Quantum Chemical Spin Densities for Radical Cations of Photosynthetic Pigment Models

The spin densities of radical cations of magnesium porphyrin, magnesium chlorine and a truncated chlorophyll a model are calculated with density-functional theory and multiconfigurational quantum chemical methods. The latter serve as a reference for approximate density-functional theory which yields spin densities that may suffer from the self-interaction error. We carried out complete active space self-consistent field calculations with increasing active orbital spaces to systematically converge qualitatively correct spin densities. In particular, for the magnesium chlorine and chlorophyll a model radical cations, this is not easy to achieve because of the lower symmetry compared to magnesium porphyrin. Strategies had to be employed which allowed us to consider very large active orbital spaces. We explored restricted active space self-consistent field and density-matrix renormalization group calculations. Based on these reference data, we assessed the accuracy of different density-functional approximations. We show that in particular, exchange-correlation model potentials with correct asymptotic behavior yield good spin densities, and we find, in agreement with previous studies on different classes of compounds, that hybrid functionals systematically increase spin-polarization effects with increasing amounts of exact exchange. Our results provide a starting point for investigations of spin densities of more complex systems such as the hinge model for the primary electron donor in photosystem II.