Thomas–Fermi–Dirac models of atoms constrained by nuclear cusp and long-range conditions

The traditional Thomas–Fermi–Dirac model of the electronic structure for a neutral atom is deficient in that it predicts an infinite electron density at the nucleus and a sharp cutoff of the electron density at a finite radius. This study was carried out to remedy these faults in the model. Extending an idea used earlier in Thomas–Fermi (TF ) theory Proc. Natl. Acad. Sci. U.S.A. 83 , 3577 (1985)], the Thomas–Fermi–Dirac (TFD ) energy functional is minimized under constraints ∫ρ( r ) d r = N, ∫e^?2kr▽²ρ( r )d r < ∞ and ∫(1 ? e^?k′r)ρ^4/3( r )d r < ∞, with k and k′ determined by the nuclear cusp condition and the correct asymptotic behavior. Optimum coordinate scaling also is considered. It is found that the TFD model is substantially improved by constraining the minimization search domain of the energy functional in this way. Energies are given for five noble gas atoms, and Compton profiles for these atoms are calculated. The behavior of electrons in momentum space is improved in both this modified TFD model and in the corresponding modified TF model.