Ornstein-Zernike function and Coulombic correlation in the homogeneous electron liquidOrnstein-Zernike function and Coulombic correlation in the homogeneous electron liquid
Faculty of Sciences. Physics

Department of Physics

article

2007 2007

Physics

Physical review B

76(2007):19, p. 1-8

195104

000251326800039

E-only publicatie

English (eng)

University of Antwerp

Adopting the original Ornstein-Zernike (OZ) definition of the direct correlation function c(r), the present study deals with the deviation Delta(r) of c(r) induced by Coulomb correlation in the homogeneous electron liquid beyond the OZ function c(FH)(r) for purely Fermi hole (FH) statistical correlations. It is first stressed that Delta(r) at large r is proportional to the Coulomb potential energy e(2)/r, suitably scaled with the plasma frequency. Both r space and k space formulations are presented. In k space, direct numerical use is made of inequalities due to Kugler [Phys. Rev. A 1, 1688 (1970)] by employing analytic representations of the pair correlations due to Gori-Giorgi [Phys. Rev. B 61, 7353 (2000)] as a function of the uniform electron density. Then, in r space, consideration is given to differential equations proposed by Dawson and March [Phys. Chem. Liq. 14, 131 (1984)] and also in the recent study of Nagy and Amovilli [J. Chem. Phys. 121, 6640 (2004)]. In both approaches, one-body potentials enter, into which Coulombic interelectronic repulsions are subsumed. Finally, Gaskell's [Proc. Phys. Soc. London 77, 1182 (1961)] variational ground-state wave function is shown to be related to the OZ direct correlation function in k space.

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