On the Kirzhnits gradient expansion in two dimensions

Abstract

We derive the semiclassical Kirzhnits expansion of the D-dimensional one-particle density matrix up to the second order in $\hslash$. We focus on the two-dimensional (2D) case and show that all the gradient corrections both to the 2D one-particle density and to the kinetic energy density vanish. However, the 2D Kirzhnits expansion satisfies the consistency criterion of Gross and Proetto [J. Chem. Theory Comput. 5, 844 (2009)] for the functional derivatives of the density and the noninteracting kinetic energy with respect to the Kohn-Sham potential. Finally we show that the gradient correction to the exchange energy diverges in agreement with the previous linear-response study.

References in corpus (4)

• Kirzhnits gradient expansion for a D-dimensional Fermi gas
• Density gradients for the exchange energy of electrons in two dimensions
• Parameter-free density functional for the correlation energy in two dimensions
• Laplacian-level density functionals for the exchange-correlation energy of low-dimensional nanostructures

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• Preserving the Hermiticity of the One-Body Density Matrix for a Non-Interacting Fermi Gas