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 (⅛)∫(∇ρ·∇ρ/ρ) d τ and T 0 is the Thomas-Fermi quantity C F ∫ ρ 5 / 3 d τ. 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 δ T /δρ 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 ⅓ ) T 0 gives an incorrect statistical estimate of that energy. An alternative correction -( C/N ⅓ ) T gives even better results.