Hartree-Fock equations/theory many-body perturbation

The pioneering work on the application of the many-body perturbation theory to atomic and molecular systems was performed by Kelly.5-17-21 He applied the method to atoms using numerical solutions of the Hartree-Fock equations. Many other calculations on atomic systems were subsequently... 

In Volume 5 of this series, R. J. Bartlett and J. E Stanton authored a popular tutorial on applications of post-Hartree-Fock methods. Here in Chapter 2, Dr. T. Daniel Crawford and Professor Henry F. Schaefer III explore coupled cluster theory in great depth. Despite the depth, the treatment is brilliantly clear. Beginning with fundamental concepts of cluster expansion of the wavefunction, the authors provide the formal theory and the derivation of the coupled cluster equations. This is followed by thorough explanations of diagrammatic representations, the connection to many-bodied perturbation theory, and computer implementation of the method. Directions for future developments are laid out. 

The 1960s saw the applications of the many-body perturbation theory developed during the 1950s by Brueckner [13], Goldstone [38] and others to the atomic structure problem by Kelly [63-72]." These applications used the numerical solutions to the Hartree-Fock equations which are available for atoms because of the special coordinate system. Kelly also reported applications to some simple hydrides in which the hydrogen atom nucleus is treated as an additional perturbation. 

The many-body perturbation theory was applied to atoms and some simple molecular systems by Kelly using a reference function obtained from finite difference solutions of the Hartree-Fock equations. The introduction of the algebraic approximation using finite basis sets during the 1970s opened up applications to arbitrary polyatomic molecular systems. 

The theory outlined in the previous sections is formally applicable to arbitrary interacting closed-shell systems. However, it cannot be applied in practice to systems larger than two-electron monomers since the resulting perturbation theory equations are too difficult to. solve without some systematic approach to the many-electron problem. The obstacle encountered here is analogous to the standard electron correlation issue and its solution requires techniques quite similar to those of the conventional many-body perturbation theory (MBPT). One takes the product of monomer Hartree-Fock determinants... 

Using numerical solutions to the Hartree-Fock equations, Kelly applied the many-body perturbation theory to the correlation problem first in atoms [37-39] and... 

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