On the Kirzhnits gradient expansion in two dimensions

Details On the Kirzhnits gradient expansion in two dimensions On the Kirzhnits gradient expansion in two dimensions

2011-11-28

arxiv.org/abs/1111.6474v1

Phys. Rev. B 85, 165101 (2012)

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

10.1103/PhysRevB.85.165101

We derive the semiclassical Kirzhnits expansion of the D-dimensional one-particle density matrix up to the second order in $\hbar$. 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.

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