Abstract
Ab initio calculations of natural orbitals, ionization potentials, and total ground state energies for the closed shell systems helium and beryllium are given using the technique of many-body Green's functions. The necessary formalism for application of the Green's function theory to finite, nonuniform, many-body systems is developed following the work of Layzer; connections with standard perturbation theory are made. The natural orbitals obtained were of high quality. Analysis of the diagrammatic expansion of the Green's function led to the surprising result that the main effect of the infinite-order summations implicit in the solution of Dyson's equation was to ``renormalize'' the second-order perturbation corrections.
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