Theoretical Elucidation of Geometrical Structures of the CaMn₄O₅ Cluster in Oxygen Evolving Complex of Photosystem II Scope and Applicability of Estimation Formulae of Structural Deformations via the Mixed-Valence and Jahn–Teller Effects

Atmospheric oxygenation and evolution of aerobic life on our earth are a result of water oxidation by oxygenic photosynthesis in photosystem II (PSII) of plants, algae, and cyanobacteria. The water oxidation in the oxygen-evolving complex (OEC) of PSII is expected to proceed through five oxidation states, known as the S_i (i = 0, 1, 2, 3, and 4) states in the Kok cycle, with the S₁ being the most stable state in the dark. The OEC in PSII involves the active catalytic site made of four Mn ions and one Ca ion, namely the CaMn4O5 cluster. Past decades, molecular structures of the CaMn4O5 cluster in OEC of PSII have been investigated by the extended X-ray absorption fine structure (EXAFS). The magnetostructural correlations were extensively investigated by EPR spectroscopy. Recently, Kamiya and Shen groups made a great breakthrough for determination of the S1 structure of OEC of PSII by the X-ray diffraction (XRD) and X-ray free electron laser (XFEL) experiments, providing structural foundations that are crucial for theoretical investigations of structure and reactivity of the CaMn₄O₅ cluster. Large-scale QM/MM calculations starting from the XRD structures elucidated geometrical, electronic, and spin structures of the CaMn₄O₅ cluster, indicating an important role of the Jahn–Teller (JT) effect of Mn(III) ions. This review fully examines our theoretical formulae for estimation of the Jahn–Teller deformations of the CaMn₄O₅ cluster in OEC of PSII. Scope and applicability of the JT deformation formulae are elucidated in relation to several different structures of the CaMn₄O₅ cluster proposed by XRD, XFEL, EXAFS, and other experiments. Subtle differences among XRD, XFEL, and EXAFS structures in the S₁ state are examined in relation to environmental effects for the CaMn₄O₅ cluster in OEC of PSII. The X-ray damage of the serial femtosecond crystallography (SFX) by XFEL is also examined in relation to the damage-free low-dose (LD) XRD structure. The JT deformation formulae are also applied to theoretical analysis of the S₃ structures by SFX. Implications of the computational results are discussed for further refinements of geometrical parameters of the CaMn₄O₅ cluster in OEC of PSII and possible mechanisms of water oxidation in OEC of PSII.