Partly occupied Wannier functions: Construction and applications

TL;DR

This paper introduces a practical method for constructing partly occupied, maximally localized Wannier functions that improve localization and symmetry by including selected unoccupied states, demonstrated on various systems.

Contribution

A new scheme for constructing Wannier functions that incorporates unoccupied states to enhance their localization and symmetry properties.

Findings

Successfully applied to silicon, copper, and surface systems.

Achieved Wannier functions with maximal average localization.

Demonstrated improved symmetry and localization properties.

Abstract

We have developed a practical scheme to construct partly occupied, maximally localized Wannier functions (WFs) for a wide range of systems. We explain and demonstrate how the inclusion of selected unoccupied states in the definition of the WFs can improve both their localization and symmetry properties. A systematic selection of the relevant unoccupied states is achieved by minimizing the spread of the resulting WFs. The method is applied to a silicon cluster, a copper crystal, and a Cu(100) surface with nitrogen adsorbed. In all cases we demonstrate the existence of a set of WFs with particularly good localization and symmetry properties, and we show that this set of WFs is characterized by a maximal average localization.