Screening in orbital-density-dependent functionals

TL;DR

This paper introduces a linear-response based method to incorporate orbital-specific screening effects into Koopmans' functionals, improving the accuracy of ionization potential predictions for complex transition-metal systems.

Contribution

The authors develop a general linear-response approach for orbital-by-orbital screening in Koopmans' functionals, enhancing their applicability to diverse chemical systems.

Findings

Achieved a mean absolute error of ~0.2 eV for ionization potentials.

Demonstrated the importance of orbital localization in screening effects.

Validated the method on 46 transition-metal complexes with good agreement to experiment.

Abstract

Electronic-structure functionals that include screening effects, such as Hubbard or Koopmans' functionals, require to describe the response of a system to the fractional addition or removal of an electron from an orbital or a manifold. Here, we present a general method to incorporate screening based on linear-response theory, and we apply it to the case of the orbital-by-orbital screening of Koopmans' functionals. We illustrate the importance of such generalization when dealing with challenging systems containing orbitals with very different chemical character, also highlighting the simple dependence of the screening on the localization of the orbitals. We choose a set of 46 transition-metal complexes for which experimental data and accurate many-body perturbation theory calculations are available. When compared to experiment, results for ionization potentials show a very good performance with a mean absolute error of $~0.2$ eV, comparable to the most accurate many-body perturbation theory approaches. These results reiterate the role of Koopmans' compliant functionals as simple and accurate quasiparticle approximations to the exact spectral functional, bypassing diagrammatic expansions and relying only on the physics of the local density or generalized-gradient approximation.