  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.
