Orbital Anatomy of Self-Interaction in Kohn-Sham Density Functional Theory

TL;DR

This paper investigates the orbital-dependent nature of self-interaction errors in Kohn-Sham DFT, proposing a unique decomposition of energies and analyzing the impact of self-interaction corrections on various functionals.

Contribution

It introduces a method to uniquely define and decompose self-interaction and exchange energies into orbital contributions using an orthogonal Hartree ansatz.

Findings

Per-orbital energy breakdown reveals error cancellations between core and valence orbitals.

Self-interaction correction disrupts error cancellation, explaining its limited effect on some functionals.

Analysis of Jacob's ladder functionals shows varying accuracy in predicting exchange energies.

Abstract

Self-interaction is a fundamental flaw of practical Kohn-Sham Density Functional Theory (KS DFT) approximations responsible for numerous qualitative and even catastrophic shortcomings. Whereas self-interaction is easy to characterize in one-electron systems, its orbital-dependent nature makes it difficult to uniquely define and decompose it and other components of the KS energy into orbital components. By starting from the orthogonal Hartree ansatz as the exchange-free self-interaction-free model, it is possible to uniquely define self-interaction and genuine exchange total energies as well as their decomposition into orbital contributions. Using Edmiston-Ruedenberg orbitals as a close numerical surrogate of the Hartree orbitals we investigate the accuracy of genuine exchange energies predicted by several levels of Jacob's ladder of functionals and their Perdew-Zunger (PZ) self-interaction corrected counterparts. Among several notable insights provided by the per-orbital breakdown of the KS energies the key is the delicate cancellation of errors between core and valence orbitals that belies the remarkable accuracy of many functionals (particularly, GGAs). Disruption of the cancellation by the PZ correction accounts for its relatively modest impact on GGAs and other semilocal functionals.