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arXiv · 1111.6474

On the Kirzhnits gradient expansion in two dimensions

A. Putaja·E. Rasanen·R. van Leeuwen·J. G. Vilhena·M. A. L. Marques
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Abstract

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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A. Putaja, E. Rasanen, R. van Leeuwen, J. G. Vilhena, M. A. L. Marques. 2011-11-28. On the Kirzhnits gradient expansion in two dimensions. https://doi.org/10.1103/physrevb.85.165101

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