Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue

TL;DR

This study demonstrates that ensemble generalization improves the accuracy of ionization potential predictions in density-functional theory across various exchange-correlation functionals without sacrificing total energy accuracy, and reduces parameter dependence in hybrid functionals.

Contribution

The paper applies ensemble generalization to various exchange-correlation functionals, showing systematic improvements in ionization potential predictions and reduced parameter sensitivity in hybrid functionals.

Findings

Ensemble generalization improves ionization potential predictions.

It maintains total energy accuracy across tested systems.

Reduces parameter dependence in hybrid functionals.

Abstract

There are several approximations to the exchange-correlation functional in density-functional theory that accurately predict total energy-related properties of many-electron systems, such as binding energies, bond lengths, and crystal structures. Other approximations are designed to describe potential-related processes, such as charge transfer and photoemission. However, the development of a functional which can serve the two purposes simultaneously is a long-standing challenge. Trying to address it, we employ in the current work the ensemble generalization procedure proposed in Phys. Rev. Lett. 110, 126403 (2013). Focusing on the prediction of the ionization potential via the highest occupied Kohn-Sham eigenvalue, we examine a variety of exchange-correlation approximations: the local spin-density approximation, semi-local generalized gradient approximations, and global and local hybrid functionals. Results for a test set of 26 diatomic molecules and single atoms are presented. We find that the aforementioned ensemble generalization systematically improves the prediction of the ionization potential, for various systems and exchange-correlation functionals, without compromising the accuracy of total energy-related properties. We specifically examine hybrid functionals. These depend on a parameter controlling the ratio of semi-local to non-local functional components. The ionization potential obtained with ensemble-generalized functionals is found to depend only weakly on the parameter value, contrary to common experience with non-generalized hybrids, thus eliminating one aspect of the so-called `parameter dilemma' of hybrid functionals.