Electronic and Spin Structures of the CaMn ₄ O ₅ (H ₂ O) ₄ Cluster in OEC of PSII Refined to 1.9Å X-ray Resolution

UB3LYP calculations have been performed to elucidate electronic and spin states of the CaMn(III) _4-m Mn(IV) _m X(H ₂ O) ₄ cluster (X=O ₅ (1) and O ₄ (OH)) (2) as active catalytic site for water-splitting reaction in oxygen-evolving complex of PSII refined to 1.9Å X-ray resolution. Both charge- and spin-fluctuated structures have been considered for the mixed-valence (MV) states of 1 and 2. Total energies obtained by these calculations have elucidated quasi-degenerated electronic and spin states that are characterized by charge and spin density populations. The energy levels revealed by UB3LYP are analyzed on the basis of the Heisenberg spin Hamiltonian model, providing the effective exchange integrals between manganese ions at an MV structure. The charge-fluctuation model is also introduced to analyze relative stabilities between MV structures of 1 and 2. The natural orbital (NO) analysis of the UB3LYP solutions has also been performed to elucidate the nature of chemical bonds of 1 and 2: classification of localized d-electrons, labile chemical bonds, and closed-shell orbitals based on their occupation numbers. The localized d-electrons characterized by the NO analysis are responsible for redox reactions, and the origins for the Heisenberg model, namely valence-bond (VB) description of the chemical bonds. On the other hand, labile d-p bonds in 1 and 2 are grasped with the molecular orbital (MO) model: occupation numbers of the NO are used for computations of effective bond order (b), diradical character (y), and spin density indices (Q). Thus, the universal MO-VB model based on the broken-symmetry (BS) calculations followed by the NO analysis is a practical and handy procedure for theoretical approaches to multinuclear transition metal complexes that are hardly investigated by the symmetry-adapted (SA) multireference approaches such as complete active space (CAS) DFT, CASPT2, and CASCC: these SA calculations for related small clusters are performed for examination of scope and applicability of UB3LYP and related DFT functions for target large systems such as 1 and 2.