Paradox of Self-Interaction Correction

Abstract

Popular local, semilocal, and hybrid density functional approximations to the exchange-correlation energy of a many-electron ground state make a one-electron self-interaction error which can be removed by its orbital-by-orbital subtraction from the total energy, as proposed by Perdew and Zunger in 1981. This makes the functional exact for all one-electron ground states, but it does much more as well: It greatly improves the description of negative ions, the dissociation curves of radical molecules and of all heteronuclear molecules, the barrier heights for chemical reactions, charge-transfer energies, etc. PZ SIC even led to the later discovery of an exact property, the derivative discontinuity of the energy. It is also used to understand strong correlation, which is beyond the reach of semilocal approximations. The paradox of SIC is that equilibrium properties of molecules and solids, including atomization energies and equilibrium geometries, are at best only slightly improved and more typically worsened by it, especially as we pass from local to semilocal and hybrid functionals which by themselves provide a ladder of increasing accuracy for these equilibrium properties. The reason for this puzzling ambivalence remains unknown. In this speculative chapter, we suggest that the problem arises because the uncorrected functionals provide an inadequate description of compact but noded one-electron orbital densities. We suggest that a meta-generalized gradient approximation designed to satisfy a tight lower bound on the exchange energy of a one-electron density could resolve the paradox, providing after self-interaction correction the first practical “density functional theory of almost everything.”