Abstract
We derive the semiclassical Kirzhnits expansion of the -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