Plane wave and orthogonalized plane wave many-body Green's function calculations of photoionization intensities

General equations for the calculation of correlated single-channel photoionization cross-sections of randomly oriented molecules are presented. These equations, employing a plane wave orthogonalized to all (occupied and virtual) bound molecular orbitals as a wavefunction for the photoelectron, are derived in a many-body Green's function framework. Several decoupling approximations for the expansion of the one-particle propagator are then used to compute angle-averaged photoionization cross-sections for a Mg Kα photon source and for a representative set of molecules: CH4, H2O, C2H2, N2, and CO. Both orthogonality corrections to the continuum orbital and many-body corrections in the description of the ionization process are shown to be important for accurate simulations of soft X-ray ionization spectra.