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

TL;DR

This paper extends the Becke-Johnson exchange potential to two-dimensional systems, addressing divergence issues and improving accuracy over local-density approximations in quasi-two-dimensional test cases.

Contribution

It introduces a gauge-invariant, asymptotically correct extension of the Becke-Johnson exchange potential for 2D systems, overcoming divergence problems.

Findings

The extended potential is highly accurate compared to exact exchange.

It significantly outperforms local-density approximation in test systems.

The approach ensures gauge invariance and proper asymptotic behavior.

Abstract

We extend the Becke-Johnson approximation [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.