Local behavior of the kinetic energy in density functional theory

Abstract

AbstractThe local behavior of several approximate kinetic energy functionals is analyzed, for the case of free atoms and ions, by comparison with the local kinetic energy of Hartree–Fock theory. The atomic electron densities used are, in all cases, Hartree–Fock electron densities. The kinetic energy functional obtained by the gradient expansion method (with a small number of terms) is, locally, not very accurate, but its integrated value is fortuitously accurate, due to a strong cancellation of errors. Functionals which have the Weizsäcker term tw = (Δ ρ)2/8ρ as a key ingredient are more accurate locally. The explicit incorporation of the shell structure and nonlocal density effects into the kinetic energy functional leads to the best results. The motivation for this work is that only a kinetic energy functional with an accurate local behavior will give good electron densities on solution of the Euler equation derived from it.