Koopmans-compliant spectral functionals for extended systems

TL;DR

This paper extends Koopmans-compliant spectral functionals to large extended systems, demonstrating their accuracy in predicting band gaps and ionization potentials comparable to advanced many-body techniques.

Contribution

It introduces a formalism for applying Koopmans-compliant functionals to extended systems, emphasizing orbital localization for the thermodynamic limit.

Findings

Accurate band gap predictions for solid-state systems.

Ionization potentials are roughly twice as accurate as previous methods.

Formalism successfully applied to one-dimensional molecular systems.

Abstract

Koopmans-compliant functionals have been shown to provide accurate spectral properties for molecular systems; this accuracy is driven by the generalized linearization condition imposed on each charged excitation - i.e. on changing the occupation of any orbital in the system, while accounting for screening and relaxation from all other electrons. In this work we discuss the theoretical formulation and the practical implementation of this formalism to the case of extended systems, where a third condition, the localization of Koopmans' orbitals, proves crucial to reach seamlessly the thermodynamic limit. We illustrate the formalism by first studying one-dimensional molecular systems of increasing length. Then, we consider the band gaps of 30 paradigmatic solid-state test cases, for which accurate experimental and computational results are available. The results are found to be comparable with the state-of-the-art in diagrammatic techniques (self-consistent many-body perturbation theory with vertex corrections), notably using just a functional formulation for spectral properties and the physics of the generalized-gradient approximation; when ionization potentials are compared, the results are roughly twice as accurate.