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The primary coordination sphere of the multinuclear cofactor (Mn4CaOx) in the oxygen-evolving complex (OEC) of photosystem II is absolutely conserved to maintain its structure and function. Recent time-resolved serial femtosecond crystallography identified large reorganization of the primary coordination sphere in the S-2 to S-3 transition, which elicits a cascade of events involving Mn oxidation and water molecule binding to a putative catalytic Mn site. We examined how the crystallographic fields, created by transient conformational states of the OEC at various time points, affect the thermodynamics of various isomers of the Mn cluster using DFT calculations, with an aim of comprehending the functional roles of the flexible primary coordination sphere in the S-2 to S-3 transition and in the recovery of the S-2 state. The results show that the relative movements of surrounding residues change the size and shape of the cavity of the cluster and thereby affect the thermodynamics of various catalytic intermediates as well as the ability to capture a new water molecule at a coordinatively unsaturated site. The implication of these findings is that the protein dynamics may serve to gate the catalytic reaction efficiently by controlling the sequence of Mn oxidation/reduction and water binding/release. This interpretation is consistent with EPR experiments; g similar to 5 and g similar to 3 signals obtained after near-infrared (NIR) excitation of the S-3 state at 4 K and a g similar to 5 only signal produced after prolonged incubation of the S-3 state at 77 K can be best explained as originating from water-bound S-2 clusters (S-total = 7/2) under a S-3 ligand field, i.e., the immediate one-electron reduction products of the oxyl-oxo (S-total = 6) and hydroxo-oxo (S-total = 3) species in the S-3 state.

The effect of periodic structure on the effective exchange integral (Jab) was investigated using density functional theory calculations with plane-wave basis and approximate spin projection scheme ...

The fully optimized geometrical structures of the CaMn4Ox (x = 5, 6) clusters in the Si (i = 0–3) states of the Kok cycle of photosynthetic water oxidation by the large-scale quantum mechanics/molecular mechanics (QM/MM) calculations were compared to recent experimental results based on serial femtosecond crystallography (SFX). The Mn Mn and Ca Mn distances obtained by the QM/MM calculations were found to be totally comparable to the SFX experiments, elucidating the entire Kok cycle involving the S4 transition state during the O O bond formation for water oxidation in the oxygen evolving complex (OEC) of photosystem II (PSII).

The optimized geometries of the CaMn4 OX (X = 5, 6) cluster in the oxygen evolving complex (OEC) of photosystem II (PSII) by large-scale quantum mechanics (QM) and molecular mechanics (MM) calculations are compared with recent serial femtosecond crystallography (SFX) results for the Si (i = 0-3) states. The valence states of four Mn ions by the QM/MM calculations are also examined in relation to the experimental results by the X-ray emission spectroscopy (XES) for the Si intermediates. Geometrical and valence structures of right-opened Mn-hydroxide, Mn-oxo and Mn-peroxide intermediates in the S3 state are investigated in detail in relation to recent SFX and XES experiments for the S3 state. Interplay between theory and experiment indicates that the Mn-oxo intermediate is a new possible candidate for the S3 state. Implications of the computational results are discussed in relation to possible mechanisms of the oxygenoxygen bond formation for water oxidation in OEC of PSII.

Photosynthetic water oxidation is catalyzed by a Mn4CaO5-cluster in photosystem II through an S-state cycle. Understanding the roles of heterogeneity in each S-state, as identified recently by the EPR spectroscopy, is very important to gain a complete description of the catalytic mechanism. We performed herein hybrid DFT calculations within the broken-symmetry formalism and associated analyses of Heisenberg spin models to study the electronic and spin structures of various isomeric structural motifs (hydroxo–oxo, oxyl–oxo, peroxo, and superoxo species) in the S3 state. Our extensive study reveals several factors that affect the spin ground state: (1) (formal) Mn oxidation state; (2) metal–ligand covalency; (3) coordination geometry; and (4) structural change of the Mn cluster induced by alternations in Mn···Mn distances. Some combination of these effects could selectively stabilize/destabilize some spin states. We found that the high spin state (Stotal = 6) of the oxyl–oxo species can be causative for cat...

Large-scale quantum mechanics/molecular mechanics (QM/MM) calculations were performed to elucidate the possible intermediates in the S3 state of the oxygen-evolving complex of photosystem II. We have investigated nine S3 candidates in the R-/L-opened Mn-hydroxide, Mn-oxo, Mn-peroxide and Mn-superoxide intermediate states, and their optimized CaMn4O6 structures and the Mn valence states were compared to the experimental results revealed by recent serial femtosecond crystallography (SFX) and X-ray emission spectroscopy (XES). By using the Jahn-Teller (JT) deformation formulae, the Mn4-O(5) and O(5)-O(6) distances were estimated from the Mn4-Mn3 distances. Among all the calculated S3 intermediates, not only the right-opened hydroxo intermediate (R-hydroxo), but also the right-opened Mn-oxo intermediate (R-oxo(4444)) were found to be plausible based on the calculated CaMn4O6 structure and the Mn valence state (4444).

We here precisely analyzed the electronic structures during the oxygen-oxygen (O-O) bond formation of the oxygen-evolving complex (OEC) in photosystem II (PSII) based on the quantum mechanics/molecular mechanics (QM/MM) calculations. Changes in the spin density and the chemical indices derived from the natural orbitals suggested that the O(5)-O(6) bond formation proceeds with a concerted bond breaking of the Mn4-O(5) coupled with the through-bond one-electron transfer from the O(6) site to the Mn4 site (Mn4(IV) → Mn4(III)). This mechanism can be best described as a Concerted Bond Switching (CBS) mechanism, which is a non-radical reaction of the O(5)-O(6) bond formation.

Molecular quantum mechanics (MQM) investigations have been performed for elucidation of fundamental principles of the photo-induced water oxidation in oxygen evolving complex (OEC) of photosystem II (PSII). To this end, as a first theoretical step, broken symmetry (BS) quantum mechanics (QM) and QM(BS)/molecular mechanics (MM) calculations have been conducted for elucidation of geometrical, electronic and spin structures of the CaMn4Ox (X = 5, 6) cluster in the five steps Si (i = 0∼4) of the Kok cycle for water oxidation. The QM and QM/MM calculations have provided full optimised geometries of short-lived key intermediates and transition state structure for the O-O bond formation in the native solar-energy conversion. The interplay between theory and experiment have clearly indicated that the CaMn4O5 cluster in OEC of PSII exhibits typical physicochemical properties of strong correlation electron system (SCES) confined with effective protein field. Our QM and QM/MM computational results for key intermediates and transition structure for the O-O bond formation in the Kok cycle are now plentiful for derivation of fundamental principles (FP) for understanding of photo-induced water oxidation in OEC of PSII. We summarize twenty nine fundamental principles (FPs) in systematic manner by QM and QM/MM calculations for understanding of water oxidation in Oxygen Evolving Complex(OEC) of Photosystem II(PSII). One of our final aims is theoretical design of the next-generation artificial photosystem materials composed of abundant metal ions.

Relative stability between manganese hydroxide (H2O)2(OH)4Mn(IV) OH (1) and manganese oxo (H2O)3(OH)3Mn(IV) O (2) species were investigated by coupled cluster (CC) SD and SD(T), DMRG CASCI, CASSCF, CASPT2 and CASDFT methods. The DMRG CASCI and DMRG CASSCF based on thirteen active orbitals and thirteen active electrons {13, 13} CAS space indicted the greater stability of 2 than 1. On the other hand, the relative stability between 1 and 2 was reversed by UCC SD, DLPNO-UCC SD, CASPT2 and CAS-DFT, indicating an important role of dynamical electron correlation corrections. Implications of present results are discussed to elucidate scope and applicability of hybrid DFT (HDFT) methods for 1 and 2.

The O2 release of the oxygen-evolving complex of the photosystem II (PSII) is one of the essential processes responsible for the highly efficient O2 production. Despite its importance, the detailed molecular mechanism is still unsolved. In the present study, we show that the O2 release is directly coupled with water insertion into the Mn cluster based on the quantum mechanics/molecular mechanics (QM/MM) calculations. In this mechanism, the O2 molecule first dissociates from the Mn sites in order, that is, the O atom coordinating to the Mn3 (O5a) first dissociates, then the other O atom coordinating to the Mn1 (O5d) dissociates in the next step in the late S4 state (1 → 2). Next, the O2 migrates to a space surrounded by the Val185 and His332 side chains as one water molecule coordinating to the Ca2+ ion (W3) comes into the O2 bonded site (2 → 3). Finally, a pre-S0 state (4) is formed after a proton transfer from the inserted water to the other proton acceptor site (W2) (3 → 4). The highest activation barri...

The reaction mechanism of the O2 formation in the S4 state of the oxygen-evolving complex of photosystem II was clarified at the quantum mechanics/molecular mechanics (QM/MM) level. After the Yz (Y161) oxidation and the following proton transfer in the S3 state, five reaction steps are required to produce the molecular dioxygen. The highest barrier step is the first proton transfer reaction (0 → 1). The following reactions involving electron transfers were precisely analyzed in terms of their energies, structures and spin densities. We found that the one-electron transfer from the Mn4Ca cluster to Y161 triggers the O–O sigma bond formation.

Possible mechanisms for water cleavage in oxygen evolving complex (OEC) of photosystem II (PSII) have been investigated based on broken-symmetry (BS) hybrid DFT (HDFT)/def2 TZVP calculations in combination with available XRD, XFEL, EXAFS, XES and EPR results. The BS HDFT and the experimental results have provided basic concepts for understanding of chemical bonds of the CaMn4O5 cluster in the catalytic site of OEC of PSII for elucidation of the mechanism of photosynthetic water cleavage. Scope and applicability of the hybrid DFT (HDFT) methods have been examined in relation to relative stabilities of possible nine intermediates such as Mn-hydroxide, Mn-oxo, Mn-peroxo, Mn-superoxo, etc., in order to understand the O–O (O–OH) bond formation in the S3 and/or S4 states of OEC of PSII. The relative stabilities among these intermediates are variable, depending on the weight of the Hartree–Fock exchange term of HDFT. The Mn-hydroxide, Mn-oxo and Mn-superoxo intermediates are found to be preferable in the weak, intermediate and strong electron correlation regimes, respectively. Recent different serial femtosecond X-ray (SFX) results in the S3 state are investigated based on the proposed basic concepts under the assumption of different water-insertion steps for water cleavage in the Kok cycle. The observation of water insertion in the S3 state is compatible with previous large-scale QM/MM results and previous theoretical proposal for the chemical equilibrium mechanism in the S3 state . On the other hand, the no detection of water insertion in the S3 state based on other SFX results is consistent with previous proposal of the O–OH (or O–O) bond formation in the S4 state . Radical coupling and non-adiabatic one-electron transfer (NA-OET) mechanisms for the OO-bond formation are examined using the energy diagrams by QM calculations and by QM(UB3LYP)/MM calculations . Possible reaction pathways for the O–O and O–OH bond formations are also investigated based on two water-inlet pathways for oxygen evolution in OEC of PSII. Future perspectives are discussed in relation to post HDFT calculations of the energy diagrams for elucidation of the mechanism of water oxidation in OEC of PSII.

Tanaka et al. (J. Am. Chem. Soc., 2017, 139, 1718) recently reported the three‐dimensional (3D) structure of the oxygen evolving complex (OEC) of photosystem II (PSII) by X‐ray diffraction (XRD) using extremely low X‐ray doses of 0.03 and 0.12 MGy. They observed two different 3D structures of the CaMn4O5 cluster with different hydrogen‐bonding interactions in the S1 state of OEC keeping the surrounding polypeptide frameworks of PSII the same. Our Jahn–Teller (JT) deformation formula based on large‐scale quantum mechanics/molecular mechanics (QM/MM) was applied for these low‐dose XRD structures, elucidating important roles of JT effects of the MnIII ion for subtle geometric distortions of the CaMn4O5 cluster in OEC of PSII. The JT deformation formula revealed the similarity between the low‐dose XRD and damage‐free serial femtosecond X‐ray diffraction (SFX) structures of the CaMn4O5 cluster in the dark stable state. The extremely low‐dose XRD structures were not damaged by X‐ray irradiation. Implications of the present results are discussed in relation to recent SFX results and a blue print for the design of artificial photocatalysts for water oxidation.

In this study, the zero-field splitting parameters ( D , E ) and effective exchange integrals ( J ) for a Mn 12 /Mn 11 Cr mixed crystal were evaluated using ab initio molecular orbital (MO) computations based on the hybrid density functional theory (DFT) methods for Mn 11 Cr ∗ -acetate cluster (Mn 12 and Mn 11 Cr mixing). In this study, Mn 12 -acetate, Mn 11 Cr-acetate, and Mn 12− n Cr n -acetate clusters were focused on. The zero-field splitting (ZFS) parameters are obtained by UB3LYP methods, i.e. −0.339 cm −1 (Mn 12 -acetate) and −0.351 cm −1 (Mn 11 Cr-acetate). The energy barriers were estimated to be 53.7 K and 50.4 K, which showed good agreement with previously reported experimental values of 68.8 K and 56.8 K, respectively. The origin of such anisotropy is assumed to be the eight Mn III ions with d 4 -electrons in their outer ring subunits, where elongated conformation along the axial direction becomes very important and leads to negative D values. The spin networks in these clusters were discussed by using the effective exchange integral sets. The J s value, as estimated by the UB3LYP method revealed that the J 2 , J 3 , and J 3 ′ interactions played important roles in describing the parallel spin ordering in cubane and ring subunits as well as the antiferromagnetic coupling between two subunits. The other interactions, i.e. J 1 , J 1 ′, J 4 , and J 4 ′ somewhat disturbed the spin ordering in the Mn 12 -acetate cluster. The substitution of Mn IV by Cr III did not change the spin network. However, the total S value changed after the substitution.

In this work, we show that the natural orbitals of unrestricted hybrid density functional theory (UHDFT) can be used as the active space orbitals to perform multireference (MR) calculations, for example, the density matrix renormalisation group (DMRG) and Mukherjee-type (Mk) MR coupled-cluster (CC) method. By including a sufficiently large number of these natural orbitals, full-valence (FV) active space can be identified without recourse of the expensive self-consistent procedures for DMRG-SCF. Several useful chemical indices are derived based on the occupation numbers of the natural orbitals for seamless continuation from broken-symmetry (BS) to symmetry-adapted (SA) methods. These procedures are used on 1,3-didehydrobenzene (meta-benzyne) to calculate its singlet (S)-triplet (T) gap. We compare our results to available experiments and computational results obtained by several other groups. We see our procedures as a seamless bridge between single-reference BS methods, such as UHDFT, and the SA MR methods, such as FV DMRG and MkMRCC.

Theoretical examinations of the ferromagnetic coupling in the m-phenylene-bis-methylene molecule and its oligomer were carried out. These systems are good candidates for exchange-coupled systems to investigate strong electronic correlations. We studied effective exchange integrals (J), which indicated magnetic coupling between interacting spins in these species. First, theoretical calculations based on a broken-symmetry single-reference procedure, i.e. the UHF, UMP2, UMP4, UCCSD(T) and UB3LYP methods, were carried out with a GAUSSIAN program code under an SR wave function. From these results, the J value by the UHF method was largely positive because of the strong ferromagnetic spin polarisation effect. The J value by the UCCSD(T) and UB3LYP methods improved an overestimation problem by correcting the dynamical electronic correlation. Next, magnetic coupling among these spins was studied using the CAS-based method of the symmetry-adapted multireference methods procedure. Thus, the UNO DMRG CASCI (...

Large-scale QM/MM calculations were performed to elucidate an optimized geometrical structure of a CaMn4O5 cluster with and without water insertion in the S3 state of the oxygen evolving complex (OEC) of photosystem II (PSII). The left (L)-opened structure was found to be stable under the assumption of no hydroxide anion insertion in the S3 state, whereas the right (R)-opened structure became more stable if one water molecule is inserted to the Mn4Ca cluster. The optimized Mna(4)–Mnd(1) distance determined by QM/MM was about 5.0 Å for the S3 structure without an inserted hydroxide anion, but this is elongated by 0.2–0.3 Å after insertion. These computational results are discussed in relation to the possible mechanisms of O–O bond formation in water oxidation by the OEC of PSII.

We applied our analysis, based on a linear response function of density and spin density, to two typical transition metal complex systems-the reaction centers of P450, and oxygen evolving center in Photosystem II, both of which contain open-shell transition metal ions. We discuss the relationship between LRF of electron density and spin density and the types of units and interactions of the systems. The computational results are discussed in relation to quantum mechanics (QM) cluster and quantum mechanics/molecular mechanics (QM/MM) modeling that are employed to compute the reaction centers of enzymes.

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 Si (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.

Estimation and the importance of spin contamination errors (SCEs) in theoretical calculations related to open-shell molecular systems are well known. However, there is no estimation scheme available for density functional theory (DFT)/plane-wave, a standard first-principles method for solid materials. Therefore, in this study, we established the estimation scheme of SCE in DFT/plane-wave using approximate spin projection, and the new scheme was applied to typical models with stable antiferromagnetic states to illustrate the importance of SCE correction in solid systems.

Photosynthetic oxidation of water to dioxygen is catalyzed by the Mn4CaO5 cluster in the protein-cofactor complex photosystem II. The light-driven catalytic cycle consists of four observable intermediates (S0, S1, S2, and S3) and one transient S4 state. Recently, using X-ray free-electron laser crystallography, two experimental groups independently observed incorporation of one additional oxygen into the cluster during the S2 to S3 transition, which is likely to represent a substrate. The present study implicates two competing reaction routes encountered during the structural rearrangement of the catalyst induced by the water binding and immediately preceding the formation of final stable forms in the S3 state. This mutually exclusive competition involves concerted versus stepwise conformational changes between two isomers, called open and closed cubane structures, which have different consequences on the immediate product in the S3 state. The concerted pathway involves a one-step conversion between two isomeric hydroxo forms without changes to the metal oxidation and total spin (Stotal = 3) states. Alternatively, in the stepwise process, the bound waters are oxidized and transformed into an oxyl–oxo form in a higher spin (Stotal = 6) state. Here, density functional calculations are used to characterize all relevant intermediates and transition structures and demonstrate that the stepwise pathway to the substrate activation is substantially favored over the concerted one, as evidenced by comparison of the activation barriers (11.1 and 20.9 kcal mol−1, respectively). Only after formation of the oxyl–oxo precursor can the hydroxo species be generated; this occurs with a slow kinetics and an activation barrier of 17.8 kcal mol−1. The overall thermodynamic driving force is likely to be controlled by the movements of two glutamate ligands, D1-Glu189 and CP43-Glu354, in the active site and ranges from very weak (+0.4 kcal mol−1) to very strong (–23.5 kcal mol−1).

Radical abstraction reactions by the cytochrome P450 compound I are investigated on the basis of the one quartet two doublet model consisted of three configurations; 4{2[↑• +Por]–[↑• 3Fe(IV)=O •↑]} (4CpdI; S = 3/2), 2{2[↓• +Por]–[↑• 3Fe(IV)=O •↑]} (2CpdIa; S = 1/2) and 2{1[Por(↑↓)]–2[↑• Fe(V)=O]} (2CpdIb; S = 1/2) where Por denotes porphyrin and axial cysteine anion (–SR) is neglected. The dπ-pπ bond of 2CpdIb was highly spin-polarized in the transition-state region of hydrogen abstraction reactions, providing the doublet configuration; 2{1[Por(↑↓)]–2[↑↑•• Fe(IV)–O •↓]} (2CpdIb,oxyl). The oxyl-radical character of 2CpdIb,oxyl plays an important role for hydrogen radical abstraction from alkanes. The spin populations on the iron atom at the transition structures by available density functional theory (DFT) results were about 2.0 for 2CpdIb,oxyl, whereas they were about 1.0 for 4CpdI and 2CpdIa. On the other hand, the spin density population on the carbon atom of alkyl radical were negative and positive in sign for 2CpdIb,oxyl and 4CpdI, respectively, in consistent with their spin structures. In order to elucidate possible reaction pathways by the cytochrome P450 compound I, relative stabilities between 4CpdI and 2CpdIb were examined on the basis of available DFT and beyond DFT results. The refined DFT results obtained by the beyond DFT elucidated one of the possible reaction pathways for hydrogen abstractions; 2CpdIa → 2Cpdb → 2CpdIb,oxyl → 2(TS) → (rebound). Implications of the computational results are also discussed in relation to water oxidation in artificial catalysts.

Fundamental concepts and basic theories for the broken-symmetry (BS) methods have been reviewed in relation to theoretical elucidation and understanding of the mechanism for water oxidation in the oxygen evolving complex (OEC) of photosystem II (PSII). The HOMO-LUMO mixings by the BS method have provided the BS orbitals which are mainly localized on the metal and oxygen sites of the high-valent transition-metal oxo (M O) bonds, respectively. The oxyl-radical character ( M–O ) is responsible for radical reactivity such as the radical coupling in accord with various experimental results. The Lewis acids play important roles for reduction of the oxyl-radical character, indicating the participation of the water-coordinated Ca(II) ion of the CaMn3O4 cubane to stabilization of the Mn(V)=O…Ca(II) bond for essentially non-radical reactions. Several chemical indices have been calculated to elucidate the radical character for quantitative purpose. Implications of the computational results are discussed in relation to possible mechanisms of water oxidation in OEC of PSII.

Large-scale QM/MM calculations including hydrogen-bonding networks in the oxygen evolving complex (OEC) of photosystem II (PSII) were performed to elucidate the geometric structures of the CaMn 4 O 5 cluster in the key catalytic states (S i ( i = 0–3)). The optimized Mn–Mn, Ca–Mn and Mn–O distances by the large-scale QM/MM starting from the high-resolution XRD structure were consistent with those of the EXAFS experiments in the dark stable S 1 state by the Berkeley and Berlin groups. The optimized geometrical parameters for other S i ( i = 0, 2, 3) states were also consistent with those of EXAFS, indicating the importance of the large-scale QM/MM calculations for the PSII-OEC.

Organic ferromagnets and advanced magneticmetals have received continued interest over many decades. The systematic investigation of open-shell radicals had been reported by Morita and co-workers. ...

Water oxidation by photosystem II (PSII) converts light energy into chemical energy with the concomitant production of molecular oxygen, both of which are indispensable for sustaining life on Earth. This reaction is catalyzed by an oxygen-evolving complex (OEC) embedded in the huge PSII complex, and its mechanism remains elusive in spite of the extensive studies of the geometric and electronic structures. In order to elucidate the water-splitting mechanism, synthetic approaches have been extensively employed to mimic the native OEC. Very recently, a synthetic complex [Mn4CaO4(ButCOO)8(py)(ButCOOH)2] (1) closely mimicking the structure of the native OEC was obtained. In this study, we extensively examined the geometric, electronic and spin structures of 1 using the density functional theory method. Our results showed that the geometric structure of 1 can be accurately reproduced by theoretical calculations, and revealed many similarities in the ground valence and spin states between 1 and the native OEC. We also revealed two different valence states in the one-electron oxidized state of 1 (corresponding to the S2 state), which lie in the lower and higher ground spin states (S = 1/2 and S = 5/2), respectively. One remarkable difference between 1 and the native OEC is the presence of a non-negligible antiferromagnetic interaction between the Mn1 and Mn4 sites, which slightly influenced their ground spin structures (spin alignments). The major reason causing the difference can be attributed to the short Mn1–O5 and Mn1–Mn4 distances in 1. The introduction of the missing O4 atom and the reorientation of the Ca coordinating ligands improved the Mn1–O5 and Mn1–Mn4 distances comparable to the native OEC. These modifications will therefore be important for the synthesis of further advanced model complexes more closely mimicking the native OEC beyond 1.

We have performed hybrid density functional theory (DFT) calculations to investigate how chemical equilibria can be described in the S3 state of the oxygen-evolving complex in photosystem II. For a chosen 340-atom model, 1 stable and 11 metastable intermediates have been identified within the range of 13 kcal mol(-1) that differ in protonation, charge, spin, and conformational states. The results imply that reversible interconversion of these intermediates gives rise to dynamic equilibria that involve processes with relocations of protons and electrons residing in the Mn4CaO5 cluster, as well as bound water ligands, with concomitant large changes in the cluster geometry. Such proton tautomerism and redox isomerism are responsible for reversible activation/deactivation processes of substrate oxygen species, through which Mn-O and O-O bonds are transiently ruptured and formed. These results may allow for a tentative interpretation of kinetic data on substrate water exchange on the order of seconds at room temperature, as measured by time-resolved mass spectrometry. The reliability of the hybrid DFT method for the multielectron redox reaction in such an intricate system is also addressed.

Full geometry optimizations of ([CaMn4O4(CH3COO)8(py)(CH3COOH)2], (py: pyridine) (1)) were performed at the UB3LYP theoretical level. 1 is a theoretical model for the synthetic model ([CaMn4O4(ButCOO)8(py)(ButCOOH)2], (But: t-butyl) (2)) which closely mimicks the native oxygen evolving complex (OEC) in photosystem II. It was shown that the X-ray structure of 2 was well reproduced by 1 in the (Mn1(III), Mn2(IV), Mn3(IV), Mn4(III)) valence state with the unprotonated O5 (O5 = O2−), and two different valence states were obtained in the one-electron oxidized state. Importance of the Jahn–Teller effect of the Mn(III) site for the structural deformations was presented.

Fundamental principles for theoretical understanding and elucidation of structure and reactivity of iron-sulfur (Fe-S) FenSm (n, m=2∼8) clusters are investigated and elucidated on the theoretical and experimental grounds. To this end, the nature of chemical bonds of these clusters is investigated by three methods; (1) the spin Hamiltonian model for analysis of EPR results, (2) broken-symmetry (BS) hybrid density functional theory (HDFT) methods for full geometry optimisations and elucidations of complete active spaces (CAS) for one-electron transfers reactions and (3) beyond HDFT methods such as CAS configuration interaction (CI) and MR CI for high precision energy calculations on classical and quantum computers. Theoretical concepts revealed are applied for elucidation of the mechanism of nitrogen fixation with FeMoco (Fe7MoS9C) cluster, indicating an important role of proton-coupled (PC) one electron spin transfer (OEST) processes instead of radical reaction mechanisms.

The seamless continuation from single reference (SR) broken-symmetry (BS) to multi-reference (MR) methods such as the density matrix renormalization group (DMRG) was revisited to elucidate natural orbitals (UNO) and their occupation numbers for iron-sulfur clusters such as P- and FeMoco clusters in nitrogenase. Fractional occupation numbers of UNO for these clusters by SR-BS were consistent with those of open-shell orbitals by MR-DMRG, supporting the UNO-CI calculations of large Fe-S clusters on classical and quantum computers.

The optimized geometries of the CaMn

Domain-based local pair natural orbital (DLPNO) coupled cluster single and double (CCSD) with triple perturbation (T) correction methods were applied for fourteen different S2 structures of the CaMn4O5 cluster in oxygen evolving complex (OEC) of photosystem II (PSII). The DLPNO-CCSD(T0) calculations elucidated that the right (R)-opened S2aYZ structure (a = O2− at the O(5) site, Y = W2 and Z = W1) with the low spin (LS) (S = 1/2, g = 2) state and two left (L)-opened S2aYZ structures with the high spin (HS) (S = 5/2, g = 4; g > 4) state were nearly degenerated in energy, supporting previous one LS-two HS model for the S2 state in compatible with recent EXAFS and EPR results.

Both direct exchange and super-exchange interactions cooperate to realize inter-spin magnetic interaction in binuclear manganese complex Mn(IV)

QM(UB3LYP)/MM(AMBER) calculations were performed for the locations of the transition structure (TS) of the oxygen–oxygen (O–O) bond formation in the S4 state of the oxygen-evolving complex (OEC) of photosystem II (PSII). The natural orbital (NO) analysis of the broken-symmetry (BS) solutions was also performed to elucidate the nature of the chemical bonds at TS on the basis of several chemical indices defined by the occupation numbers of NO. The computational results revealed a concerted bond switching (CBS) mechanism for the oxygen–oxygen bond formation coupled with the one-electron transfer (OET) for water oxidation in OEC of PSII. The orbital interaction between the σ-HOMO of the Mn(IV)4–O(5) bond and the π*-LUMO of the Mn(V)1=O(6) bond plays an important role for the concerted O–O bond formation for water oxidation in the CaMn4O6 cluster of OEC of PSII. One electron transfer (OET) from the π-HOMO of the Mn(V)1=O(6) bond to the σ*-LUMO of the Mn(IV)4–O(5) bond occurs for the formation of electron transfer diradical, where the generated anion radical [Mn(IV)4–O(5)]-• part is relaxed to the •Mn(III)4 … O(5)- structure and the cation radical [O(6)=Mn(V)1]+ • part is relaxed to the +O(6)–Mn(IV)1• structure because of the charge-spin separation for the electron-and hole-doped Mn–oxo bonds. Therefore, the local spins are responsible for the one-electron reductions of Mn(IV)4->Mn(III)4 and Mn(V)1->Mn(IV)1. On the other hand, the O(5)- and O(6)+ sites generated undergo the O–O bond formation in the CaMn4O6 cluster. The Ca(II) ion in the cubane- skeleton of the CaMn4O6 cluster assists the above orbital interactions by the lowering of the orbital energy levels of π*-LUMO of Mn(V)1=O(6) and σ*-LUMO of Mn(IV)4–O(5), indicating an important role of its Lewis acidity. Present CBS mechanism for the O–O bond formation coupled with one electron reductions of the high-valent Mn ions is different from the conventional radical coupling (RC) and acid-base (AB) mechanisms for water oxidation in artificial and native photosynthesis systems. The proton-coupled electron transfer (PC-OET) mechanism for the O–O bond formation is also touched in relation to the CBS-OET mechanism.

We have investigated nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function to examine theoretical foundation of contemporary computational chemistry such as quantum mechanics/molecular mechanics methods. In this study, we introduce several nearsightedness-related indices to assess the magnitude of localisability of responses for one-dimensional finite model systems. We started from two electrons' systems, which are beyond the scope of the original concept of NEM, and increased the number of electrons (N) to a hundred electrons to analyse dependency of such indices on N. In the process of construction of the indices, we analysed the factors, because of which the magnitude of nonlocal parts of linear response functions becomes small, into several ones, and extracted purely the magnitude of propagation of responses.

Several key concepts and geometrical rules for the Mn–Mn and Mn–O distances of the CaMn 4 O 5 cluster in the oxygen evolving complex (OEC) of photosystem II (PSII) by previous and present theoretical calculations were examined for a clear understanding of the damage-free S 1 structure revealed by X-ray free electron laser (XFEL). A simple equation to estimate the Mn a –Mn b distance in relation to the Mn a –O (5) distance was derived taking into consideration the Jahn–Teller (JT) effects for Mn centers, indicating that the XFEL structure is regarded as a slightly right-elongated quasi-central structure in contradiction to a right-opened structure proposed by the EXAFS measurements.

The structure of the oxygen evolving complex (OEC) of photosystem II (PSII) was recently analyzed by crystallography at 1.95 A resolution using X-ray free electron laser (XFEL), but the positions of hydrogen atoms were not determined. We have examined the XFEL structure theoretically under the assumption of four protonation cases. The spin densities obtained by the high-spin UB3LYP revealed that a partial internal reduction of the high-valent Mn ions in the CaMn4O4X(H2O)3Y cluster occurs for the O(5)(=X) = O2− case, entailing its protonation (X = OH−) in the XFEL structure.