关键词: Thomas-Fermi理论, Hohenberg-Kohn理论, Kohn-Sham方法, 动能密度

Abstract: Kirzhnits method is extended in the gradient expansion of the Dirac density matrix of a many electron system to the two dimension case. The zeroth-order and second-order expansion for the Dirac density matrix in two dimensions is derived. From it, the expansion for the density and kinetic energy are further derived. The results show that, in contrast to the case of the three dimensions, to the second order of the gradient expansion, there is only the Laplacian type of term Δ²k_F², while the gradient term of (Δk_F²)² is absent in the two dimensional case. The result should be useful in the application of density functional theory to two dimensional systems.

Key words: Thomas-Fermi theory, Hohenberg-Kohn theory, Kohn-Sham method, kinetic energy density