Many-Electron Theory of Atoms and Molecules. II

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Abstract
It was shown in Paper I that to calculate the correlation energy of an N-electron system only the unique pairs of Hartree—Fock electrons need be considered. Methods for obtaining these pair correlations are developed. Each pair satisfies a Schrödinger equation similar to that of, say, He or H2. For π electrons the corresponding equation turns out to be just the ``π-electron Hamiltonian.'' In a closed-shell system, to obtain any of the pair functions one minimizes the energy of just that pair. There is no ``nightmare of inner shells.'' With the procedure given, any well-known two-electron method such as Hylleraas' r12-coordinate, ``open shell'' or even Heitler—London can be used for an Hartree—Fock pair depending on the nature of the pair. This ``exact pair'' theory leads to ``first-order'' pairs and to a Brueckner-type theory for finite systems upon further approximation.