Understanding Two Different Structures in the Dark Stable State of the Oxygen‐Evolving Complex of Photosystem II: Applicability of the Jahn–Teller Deformation Formula

Abstract

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 Mn^III 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.

1. Introduction

A number of experimental studies for oxygen evolving complex (OEC) of photosystem II (PSII) have been performed using several kinds of experimental techniques.1, 2 Structural parameters, particularly Mn‐Mn distances, of the CaMn₄O₅ cluster in OEC of PSII have been investigated by the extended X‐ray absorption fine structure (EXAFS).3, 4, 5, 6, 7, 8, 9, 10 On the other hand, X‐ray diffraction (XRD) experiments11, 12, 13, 14, 15, 16, 17, 18, 19 play an important role for elucidation of complex, three‐dimensional (3D) structures of transition metal‐containing enzymes such as OEC of PSII, providing structural bases for successive investigations by spectroscopic methods such as EPR and FTIR.1, 2 However a critical issue of the XRD11, 12, 13, 14, 15, 16, 17, 18, 19 for redox‐active OEC of PSII is the radiation damage with intense synchrotron radiation as compared with EXAFS.3, 4, 5, 6, 7, 8, 9, 10 In the past six years, serial femtosecond X‐ray (SFX) diffraction method, known as “diffraction‐before‐degradation”, using the X‐ray free‐electron laser (XFEL)20, 21, 22, 23, 24, 25, 26, 27, 28, 29 have been developed to obtain damage‐free XRD structures of redox‐active enzymes such as OEC of PSII. On the other hand, low dose XRD experiments have been also desired for suppression of the X‐ray damage.6, 7 Tanaka et al.30 recently reported the 3D structures of the CaMn₄O₅ cluster in OEC of PSII by XRD using extremely low X‐ray doses of 0.03 and 0.12 MGy, for which the external Mn reductions were estimated to be less than 1 and 3.5 (%), respectively.6, 7, 30 They observed that geometrical structures of the A‐monomer were different from those of the B‐monomer in the dimer units of both 5B5E with 0.03 MGy and 5B66 with 0.12 MGy XRD results even in the S₁ state of the Kok cycle,31, 32 although the surrounding polypeptide frameworks of PSII were the same.30

In the past decade we have performed broken‐symmetry (BS) hybrid DFT (UB3LYP) calculations33, 34, 35, 36 of the CaMn₄O₅ cluster in OEC of PSII starting from the 3D XRD (0.43 MG) structure18 for theoretical investigation of geometrical, electronic and spin structures of OEC of PSII. The UB3LYP calculations were performed for total 48 (=8×6) valence configurations obtained by 8 spin states for 6 mixed valence structures (see SV).37 The energy diagrams for all the configurations elucidated that the ground valence configuration of the cluster in the dark stable S₁ state was the Ca^IIMn^III _4(a)Mn^IV _3(b)Mn^IV _2(c)Mn^III _1(d), that was abbreviated as (3443). Moreover the DFT calculations elucidated that the nature of the Mn₄−O₍₅₎−Mn₁ bond of the cluster was labile,33 indicating structural symmetry breaking (SSB)35, 36 because of the Jahn–Teller (JT) effects of the Mn^III _4(a) ion. Full geometry optimizations of OEC of PSII by large‐scale QM/MM methods37, 38 indeed elucidated four different topological structures based on the JT effects as illustrated in the Supporting Information Figure S1 (see SII.1). An estimation formula39 of the JT deformations of the cluster also emerged on the basis of a number of the optimized geometries by QM and QM/MM,33, 34, 35, 36, 37, 38, 39 together with available experimental geometrical parameters of manganese oxides clusters. In this paper, we apply our JT deformation formula for two different S₁ structures by the low‐dose XRD experiments of Tanaka et al.,30 proposing a unified view of the EXAFS,3, 4, 5, 6, 7, 8, 9, 10 XRD11, 12, 13, 14, 15, 16, 17, 18, 19 and XFEL27, 28, 29 structures and theoretical models33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44 of the S₁ state of OEC of PSII. Implication of present results is discussed in relation to recent SFX results and a blue print for the design of artificial photo‐catalysts using abundant 3d‐transition metals.

2. Theoretical Background

2.1. Structural Symmetry Breaking of the CaMn₄O₅ Cluster in the OEC of PSII

The high‐resolution XRD18 experiments first elucidated the 3D structure of the CaMn₄O₅ cluster with almost central (C) conformation, as illustrated in Figure S1. Our QM and QM/MM computations33, 34, 35, 36, 37, 38, 39 revealed slightly right (C_R)‐ and left (C_L)‐elongated quasi‐central structures as well as right (R)‐ and left (L)‐opened structures of the CaMn₄O₅ cluster of OEC (see Figure S1). The structural symmetry breaking (SSB) parameter defined by using the distances of the Mn_1(d)−O₍₅₎ and Mn_4(a)−O₍₅₎ bonds is as follows [Eq. (1)]:37, 38, 39

$${\displaystyle \delta =[\mathrm{R}(\mathrm{Mn}{}_{1\left(\mathrm{d}\right)}-\mathrm{O}{}_{\left(5\right)})-\mathrm{R}(\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}-\mathrm{O}{}_{\left(5\right)})/2}$$ (1)

The δ‐value was 0.05 Å for the 3ARC XRD central (C) structure18 of the CaMn₄O₅ cluster. The δ‐values were 0.12 and 0.16 (Å) for A‐ and B‐monomers of 3WU2,18 namely refined 3ARC structure, indicating the C_R structure. The δ‐values for 4UB6A, 4UB6B, 4UB8A and 4UB8B by the damage‐free XFEL method27 were 0.20, 0.23, 0.15 and 0.20 (Å) respectively, exhibiting the C_R structure in Figure S1. Thus the SSB parameters for 3WU2, 4UB6 and 4UB8 are smaller than 0.25 Å.

The SSB (δ) parameter was 0.71 Å for the full‐optimized low‐spin (LS) S₁ structure of the CaMn₄O₅ cluster by large‐scale QM/MM method37, 38 on the assumption that the O₍₅₎ site was oxygen dianion (O²⁻), indicating the R‐structure in Figure S1. The optimized S₁‐structures obtained by other and our groups under the same assumption of O₍₅₎=O²⁻ were also the R‐structure.40, 41, 42, 43, 44, 45, 46, 47 The large δ‐value (>0.5 Å) obtained by the theoretical calculations is one of the reasons for the claim44, 46 that the XFEL structure with small δ‐value (<0.25 Å)27 might be the S₀ structure induced by the radical addition to the CaMn₄O₅ cluster. On the other hand, we have shown that the C_R structure for the S₁ state can be reproduced under the assumption of the protonation of the O₍₅₎ site, namely O₍₅₎=OH^−[35–39] and/or the rotation of the JT deformation axis (d${}_{\mathrm{z}{}^2}$ →d${}_{\mathrm{x}{}^2}$ ) for O₍₅₎=O²⁻.39 Therefore, theoretical analysis of the damage‐free low dose XRD structure30 is very important for elucidation of the most plausible S₁ structure and scope and reliability of the XFEL27 and SFX structures.28, 29

2.2. Theoretical Modeling of Structural Symmetry Breaking in the CaMn₄O₅ Cluster

Our QM and QM/MM calculations33, 34, 35, 36, 37, 38, 39 of OEC in PSII revealed that the Mn_4(a)−Mn_3(b) distance was correlated with Mn_4(a)−O₍₅₎ distance in the CaMn₄O₅ cluster of OEC of PSII. We have already presented a practical estimation equation37, 38, 39 of the Mn_4(a)−Mn_3(b) distance by the use of the Mn_4(a−O₍₅₎ distance (see Figure S2 in SII.1) as follows [Eq. (2)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}-\mathrm{Mn}{}_{3\left(\mathrm{b}\right)})=2.80+x/2n}$$ (2)

where the deformation parameter x is defined by [Eqs. (3a)a) and (3b)b)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}-\mathrm{O}{}_{\left(5\right)})=2.18+x}$$ (3a)

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{1\left(\mathrm{d}\right)}-\mathrm{O}{}_{\left(5\right)})=2.88-x\left(\AA \mathrm{unit}\right).}$$ (3b)

The n‐values were taken to be 1 for O₍₅₎=OH^−. and 2 for O₍₅₎=O²⁻ respectively, depending on the strength of the Mn_4(a)−O₍₅₎ bond (see Figure S2 in the Supporting Information). The x‐value was determined using the calculated Mn_4(a)−O₍₅₎ distance, R(Mn_4(a)−O₍₅₎), by QM and QM/MM methods. The SSB parameter was defined by Equation (1). The x value and Mn_4(a)−O₍₅₎ distance were in turn estimated using R(Mn_4(a)−Mn_3(b)) values by the EXAFS,8, 10 XRD,18, 30 XFEL27, 28, 29 and computational methods.33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47

The Mn_4(a)−O₍₅₎ distances were estimated to be 2.00 and 1.82 (Å) for O₍₅₎=OH⁻ and O₍₅₎=O²⁻ respectively, assuming the short Mn_4(a)−Mn_3(b) distance (2.71 Å by EXAFS10) of the CaMn₄O₅ cluster [see Eq. (3a)]. The optimized Mn_4(a)−O₍₅₎ distance by low‐spin QM/MM under the assumption of O₍₅₎=O^{2−[37, 38, 47]} was equivalent to the latter value (1.82 Å), confirming the reliability of Equations (2) and (3a) for estimation based on the QM/MM results. The optimized Mn_4(a)−Mn_3(b) distances obtained by QM calculations by ours and other groups39, 40, 41, 42, 43, 44, 45, 46, 47 also provided 1.8∼1.9 (Å) for the Mn_4(a)−O₍₅₎ distance in accord with the assumption of O₍₅₎=O²⁻ as shown in Figure 1 A. These short Mn_4(a)−O₍₅₎ distances in turn were considered to support the assumption of O₍₅₎=O²⁻ in the geometry optimizations by QM since the Mn_4(a−Mn_3(b) distance of EXAFS by Glöckner et al.10 was about 2.7 Å (see Table S6). However, the observed Mn−O distances of the CaMn₄O₅ cluster by the EXAFS6, 7 are classified into two groups with about 1.8 and 2.0 (Å), respectively, indicating the difficulty for discrimination between R(Mn_4(a)−O₍₅₎) ≈1.8 Å and R(Mn_4(a)−Mn_3(b)) ≈2.7 Å for O₍₅₎=O²⁻ and R(Mn_4(a)−O₍₅₎) ≈2.0 Å and R(Mn_4(a)−Mn_3(b)) ≈2.7 Å for O₍₅₎=OH⁻. Therefore precise determination of R(Mn_4(a)−O₍₅₎) by other experimental methods such as the low dose XRD30 is crucial for discrimination between O₍₅₎=O²⁻ and O₍₅₎=OH⁻ in the CaMn₄O₅ cluster of OEC of PSII to elucidate the possibility of the X‐ray damage of the XFEL27 and SFX structures.28, 29 Furthermore, it is noteworthy that discrimination between OH⁻ and O²⁻ at the O₍₅₎ site in the S₁ state is not at all trivial because possible mechanisms for water oxidation may be different by protonation of the site.

Figure 1.

Three different Jahn–Teller (JT) deformation structures at the Mn^III _4(a) site of the CaMn₄O₅ cluster in OEC of PSII by QM and QM/MM computations; A) d${}_{\mathrm{z}{}^2}$ JT, B) d${}_{\mathrm{y}{}^2}$ JT and C) d${}_{\mathrm{x}{}^2}$ JT.

2.3. Jahn–Teller Effect of the Mn^III Ion

The high‐resolution XRD18 experiment revealed that ligand fields of Mn ions are essentially octahedral in the CaMn₄O₅ cluster in OEC of PSII.1, 2 The first QM computation33, 34 of the S₁ structure of the CaMn₄O₅ cluster by 3WU218 elucidated the (3443) valence configuration of the CaMn₄O₅ cluster as mentioned above. Therefore, the Jahn–Teller (JT) effect of the Mn^III _4(a) ion plays important roles for subtle deformations of the CaMn₄O₅ cluster.37, 38, 39 The JT elongation axis responsible for the d${}_{\mathrm{z}{}^2}$ orbital was vertical (v) to (W₁)O−Mn^III _4(a)−O₍₅₎ bond for the short Mn_4(a)−Mn_3(b) distance (2.7 Å) as shown in Figure 1 A, suggesting the Mn_4(a−O₍₅₎ distance with about 2.0 Å for O₍₅₎=OH⁻ or about 1.8 Å for O₍₅₎=O²⁻. The intermediate Mn_4(a)−Mn_3(b) distance (2.75 Å) provided the Mn_4(a)−O₍₅₎ distances with about 2.1 and 2.0 (Å) for O₍₅₎=OH⁻ and O₍₅₎=O²⁻ respectively, because the JT deformation was the d${}_{\mathrm{y}{}^2}$ type, as shown in Figure 1 B. On the other hand, the JT axis for the d${}_{\mathrm{x}{}^2}$ orbital becomes almost parallel to the (W₁)O−Mn^III _4(a)−O₍₅₎ bond, namely horizontal (h), as shown in Figure 1 C. In this case the Mn_4(a)−Mn_3(b) distance is 2.80 Å for which the Mn_4(a)−O₍₅₎ distances are about 2.2 Å for both O₍₅₎=OH⁻ and O₍₅₎=O²⁻(see Figure S2 in SII.1). The horizontal JT (d${}_{\mathrm{x}{}^2}$ ) distortion is also operative for R(Mn_4(a)−Mn_3(b))=2.85 Å, although the Mn_4(a)−O₍₅₎ distances are about 2.3 and 2.4 (Å) for O₍₅₎=OH⁻ and O₍₅₎=O²⁻ respectively.

The estimation formula (2) and (3) are not effective for discrimination between O₍₅₎=OH⁻ and O₍₅₎=O^{2−[37–39]} near the crossing region, R(Mn_4(a)−O₍₅₎)=2.2 Å in Figure S2 (see Tables 1 and 5). The Mn_3(b−O₍₅₎ distance can be employed as second JT deformation index in the region. Thus, the orbital degree of freedom at the Mn_3(b) site is one of the important factors for subtle geometrical deformation of the CaMn₄O₅ cluster that is regarded as a characteristic property of strongly correlated electron system (SCES).35, 39, 45

Table 1.

The Mn₄−Mn₃ distances [Å] of the CaMn₄O₅ cluster in the S₁ state of OEC of PSII by the low‐dose (LD) XRD30 and the estimation procedure [Eqs. (2) and (3)].

Structures	Mn4−Mn3	Mn4−Mn3 [a]	Mn4−O(5) [b]	Mn3−O(5) [c]	O(5) [d]	SSB[e]	Topology[f]
	XRD	(Estimation)	Exp.(Est.)	Exp.
5B5EA	2.82	(2.83)[a1]	2.24	2.09	O(5)=OH−	0.29	CR
		(2.82)[a2]	2.24	2.09	O(5)=O2−	0.29	CR
	2.82		(2.22)[b1]	(2.0)[c1]	O(5)=OH−	0.31	CR
	2.82		(2.26)[b2]	(1.8)[c2]	O(5)=O2−	0.27	CR
5B5EB	2.75	(2.79)[a1]	2.17	2.07	O(5)=OH−	0.36	R
		(2.80)[a2]	2.17	2.07	O(5)=O2−	0.36	R
	2.75		(2.08)[b1]	(2.0)[c1]	O(5)=OH−	0.45	R
	2.75		(1.98)[b2]	(1.8)[c2]	O(5)=O2−	0.55	R
5B66A	2.85	(2.85)[a1]	2.28	2.14	O(5)=OH−	0.25	CR
		(2.83)[a2]	2.28	2.14	O(5)=O2−	0.25	CR
	2.85		(2.28)[b1]	(2.0)[c1]	O(5)=OH−	0.25	CR
	2.85		(2.38)[b2]	(1.8)[c2]	O(5)=O2−	0.15	CR
5B66B	2.77	(2.77)[a1]	2.12	2.02	O(5)=OH−	0.41	R
		(2.78)[a2]	2.12	2.02	O(5)=O2−	0.41	R
	2.77		(2.12)[b1]	(2.0)[c1]	O(5)=OH−	0.41	R
	2.77		(2.06)[b2]	(1.8)[c2]	O(5)=O2−	0.47	R

[a] The Mn_4(a)−Mn_3(b) distances were estimated by using the experimental Mn_4(a)−O₍₅₎ distance in Equation (2) and (3) under the assumption of a1) O₍₅₎=OH⁻ and a2) O²⁻. [b] The Mn_4(a)−O₍₅₎ distances were estimated by using the experimental Mn_4(a)−Mn_3(b) distance in Equation (2) and (3) under the assumption of b1) O₍₅₎=OH⁻ and b2) O²⁻. [c] The Mn_3(b)−O₍₅₎ distances were estimated to be 2.0 and 1.8 for c1) O₍₅₎=OH⁻ and c2) O²⁻, respectively. [d] Assignment of the O₍₅₎ site. [e] Structural symmetry breaking (SSB) parameter. [f] Topology.

Table 5.

The Mn₄−Mn₃ distances [Å] of the CaMn₄O₅ cluster in the S₁ state of OEC of PSII by SFX28, 29 with and without preflash and estimation procedure [Eqs. (2) and (3)].

Structures	Mn4−Mn3	Mn4−Mn3 [a]	Mn4−O(5) [b]	Mn3−O(5) [c]	O(5) [d]	SSB[e]	Topology[f]
	XRD	(Estimation)	Exp.(Est.)	Exp.
5GTHA	2.98	(2.88)[a1]	2.33	2.03	O(5)=OH−	0.20	CR
(no preflash		(2.84)[a2]	2.33	2.03	O(5)=O2−	0.20	CR
dark SFX)	2.98		(2.54)[b1]	(2.0)[c1]	O(5)=OH−	−0.01	C
	2.98		(2.90)[b2]	(1.8)[c2]	O(5)=O2−	−0.37	CL
5GTHB	2.91	(2.88)[a1]	2.34	2.02	O(5)=OH−	0.19	CR
(no preflash		(2.84)[a2]	2.34	2.02	O(5)=O2−	0.19	CR
dark SFX)	2.91		(2.40)[b1]	(2.0)[c1]	O(5)=OH−	0.13	CR
	2.91		(2.62)[b2]	(1.8)[c2]	O(5)=O2−	−0.09	C
5WS5A	2.77	(2.86)[a1]	2.29	2.02	O(5)=OH−	0.24	CR
(preflash dark		(2.83)[a2]	2.29	2.02	O(5)=O2−	0.24	CR
SFX)	2.77		(2.12)[b1]	(2.0)[c1]	O(5)=OH−	0.41	R
	2.77		(2.06)[b2]	(1.8)[c2]	O(5)=O2−	0.47	R
5WS5B	2.75	(2.86)[a1]	2.29	2.03	O(5)=OH−	0.24	CR
(preflash dark		(2.83)[a2]	2.29	2.03	O(5)=O2−	0.24	CR
SFX)	2.75		(2.08)[b1]	(2.0)[c1]	O(5)=OH−	0.45	R
	2.75		(1.98)[b2]	(1.8)[c2]	O(5)=O2−	0.55	R
5KAFA(B)	2.87	(2.88)	2.33	2.20	O(5)=OH−	0.20	CR
(no preflash		(2.84)	2.33	2.20	O(5)=O2−	0.20	CR
dark SFX)	2.87		(2.32)	(2.0)	O(5)=OH−	0.21	CR
	2.87		(2.46)	(1.8)	O(5)=O2−	0.07	C

[a] The Mn_4(a)−Mn_3(b) distances were estimated by using the experimental Mn_4(a)−O₍₅₎ distance by SFX structures28, 29 with and without preflash in Equations (2) and (3) under the assumption of a1) O₍₅₎=OH⁻ and a2) O²⁻. [b] The Mn_4(a)−O₍₅₎ distances were estimated by using the experimental Mn_4(a)−Mn_3(b) distance in Equations (2) and (3) under the assumption of b1) O₍₅₎=OH⁻ and b2) O²⁻. [c] The Mn_3(b)−O₍₅₎ distances were estimated to be 2.0 and 1.8 for c1) O₍₅₎=OH^‐ and c2) O²⁻, respectively. [d] Assignment of the O₍₅₎ site. [e] Structural symmetry breaking (SSB) parameter. [f] Topology.

3. Theoretical Studies on the Low‐Dose XRD Structures of the CaMn₄O₅ Cluster

3.1. Structural Symmetry Breaking of the Low‐Dose XRD Structures

After the discovery18 of the high resolution XRD structure of the CaMn₄O₅ cluster in OEC of PSII, X‐ray damage6, 7 of the high‐valent Mn^IV ions under the high dose conditions such as 0.43 MGy18 was pointed out by several groups.40, 41, 42, 43, 44, 45, 46, 47 Tanaka et al.30 recently performed the XRD experiments using low‐doses of 0.03 (5B5EA(B)) and 0.12 MGy (5B66A(B)) for OEC of PSII. Therefore, the S₁ structure by their XRD experiments is considered to be almost X‐ray‐damage free (1∼3 %). Table 1 summarizes the observed and calculated Mn_4(a)−Mn_3(b) and Mn_4(a)−O₍₅₎ distances and SSB parameters for the low dose XRD structures.30 From Table 1, the δ‐values were 0.29 and 0.25 (Å) respectively, for A‐monomers of 5B5E and 5B66,30 exhibiting the C_R structure in our terminology (see Figure S1).35, 36, 37, 38, 39 On the other hand, the δ‐values were 0.36 and 0.41 for 5B5EB and 5B66B respectively, showing the R‐opened (R) structure near C_R. The SSB for the B‐monomers were a little larger than those of the A‐monomers in the low dose XRD structure.30 However, the δ‐values of the B‐monomers were only one half of the optimized value (about 0.7) of the CaMn₄O₅ cluster by QM and QM/MM under the assumptions of O₍₅₎=O²⁻ and the vertical JT (d${}_{\mathrm{z}{}^2}$ ) distortion (Figure 1 A).36, 38 Thus, the δ‐values of the low dose XRD structures30 are rather consistent with those of the damage‐free XFEL structures27 in contradiction to the claim based on the R‐structure (Figure 1 A).44, 46

The 5B5EA structure by low dose XRD in Figure 2 A(C) indicated that the Mn_3(b)−Mn_4(a), Mn_2(c)−Mn_3(b), Mn_1(d)−Mn_2(c), Mn_1(d)−Mn_3(b) and Mn_1(d)−Mn_4(a) distances were 2.82(2.85), 2.76(2.78), 2.74(2.72), 3.22(3.22) and 4.91(4.92) (Å) respectively, where the corresponding values for 5B66A structure30 (see also Figure 1 C) are given in parentheses. The observed Mn−Mn distances for A monomers indicated the following trend [Eq. (4a)a)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_1-\mathrm{Mn}{}_2)<\mathrm{R}(\mathrm{Mn}{}_2-\mathrm{Mn}{}_3)<\mathrm{R}(\mathrm{Mn}{}_3-\mathrm{Mn}{}_4)<\mathrm{R}(\mathrm{Mn}{}_1-\mathrm{Mn}{}_3)<\mathrm{R}(\mathrm{Mn}{}_1-\mathrm{Mn}{}_4).}$$ (4a)

Figure 2.

Three dimensional (3D) structures and Mn−Mn and Ca−Mn distances of the CaMn₄O₅ cluster in oxygen evolving complex (OEC) determined by an extremely low dose XRD experiment by Tanaka et al.:28 A) 5B5EA, B) 5B5EB, C) 5B66A and D) 5B66B.

The trend, R(Mn₂−Mn₃)< R(Mn₃−Mn₄), was also observed for 3WU218 and XFEL27 structures.

On the other hand, the corresponding Mn−Mn distances were 2.75(2.77), 2.77(2.82), 2.65(2.72), 3.22(3.24) and 4.88(4.89) (Å) respectively, for the 5B5EB (5B66B) structures as shown in Figure 2 B(D), showing a different trend [Eq. (4b)b)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_1-\mathrm{Mn}{}_2)<\mathrm{R}(\mathrm{Mn}{}_3-\mathrm{Mn}{}_4)<\mathrm{R}(\mathrm{Mn}{}_2-\mathrm{Mn}{}_3)<\mathrm{R}(\mathrm{Mn}{}_1-\mathrm{Mn}{}_3)<\mathrm{R}(\mathrm{Mn}{}_1-\mathrm{Mn}{}_4)}$$ (4b)

The reverse trend, R(Mn₃−Mn₄) < R(Mn₂−Mn₃), was also observed for the EXAFS structure reported by Yano and co‐workers.8, 10 The average Mn–Mn distances of Mn_3(b)−Mn_4(a), Mn_2(c)−Mn_3(b) and Mn_1(d)−Mn_2(c) are 2.77, 2.78, 2.72 and 2.77 (Å) respectively for 5B5EA, 5B66A, 5B5EB and 5B66B28 in agreement with the average Mn−Mn distances revealed by the damage‐free XFEL,27 namely 2.72 Å for 4UB6, and 2.78 Å for 4UB8, and 2.73 Å for EXAFS.8, 10 Thus, there is no serious differences (namely within the experimental uncertainty) of the average Mn−Mn distance among the low dose XRD,30 XFEL27 and EXAFS10 structures. On the other hand, the corresponding average Mn−Mn distances were 2.91 and 2.86 (Å) for 3WU2A and 3WU2B,18 respectively, indicating non‐negligible elongations (0.1∼0.2 Å) because of the X‐ray damage.27, 30, 45 However, the topological structure of 3WU2 [see Eq. (4a)] is similar to that of XFEL,27 namely 5 % reduction of the Mn−Mn distances of 3WU218 is necessary for production of the XFEL structure.27

The Ca−Mn_4(a), Ca−Mn_3(b), Ca−Mn_2(c) and Ca−Mn_1(d) distances were 3.75(3.77), 3.39(3.40), 3.35(3.34) and 3.50(3.51) (Å) respectively for 5B5EA(5B66A). The corresponding Ca−Mn distances were 3.78(3.74), 3.40(3.39), 3.29(3.30) and 3.51(3.48) respectively for 5B5EB(5B66B).

The Ca−Mn distances were not so different between A‐ and B‐monomers of the dimer structure of OEC of PSII in both samples, indicating a general tendency referred to as the rule IIa35, 36, 37, 38, 39 for the XRD18 and XFEL27 structures [Eq. (5)].

$${\displaystyle \mathrm{R}(\mathrm{Ca}-\mathrm{Mn}{}_2)<\mathrm{R}(\mathrm{Ca}-\mathrm{Mn}{}_3)<\mathrm{R}(\mathrm{Ca}-\mathrm{Mn}{}_1)<\mathrm{R}(\mathrm{Ca}-\mathrm{Mn}{}_4)}$$ (5)

The divalent Ca^II ion is therefore irrelevant to the X‐ray damage.

3.2. Application of the Jahn–Teller Deformation Formula to the CaMn₄O₅ Cluster

The JT deformation formula [see Eqs. (2) and (3)] were applied to the low dose XRD structures by Tanaka et. al.30 which elucidated subtle different structures between A‐ and B‐monomers. The observed Mn_4(a)−O₍₅₎ distances for 5B5EA(5B66A) were 2.24(2.28) (Å) respectively, indicating that the Mn_3(b)−Mn_4(a) distances were estimated to be 2.83(2.85) (Å) for O₍₅₎=OH⁻ and 2.82(2.83) (Å) for O₍₅₎=O²⁻ respectively, in accord with the parallel JT (d${}_{\mathrm{x}{}^2}$ ) elongation illustrated in Figure 1 C. On the other hand, the Mn_4(a)−O₍₅₎ distances were estimated to be 2.22(2.28) (Å) for O₍₅₎=OH⁻ and 2.26(2.38) (Å) for O₍₅₎=O²⁻ respectively, using the Mn_3(b)−Mn_4(a) distances, namely 2.82 (2.85) (Å) for 5B5EA(5B66A). The Equations (2) and (3) using the Mn_3(b)−Mn_4(a) and Mn_4(a)−O₍₅₎ distances were not conclusive for discrimination between O₍₅₎=OH⁻ and O₍₅₎=O²⁻ (except for 5B66A for which O₍₅₎=OH⁻) near the crossing region of the JT deformation lines (see Figure S2 in SII.1). Therefore, the second criterion, namely Mn_3(b)−O₍₅₎ distance, was employed for the discrimination.37, 38, 39 As shown in Table 2, the observed Mn_3(b)−O₍₅₎ distances by the LD XRD were 2.09 and 2.14 (Å) for 5B5EA and 5B66A respectively. These values are rather consistent with the assumption of O₍₅₎=OH⁻ in Table S1, supporting the S₁ structure by XFEL27 and structure of A monomer of LD XRD.30

Table 2.

The Mn_4(a)−O₍₅₎ and Mn_3(b)−O₍₅₎ distances [Å] of the CaMn₄O₅ cluster in the S₁ state of OEC of PSII based on the estimation procedure using the Mn₄−Mn₃ distance [Å] obtained by the mixing of the S₁(C_R) and S₀(C_L) structures [Eq. (7)].

Structures[a]	Mn4−Mn3	α(CL) [%][b]	Mn4=O(5) [c]	Mn3−O(5) [d]	SSB[e]	Topology[f]
S1(CR)	2.80	0.0	2.18	2.00	0.35	R
	2.81	3.3	2.20	2.01	0.33	R
	2.82	6.7	2.22	2.03	0.31	CR
	2.83	10.0	2.24	2.04	0.29	CR
	2.84	13.3	2.26	2.05	0.27	CR
(1−α) S1(CR)	2.85	16.7	2.28	2.07	0.25	CR
+ α S0(CL)	2.86	20.0	2.30	2.08	0.23	CR
	2.87	23.3	2.32	2.09	0.21	CR
	2.88	26.7	2.34	2.11	0.19	CR
	2.89	30.0	2.36	2.12	0.17	CR
	2.90	33.3	2.38	2.13	0.15	CR
	2.91	36.7	2.40	2.15	0.13	CR
	2.92	40.0	2.42	2.16	0.11	CR

[a] The geometrical parameters are given by the mixing of the S₁(C_R) and S₀(C_L) structures. [b] The mixing ratio α(C_L) for the C_R structure. [c] The Mn_4(a)−O₍₅₎ distance for the (1−α)S₁(C_R) + αS₀(C_L) structure. [d] The Mn_3(b)−O₍₅₎ distance for the mixed (1−α) S₁(C_R) + α S₀(C_L) structure. [e] Structural symmetry breaking (SSB) parameter. [f] The right‐opened structure (R).

The JT deformation formula were also applied to the low dose XRD structures of the B‐monomer.30 The observed Mn_4(a)−O₍₅₎ distances for 5B5EB(5B66B) were 2.17(2.12) (Å), providing that the estimated Mn_3(b)−Mn_4(a) distances were 2.79(2.77) (Å) for O₍₅₎=OH⁻ and 2.80(2.78) (Å) for O₍₅₎=O²⁻ respectively. On the other hand, the Mn_4(a)−O₍₅₎ distances for 5B5EB(5B66B) were estimated to be 2.08(2.12) (Å) for O₍₅₎=OH⁻ and 1.98(2.06) (Å) for O₍₅₎=O²⁻ respectively, using the observed Mn_3(b)−Mn_4(a) distance, namely 2.75 (2.77) (Å) for 5B5EB(5B66B). Interestingly, the Mn_4(a)−O₍₅₎ distance estimated using the Mn_3(b)−Mn_4(a) distance (2.75 Å) of 5B5EB was about 2.1 Å in agreement with the assumption of O₍₅₎=OH⁻ in Table S1. The observed Mn_3(b)−O₍₅₎ distance for 5B5EB was 2.07 Å, further supporting the assumption of O₍₅₎=OH⁻. The protonation of the O₍₅₎ site is also consistent with the Mn_4(a)−O₍₅₎ distance (2.12) for 5B66B. Thus the JT distortion for the B‐monomer was consistent with the JT (d${}_{\mathrm{y}{}^2}$ ) deformation in Figure 1 B. Interestingly, the longer Mn_4(a)−O₍₅₎ distances of the B‐monomers are rather consistent with the longer Mn_4(a)−O₍₅₎ distance (about 2.0 Å) by EXAFS.6 This indicates the d${}_{\mathrm{y}{}^2}$ ‐JT‐type B‐structure (see Figure 1 B) for the EXAFS results8, 10 as shown in Table S6 (see the Supporting Information).

In order to confirm the above assignments, the Mn−O distances of the octahedral ligand fields for the Mn^III _4(a) ion were depicted in Figure 3. The observed Mn_4(a)−O₍₅₎ and Mn_4(a)−O(W1) distances for 5B5EA(5B66A) were 2.24(2.28) and 2.19(2.19) (Å) respectively, as shown in Figure 3 A(D), indicating the parallel JT elongation (d${}_{\mathrm{x}{}^2}$ ) illustrated in Figure 1 C. The observed Mn_4(a)−O₍₅₎ and Mn_4(a)−O(W1) distances for 5B5EB(5B66B) were 2.17(2.12) and 2.10(2.10) (Å) respectively, as shown in Figure 3 B(E), showing the shortening of 0.07(0.16) and 0.09(0.09) as compared with those of 5B5EA(5B66A). On the other hand, the Mn_4(a)−O₍₄₎ and Mn_4(a)−O(W2) distances for 5B5EA(5B66A) were 1.87(1.84) and 2.04(2.13) (Å), respectively, as shown in Figure 3 A(D). The corresponding values for 5B5EB(5B66B) are 2.07(2.10) and 2.17(2.15) (Å) as shown in Figure 3 B(E), indicating the elongations of 0.20(0.26) and 0.13(0.02) (Å) respectively, as shown in Figure 3 C(F) in accord with the JT (d${}_{\mathrm{y}{}^2}$ ) deformation. Therefore, 5B5EB(5B66B) are regarded as a JT (d${}_{\mathrm{y}{}^2}$ ) deformed structure in Figure 1 B, also suggesting that the EXAFS structure8, 10 with the different topology [see Eq. (4b)] may be explained with the B‐structure by the LD XRD.30 The LD XRD structures with no significant X‐ray damage30 was not consistent with the R‐structure with the JT (d${}_{\mathrm{z}{}^2}$ ) distortion in Figure 1 A, where the Mn_3(b)−Mn_4(a) and Mn_4(a)−O₍₅₎(=O²⁻) distances are estimated to be about 2.7 and 1.8 (Å), respectively.

Figure 3.

Schematic illustration of the Mn−O bond lengths in the octahedral ligand field of the Mn_4(a) ion in the CaMn₄O₅ cluster in OEC for A) 5B5EA, B) 5B5EB(a), D) 5B66A and E) 5E66B(a). Differences of the Mn−O distances between the A and B(a) monomers in 5B5E and 5B66 are shown in (C) and (F), respectively.

3.3. Importance of the Mn_3(b)−O₍₅₎ Distances in the CaMn₄O₅ Cluster

The discrimination between O²⁻ and OH⁻ at the O₍₅₎ site is hardly possible based on the JT deformation formula in the region of the R(Mn_4(a)−O₍₅₎)=2.2 Å (see Figure S2). In this situation, the Mn_3(b)−O₍₅₎ bond lengths become an important JT deformation index for discrimination between O²⁻ and OH⁻ at the O₍₅₎ site of the CaMn₄O₅ cluster. The Mn^IV _3(b)−O₍₅₎ bond lengths are usually about 1.8∼1.9 Å for O₍₅₎=O²⁻ because of no JT effect of Mn^IV ion, as shown previously (see Tables 5 and S5).39 The Mn^IV _3(b)−O₍₅₎H bond length after protonation of the O₍₅₎ site is 2.0∼2.1 (Å) because of no JT effect. On the other hand, the Mn^III _3(b)−O₍₅₎H bond length may be elongated to 2.3∼2.4 Å if the JT elongation axis is parallel to the HO₍₅₎−Mn_b(3)−O(Glu 354) bond in the CaMn₄O₅ cluster. In fact, Mn_3(b)−O₍₅₎ bond length by 3WU2 structure18 was 2.4 Å because of the reduction of Mn^IV _3(b) into Mn^III _3(b).30 Thus, the JT deformation formula revealed by the computational results35, 36, 37, 38, 39 and available experiments for Mn complexes provide guiding principles for understanding of variations of Mn−O bond lengths of the CaMn₄O₅ cluster of OEC of PSII.

Nevertheless, several theoretical papers41, 42, 44, 46 suggested the possibility of the radiation damage of the XFEL structure.27 Previously39 we have estimated the fraction of the S₀ component in the observed XFEL structure27 on the basis of the following equation under the assumption of 2.0 and 2.4 (Å) for the Mn_3(b)−O₍₅₎ distances of the C_R structures in the S₁ and S₀ states, respectively [Eq. (6)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{O}{}_{\left(5\right)})=(1-\alpha )\mathrm{R}(\mathrm{Mn}{}^{\mathrm{IV}}{}_{3\left(\mathrm{b}\right)}-\mathrm{OH}{}_{\left(5\right)})=2.0\mathrm{for}\mathrm{S}{}_1\left(\mathrm{C}{}_{\mathrm{R}}\right)+\alpha \mathrm{R}(\mathrm{Mn}{}^{\mathrm{III}}{}_{3\left(\mathrm{b}\right)}-\mathrm{OH}{}_{\left(5\right)})=2.4\mathrm{for}\mathrm{S}{}_0\left(\mathrm{C}{}_{\mathrm{R}}\right))}$$ (6)

where the C_R structures are used for both S₁ and S₀ states. Here the Equation (6) was applied for the low dose XRD structures.30 The weight (α) of the S₀ component was estimated to be 17.5 and 35 (%) respectively for 5B5EA and 5B66A structures. The estimated contribution of the S₀(C_R) component for 5B5EA is smaller than the estimated value (25 %) for the no pre‐flash experiment, whereas it seems non negligible for 5B66A structure46 under the assumption of no experimental uncertainty. However, the contamination of the S₀(C_R) structure in 5B66A resulted in a very small elongation (2.85–2.82=0.03 Å) of the Mn_3(b)−Mn_4(a) distance because of the same C_R topology. Therefore, the observed structure of the A monomer by the LD XRD experiment30 is fully compatible with the damage‐free XFEL structure,27 particularly 4UB6 structure and reassigned EXAFS structure39 (see Table S6).

The estimated fractions (α) of the S₀(C_R) component by Equation (6) were 22 and 5 (%) respectively, for 5B5EB and 5B66B structures.30 The estimated contribution of the S₀ structure for 5B5EB is smaller than 25 %, whereas it seems negligible for 5B66B structure for which the observed Mn_3(b)−O₍₅₎ distance is 2.02 Å. Therefore, the observed structure of the B monomer by the low dose (LD) XRD experiment30 is fully compatible with the JT (d${}_{\mathrm{y}{}^2}$ ) deformed structure in Figure 1 B instead of the JT (d${}_{\mathrm{z}{}^2}$ ) structure in Figure 1 A. Thus, the nature of the chemical bonds of the CaMn₄O₅ cluster of OEC is labile,33 indicating the structural deformations (see Figure 4).

Figure 4.

The Mn−O distances and hydrogen bonding interactions in the dimer of OEC of PSII by low‐dose XRD experiments.28 A) A‐monomers by 5B5EA(5B66A) and B) B‐monomers of 5B5EB(5B66B).

3.4. Estimation of Radiation Damage by the Mn_3(b)−Mn_4(a) Distances in the CaMn₄O₅ Cluster

The pre‐flash procedure for generation of the pure S₁ state was not performed for the LD XRD experiments,30 indicating a possibility of the contamination of the S₀ component. The JT deformation formula indicate that the Mn_3(b)−Mn_4(a) distances can be used for estimation of the possible fraction of the S₀ component, under the assumption of reduction of the high‐valent Mn^IV _3(b) ion into Mn^III _3(b) as follows [Eq. (7)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)})=(1-\alpha )\mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}=2.80)\mathrm{for}\mathrm{S}{}_1\left(\mathrm{C}{}_{\mathrm{R}}\right)+\alpha \mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}=3.10)\mathrm{for}\mathrm{S}{}_0\left(\mathrm{C}{}_{\mathrm{L}}\right)}$$ (7)

where the C_L structure for the S₀(3343) state was employed for estimation. The mixing coefficient (α) are summarized in Table 2. The α‐values are 6.7 and 16.7 (%) respectively, for 5B5EA and 5B66A for which the Mn_3(b)−Mn_4(a) distances are 2.82 and 2.85 (Å) respectively. Therefore, the S₀ components for the A‐monomers are smaller than 25 %, showing the normal behavior. The Mn_4(a)−O₍₅₎ distances estimated by the α‐values are 2.22(2.24) and 2.28(2.28) (Å) respectively, where the observed distances are given in parentheses. The estimated (observed) Mn_3(b−O₍₅₎ distances are 2.03(2.09) and 2.07(2.14) (Å), respectively. The JT deformation formulae [see Eqs. (2) and (3)] work well for examination of the S₀ contamination for the LD XRD structures.30 The A‐monomer by the LD XRD30 is essentially regarded as the S₁(C_R) structure even if the partial S₀(C_L) contamination is taken into account.

We have assumed the reduction of the high‐valent Mn^IV _3(b) into the Mn^III _3(b) ion in the S₁ to S₀ transition in Equation (7). However, the reduction of Mn^III _4(a) into Mn^II _4(a) by chemical origins45 is also conceivable, yielding the S₀ state with the (2443) valence configuration.36 The optimized Mn_3(b)−Mn_4(a), Mn_2(c−Mn_3(b), Mn_1(d)−Mn_2(c), Mn_1(d)−Mn_3(b) and Mn_4(a)−O₍₅₎ distances were 2.97, 2.81, 2.75, 3.32 and 2.44 (Å) respectively for the S₀(C_R)′ state with the (2443) configuration.36 Therefore the Mn_3(b)−Mn_4(a) distances are also estimated as follows [Eq. (8)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)})=(1-\alpha )\mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}=2.80)\mathrm{for}\mathrm{S}{}_1\left(\mathrm{C}{}_{\mathrm{R}}\right)+\alpha \mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}=2.97)\mathrm{for}\mathrm{S}{}_0\left(\mathrm{C}{}_{\mathrm{R}}\right){}^{\text{'}}.}$$ (8)

The α‐values calculated by using R(Mn_3(b)−Mn_4(a)) distance of S₀(C_R)′ are 11.8 and 29.4 (%), respectively. Therefore the estimated Mn_4(a)−O₍₅₎ distances for 5B5EA and 5B66A are 2.21(2.24) and 2.26(2.28) (Å) respectively, where the observed distances are given in parentheses. The main component of the A‐monomer30 based on the Mn_3(b)−Mn_4(a) and Mn_4(a)−O₍₅₎ distances is regarded as the S₁(C_R) structure in Figure 1 C.

Several theoretical papers44, 46 claimed that the “damage‐free” XFEL structure27 may be regarded as the S₀ structure. The α‐values by Equation (7) assuming the mixing of the S₀(C_R)(3343) configuration are 20, 10, 27 and 37 (%) respectively for 4UB6A(2.86 Å), 4UB6a(2.83 Å), 4UB8A(2.88 Å) and 4UB8a(2.91 Å)27 for which the observed Mn_3(b)−Mn_4(a) distances are given in parentheses. On the other hand, the corresponding α‐values by Equation (8) assuming the mixing of the S₀(C_R)′(2443) configuration are 35 (92), 18 (62), 47(77) and 65 (67) (%) respectively, where the corresponding values estimated by the EXAFS line simulations using 2.83, 2.86, 2.83 and 2.88 (Å) for R(Mn_3(b)−Mn_4(a)) respectively, are given in parentheses.46 High(HO)‐ and low(LO)‐oxidation paradigms2, 47 have been proposed for the valence state of the CaMn₄O₅ cluster in OEC of PSII (see Ref. 47 and section SV in the Supporting Information). According to the HO and LO paradigms,2, 47 Mn^III and Mn^II ions are involved in the S₀ state, respectively. The Equation (7), consistent with the HO paradigm, suggests that the fraction of the S₀‐component for 4UB6 is normal for the no pre‐flash experiment,27 whereas the estimated value for 4UB8a suggests the non‐negligible uncertainty.44, 46 4UB6 is also acceptable for the Equation (8) for the LO paradigm.47 Therefore, our conclusion is different from the assumption of the better quality of 4UB8 than that of 4UB6 employed for the electron density maps analysis by Wang et al.,46 which predicted 100, 88, 77 and 78 (%) S₁ to S₀ reductions for 4UB6A, 4UB6B, 4UB8A and 4UB8B respectively. The LO paradigm reported by Petrie et al.47 provided different explanations of the XRD structure18 as described in the Supporting Information, Section SV.

The spin densities (Q) on the Mn₁, Mn₄ and O₍₄₎ atoms are another chemical index37, 39 for elucidation of the reduction of the Mn^III and Mn^IV ions, for which the Q values are about 4.0 and 3.0 respectively. Table 3 summarizes the calculated Q values by the QM (UB3LYP) method.48 The spin densities on the Mn_4(a) are in the range; 4.23∼4.37, indicating the internal reduction by the spin polarization (SP) of the Mn_4(a)−O₍₄₎ bond under the assumption of W2=H₂O and O₍₅₎=O²⁻. Therefore, the renormalized spin densities (Q_R) are obtained by using the negative spin densities on the O₍₄₎ atom (see Table 3). The Q values for the Mn_4(a) ion are about 4.0, indicating the Mn^III valence state. The SP effect for the Mn_4(a)‐O₍₄₎ bond is small for the case; W2=O₍₅₎=OH⁻, indicating Q≈4.0 on Mn_4(a). The spin densities (Q) on the Mn_1(d) ion are also 3.7∼3.8 in agreement with the Mn^III valence state. The Q‐values on the Mn_2(c) ion are 2.9∼3.2 in compatible with the Mn^IV valence state. On the other hand, spin densities (Q) on the Mn_3(b) ion are 3.21, 3.11, 3.49 and 3.64, respectively, for 4UB6A, 4UB6B, 4UB8A and 4UB8B. The spin densities of the Mn_3(b) site for 4UB8 were significantly larger than 3.0, suggesting that non‐negligible reduction of the Mn^IV _3(b) into Mn^III _3(b), namely, the mixing of S₀(C_R)(3343) under the assumption of no experimental uncertainty. Present and previous39 computational results indicate that the XFEL structure (4UB6) by Suga et al.27 corresponds to the S₁ structure against the claim by other groups44, 46 and it is compatible with the structure of A monomer by LD XRD.30 Young et al. also used the XFEL structure27 for analysis of the new SFX results (5KAF)29 for dark stable state.

Table 3.

The spin densities on the Mn_1(d), Mn_2(c), Mn_3(b), Mn_4(a) and O₍₄₎ ions of the XFEL structures27 of the CaMn₄O₅ cluster of OEC of PSII by UB3LYP method.48

Sites	Case I	(X=O2−,	Y=H2O)		Case II	(X=OH−,	Y=OH−)
	4UB6A	4UB6a	4UB8A	4UB8a	4UB6A	4UB6a	4UB8A	4UB8A
Mn4	4.23	4.29	4.34	4.29	4.07	4.04	4.14	4.12
	(3.86)[a]	(3.89)[a]	(3.96)[a]	(3.95)[a]	(3.93)[a]	(3.96)[a]	(4.05)[a]	(4.06)[a]
Mn3	3.33	3.14	3.68	3.60	3.21	3.11	3.68	3.60
Mn2	3.12	2.88	3.18	3.07	3.11	2.88	3.18	3.07
Mn1	3.78	3.75	3.73	3.70	3.79	3.76	3.73	3.69
O(4)	−0.37	−0.40	−0.41	−0.34	−0.14	−0.08	−0.09	−0.06

[a] The renormalized spin density Q_R=Q(Mn₄)+Q(O₍₄₎) to remove the internal reduction of Mn ion by the spin polarization of the Mn₄−O₍₄₎ bond is given in parentheses.

4. Discussion

4.1. Examination of the Right‐Opened structure in the S₁ State

The structures of A‐monomers with R(Mn_3(b)−Mn_4(a)) >2.8 Å by the LD XRD30 are compatible with the XFEL structures30 and the re‐assigned EXAFS structure (see Table S6).37, 38, 39 On the other hand, the Mn_3(b)−Mn_4(a) distances of 5B5EB and 5B66B30 are shorter than 2.80 Å, suggesting that the geometrical structures of B‐monomers may be explained by mixing of the right‐opened (R) S₁ structure (see Figure 1 A) with the slightly right (C_R)‐ and left (C_L)‐elongated quasi‐central S₀ structures (see Figure S1) as follows (X=R or L) [Eq. (9)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)})=(1-\alpha )\mathrm{R}(\mathrm{Mn}{}_{3(\mathrm{b}}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}=2.70)\mathrm{for}\mathrm{S}{}_1\left(\mathrm{R}\right)+\alpha \mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}=\mathrm{R}{}_{\mathrm{cal}})\mathrm{for}\mathrm{S}{}_0\left(\mathrm{C}{}_{\mathrm{X}}\right))}$$ (9)

where R_cal are 2.80 and 3.10 (Å) for S₀(C_R) and S₀(C_L) respectively. Table S2 summarizes the mixing coefficients (α) and estimated Mn_4(a)−O₍₅₎ and Mn_3(b)−O₍₅₎ distances. From Table S2 (see SII.2), the Mn_4(a)−O₍₅₎ distances for the mixed structures are estimated to be in the range; 1.82≈1.90 (Å) under the assumptions of R(Mn_3(b)−Mn_4(a))=2.71∼2.74 (Å).

The α‐values calculated by using R(Mn_3(b)−Mn_4(a))=2.75 Å for 5B5EB are 25 and 12.5 (%), respectively, for the S₀(C_R) and S₀(C_L) mixings into the S₁(R) structure, indicating that the S₁(R)‐structure is acceptable for 5B5EB. However, the calculated Mn_4(a)−O₍₅₎ distance is 1.93 Å for both mixing cases, and in contradiction to the observed value of 2.17 Å. The calculated Mn_3(b−O₍₅₎ distances are 1.95 and 1.88 Å, respectively, for the S₀(C_R) and S₀(C_L) mixings, but the observed value is 2.07 Å. Therefore the observed Mn_4(a)−O₍₅₎ and Mn_3(b)−O₍₅₎ distances for 5B5EB are hardly explained by the mixing in Equation (9) based on the Mn−Mn distances.

The α‐values for 5B66B with R(Mn_3(b)−Mn_4(a))=2.77 Å30 are calculated to be 35 and 17.5 (%) respectively, for the S₀(C_R) and S₀(C_L) mixings into the S₁(R) structure, indicating that the former value for the S₀(C_R) mixing is over the normal value (25 %). On the other hand, the latter value for the S₀(C_L) mixing is normal, indicating that the S₁(R)‐structure in Figure 1 A seems feasible for 5B66B. The calculated Mn_4(a)−O₍₅₎ and Mn_3(b)−O₍₅₎ distances for the latter mixing are 1.99(2.12) and 1.91(2.02) (Å) respectively, where the corresponding observed values are given in parentheses (see Section SII in the Supporting Information). The high‐resolution LD XRD structure with experimental uncertainty smaller than 0.1 Å is desirable for further discussion of the S₁(R) structure in Figure 1 A.

The mixing for S₁(R) with S₀(C_R)′ is also conceivable as follows [Eq. (10)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{3(\mathrm{b}}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)})=(1-\alpha )\mathrm{R}(\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}=2.70)\mathrm{for}\mathrm{S}{}_1\left(\mathrm{R}\right)+\alpha \mathrm{R}(\mathrm{Mn}{}_{3(\mathrm{b}}-\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}=2.97)\mathrm{for}\mathrm{S}{}_0\left(\mathrm{C}{}_{\mathrm{R}}\right){}^{\text{'}}.}$$ (10)

The estimated α‐values are 18.5 and 25.9 (%) respectively, for 5B5EB and 5B66B, indicating that the d${}_{\mathrm{z}{}^2}$ ‐JT type R‐structure seems acceptable. However, the elongated Mn_4(a)−O₍₅₎ distances for 5B5EB and 5B66B are estimated to be 1.90 (2.17) and 1.95(2.12) (Å) respectively, where the corresponding observed values are given in parentheses. Therefore the observed Mn_4(a)−O₍₅₎ and Mn_3(b−O₍₅₎ distances for 5B5EB are hardly explained by the mixing in Equation (10).

The valence configuration of the Mn_3(b) site should be smaller than the formal Mn^IV (Q=3.0) of the pure S₁ configuration if the S₀(C_R) or S₀(C_L) with the (3343) configuration were mixed in the LD XRD structure without the pre‐flash (see Table 3). On the other hand, the valence configuration of the Mn_4(a) site should be smaller than the formal Mn^III(Q=4.0) with mixing of the S₀(C_R)′ with the (2443) configuration. Therefore, precise determination of the valence state of each Mn ion in the LD XRD structures by the X‐ray spectroscopy is desirable for discrimination between the mixing schemes (9) and (10) on the experimental ground.2 The HO and LO paradigms2, 47 relating to valence states of Mn ions are discussed in the Supporting Information, Section SV.

4.2. X‐ray Induced Atomic Displacements by XFEL

Several experimental and theoretical studies49, 50, 51, 52 on X‐ray‐induced atomic displacements within the XFEL pulse durations have been performed in relation to X‐ray damages of serial femtosecond crystallography (SFX) (see SIII). Nagaya et al.49, 50 investigated the electronic and nuclear dynamics of I‐containing organic molecules such as 5‐iodouracil (5‐IU) induced by intense hard X‐ray pulses at the XFEL facility (SACLA), elucidating that the changes of C−O, C−N and C−C distances of 5‐IU were less than several % at the 10 fs pulse duration, and in contrast, the I−C length of 5‐IU did not change in 30 fs. Amin et al.51, 52 performed ab initio molecular dynamics simulation of OEC, where the nuclei move classically in a full quantum potential created by electron density under the effect of strong laser pulse in the Ehrenfest dynamics regime (see details SIII). The computational results51, 52 showed that the Mn‐Mn and Mn‐Ca distances were less affected by radiation damage due to their heavy masses, while the O₍₅₎ atom moved significantly. The Mn_4(a)−Mn_3(b) (Ca−O₍₅₎) distances for the S₁ structure (see Figure 1 A) were calculated to be 2.89(2.47), 2.90(2.47) and 3.08(2.53) (Å) respectively, after 0, 10 and 50 fs duration of the XFEL pulse.51, 52 Therefore, the elongations by X‐ray damage were 0.01(0.00) and 0.19(0.06) (Å) for 10 and 50 fs irradiations, respectively. The calculated Mn_4(a)−O₍₅₎ (Mn_3(b−O₍₅₎) distances51, 52 for the S₁ structure were 1.88(1.87), 1.92(1.89) and 2.34(2.01) (Å) respectively, after 0, 10 and 50 fs irradiation of XFEL. The elongations by X‐ray damage were 0.04(0.02) and 0.46(0.14) (Å) for 10 and 50 fs irradiations, respectively, indicating the 2.13(1.07) and 24.4 (7.49) % elongations. The Mn^III _4(a)−O₍₅₎ bond was sensitive to the radiation damage as compared with the Mn^IV _3(b)−O₍₅₎ bond.

According to the above computational results,51, 52 the Mn^III _4(a)−O₍₅₎ bond lengths of the XFEL structures27 were estimated using the Coulomb explosion distance (Δ_XFEL) as follows [Eq. (11)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}-\mathrm{O}{}_5){}_{\mathrm{correct}.}=\mathrm{R}(\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}-\mathrm{O}{}_5){}_{\mathrm{XFEL}}-\Delta {}_{\mathrm{XFEL}}}$$ (11)

where Δ_XFEL were given by the above 2.13 (10 fs) and 24.4 (50 fs) % elongations of the Mn_4(a)−O₅ distance of XFEL structures.27 The 5 and 10 (%) elongations were also examined for weak and medium explosions, respectively. Table 4 summarizes the calculated Mn_4(a)−O₅ distances, for which the Mn_4(a)−Mn_3(b) distances are estimated using Equation (3). The explosion distances (Δ_XFEL) were about 0.05, 0.1, 0.2 and 0.6 (Å) respectively, for 2.13 (10 fs), 5 (a fs), 10 (b fs) and 24.4 (50 fs) % elongations, where 10<a<b<50. The slightly elongated Mn_4(a−O₅ distances (about 2.3 Å) of the XFEL structures at 10 fs pulse duration (SACLA)27 are shortened by about 0.05∼0.1 Å, and the corrected Mn_4(a)−O₅ distances by Equation (11) are therefore compatible with those of the A‐monomers of the LD XRD structure.30 On the other hand, the corrected Mn_4(a)−O₅ distances for the medium (10 %) and long (50 fs) pulse durations are formally compatible with the Mn_4(a)−O₅ distances of the B‐monomers of the LD XRD30 and R‐structures in Figure 1 A, respectively. The computational results suggest that the atomic displacement of the Mn^III _4(a)−O₍₅₎ bond of the CaMn₄O₅ cluster by XFEL27 is small (<0.1 Å) because of the short pulse width (10 fs) at SACLA.53 The situation is the same for the Mn^III _3(b)−O₍₅₎ bond (see Table S5). The high‐resolution XFEL (∼40 fs) structure at LCLS29 is really desirable for comparison (see SIII).

Table 4.

The calculated Mn₄‐Mn₃ distances [Å] of the XFEL27 and SFX28, 29 structures of the CaMn₄O₅ cluster of OEC of PSII based on the Mn_4(a)−O₍₅₎ distances [Å] shortened by the corrections of the XFEL expansions.^[a]

Structures	Distance[b]		Duration	Time
		0 fs	10 fs	a fs	b fs	50 fs
Difference (Δ)		0 %	2.13 %	5 %	10 %	24.4 %	Type
4UB6A	Mn4(a)−O(5)	2.32	2.27	2.20	2.09	1.75
	Mn4(a)−Mn3(b)	2.87	2.85	2.81	2.75		O(5)=OH−
	Mn4(a)−Mn3(b)	2.84	2.82	2.81	2.78	2.69	O(5)=O2−
4UB6B	Mn4(a)−O(5)	2.30	2.25	2.19	2.07	1.74
	Mn4(a)−Mn3(b)	2.86	2.84	2.81	2.76		O(5)=OH−
	Mn4(a)−Mn3(b)	2.83	2.82	2.81	2.78	2.69	O(5)=O2−
4UB8A	Mn4(a)−O(5)	2.38	2.33	2.26	2.14	1.80
	Mn4(a)−Mn3(b)	2.90	2.88	2.84	2.78		O(5)=OH−
	Mn4(a)−Mn3(b)	2.85	2.84	2.82	2.79	2.70	O(5)=O2−
4UB8B	Mn4(a)−O(5)	2.33	2.28	2.21	2.10	1.76
(5GTHA)[c]	Mn4(a)−Mn3(b)	2.88	2.85	2.82	2.76		O(5)=OH−
(5KAFA(B))[c]	Mn4(a)−Mn3(b)	2.84	2.83	2.81	2.78	2.69	O(5)=O2−
(5GTHB)[c]	Mn4(a)−O(5)	2.34	2.29	2.22	2.11	1.82
	Mn4(a)−Mn3(b)	2.88	2.85	2.82	2.76		O(5)=OH−
	Mn4(a)−Mn3(b)	2.84	2.83	2.81	2.78	2.69	O(5)=O2−
5WS5A(B)	Mn4(a)−O(5)	2.29	2.24	2.18	2.06	1.73
	Mn4(a)−Mn3(b)	2.86	2.84	2.81	2.76		O(5)=OH−
	Mn4(a)−Mn3(b)	2.83	2.82	2.81	2.78	2.69	O(5)=O2−

[a] The Mn_4(a)−O₍₅₎ distances of the XFEL structures27 were estimated by using the Coulomb explosion distance (Δ_XFEL) in Equation (11). [b] The Mn_4(a−Mn_3(b) distances were estimated by using Equations (2) and (3) under the assumption of a1) O₍₅₎=OH⁻ and a2) O₍₅₎=O²⁻. [c] The Mn_4(a)−O₍₅₎ distances for 5GTHA(B)28 and 5KAFA(B)29 by SFX were the same as that of 4UB8B, providing the same estimation results.

4.3. Comparisons Between Low‐Dose XRD and New SFX Structures

The d${}_{\mathrm{y}{}^2}$ ‐JT type structures (see Figure 1 B) of B‐monomers by LD XRD30 were in agreement with the EXAFS structure with the {2, 1, 0} Mn‐Mn distances10 under the assumption of protonation of the O₍₅₎ site (O₍₅₎=OH⁻). Detailed discussions on the EXAFS results2, 3 relating to LD XRD30 were given in Section SIV in the Supporting Information.39 Here the JT deformation Equations (1)–(3) applied for the analysis of very recent SFX structures with and without preflash in the dark stable state reported by Suga et al.28 and Young et al.29. Table 5 summarizes the observed and calculated Mn_4(a)−Mn_3(b) and Mn_4(a)−O₍₅₎ distances and SSB parameters for these SFX structures. From Table 5, the SFX results for A‐monomer of 5GTH without preflash28 elucidated that the Mn_4(a)−Mn_3(b), Mn_4(a)−O₍₅₎ and Mn_3(b)−O₍₅₎ distances were 2.98(2.91), 2.33(2.34), 2.03(2.02) and 0.20(0.19) (Å) respectively, where the corresponding values for B‐monomer were given in parentheses. The Mn_4(a)−Mn_3(b) distances estimated by using the observed Mn_4(a)−O₍₅₎ distance for 5GTHA(B) were 2.88(2.88) and 2.84(2.84) (Å) for O₍₅₎=OH⁻ and O²⁻, respectively. On the other hand, the Mn_4(a)−O₍₅₎ distances estimated by using the observed Mn_4(a)−Mn_3(b) distance for 5GTHA(B) were 2.54(2.40) and 2.90(2.62) (Å) for O₍₅₎=OH⁻ and O²⁻, respectively. The estimated Mn_4(a)−O₍₅₎ distances supported O₍₅₎=OH⁻. The structural parameters for 5GTHA(B) without preflash were fully consistent with those of previous SFX structure without preflash.27 They were also compatible with 5KAFA(B) structure without preflash by Young et al.,29 the structure of A monomer by LD XRD30 and the reassigned EXAFS structure (see Tables S6 and S7).39

The SFX results for A(B)‐monomer of 5WS5 with preflash28 indicated that the Mn_4(a)‐Mn_3(b), Mn_4(a)−O₍₅₎ and Mn_3(b)−O₍₅₎ distances for were 2.77(2.75), 2.29(2.29), 2.02(2.03) and 0.24(0.24) (Å), respectively. The Mn_4(a)−Mn_3(b) distances estimated by using the observed Mn_4(a)−O₍₅₎ distance for 5WS5A(B) were 2.86(2.86) and 2.83(2.83) (Å) for O₍₅₎=OH⁻ and O²⁻, respectively. The estimated Mn_4(a)−Mn_3(b) distances were longer by about 0.1 Å than the corresponding observed values. On the other hand, the Mn_4(a)−O₍₅₎ distances estimated by using the observed Mn_4(a)−Mn_3(b) distance for 5WS5A(B) with preflash were 2.12(2.08) and 2.06(1.98) (Å) for O₍₅₎=OH⁻ and O²⁻, respectively. The estimated Mn_4(a)−O₍₅₎H distances were shorter by about 0.2 Å than the observed value, indicating the similarity to the corresponding observed values of B‐monomer of LD XRD.30 Moreover, the Mn_4(a)−O₍₅₎ distance estimated by 5 % reduction of the observed values of 5WS5A(B) by SFX(SACLA) is 2.18(2.18) which is in compatible with those of the B‐monomer of LD XRD at 1.85 Å resolution as shown in Table 4. Judging from the estimated Mn_4(a)−O₍₅₎ distances, and the observed Mn_4(a)−Mn_3(b) and Mn_3(b)−O₍₅₎ distances, 5WS5A(B) structure with preflash was similar to B‐monomer of LD XRD.30 Preflash effect was significant for successive investigation of the S₁‐to‐S₃ transition investigated by SFX.28, 29 Further examinations of the SFX results after two flash illuminations were given in the Section SV in the Supporting Information (Table S8).

4.4. Importance of Hydrogen‐Bonding Interactions in the Protein Field

Subtle structural differences between A‐ and B‐monomers by low‐dose XRD30 were examined for elucidation of important roles of the environmental effects around the CaMn₄O₅ cluster. Figure 4 illustrates the observed Mn‐O distances, together with hydrogen bonding interactions for the CaMn₄O₅ cluster. The O₍₃₎−N(His 337) distances for 5B5EA(5B66A) and 5B5EB(5B66B) were 2.46(2.48) and 2.75(2.74) (Å), respectively. The O₍₃₎‐N distances of the A‐monomers are shorter by 0.29(0.26) Å than those of the B‐monomers, indicating that the O₍₃₎−H−N(His 337) hydrogen bonding interaction30 is very strong for the A‐monomers. The Mn_3(b)−O₍₃₎ bond lengths for 5B5EA(5B66A) and 5B5EB(5B66B) were 2.27(2.18) and 1.96(1.95) (Å), respectively. The Mn_3(b)−O₍₃₎ distances of the A‐monomers are longer by 0.31(0.23) Å than those of the B‐monomers, indicating the elongation induced by the strong hydrogen bonding interaction.30

The O₍₄₎−O₍₁₁₎(W11) distances for 5B5EA(5B66A) and 5B5EB(5B66B) were 2.66(2.71) and 2.44(2.45) (Å), respectively. The O₍₄₎−O₍₁₁₎ distances of the B‐monomers are shorter by 0.22(0.26) Å than those of the A‐monomers, indicating very strong O₍₄₎−H−O₍₁₁₎(W11) hydrogen bonding interaction. The Mn_4(a)−O₍₄₎ bond lengths for 5B5EA(5B66A) and 5B5EB(5B66B) were 1.87(1.84) and 2.07(2.10) (Å), respectively. The Mn_4(a)−O₍₄₎ distances of the B‐monomers are longer by 0.20(0.26) Å than those of the A‐monomers, indicating the elongation induced by the very strong hydrogen bonding interaction. The elongation of the Mn_4(a)−O₍₄₎ distance is consistent with the JT distortion in Figure 1 B.38 Thus, the LD XRD experiments30 opened the door for understanding important roles of confinement effects37, 45 of protein such as hydrogen bonding networks for subtle geometry changes of the CaMn₄O₅ cluster in OEC of PSII, indicating the following structural fluctuations (ΔR_protein<0.1 Å) depending on states of protein fields [Eq. (12)]:

$${\displaystyle \mathrm{R}(\mathrm{Mn}{}_{4\left(\mathrm{a}\right)}-\mathrm{Mn}{}_{3\left(\mathrm{b}\right)}){}_{\mathrm{protein}}=2.80\pm \Delta \mathrm{R}{}_{\mathrm{protein}}\left(\AA \right)}$$ (12)

The large‐scale QM/MM models involving hydrogen bonding networks36, 37, 38 are necessary for theoretical investigation of ΔR_protein at the atomic level for the CaMn₄O₅ cluster controlled by several environmental effects,1, 2 such as pH,54 hydrogen bonding and packing structures27, 28, 29, 30 of OEC of PSII.

4.5. Implication of Present Results in Artificial Photosynthesis

The CaMn₄O₅ cluster in OEC of PSII examined here is a road‐map for artificial photosynthesis. Present results indicate importance of design of appropriate reaction fields for the purpose.36, 37, 38, 39 Hole‐doped Mn oxides such as the CaMn₄O₅ cluster33, 34, 35 are typical strongly correlated electron systems (SCES),39 for which orbital, charge and spin degrees of freedom play important roles for emergence of various important properties and functions such as magneto‐resistance,55 single molecule magnets56 and spin frustration.57 We have already investigated the charge and spin degrees of the CaMn₄O₅ cluster33, 34, 35, 36, 37, 38, 39 in relation to the mixed‐valence (MV) states revealed by EXAFS2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and ground spin states observed by EPR.1, 44 In this paper, the orbital degree of freedom and related Jahn–Teller (JT) deformation of the CaMn₄O₅ cluster were investigated to elucidate possible origins of the two different geometrical structures by low dose (LD) XRD.30 Hydrogen bonding networks around the CaMn₄O₅ cluster play important roles for subtle regulation of its geometrical structures.

Present theoretical results in turn indicate that SCES such as magnetic transition‐metal clusters developed in the field of molecular magnetism55, 56, 57 may be converted into active catalysts for water oxidation in artificial photosynthesis, as proposed previously.35, 58, 59 To this end, the CaMn₄O₅ cluster in OEC of PSII can be replaced with other SCESs constructed of abundant 3d transition metals such as Fe, Co, Cu etc. for development of artificial photo‐catalysts for which precious metals have been used for catalytic sites. Protein field is also replaced with other robust confinement materials such as metal organic framework (MOF), polyoxo metallate (POM), nanotube (NT) as illustrated in Figure 5.35, 58, 59 Masaoka et al.60 very recently made a great breakthrough for conversion of the Fe₅ magnetic cluster57 into an active catalyst for water conversion by electrochemical hole‐doping techniques. Design of appropriate ligands35, 58, 59 for hole doping by solar energy are desirable for future developments of molecular catalysts for water oxidation.

Figure 5.

Our theoretical proposal of artificial photosynthesis where the protein field of OEC of PSII confines the CaMn₄O₅ cluster which is a typical example of hole‐doped strongly correlated electron systems (SCES).33 The CaMn₄O₅ cluster can be replaced with other SCESs constructed of abundant 3d transition, such as, for example, Mn, Fe, and Co. The protein field is replaced with other confinement materials, such as metal–organic frameworks (MOF), polyoxometallates (POM) and nanotubes (NT).

5. Conclusions

The JT deformation formula37, 38, 39 are found to be useful and applicable for understanding and qualitative prediction of JT deformations of the CaMn₄O₅ cluster in OEC of PSII. In fact, the JT deformation formula37, 38, 39 was successfully applied for elucidation of structural deformations of the CaMn₄O₅ cluster in the A‐ and B‐monomers of the dimer structure of PSII by the XRD experiments under low dose 0.03 MGy (5B5E) and 0.12 MGy (5B66) conditions.30 The Mn_3(b)−Mn_4(a), Mn_4(a)−O₍₅₎ and Mn_3(b)vO₍₅₎ distances of the A‐monomer are about 2.8, 2.2 and 2.0 (Å) respectively, showing the JT (d${}_{\mathrm{x}{}^2}$ ) elongation of the Mn_4(a)−O₍₅₎ distance responsible for the C_R structure in Figure 1 C. The corresponding distances of the B‐monomer are 2.75, 2.1 and 2.0 (Å) respectively, indicating the JT (d${}_{\mathrm{y}{}^2}$ ) deformation (see Figure 1 B). The structure of the A‐monomer by LD XRD30 is consistent with the refined SFX structure without XFEL damage27, 28, 29 (see Table 4) and the reassigned EXAFS37, 38, 39 structures, whereas the structure of the B‐monomer by LD XRD is compatible with the original EXAFS structure10 (see Table S5) and the recent SFX structure with preflash28 (see Table 5). The EXAFS structure10 has been referred to as the reference structure to support the theoretical S₁ models with the vertical JT (d${}_{\mathrm{z}{}^2}$ ) deformation (see Figure 1 A), for which the Mn_3(b)−Mn_4(a), Mn_4(a)−O₍₅₎ and Mn_3(b)−O₍₅₎ distances are 2.7, 1.8 and 1.8 (Å), respectively. The last structure40 is therefore similar to the R‐opened S₂ structure of the CaMn₄O₅ cluster.35, 36, 37 Thus the LD XRD structures30 have provided structural foundations for reasonable explanation and understanding of the XRD,3, 4, 5, 6, 7, 8, 9, 10 XFEL,27, 28, 29 EXAFS8, 10 structures and computational models33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47 in the S₁ state of OEC of PSII. In conclusion, the CaMn₄O₅ cluster in OEC of PSII is labile33 for catalytic water oxidation, exhibiting subtle geometry changes induced by hydrogen bonding interactions, JT effects of the Mn^III ion and other environmental effects such as pH55 and packing structures.27, 28, 29, 30 Large‐scale QM/MM calculations37, 38 were necessary for elucidation of subtle structural fluctuations of the CaMn₄O₅ cluster by the protein field of PSII at atomic scale. The JT deformation formulae were successfully applied for theoretical analysis of the recent SFX results28,29 after two flash (see Section SV in the Supporting Information). Finally, implications of the present results for artificial photosynthesis by the use of abundant transition metals56, 57, 58, 59, 60 have been touched briefly.

Conflict of interest

The authors declare no conflict of interest.

Supporting information

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Supplementary

M. Shoji, H. Isobe, A. Tanaka, Y. Fukushima, K. Kawakami, Y. Umena, N. Kamiya, T. Nakajima, K. Yamaguchi, ChemPhotoChem 2018, 2, 257.