Many-Electron Theory of Atoms and Molecules. II

TLDR

The correlation energy of an N‑electron system can be obtained by considering only unique Hartree–Fock electron pairs, avoiding complications from inner shells. The study develops methods for obtaining pair correlations among Hartree–Fock electrons. Each electron pair is treated by solving a Schrödinger equation—e.g., the π‑electron Hamiltonian for π pairs—and its energy is minimized, allowing the use of any two‑electron method such as Hylleraas, open‑shell, or Heitler–London. The exact pair theory yields first‑order pairs and, with further approximation, a Brueckner‑type theory for finite systems.

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.