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

Universal correction for the Becke-Johnson exchange potential