Becke-Johnson-type exchange potential for two-dimensional systems

We extend the Becke-Johnson approximation [A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 (2006)] of the exchange potential to two dimensions. We prove and demonstrate that a direct extension of the underlying formalism may lead to divergent behavior of the potential. We derive a cure to the approach by enforcing the gauge invariance and correct asymptotic behavior of the exchange potential. The procedure leads to an approximation which is shown, in various quasi-two-dimensional test systems, to be very accurate in comparison with the exact-exchange potential and thus a considerable improvement over the commonly applied local-density approximation.