A polarization propagator for x-ray spectra is outlined and implemented in density functional theory. It rests on a formulation of a resonant-convergent first-order polarization propagator approach which makes it possible to directly calculate the x-ray absorption cross section at a particular frequency without explicitly addressing the excited states. The quality of the predicted x-ray spectrum relates only to the type of density functional applied without any separate treatment of dynamical relaxation effects.

An experimental and theoretical study of the electronic structure of copper phthalocyanine (CuPc) molecule is presented. We performed x-ray photoemission spectroscopy (XPS) and photoabsorption [x-ray absorption near-edge structure (XANES)] gas phase experiments and we compared the results with self-consistent field, density functional theory (DFT), and static-exchange theoretical calculations. In addition, ultraviolet photoelectron spectra (UPS) allowed disentangling several outer molecular orbitals. A detailed study of the two highest occupied orbitals (having a1u and b1g symmetries) is presented: the high energy resolution available for UPS measurements allowed resolving an extra feature assigned to vibrational stretching in the pyrrole rings. This observation, together with the computed DFT electron density distributions of the outer valence orbitals, suggests that the a1u orbital (the highest occupied molecular orbital) is mainly localized on the carbon atoms of pyrrole rings and it is doubly occupied, while the b1g orbital, singly occupied, is mainly localized on the Cu atom. Ab initio calculations of XPS and XANES spectra at carbon K edge of CuPc are also presented. The comparison between experiment and theory revealed that, in spite of being formally not equivalent, carbon atoms of the benzene rings experience a similar electronic environment. Carbon K-edge absorption spectra were interpreted in terms of different contributions coming from chemically shifted C 1s orbitals of the nonequivalent carbon atoms on the inner ring of the molecule formed by the sequence of CN bonds and on the benzene rings, respectively, and also in terms of different electronic distributions of the excited lowest unoccupied molecular orbital (LUMO) and LUMO+1. In particular, the degenerate LUMO appears to be mostly localized on the inner pyrrole ring.