On a Solution of the Self-Interaction Problem in Kohn-Sham Density Functional Theory

TL;DR

This paper introduces a new formalism in Kohn-Sham density functional theory that explicitly removes self-interaction effects by deriving an analytic exchange potential, demonstrated on model systems and atoms.

Contribution

A novel method for calculating the Coulomb potential and exchange energy explicitly as a functional of the density, eliminating self-interaction errors in Kohn-Sham DFT.

Findings

The new approach yields total energies higher than Hartree-Fock and OEP, indicating greater variational flexibility.

Application to atoms from Helium to Krypton demonstrates the method's effectiveness.

Comparison shows the hierarchy E_HF ≤ E_OEP ≤ E_SIF, reflecting the method's properties.

Abstract

We report on a methodology for the treatment of the Coulomb energy and potential in Kohn-Sham density functional theory that is free from self-interaction effects. Specifically, we determine the Coulomb potential given as the functional derivative of the Coulomb energy with respect to the density, where the Coulomb energy is calculated explicitly in terms of the pair density of the Kohn-Sham orbitals. This is accomplished by taking advantage of an orthonormal and complete basis that is an explicit functional of the density that then allows for the functional differentiation of the pair density with respect to the density to be performed explicitly. This approach leads to a new formalism that provides an analytic, closed-form determination of the exchange potential. This method is applied to one-dimensional model systems and to the atoms Helium through Krypton based on an exchange only implementation. Comparison of our total energies (denoted SIF) to those obtained using the usual Hartree-Fock (HF) and optimized effective potential (OEP) methods reveals the hierarchy $E_{\rm HF} \le E_{\rm OEP} \le E_{\rm SIF}$ that is indicative of the greater variation freedom implicit in the former two methods.