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

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.

submitted to Phys. Rev. B on July 9th, 2009

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• Comparison between exact and semilocal exchange potentials: An all-electron study for solids
• Interaction-Induced Spin Polarization in Quantum Dots
• Pauli energy contribution to nucleus-nucleus interaction
• Parameter-free density functional for the correlation energy in two dimensions
• Laplacian-level density functionals for the exchange-correlation energy of low-dimensional nanostructures
• Energetics of the AK13 Semi-Local Kohn-Sham Exchange Energy Functional
• Semi-local Exchange Energy Functional For Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations
• Correlation energy of anisotropic quantum dots
• Colle-Salvetti-type local density functional for the exchange-correlation energy in two dimensions
• Exchange-correlation potentials for inhomogeneous electron systems in two dimensions from exact diagonalization: comparison with the local-spin-density approximation
• Inhomogeneity Induced and Appropriately Parameterized Semilocal Exchange and Correlation Energy Functionals in Two-Dimensions
• Semilocal approximations to the Kohn-Sham exchange potential as applied to a metal surface
• Density-functional approach to the band gaps of finite and periodic two-dimensional systems