Contracted Plane Wave satisfying periodic gauge

TL;DR

The paper introduces contracted plane waves (CPWs) that satisfy the periodic gauge in the Brillouin zone, simplifying the interpolation of physical quantities and complementing Gaussian bases.

Contribution

It presents a new class of CPWs that are simple sums of plane waves satisfying the periodic gauge, enabling improved interpolation and basis set expansion.

Findings

CPWs satisfy the periodic gauge in the Brillouin zone.

CPWs can replace Wannier functions for physical quantity interpolation.

CPWs facilitate complementing Gaussian basis sets.

Abstract

We introduce the contracted plane waves (CPWs), which satisfy the periodic gauge in the Brillouin-zone torus as in the case of usual Wannier functions. CPWs are very simply given as the sum of plane waves. We will be able to use CPWs instead of the Wannier functions for the interpolation of physical quantities given as the function of wave vectors in BZ. Furthermore, it will be easy to complement the set of Gaussian bases by CPWs.