Electron propagator calculations of the photoelectron spectrum for open shell molecules with applications to the oxygen molecule

An approximate self−energy for the electron propagator is derived using the Grand Canonical averaging procedure for open shell molecules. The connection between the overlap amplitudes and the photoionization cross section is discussed. A direct pole and residue search is employed to solve the Dyson equation with a second order self−energy for the oxygen molecule, yielding a theoretical photoelectron spectrum in good agreement with experimental x−ray induced spectra.