A self-interaction-free local hybrid functional: Accurate binding energies vis-\`a-vis accurate ionization potentials from Kohn-Sham eigenvalues

TL;DR

This paper introduces a new exchange-correlation functional for Kohn-Sham DFT that is free of one-electron self-interaction, aiming to improve binding energies and ionization potential predictions, but with some limitations in accuracy.

Contribution

A novel self-interaction-free local hybrid functional combining exact exchange with non-local correlation, optimized for accurate binding energies and ionization potentials.

Findings

Accurate binding energies achieved with parameter optimization.

Improved dissociation energy curves and Kohn-Sham eigenvalues.

Discrepancy between eigenvalues and experimental ionization potentials.

Abstract

We present and test a new approximation for the exchange-correlation (xc) energy of Kohn-Sham density functional theory. It combines exact exchange with a compatible non-local correlation functional. The functional is by construction free of one-electron self-interaction, respects constraints derived from uniform coordinate scaling, and has the correct asymptotic behavior of the xc energy density. It contains one parameter that is not determined ab initio. We investigate whether it is possible to construct a functional that yields accurate binding energies and affords other advantages, specifically Kohn-Sham eigenvalues that reliably reflect ionization potentials. Tests for a set of atoms and small molecules show that within our local-hybrid form accurate binding energies can be achieved by proper optimization of the free parameter in our functional, along with an improvement in dissociation energy curves and in Kohn-Sham eigenvalues. However, the correspondence of the latter to experimental ionization potentials is not yet satisfactory, and if we choose to optimize their prediction, a rather different value of the functional's parameter is obtained. We put this finding in a larger context by discussing similar observations for other functionals and possible directions for further functional development that our findings suggest.