Abstract
Electron propagator or Green's function methods are discussed using the algebraic methods of superoperators, inner and outer projections on a linear space of fermionlike electron field operator products, partitioning, and perturbation theory. The problems of accurate determination of molecular electron binding energies from the core through the valence region are addressed. The complications of diagonalization of very large matrices in the self-energy expressions are pointed out and various diagonal approximations are discussed with the use of renormalization theory.Simple applications to the photoelectron spectra of water and acetylene are presented for illustrative purposes.
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