On the atomic kinetic energy functionals with full Weizsacker correction

The functional proposed by Acharya, Bartolotti, Sears, and Parr for representing the kinetic energy of the ground state of an N electron atom or ion in terms of its electron density, namely T[ρ] = Tw[ρ] +γ(N, Z) TTF[ρ] [TW is the Weizsacker term, TTF is the Thomas–Fermi term and γ(N, Z) = 1−C0/N1/3] is derived by: (1) considering explicitly the variation of the charge density in an atom, and (2) approximating the pair correlation function for parallel spin electrons by that of a uniform free-electron gas, but including the corrections to the momentum at the Fermi level and the appropriate boundary conditions that result from taking into account that the number of electrons in an atom is finite. The first consideration leads in a natural way to the full Weizsacker correction, while the second consideration yields γ(N, Z) = (1−2/N)(1−C0/N1/3−C1/N1/3) times the Thomas–Fermi term. Thus, the functional obtained is exact for one-electron atoms and two-electron Hartree–Fock atoms, yields an adequate functional derivative, is in agreement with the leading correction to Thomas–Fermi, and provides an excellent representation of the kinetic energy of atoms 2⩽Z⩽54 when Hartree–Fock densities are used.