We discuss the recent progress in the development of the single center (SC) method for computation of highly-delocalized discrete and partial photoelectron wave continuous functions of molecules. Basic equations of the SC method are presented, and an efficient scheme for the numerical solution of a system of coupled Hartree–Fock equations for a photoelectron is described. Several illustrative applications of the method to photoionization and electronic excitation processes in diatomic molecules are considered. Thereby, we demonstrate its potential for theoretically studying angularly resolved molecular photoionization processes.

The photoionization and photodissociation of an oxygen molecule are investigated theoretically by the method of coupled differential equations. The molecular orbitals of the core are calculated in the MO LCAO approximation. The molecular orbitals of a photoelectron in the discrete and continuous spectra are determined by the single-center method. The wave functions of vibrational motion of the oxygen molecule are obtained within the diabatic approach. The described method is used for calculating the predissociation and autoionization widths of the 2σ _u ⁻¹ (c ⁴Σ _u ⁻ )n/σ_g, v Rydberg states of the oxygen molecule. The total cross sections of the resonant photoionization and neutral predissociation calculated for the oxygen molecule in the excitation energy range 20.6–24.8 eV are in good agreement with the available experimental data.