Alternative Decouplings of the Electron Propagator

Abstract:
Several alternative decouplings of the electron propagator are investigated in this dissertation in an attempt to derive more accurate and more tractable computational schemes for extracting the physical information available. When the electron propagator is defined as a single-time, Green's function, the decoupling approximation and the choice of reference state average are shown to be independent approximations, and the use of uncorrelated, Hartree-Fock reference states is advocated. The derivation of each decoupling approximation utilizes the superoperator formalism and emphasizes elementary algebraic manipulations. In Chapter 1, operator product decouplings are reviewed and critically discussed. In Chapter 2, moment-conserving decouplings, which consist of Pade' approximants to the propagator moment expansion, are investigated. In Chapter 3, a partitioning of the superoperator Hamiltonian is invoked, and a perturbation expansion of the superoperator resolvent is developed. This development leads straightforwardly to the derivation of the Dyson equation and permits an identification of wave and reaction superoperators. Two types of diagram-conserving decouplings are then examined, and equivalences with the diagrammatic expansion method are demonstrated. Finally in Chapter 4, renormalized decouplings are considered, and the two-particle, one-hole, Tamm-Dancoff approximation is specifically derived and investigated. In each of the first four chapters, the decoupling approximations are evaluated on the basis of computational applications in which the propagator poles are compared to experimentally measured ionization energies for several molecules. In order to avoid a possible bias with this evaluation criterion, the quality of the Feynman-Dyson amplitudes is examined in Chapter 5 via the calculation of relative photo-ionization intensities. The four decoupling approximations are finally summarized as various approximations to the wave and reaction superoperators, and several extensions of these investigations are proposed.
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