Hartree-Fock-Wigner method

We recently presented a correlation method based on the Wigner intracule, in which correlation energies are calculated directly from a Hartree-Fock waveftmction. We now describe a self-consistent form of this approach which we term the Hartree-Fock-Wigner method. The efficacy of the new scheme is demonstrated using a simple weight function to reproduce the correlation energies of the first- and second-row atoms with a mean absolute deviation of 2.5 m h. 

In principle, the correspondence between the two theories is not complete, because scattering theory is the more general formulation. For our purposes, however, the fact that the applications to atomic physics obtained by both methods are quite consistent with each other is an important and useful conclusion. The same result and connections have been obtained independently by Komninos and Nicolaides [378]. Both [373] and [378] noted that the derivation of MQDT from Wigner s scattering theory establishes its basic structure and theorems without special assumptions about the asymptotic forms of wavefunctions. The approach of Komninos and Nicolaides [378] is designed for applications involving Hartree-Fock and multiconfigurational Hartree-Fock bases. In the present exposition, we follow the approach and notation of Lane [379] and others [380, 381], who exploit the analytic K-matrix formalism and include photon widths explicitly when interferences occur. 

The original CS correlation functional was proposed as an electron correlation correction for the Hartree-Fock method in 1975. Assuming that the volume of the region where electrons are excluded (excluded volume) is proportional to Wigner s excluded volume (Wigner 1934 Wigner and Seitz 1933), the following equation... 

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