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Flocco M , Gao XQ , Massa L
A Study of the Colle-Salvetti Formula for the Calculation of the Correlation-Energy
International Journal of Quantum Chemistry. 1990 :213-223
PMID: ISI:A1990EQ16800019   
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The formalism of Colle and Salvetti for the calculation of the correlation energy of electronic systems has proven to be highly successful in a wide variety of applications. Several authors have applied the method and analyzed its usefulness. The Colle and Salvetti ansatz for the correlation energy is [GRAPHICS] where b is a correlation factor of simple form and depends solely on the electron density. Other symbols have their usual meaning. Colle and Salvetti approximate the correlation energy of Eq. (1) using a Taylor series expansion of P2HF and obtain the expression. [GRAPHICS] where rho-(R) is the electron density evaluated at the center of mass coordinate R. The one dimensional integral, whose empirical constants are fit to the correlation energy of helium, is evaluated numerically. We test the limits of validity for expression (2) by applying it to the series of ions isoelectronic with helium, (two-electron case) and beryllium, (four-electron case). We find that the approximation breaks down for sufficiently high Z. We also compare the results given by Eqs. (1) and (2). We find that although both expressions give the same result for the neutral He atom, in general they do not.