield Wannier functions following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)]. This approach circumvents the a posteriori application of the Wannier transformation to Bloch functions. I give a novel and rigorous derivation of the relevant equations by introducing an orthogonalizing potential to ensure the orthogonality among the resulting functions. The properties of these, so-called a priori Wannier functions, are analyzed and the relation of the modified Hartree-Fock equations to the conventional, Bloch-function-based equations is elucidated. It is pointed out that the modified equations offer a different route to maximally localized Wannier functions. Their computational solution is found to involve an effort that is comparable to the effort for the solution of the conventional equations. Above all, I show how a priori Wannier functions can be obtained by a modification of the Kohn-Sham equations of density-functional theory.