Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange

TL;DR

This paper introduces an efficient iterative method to compute the optimized effective potential for orbital functionals, including exact exchange, by solving PDEs instead of integral equations, improving accuracy and computational efficiency.

Contribution

The authors develop a novel iterative approach to obtain the OEP for orbital functionals, avoiding unoccupied orbitals and solving PDEs, which enhances practicality and precision.

Findings

Method accurately computes OEP for atoms and clusters.

Avoids calculation of unoccupied orbitals, saving computational resources.

Reveals new asymptotic behaviors of the exact OEP.

Abstract

For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential $V_{\mathrm{xc}\sigma}(\re)$ must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very demanding and has limited the use of orbital functionals like exact exchange. We demonstrate that the OEP can be obtained iteratively by solving a system of partial differential equations instead of an integral equation. This amounts to calculating the orbital shifts that exactify the Krieger-Li-Iafrate (KLI) approximation. Unoccupied orbitals do not need to be calculated. Accuracy and efficiency of the method are shown for atoms and clusters using the exact exchange energy. Counter-intuitive asymptotic limits of the exact OEP, not accessible from previous constructions, are presented.