Kirzhnits gradient expansion in two dimensions

A. Putaja, E. Räsänen, R. van Leeuwen, J. G. Vilhena, and M. A. L. Marques
Phys. Rev. B 85, 165101 – Published 2 April 2012

Abstract

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

  • Received 22 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.165101

©2012 American Physical Society

Authors & Affiliations

A. Putaja1, E. Räsänen1,2,*, R. van Leeuwen1, J. G. Vilhena3, and M. A. L. Marques3

  • 1Nanoscience Center, Department of Physics, University of Jyväskylä, FI-40014 Jyväskylä, Finland
  • 2Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
  • 3Université de Lyon, F-69000 Lyon, France and LPMCN, CNRS, UMR 5586, Université Lyon 1, F-69622 Villeurbanne, France

  • *erasanen@jyu.fi

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Vol. 85, Iss. 16 — 15 April 2012

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