Homogeneities in density of various LDA energy functionals

Abstract

Expanding on the work of March (Phys. Rev. A 56 (1997) 1025), partial differential equations are obtained for self-consistent atomic electron densities in the local density approximation. Local models treated include the Thomas–Fermi model, the Thomas–Fermi–Dirac model, and the Thomas–Fermi–Dirac model plus correlation. It is shown that within these models, the Thomas–Fermi kinetic energy functional can be expressed as a functional homogeneous of degree one with respect to the self-consistent-density scaling. In addition, the Dirac exchange functional and the Liu–Parr correlation functional each also can be rewritten as a functional homogeneous of degree one in the density scaling.