One- and many-electron self-interaction error in local and global hybrid functionals

Abstract

Electronic self-interaction poses a fundamental challenge in density-functional theory. It greatly limits, e.g., the physical interpretation of eigenvalues as electron removal energies. We here investigate whether local hybrid functionals that are designed to be free from one-electron self-interaction lead to occupied Kohn-Sham eigenvalues and orbitals that approximate photoemission observables well. We compare the local hybrid results to the ones from global hybrid functionals that only partially counteract the self-interaction, and to the results that are obtained with a Perdew-Zunger-type self-interaction correction. Furthermore, we check whether being nominally free from one-electron self-interaction translates into a reduced many-electron self-interaction error. Our findings show that this is not the case for the local hybrid functionals that we studied: In practice they are similar to global hybrids in many respects, despite being formally superior. This finding indicates that there is a conceptual difference between the Perdew-Zunger way and the local hybrid way of translating the one-electron condition to a many-electron system. We also point out and solve some difficulties that occur when using local hybrid functionals in combination with pseudopotentials.