Generalized approximate spin projection calculations of effective exchange integrals of the CaMn₄O₅ cluster in the S₁ and S₃ states of the oxygen evolving complex of photosystem II

Full geometry optimizations followed by the vibrational analysis were performed for eight spin configurations of the CaMn₄O ₄X(H₂O)₃Y (X = O, OH; Y = H₂O, OH) cluster in the S₁ and S₃ states of the oxygen evolution complex (OEC) of photosystem II (PSII). The energy gaps among these configurations obtained by vertical, adiabatic and adiabatic plus zero-point-energy (ZPE) correction procedures have been used for computation of the effective exchange integrals (J) in the spin Hamiltonian model. The J values are calculated by the (1) analytical method and the (2) generalized approximate spin projection (AP) method that eliminates the spin contamination errors of UB3LYP solutions. Using J values derived from these methods, exact diagonalization of the spin Hamiltonian matrix was carried out, yielding excitation energies and spin densities of the ground and lower-excited states of the cluster. The obtained results for the right (R)- and left (L)-opened structures in the S₁ and S₃ states are found to be consistent with available optical and magnetic experimental results. Implications of the computational results are discussed in relation to (a) the necessity of the exact diagonalization for computations of reliable energy levels, (b) magneto-structural correlations in the CaMn₄O₅ cluster of the OEC of PSII, (c) structural symmetry breaking in the S ₁ and S₃ states, and (d) the right- and left-handed scenarios for the O-O bond formation for water oxidation.