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The local behavior of several approximate kinetic energy functionals is analyzed, for the case of free atoms and ions, by comparison with the local kinetic energy of Hartree-Fock theory. The atomic electron densities used are, in all cases, Hartree-Fock electron densities. The kinetic energy functional obtained by the gradient expansion method (with a small number of terms) is, locally, not very accurate, but its integrated value is fortuitously accurate, due to a strong cancellation of errors. Functionals which have the Weizsacker term t, = (V p)'/S p as a key ingredient are more accurate locally. The explicit incorporation of the shell structure and nonlocal density effects into the kinetic energy functional leads to the best results. The motivation for this work is that only a kinetic energy functional with an accurate local behavior will give good electron densities on solution of the Euler equation derived from it.

Simple density functional theory gives the following relation between the energy EZ,N of an ion of nuclear charge 2 and N electrons, the potential V ( 0 ) created at the nucleus by the electronic cloud, and the chemical potential y, EZ,N = $ ( Z V ( O ) + N p ) .Using Hartree-Fock values for V ( 0 ) and y, this equation has been tested in several isoelectronic series with 3 5 N 5 28. The importance of the term 3Np/7 increases as the degree of ionization increases.The knowledge of the relation between the ground-state energy E of an atom or ion and the electrostatic potential V(O), created at the nucleus by the electronic cloud,has potentially interesting applications. p(r) in Eq. (1) where 2 is the nuclear charge, and E is the one-electron energy eigenvalue. The treatment of ions or atoms with more than two electrons is more difficult. The simplest version of the density functional theory, that is, the Thomas-Fermi (TF) approximation, gives the following result for an ion with N electrons [5]

A density functional pseudopotential method is used to calculate the heat of formation and the equilibrium volume of Zn,Cdl --z as a function of the concentration 2. Then an estimation of the free energy of formation is given and the results are used to explain the main features of the solid part of the phase diagram of this alloy. The influence of the form of the pseudopotential is studied by performing the calculations both with Ashcroft's and with Shaw's pseudopotentials.Le mbthode du fonctionalle de la densite a Btb utilisbe 8, fin de calculer la chaleur de formation ainsi que le volume d'bquilibre du Zn,Cdl-, en fonction de la concentration z. A partir de 16, on fait line estimation de l'bnergie libre de formation; les rbsultats obtenus sont utilisbs pour expliquer les caractbristiques principales de la partie solide du diagramme de phase de cet alliage. L'influence de la forme du pseudopotentiel a Btk Btudibe en faisant de calculs avec les pseudopotentiels #Ashcroft et celui de Shaw respectivement.

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