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.