Universal correction for the Becke-Johnson exchange potential

TL;DR

This paper introduces a universal correction to the Becke-Johnson exchange potential, improving its accuracy for systems with external fields and non-Coulombic potentials by enforcing gauge invariance and single-electron exactness.

Contribution

The authors develop a system-independent correction to the Becke-Johnson potential that enhances its performance in external fields and for current-carrying states.

Findings

Improved potential handles external electric and magnetic fields better.

Correct asymptotic behavior for multi-electron systems achieved.

Test cases show very good results for hydrogen chain and harmonium.

Abstract

The Becke-Johnson exchange potential [J. Chem. Phys. 124, 221101 (2006)] has been successfully used in electronic structure calculations within density-functional theory. However, in its original form the potential may dramatically fail in systems with non-Coulombic external potentials, or in the presence of external magnetic or electric fields. Here, we provide a system-independent correction to the Becke-Johnson approximation by (i) enforcing its gauge invariance and (ii) making it exact for any single-electron system. The resulting approximation is then better designed to deal with current-carrying states, and recovers the correct asymptotic behavior for systems with any number of electrons. Tests of the resulting corrected exchange potential show very good results for a Hydrogen chain in an electric field and for a four-electron harmonium in a magnetic field.