Ab initio study of the magnetic exchange coupling constants of a structural model [CaMn3IIIMnII] of the oxygen evolving center in photosystem II

A new structural model for the oxygen evolving center in photosystem II was recently synthesized and characterized by Hewitt et al. (Chem. Commun., 2006, 2650). A simplified Heisenberg model Hamiltonian with only two independent constants was applied to extract the magnetic spin-coupling constants Jij of the mixed valent Mn4 system. In the present study, all six possible coupling constants are calculated by ab initio methods in order to obtain a detailed understanding of the magnetic behavior of the system. The broken symmetry approach of Noodleman is applied using density functional theory (DFT). Two different approaches are compared. On the one hand, the coupling constants are obtained from calculations on eight different determinants which describe the high-spin state as well as different broken-symmetry states of the tetranuclear cluster. On the other hand, a pair approach that permits a direct calculation of the individual coupling constants is used. For the pair approach, the coupling constants are also obtained from modified CASCI (complete active space configuration interaction) calculations. With the different sets of coupling constants, the full Heisenberg Hamiltonian of the four center problem is used to calculate the magnetic susceptibilities, which are then compared with the experimental values.