An atomic kinetic energy functional with full Weizsacker correction.

A functional is proposed for representing the electronic kinetic energy of the ground state of an N-electron atom or ion in terms of its electron density, [Formula: see text] Here T(w) is the Weizsacker quantity ((1/8))integral(nablarho.nablarho/rho)dtau and T(0) is the Thomas-Fermi quantity C(F) integral rho(5 / 3)dtau. From Hartree-Fock data on 55 neutral atoms, C = 1.412 +/- 0.033; for 1200 atoms and ions, C = 1.332 +/- 0.053. The proposed functional gives the derivative deltaT/deltarho its most important correct properties. The term T(w) is shown to give the kinetic energy of the K shell, whereas the term (C/N((1/3)))T(0) gives an incorrect statistical estimate of that energy. An alternative correction -(C/N((1/3)))T gives even better results.