Ionization potentials of atoms calculated with a nonlocal exchange and a local correlation functional

Abstract

We calculate the first ionization potential of atoms (3 5 Z 5 54) by means of a nonlocal density functional approach and the results are compared with those obtained using other recent density functional approaches based on density gradients. In these calculations, we use a nonlocal weighted spin-density approximation of exchange effects and a local spin-density approximation of Coulomb correlation, both based on novel forms of the pair-correlation functions. We also calculate the total energies of the He, Be, and Ne isoelectronic series. 0

A Combination of the Work Formalism for Exchange with an Optimized Correlation Energy Functional for Atoms

“…Among other possible alternatives [10][11][12][13][14], we have chosen a recently developed "optimized local approximation" (OLA) [10,14] which has been successfully tested for free atoms [10,14] and positive ions [15]. The OLA is based on an explicit modelling of the correlation hole arising from the Coulomb repulsion between Evidently, when we introduce correlation, Wx(r) in equation (7) has to be substituted by Wx(r) + I~°~~(r) and the correlation energy term, E)~~[ pi has to be added to the total energy in equation (10).…”

“…The exchange energy is expressed as ~wDAj ~j ~_i j j Pir)Pir~)gz~~iir r'ii rxir)) ~~~~, j~~2 jr r'j This energy can be interpreted as the electrostatic interaction between two charge distributions: one is the usual electron density p(r), and the other, (p(r')gf~~((r r'( rx jr ), is a non-local charge density representing the Fermi hole around an electron placed at r. The WDA form for the pair correlation function gx(ri, r2) is chosen as where ~x(r), which can be interpreted as the effective sum iving the exact charge of hole: so that the WDA exchange energy functional is completely free of parameters. Equation (15) indicates that ~x(r) depends in a nonlocal way on the electron density.…”