Comparative study of the gradient expansion of the atomic kinetic energy functional–isoelectronic series

In previous work, it was shown that, for the ground state of neutral atoms, the truncated gradient expansion of the kinetic energy functional T[ρ] can give very good kinetic energy values when Hartree–Fock densities are used. In this work, we use the Hodges expansion formula: T[ρ]=T0[ρ]+T2[ρ]+T4[ρ], with T0[ρ]=3/10 (3π2)2/3∫ρ5/3dτ, T2[ρ] = (1/72) ∫[(∇ρ)2/ρ]dτ, etc., to calculate the kinetic energies of heliumlike, neonlike, and argonlike atoms and ions. The errors in the values obtained depend significantly on the number of electrons, N, of the system when N is small. As N increases, the error gradually decreases.