Electron localisation in static and time-dependent one-dimensional model systems

TL;DR

This paper introduces a new measure of electron localization based on the exact many-electron wavefunction, revealing its variability across systems and its disruption under electric fields, and evaluates the accuracy of the traditional ELF in these contexts.

Contribution

It proposes a novel localization measure, compares it with the traditional ELF, and analyzes electron localization dynamics in static and time-dependent systems.

Findings

Full ELF accurately describes localization

Approximate ELF fails in time-dependent scenarios

Localization varies significantly across different systems

Abstract

Electron localization is the tendency of an electron in a many-body system to exclude other electrons from its vicinity. Using a new natural measure of localization based on the exact manyelectron wavefunction, we find that localization can vary considerably between different ground-state systems, and can also be strongly disrupted, as a function of time, when a system is driven by an applied electric field. We use our new measure to assess the well-known electron localization function (ELF), both in its approximate single-particle form (often applied within density-functional theory) and its full many-particle form. The full ELF always gives an excellent description of localization, but the approximate ELF fails in time-dependent situations, even when the exact Kohn-Sham orbitals are employed.