Electron gas model for inhomogeneous systems

Recently it has been shown that very accurate exchange and correlation potentials may be predicted from the properties of the one- and two-particle density matrices for a system with a finite number of electrons. The charge density dependence of the exchange potential thus derived is the same as that of a free electron gas (homogeneous system). In order to take into account the inhomogeneity effects, we have carried out an expansion of the charge density around the center of the Fermi hole. This leads to an exchange potential of the same form as that of the Xαβ theory. The value of β predicted for a modified Wigner form of the pair correlation function of electrons with parallel spin, f (1,2), when the number of electrons goes to infinity is 0.0020, in agreement with the theoretical value found by Liberman. Exchange, correlation, and total energies of atoms Li through Ar predicted from several models, corresponding to different forms of f (1,2), are in very good agreement with the exact values.