A DFT/TDDFT interpretation of the ground and excited states of porphyrin and porphyrazine complexes

A comprehensive treatment is given of the electronic excitation spectra of Mg, Zn and Ni complexes of porphyrin and porphyrazine using time-dependent density functional theory (TDDFT). It is emphasized that the Kohn–Sham (KS) molecular orbital (MO) method, which is the basis for the TDDFT calculations, affords a MO interpretation of the ground state electronic structure and of the nature of the excitations. This implies that a direct connection can be made to many previous MO treatments of the title compounds. We discuss in particular, how the original explanations of the intensity distribution over the lowest excitations (the Q and B bands) in terms of a cyclic polyene model, or even a free-electron model, can be reconciled with the actual molecular and electronic structure of these compounds being much more complicated than these simple models. A fragment approach is used, building the porphyrin ring from pyrrole rings and CH or N bridges. This leads directly to a simple interpretation of the orbitals of Gouterman's four-orbital model, which are responsible for the Q and B bands. It also leads to additional occupied π-orbitals which are absent in the cyclic polyene model and which need to be invoked to understand other features of the electronic spectra such as the origin of the N, L and M bands. Considerable attention is given to the intensities of the various transitions, explaining why the transitions within the so-called four-orbital model of Gouterman have large transition dipoles, why transitions from additional occupied π-orbitals have relatively small transition dipoles.