Electron localization function for non-collinear spins

TL;DR

This paper reveals limitations of the electron localization function (ELF) in non-collinear spin states and proposes a gauge-invariant extension that enhances its applicability to complex magnetic systems.

Contribution

The authors develop a gauge-invariant extension of ELF that accurately describes non-collinear spins, improving upon the traditional ELF's limitations.

Findings

ELF breaks down for non-regular quantum states.

Addressing both U(1) and SU(2) gauge invariance is essential.

Extended ELF improves description of collinear states.

Abstract

Understanding of bonding is key to modelling materials and predicting properties thereof. A widely adopted indicator of bonds and atomic shells is the electron localization function (ELF). The building blocks of the ELF are also used in the construction of modern density functional approximations. Here we demonstrate that the ELF breaks down when applied beyond regular non-relativistic quantum states. We show that for tackling general non-collinear open-shell solutions, it is essential to address both the U(1) gauge invariance -- i.e., invariance under a multiplication by a position dependent phase factor -- and SU(2) gauge invariance -- i.e. invariance under local spin rotations -- {\em conjointly}. Remarkably, we find that the extended ELF also improves the description of paradigmatic collinear states.