The S₃ State of the Oxygen-Evolving Complex: Overview of Spectroscopy and XFEL Crystallography with a Critical Evaluation of Early-Onset Models for O–O Bond Formation

Abstract

The catalytic cycle of the oxygen-evolving complex (OEC) of photosystem II (PSII) comprises five intermediate states S_i (i = 0–4), from the most reduced S₀ state to the most oxidized S₄, which spontaneously evolves dioxygen. The precise geometric and electronic structure of the S_i states, and hence the mechanism of O–O bond formation in the OEC, remain under investigation, particularly for the final steps of the catalytic cycle. Recent advances in protein crystallography based on X-ray free-electron lasers (XFELs) have produced new structural models for the S₃ state, which indicate that two of the oxygen atoms of the inorganic Mn₄CaO₆ core of the OEC are in very close proximity. This has been interpreted as possible evidence for “early-onset” O–O bond formation in the S₃ state, as opposed to the more widely accepted view that the O–O bond is formed in the final state of the cycle, S₄. Peroxo or superoxo formation in S₃ has received partial support from computational studies. Here, a brief overview is provided of spectroscopic information, recent crystallographic results, and computational models for the S₃ state. Emphasis is placed on computational S₃ models that involve O–O formation, which are discussed with respect to their agreement with structural information, experimental evidence from various spectroscopic studies, and substrate exchange kinetics. Despite seemingly better agreement with some of the available crystallographic interpretations for the S₃ state, models that implicate early-onset O–O bond formation are hard to reconcile with the complete line of experimental evidence, especially with X-ray absorption, X-ray emission, and magnetic resonance spectroscopic observations. Specifically with respect to quantum chemical studies, the inconclusive energetics for the possible isoforms of S₃ is an acute problem that is probably beyond the capabilities of standard density functional theory.

1. Introduction

In oxygenic photosynthetic organisms conversion of solar to chemical energy is initiated by the light-driven four-electron oxidation of water in the membrane protein complex Photosystem II (PSII), a water–plastoquinone oxidoreductase [1,2] (Figure 1a). The site of water oxidation in PSII is the oxygen-evolving complex (OEC) that harbors a cluster of four Mn and one Ca oxo-bridged cations (Figure 1b,c). The OEC is oxidized by successive light-induced electron transfers along a sequence of storage states S_i (i = 0–4 denotes the number of stored oxidizing equivalents) with S₄ being a transient state that evolves dioxygen resetting the cluster to S₀ (Figure 1d). Among the many open questions regarding aspects of the structure and function of PSII, the definition of the geometric/electronic structure and mechanistic principles of the OEC remain in primary focus [3,4,5,6,7,8,9,10,11,12], not least because of the potential relevance of this unique biological catalyst for the development of bioinspired artificial photosynthetic systems [13,14,15,16,17,18,19,20,21,22,23,24,25,26].

Crystallographic characterization of the dark-stable S₁ state of the OEC established the presence of an asymmetric Mn₄CaO₅ cluster as shown in Figure 1b [27,28]. According to the most widely accepted assignment of oxidation states, the two terminal Mn ions (Mn1 and Mn4) are in the +III while Mn2 and Mn3 are in the +IV oxidation state [29,30]. Loss of electrons and protons from the OEC occurs in a strictly alternating fashion [31,32,33,34] (Figure 1d), with the protein matrix playing a direct functional role. This level of description does not specify exactly how the geometric and electronic structure of the cluster evolves in each transition: these remain areas of active research [5].

A fundamental mechanistic question concerns the localization of oxidative events, that is, whether each individual S_i–S_i+1 transition involves Mn-centered or ligand-centered oxidation. In combination with the metal valence arrangement as well as the positioning and protonation states of the ligands/substrates, this, in turn, determines the range of possibilities for the critical catalytic step of O–O bond formation. There is currently little doubt that the S₀–S₁ and S₁–S₂ transitions correspond to metal-centered oxidations. There is strong evidence that the same is true for the S₂–S₃ step, but diverging views exist on the nature of this complex transition and on the nature and composition of the S₃ state itself [5].

With respect to dioxygen evolution, a long-held and currently popular view is that formation of the O–O bond occurs in the S₄ state or, more realistically, as part of a still unknown multistage S₃–S₀ transition that has so far been explored only in various computational studies [35,36,37,38]. This means that O–O coupling would be initiated only after the final light-driven oxidation of the cluster, i.e., past the S₃Y_Z· state indicated in Figure 1d. The S₄ hot species in this case might be a Mn(V)–oxo [39,40] or a Mn(IV)–oxyl group [41,42]. These two extremes imply, respectively, metal-based storage of four holes prior to O–O coupling or three-electron metal-based hole storage followed by substrate radical formation as prerequisite for O–O bond formation. A fundamentally different sequence of events had been proposed by Renger (initially formulated long before much of the current spectroscopic information was available) and posited the existence of a redox equilibrium in the S₃ state, allowing for O–O bond formation already before the S₃–S₄ transition in part of the S₃ population [43,44,45]. This is termed here “early-onset” O–O bond formation. If such a species would be predominantly representative of the S₃ state then the S₂–S₃ transition would not involve oxidation of manganese, and hence at most two metal-based oxidations would take place (in the preceding catalytic steps of S₀–S₁ and S₁–S₂). This hypothesis has found little support from the increasingly available studies on the S₃ state that kept refining our understanding of its properties in the last decade. However, two recent developments brought the early-onset O–O bond formation idea back to the fore as a credible alternative. One development was the emergence of the first crystallographic models of the S₃ state resulting from X-ray free-electron laser (XFEL) studies: these models suggested that two oxygen atoms within the cluster were within bonding distance [46] or, at least, within a distance considerably shorter than that of a hydrogen bond [47]. The second development was the suggestion by a number of computational studies of the S₃ state [48,49,50,51,52] that peroxo or superoxo redox isomers (in which some Mn ions are reduced compared to the S₂ state) can be energetically accessible or even more favorable than redox isomers in which the Mn ions are oxidized with respect to the S₂ state, suggesting that early-onset O–O bond formation is feasible.

The present review discusses these alternative possibilities for the S₃ state of the OEC. First, a summary of important experimental information on the geometric and electronic properties of the S₃ state is provided and quantum chemical structural models that have been developed to accommodate this information are described. The recent XFEL crystallographic models of the S₃ state are then presented, followed by an exposition and discussion of computational models that assume formation of the O–O bond already in the S₃ state. Evaluation of the computational models with respect to spectroscopic data suggests that O–O coupling in the S₃ state remains the least likely among currently proposed hypotheses, but it is acknowledged that the nature of the S₃ state and of the S₂–S₃ transition are not yet sufficiently understood to allow definitive structural assignments of intermediates.

2. Geometric and Electronic Information on the S₃ State

This section provides a brief overview of selected experimental information on the geometric and electronic structure parameters of the S₃ state, compiled from the numerous spectroscopic studies that were performed before the advent of XFEL crystallographic models. Associated spectroscopy-consistent models derived from quantum chemical studies (similarly prior to crystallographic suggestions for the structure of the S₃ state) will be presented in the subsequent section.

X-ray absorption fine structure (EXAFS) indicated the presence of three short Mn–Mn distances in the S₃ state, and additionally suggested potential elongation of a Mn–Mn distance in the S₂–S₃ transition compared to the previous steps [12,53,54,55]. Different groups have come up with numerically different fit sets for the short Mn–Mn distances in the S₃ state, but they are in broad agreement, falling within the range of 2.7 to 2.8 Å [53,55]. A fourth, longer Mn–Mn distance is suggested at ~3.2 Å; however, an alternative fit has been proposed without this longer distance but with four shorter ones [53]. The complex view of EXAFS for the S₂–S₃ transition implies that structural changes or rearrangements occur in connection with or in addition to simple oxidative events. This could be related to the binding of a water molecule as discussed below. Beyond geometric parameters, valuable information on the OEC is provided by techniques that probe the global and local electronic structure of the inorganic cluster, especially in the case of element-specific methods.

The shift of the Mn K-edge in X-ray absorption spectroscopy (defined by intense 1s–4p transitions of the excited core electron) has long been used to monitor redox changes upon S-state transitions (Figure 2a). X-ray absorption near-edge spectroscopy (XANES) shows a shift of the K-edge to higher energies indicating manganese oxidations (from the Mn(III) to the Mn(IV) oxidation state) in the S₀–S₁ and S₁–S₂ transitions. The observations of the S₂–S₃ transition have received two different interpretations, as consistent with either ligand radical formation [56] or, in analogy to the preceding steps, manganese-centered oxidation [57,58,59], resulting in a Mn(IV)₄ cluster in S₃. The latter interpretation is currently favored (and consistent with other spectroscopic data discussed below) and the spectral differences observed in the S₂–S₃ versus the S₁–S₂ transition are attributed not to ligand-based oxidation, but to a coordination sphere change from a five-coordinate Mn(III) to a six-coordinate Mn(IV) ion [60], presumably by coordination of an additional ligand. Mn K pre-edge features, arising from formally dipole-forbidden 1s–3d excitations that gain intensity through 4p mixing, show a gradual increase in intensity without significant shift in the peak position as the cluster advances from S₀ to S₃ [56]. A direct reading of oxidation states is not possible in this case, but simulations strongly support the interpretation of the K pre-edge features in terms of successive Mn oxidations from a Mn(III)₃Mn(IV) state (S₀) to a Mn(IV)₄ state (S₃) [30].

X-ray emission spectroscopy (XES) has also contributed greatly to the question of redox changes. The Kβ main line stems from 3p radiative electron decay to the 1s core hole and splits into Kβ′ and Kβ_1,3 features; the latter is a sensitive indicator of changes in oxidation state owing to 3p/3d interactions. Although initial XES results were suggested to be consistent with lack of Mn oxidation in the S₂–S₃ transition [56], recent room temperature Kβ_1,3 emission spectra of the OEC collected within ≤200 ms using a time-resolved energy-sampling approach and laser flash excitation of PSII were unambiguously interpreted in support of single-electron Mn-centered oxidation in the S₂–S₃ transition leading to a Mn(IV)₄ cluster in the S₃ state [61] (Figure 2b). The absolute amplitudes of Kβ_1,3 changes during both S₁–S₂ and S₂–S₃ transitions corresponded to ~25% of the changes observed for Mn(III)–Mn(IV) oxidations in reference compounds, the mean energy downshift being ~0.15 eV compared to ~0.6 eV in synthetic models, consistent with one Mn(III)–Mn(IV) oxidation in each of these S-state transitions [61].

The Kα line arises from 2p–1s decay and is similarly split by spin–orbit coupling of the 2p_3/2 and 2p_1/2 levels. Although in principle they are less sensitive to valence changes, they are an order of magnitude more intense than the Kβ_1,3 line, enabling better XES signal quality. Schuth et al. [62] reported room temperature Kα1 spectra of PSII in the S₀, S₁, S₂, and S₃ states and, by comparison of the data with model compounds in varying Mn oxidation states, they could reach the conclusion that Kα XES is consistent with the other XES results, supporting Mn oxidations in all transitions up to an all-Mn(IV) S₃ state that likely features binding of an additional water ligand [62].

The S₃ state has been particularly challenging to study by electron paramagnetic resonance (EPR) methods because of the even number of unpaired electrons in the cluster, which results in an integer value for the total spin. Early X-band EPR studies of the S₃ state documented weak low-field signals [64,65] that were considered consistent with a spin S = 1 assignment. Subsequent Q-band studies by Sanakis et al. [66] showed that only a total effective spin of S = 3 could fit both the X- and the Q-band data. This was supported by further studies [67]. The S = 3 spin state assignment was more recently confirmed by pulse W-band EPR and Rabi nutation experiments [68]. Electron-electron double resonance (ELDOR) detected nuclear magnetic resonance experiments (EDNMR) by Cox et al. [68] (Figure 3) additionally showed that all Mn ions are electronically similar and isotropic, implying they are all octahedrally coordinated Mn(IV) ions. The EDNMR results [68] therefore support Mn-centered oxidation in the S₂–S₃ transition. In terms of geometry, widely accepted structural models for the S₂ state assume the presence of a single Mn(III) ion with a formally empty coordination site. Therefore, the isotropic nature of the Mn ions documented by EDNMR suggests that either the cluster has contracted so that an oxo bridge saturates the coordination site that was empty in S₂, or that a new ligand is bound, possibly a substrate water molecule. Both would render all Mn(IV) octahedral. The former would be consistent with a particular EXAFS interpretation that favors a μ₃-oxo bridge of the S₂ state becoming μ₄-oxo in S₃ [53,69], while the latter would be consistent with water insertion in the S₂–S₃ transition, as favored by the most widely accepted interpretation of EXAFS and with numerous other independent studies in addition to the aforementioned X-ray studies, for example by flash-induced Fourier transform infrared (FTIR) difference spectroscopy [70].

The results of time-resolved mass spectrometric experiments that probe the kinetics of substrate exchange [72,73,74] are important in relation to the possible binding of an additional water molecule in the S₃ state and the likelihood of it being a substrate. These experiments indicate that the two substrate oxygen atoms exchange in two phases, a slow and a fast one. The slow phase is resolvable in all S-states, whereas the fast one is resolvable in the S₂ and S₃ states. Importantly, the exchange rate of the slow-exchanging substrate (W_s) is essentially the same in S₂ and S₃, while the exchange rate of the fast-exchanging substrate (W_f) is approximately three times slower in S₃ compared to S₂. The limited differences between these two states should be contrasted with the more dramatic changes occurring in the slow-exchanging substrate upon the S₀–S₁ transition (~500-fold decrease) and the S₁–S₂ transition (~100-fold increase). In comparison, the similarity in substrate exchange rates in the S₂ and S₃ states might signify a chemically invariant environment. However, this is not clear at present and several ideas have been proposed to account for these observations. Unfortunately, there is currently no transparent way of testing and comparing all competing hypotheses.

Overall, and while acknowledging the existence of alternative interpretations (e.g., [75,76,77,78,79]), the available information from spectroscopy is most consistent with Mn-centered oxidation in the S₂–S₃ transition resulting in an all-Mn(IV) cluster, accompanied by a structural change that renders all Mn ions six-coordinate.

In parallel to the above coherent picture, there are clear and incontrovertible indications that the S₃ state is heterogeneous, i.e., that it contains multiple forms that are spectroscopically distinct [65,80,81,82,83,84]. A somewhat simplified account of the observations is that the S₃ state contains a population (perhaps up to 30–40%) that can absorb near-infrared (NIR) light and “regress” to an S₂Y_Z·′ state. This results from electron transfer from Y_Z to a Mn ion. The prime symbol is used to indicate that this state is not the same as the one observed in the normal “forward” S₂–S₃ advancement. Two observations are crucial: (i) the signal of the S = 3 state discussed above in the context of EPR studies remains unaffected, therefore the NIR absorption is due to an alternative EPR-silent S₃ population, and (ii) the “split signal” [85,86,87,88,89] observed from the resulting S₂Y_Z·′ state differs significantly from the ”forward” S₂Y_Z· signal in that the tyrosyl radical interacts with a cluster in a higher spin state (S ≥ 5/2). This is in contrast to the low-spin S = 1/2 state of the “forward” S₂Y_Z· signal and of the dominant multiline g = 2 multiline EPR signal of the S₂ state. The main points made above are summarized in Scheme 1. A hypothesis that attempts to explain these observations will be mentioned in the following, but the implication is already clear: a single structural model for the S₃ state might not be able to accommodate all experimental observations, not simply in practice but in principle.

3. Spectroscopy-Consistent Computational Models for the S₃ State

A comprehensive historical account of computational studies on the S₃ state of the OEC cannot be provided here, and only specific models that have been explicitly demonstrated to be consistent with the experimental data discussed in the previous section will be presented. The most widely accepted structural representation of the S₃ state is the “oxo–hydroxo” model shown in Figure 4b. In the preceding S₂ state, where the manganese cluster is present as Mn(IV)₃Mn(III), all Mn(IV) ions are six-coordinate except Mn(III), which adopts a five-coordinate approximately square pyramidal geometry as a result of the strong Jahn–Teller effect. The two valence isomers of the S₂ state shown in Figure 4a [90,91,92] (“open cubane” S₂^A and “closed cubane” S₂^B) differ in the binding of the O5 bridge and the location of the unique Mn(III) ion. They correspond to the two interconvertible EPR signals associated with this state [90,93,94,95,96] (see also Scheme 1). According to the computational model of S₃ in Figure 4 (the label S₃^A,W will be used for this species in the following), the available Mn1 site of the open cubane S₂ isomer is occupied by a hydroxo group (O6H) in the all-Mn(IV) S₃ state, rendering all Mn ions six-coordinate.

An early version of this type of structure for the S₃ state was proposed as part of mechanistic studies on possible O–O bond formation pathways [36], and later refined convergently by several groups in light of the 2011 crystallographic model of PSII by Umena et al. [27]. The proton of the OH group may either point towards the O5 bridge or away from it, establishing instead a hydrogen bond with another acceptor group, for example the carboxylate of Glu189. In either case, the distance between O5 and O6 is computed at ~2.4–2.6 Å [30,48,49,50,68]. According to DFT calculations these alternative hydrogen-bonding patterns lie too close to be reliably distinguishable energetically [30].

Even though there are small variations in metal–metal distances, which are due to different methodological choices in the various “incarnations” of this model as presented by different computational groups (Figure 4d) as well as different opinions on the most preferable protonation states of terminal OH/H₂O ligands on Mn4, the oxo–hydroxo S₃ structure depicted in Figure 4b can be considered consistent with distances derived from EXAFS [30,97,98] (three Mn–Mn distances of ca. 2.8 Å or shorter [53,55]). It has also been shown to be consistent with EXAFS spectra by explicit simulations (Figure 4e) [97,98]. Although this agreement provides useful support, its significance should not be overestimated because of the insufficient information content of the original EXAFS spectra and the limitations in first-principles prediction of EXAFS for complex multinuclear systems [98,99,100].

This type of structure with an oxo bridge between Mn3 and Mn4 and a terminal OH group on Mn1, in combination with its lower S_i-state analogues, has been shown with time-dependent DFT calculations to reproduce successfully the measured Mn K-pre-edge X-ray absorption spectra of the OEC [30,56]. It is also consistent with Mn Kα X-ray emission spectroscopy that supports Mn oxidation in all three S₀–S₁, S₁–S₂, and S₂–S₃ transitions along with binding of an additional water-derived ligand in the S₃ state at a previously open Mn coordination site [62].

Additional support for this oxo–hydroxo model of the S₃ state, shown in Figure 4b, comes from the way it accommodates the local and global electronic structure parameters derived from magnetic resonance spectroscopies. First of all, the total spin state of the model as computed by broken-symmetry DFT calculations is S = 3 [30,68], resulting from a balance between ferromagnetic and antiferromagnetic interactions within the Mn1–Mn2–Mn3 unit and a moderate antiferromagnetic coupling between Mn3–Mn4 [30] (Figure 4c). The computed spin state is the same as that required by EPR [67,68], but this is not compelling because other possible geometric/magnetic topologies for S₃-state models can lead to the same ground spin state [30]. Strong evidence in favor of this type of structure comes from DFT calculations which show that its magnetic topology results in ⁵⁵Mn hyperfine coupling constants consistent with experiment [68]. As shown in

Table 1. Calculated projected ⁵⁵Mn isotropic hyperfine coupling constants (MHz) for two selected S₃ models of the type shown in Figure 4, among the several models evaluated by Krewald et al. [30], compared to experimental values for the S₃ state ordered from high to low in terms of absolute values. Superscripts in parentheses indicate assignments to individual Mn ions. Positive sign for the HFC identifies the Mn ion with minority (β) spin. The two models listed here differ in the presence (model “S₃H-1”) or absence (“S₃H-2”) of direct hydrogen bonding between O5 and the Mn1-bound O6H group.

S3 Model [30]	55Mn |Aiso|
S3H-1	−86 (Mn1)	−76 (Mn2)	−34 (Mn3)	27 (Mn4)
S3H-2	−99 (Mn2)	−88 (Mn1)	−29 (Mn4)	20 (Mn3)
Exp. [68]	−99 (Mn1 or Mn2)	−96 (Mn1 or Mn2)	−26 (Mn3 or Mn4)	≤5 (Mn3 or Mn4)

and further discussed in Ref. [30], the experimentally observed pattern of two large and two small ⁵⁵Mn hyperfine coupling constants can be reproduced by an oxo–hydroxo structural model (see associated spin projection coefficients in Figure 4c [30,68]), even though the smaller values are overestimated compared to experiment. Computationally derived structures with different bonding and magnetic topologies or with alternative oxidation states do not reproduce the magnitude and distribution of the experimental ⁵⁵Mn hyperfine coupling constants as successfully [30,50,101].

Overall, this model has a strong connection with the spectroscopy of the S₃ state. On the other hand, as mentioned above and shown in Scheme 1, EPR spectroscopy provides clear indications of heterogeneity in the S₃ state [80,81]. A crucial observation is that the S₂Y_Z·′ state formed by NIR illumination from a population of S₃ that is not yet positively identified via EPR involves the tyrosyl radical interacting with the manganese cluster in a high-spin state. For reasons that relate to the dependence of the superexchange interactions on the Mn–O–Mn angles [90,102,103] this high-spin state is a signature of a closed cubane Mn₃CaO₄ unit for the S₂ state of the OEC (Figure 4a). This geometric arrangement suppresses the antiferromagnetic interactions within the Mn1–Mn2–Mn3 trimer that in the open cubane isomer lead to the lowest possible S = 1/2; instead, the closed cubane topology of the S₂ state has a spin state of S ≥ 5/2 [90]. However, this closed cubane topology is obviously inconsistent with the computationally derived S₃-state structure shown in Figure 4b and with the binding of an additional ligand (O6H) to Mn1.

A hypothesis that attempts to accommodate all of these observations was advanced by Retegan et al. [104]. It implicates three distinct forms for the S₃ state, which are all isoelectronic in terms of Mn oxidation states, i.e., Mn(IV)₄, but not isostructural. According to this model the two forms of the S₂ state have a functional role in gating progression to S₃: the dominant open cubane form (S₂^A in Figure 4a) is the one that can most easily lose a proton from a terminal water ligand once oxidized to the S₂Y_Z· intermediate [104,105]. The group that is deprotonated is W1, computed to be the most acidic terminal ligand at this stage of the cycle [104]. Deprotonation of W1 is facilitated by a dipole reorientation on formation of the tyrosyl radical [105] and by the presence of the hydrogen-bonded proton acceptor Asp61. On the other hand, only the closed cubane topology (S₂^B in Figure 4a) allows intramolecular electron transfer between the Mn(III) ion and the tyrosyl radical, once deprotonation of W1 takes place [104]. A QM/MM molecular dynamics study by Narzi et al. independently proposed that the closed cubane form is stabilized preferentially at the level where the S₂ cluster is deprotonated and the tyrosyl radical is formed [106]. In either case, the result is that the closed cubane form of S₂ is the species that advances to the S₃ state, leading to an all-Mn(IV) intermediate where Mn4 is a five-coordinate Mn(IV) [104] (species S₃^B in Figure 5). A species with a five-coordinate Mn(IV) is unusual but has synthetic precedents, for example in the work of Borovik and coworkers [107]. Importantly, detailed EPR studies by Boussac and coworkers indicate that the multiline signal of the S₂ state (attributed here to the open cubane model S₂^A) is formed first and converts to higher-spin signals (associated here with the closed cubane topology of S₂^B) in order for the Mn ions to be oxidized by the tyrosyl radical and advance to the S₃ state [81,108,109]. This can be considered an experimental demonstration of the gating role of structural bistability in the S₂ state and of the catalytic competence of the high-spin S₂ component, providing strong support for the scheme derived from quantum chemical studies in Figure 5a.

The particular form (S₃^B), which according to the above scenario is the first structural component of the S₃ state, provides a natural explanation of the NIR absorption: this is attributed to a d_xz–d_z² excitation of the five-coordinate Mn(IV) ion [104]. If this excitation triggers electron transfer from Y_Z to this Mn site, then the alternate S₂Y_Z·′ is readily rationalized: the closed cubane Mn₃Ca subunit of the S₃^B form results in a high-spin state of the manganese cluster in S₂Y_Z·′, analogously to the S₂^B form of the S₂ state. Furthermore, the S₃^B state might be silent in X-band because of the high zero-field splitting associated with the five-coordinate Mn4 [104,107], but this has not been explicitly demonstrated yet. Binding of water at Mn4 through a channel associated with the interaction of small molecules such as methanol and ammonia [4,110,111,112,113,114,115,116,117,118,119] completes the coordination sphere of this ion leading to the structure labeled S₃^B,W in Figure 5 (where the superscript W indicates binding of an extra water molecule). This isomerizes to S₃^A,W by a simple bond rearrangement [120].

According to the above hypothesis, the prevalent structural form of the S₃ state might be represented by S₃^A,W, but this may coexist with the S₃^B,W isomer as well as with a form of the latter that lacks a sixth ligand at the terminal Mn4 (S₃^B). All these forms are in principle interconvertible [103,104,120,121], but their relative energies remain a matter of debate in the computational literature. It is noted that if they coexist as structural components of the S₃ state, these structural forms should not be considered necessarily resolvable by EXAFS because the metal–metal distances are not significantly different among them, even though the bonding topology is.

An alternative way of reaching the S₃^A,W structural form involves movement of a Ca-bound water, with concomitant deprotonation, to the available internal coordination site of the Mn1 ion directly in the “open cubane” S₂ topology of the cluster [122]. As will be discussed in the following, this is consistent with a suggested interpretation of XFEL models [47]. This pathway for water delivery is plausible, but the water movement and the deprotonation of Ca-bound water were both predicted to be energetically disfavored [104,106,123] or could not be independently reproduced in computer simulations [101]. Additionally, access to the OEC of methanol and ammonia likely proceeds through a different channel [4,110,111,112,113,114,115,116,117,118], rendering this water delivery mechanism rather unexpected. Finally, this scenario does not involve intermediates that can obviously explain the EPR and NIR phenomenology described above, either in terms of which S₂-state EPR signals correspond to species able to progress to the S₃ state, or in terms of the spectroscopic behavior of the S₃ state itself.

In summary, a lot of the spectroscopy on the S₃ state of the OEC can be rationalized by a single oxo–hydroxo type of structure, such as the one depicted in Figure 4b and Figure 5 (S₃^A,W). However, a single species cannot account for the complete experimental phenomenology. The scenario of Figure 5 has certain merits in terms of accommodating EPR and NIR observations, but at present the spectroscopic heterogeneity of the S₃ state is insufficiently understood in structural terms.

4. XFEL Crystallographic Models for the S₃ State

The experimental studies and computational models described in the preceding section were performed and developed mostly prior to reports of atomic resolution crystallographic models for the S₃ state of the OEC. In the last two years three XFEL studies have been published that advanced specific atomic-level structural representations of the S₃ state of the OEC. The first was by Young et al. [124], which suggested that the S₃ state is extremely similar to S₂, a surprising conclusion that clashed with expectations from all experimental structural and spectroscopic evidence outlined above. Fundamental aspects of this study were noted as potentially problematic, for example in terms of data processing [125], while a computational study suggested that the proposed structural model was untenable as a representation of the S₃ state [126], even on the simple grounds of correlating geometric parameters to oxidation states. Therefore, this model will not be further discussed here.

This was followed by the XFEL study of Suga et al. [46]. The structural model of the OEC for the preflash/two-flash dataset proposed in that work (2.35 Å resolution, S₃ estimated by FTIR at 46% but fixed at 80% for structural refinement) is shown in Figure 6a. A distinctive feature is the presence of an additional oxygen ligand compared to the S₁ state. Two of the centrally located oxygen atoms (O5 and O6 in Figure 6a) are within ca. 1.45 Å of each other, a distance characteristic of an O–O bond. This report has supported the reemergence of the S₃ peroxo hypothesis. Kern et al. [47] followed with a model (Figure 6b, 2.07 Å resolution, estimated S₃ 60–70%) that has similarities with that of Suga et al. but differs in important details. The additional oxygen atom is labeled “Ox” in the work of Kern et al. but here it will be labeled O6 to facilitate discussion and comparisons. The O5–O6 distance in the Kern et al. model is ~2.1 Å and the O6 is positioned within bonding distance of the calcium ion (ca. 2.5 Å, compared to over 2.9 Å in the model of Suga et al.), closer in fact to Ca than O5 (2.6 Å). O6 in this model is also much closer to Mn1, less than 1.8 Å compared to ca. 2.3 Å in the model of Suga et al., which results in an effective difference of the O6 position between the two models of ca. 1 Å.

It must be clarified from the outset that if the Suga et al. model (Figure 6a) is to be taken at face value as a single-structure representation of the S₃ state of the OEC, it is impossible to regard it as compatible with an oxo–hydroxo model, such as the spectroscopically consistent computational model depicted in Figure 4 and Figure 5. In a literal interpretation of this XFEL model the O5–O6 distance is too short to be considered anything, but a covalent O–O bond of a peroxo moiety. This assignment would agree with another characteristic feature of the model, the unmistakable signature of Mn(III) ions in the form of strong axial Jahn–Teller distortions for Mn1 and Mn4 with Mn–O distances around 2.3 Å. Such long distances are practically identical to corresponding Mn(III)–O distances in the S₁ state [28]. By contrast, normal Mn(IV)–O distances are ca. 0.3–0.4 Å shorter [28,127,128].

A bond valence sum analysis was performed for the purposes of the present review on the Suga et al. two-flash model (5WS6) using the standard Brown–Altermatt equation [129] with the 2015 Gagné–Hawthorn bond valence parameters—R₀ and B—that were derived individually for each Mn oxidation state by a generalized reduced gradient method [130]. The resulting oxidation states are +3.1, +3.7, +3.1, and +2.5 for ions Mn1–Mn4 in monomer A and +3.2, +3.5, +3.3, and +2.6 for monomer B (total average oxidation state +3.1). These suggest that only Mn2 can be more or less straightforwardly assigned as formally Mn(IV) in this model; Mn4 is better described as Mn(II)/Mn(III), while Mn1 and to a lesser extent Mn3 justify a formal oxidation state of Mn(III) rather than Mn(IV). As a “sanity check”, the same approach applied to the computational S₃ model of Figure 4b with coordinates obtained from Cox et al. [68] yields bond valences of +3.7 for all Mn ions, consistent with a formal Mn(IV)₄ state.

The presence of Mn(III) ions, i.e., reduction of metal ions in the S₂–S₃ transition, is precisely what should accompany peroxo formation in the S₃ state. However this interpretation contradicts the spectroscopic evidence discussed above: XAS, XES, and EPR studies concur that the S₁–S₂–S₃ transitions involve two successive Mn-based oxidations and that the S₃ state is most consistent with Mn(IV)₄. Even if the possibility of ligand-centered oxidation in the S₂–S₃ transition can still be entertained, and even if alternative hypotheses can be advanced about the total oxidation level of the inorganic cluster (e.g., the “low-oxidation state” hypothesis [75,76,77]), there is no interpretation of the currently available spectroscopic data that can accommodate Mn oxidation in S₁–S₂ followed by Mn reduction in the S₂–S₃ step; this redox transformation would revert the metal ions of the cluster to the electronic structure of the resting dark-stable S₁ state. Other aspects of the Suga et al. XFEL study [46] call for further scrutiny, for example, uncertainty in the positive identification of O6 in the difference Fourier map and S_i-state quantification. Localization of light atoms in the vicinity of electron-rich Mn ions is intrinsically difficult [131]. The S_i-state composition is also open to discussion. This is because S_i-state conversion is imperfectly synchronized due to “misses” as well as “double hits”. At the same time, the dark-adapted sample might have contained an uncertain amount of S₀ state, either physiologically or as a result of XFEL-induced Mn reduction [132,133]. All these considerations impact the quantification of the S₃ state. It is noted that if the suggested percentage of 46% S₃ in the two-flash sample is approximately correct, this could imply the presence of more than 50% S₂ state in this sample, a situation that is not clearly accounted for.

Based on the two main observations above, namely the clear presence of Mn(III) ions and the problems with quantification of S_i-state populations, we would like to describe an alternative hypothesis that could partially explain [5] the peculiar geometric parameters in the Suga et al. XFEL model. Specifically, it is suggested that the refinement of OEC core atom positions, especially the light ones such as the O5 and O6 bridges, may reflect the compromised result of the attempt to elicit a unique model out of the data despite the presence of multiple structural components. By simply superimposing the 1.95 Å resolution XFEL model of the S₁ state with a combination of the spectroscopically consistent computational models of the S₂ and S₃ states (Figure 4) it is possible to approximate an averaged value of ca. 1.5 Å for an “effective” distance between O5 and O6. In an average sense, this can create the illusion of bonding between these two atoms without ever such a short O–O distance being present in any of the individual structures that contribute to the averaged model. This could also rationalize the fractional occupancies of the O5 and O6 atoms. According to the superposition hypothesis the observation of Jahn–Teller distorted terminal Mn(III) ions in the model of Suga et al. is naturally explained as arising from the contribution of insufficiently eliminated lower S_i states, not from the S₃.

In the Kern et al. model [47] (Figure 6b), a direct reading of the O5–O6 interaction is complicated by the fact that the O–O distance is too long by ca. 0.5 Å to be a bond, yet too short by almost the same extent to represent a hydrogen bonding interaction; these chemical situations are nonoverlapping in terms of distances. The close but nonbonding contact between the O atoms in the Kern et al. model implies that O6 (“Ox” in the original report) should be considered as fully deprotonated, which might justify the peculiarly short Mn1–O bond length of 1.79 Å. On the other hand, this Mn–O distance might be considered too short if it is assumed that O6 is not a terminal oxo but acts as a bridge between Mn1 and Ca as implied by the Ca–O6 distance. The position of O6 leads to a highly unusual coordination geometry for Mn1, with significant distortion away from octahedral symmetry. The movement of Glu189 in combination with intermediate “snapshots” obtained late in the S₂–S₃ transition was interpreted in support of water insertion from Ca to Mn1, a suggestion that at first sight seems inconsistent with the documented absence of significant adverse effects in Glu189 mutants [134]. The Kern et al. model presents a situation that requires further analysis to be properly evaluated, but given that the O5–O6 distance falls in-between the distances associated with a covalent O–O bond and a hydrogen bond, an interpretation in line with incipient O–O bond formation cannot be strictly eliminated. However, this would present the same problem with respect to the requirement for Mn reduction as above; Kern et al. already pointed out that their in situ XES data was obtained in the same study conflict with this interpretation since they are consistent with Mn oxidation upon the S₂–S₃ transition. In line with this point, the Jahn–Teller elongated Mn–O distances discussed above for the Suga et al. model are much shorter here and more typical of Mn(IV) ions. It is thus unclear whether all issues discussed above for the Suga et al. XFEL model are entirely resolved. Overall, however, the model of Kern et al. is distinct in fundamental ways from that of Suga et al. and can be considered as posing an alternative type of “double-oxo” structural type for the S₃ state. As such, it is also distinct from the spectroscopically consistent computational models discussed in the preceding section.

It has not yet been examined explicitly whether a quantum chemically refined “double-oxo” model can be an acceptable alternative to the “oxo–hydroxo” model in terms of consistency with EPR and X-ray spectroscopies. It is likely that imperfect elimination of lower S-state contributions and structural heterogeneity may also affect this model to some degree. In any case, it is important to keep in mind that the picture from spectroscopic studies on the S₃ state describes a more complex situation than might be possible to capture by a single averaged crystallographic fit. Therefore, it seems premature and counterproductive to regard any of the current XFEL models as a definitive representation of exclusively the S₃ state, or indeed of any single structural entity.

5. Peroxo/Superoxo Models for the S₃ State

The heterogeneity model for the S₃ state described in Figure 5 [104] assumes the presence of distinct geometric forms but all with the same oxidation states of ligands and metals, i.e., Mn(IV)₄. The computational models for the S₃ state discussed in the present section differ profoundly from the above concept in that they implicate redox isomers with distinct electronic/valence structures. In this scenario, an all-Mn(IV) form is but one of several possible components of the S₃ state; additional isomeric forms arise through intramolecular redox processes that involve formation of peroxidic or superoxidic bonds with concomitant reduction of Mn(IV) ions to the Mn(III) level. In at least one of those possible isomers a structure very similar to the XFEL model of Suga et al. [46] (Figure 6a) would be obtained. In terms of the S_i-state progression redox isomers that involve O–O bond formation require a reversal of the regular oxidative advancement with Mn reduction in the S₂–S₃ transition.

Isobe et al. [48] presented detailed computational models in which the S₃ state of the OEC contains redox isomers with Mn oxidation states (IV)₄, (IV)₃(III), (IV)₂(III)₂, and (IV)(III)₃, the latter three in various valence arrangements. Note that all these states are isoelectronic, the difference between them being how many of the electrons are spin-paired and how many remain unpaired (on metal ions or ligand radicals). The isomeric forms with one Mn(III) ion correspond to formation of a terminal oxyl radical group, while the redox isomers that contain two and three Mn(III) ions correspond to peroxide and superoxide formation, respectively. For a large 340-atom quantum mechanical model, twelve distinct forms, which differ in protonation, charge, spin, and conformation, could be located within an energy range of 13 kcal·mol⁻¹ using the B3LYP functional [135,136] with variable percentages of Hartree–Fock (HF) exchange. Figure 7 reproduces a scheme from the study of Isobe et al. [48] that depicts the four Mn ions and the two centrally located oxygen atoms in the various redox states identified in that study. Model H(open) (Figure 7) is an oxo–hydroxo species with a Mn(IV)₄ valence structure and is equivalent to the oxo–hydroxo model discussed above (S₃^A,W, Figure 4b and Figure 5). The O–O distances in the models of Figure 7 are consistent with expectations with respect to the formal oxidation states. Model P(open) (Figure 7) is a close geometric analogue to the Suga et al. model [46] in terms of the formal oxidation states assigned to the Mn ions (III, IV, IV, and III) and the presence of a peroxo moiety in the center of the cluster with an O5–O6 distance of ca. 1.4 Å.

A critical issue when discussing the relevance of all these computational models for understanding the natural system is their relative energies. Isobe et al. [48] reported pronounced sensitivity of computed relative energies for the redox isomers on the percentage of Hartree–Fock (HF) exchange included in the functional. Three different versions of the B3LYP functional were employed with 10%, 15%, and 20% HF exchange, the latter corresponding to the original definition of the functional [135,136]. According to Isobe et al. [48] the version of the functional with 10% HF exchange led to H(open) (see Figure 7, top) being the ground state of the system, O*(open) being less than 2 kcal·mol⁻¹ higher in energy, the peroxo forms at ca. 9–10 kcal·mol⁻¹ and, finally, the superoxo forms at ca. 8–10 kcal·mol⁻¹. Increasing the HF exchange to 15% led to the superoxo forms being 3–5 kcal·mol⁻¹ lower in energy than H(open). With 15% HF exchange the latter was practically isoenergetic (within 1 kcal·mol⁻¹) with O*(open) and the two peroxo P forms. Finally, using 20% HF exchange the results were strongly in favor of the superoxo and peroxo forms: S_singlet was computed to be almost 18 kcal·mol⁻¹ lower than H(open) and both peroxo forms more than 7 kcal·mol⁻¹ lower than H(open). In view of this extreme sensitivity of computed relative energies on the technical parameters of the DFT method, as well as because of the absence of obvious interconversion pathways in most cases, Isobe et al. suggested that at the very least these results could leave open the possibility of interconversion between some of these forms at room temperature, leading to reversible activation/deactivation of substrate oxygens in the S₃ state [48].

The idea of an S₃ state with a configuration that is “primed” to form an O–O bond was also explored by Pushkar and coworkers [49]. A characteristic feature of the proposed model is the formation of a terminal Mn1(IV)=O oxo unit in the S₃ state. This appears to interact with Ca, effectively forming a Mn1(IV)–O–Ca bridge. In this sense, the proposed computational structure [49] bears similarities with the XFEL model of Kern et al. [47], in that both of the centrally located oxygen ligands are fully deprotonated and both are positioned between Ca and Mn1 or Ca and Mn4, although a more chemically realistic distance of ca. 2.5 Å is reported for the O5–O6 separation by Pushkar et al. [49] compared to the XFEL model [47]. A high spin population of ca. 0.4 was computed for the oxo unit [49], which might therefore more appropriately be described as an oxyl radical attached to a Mn(III) ion rather than a Mn(IV)-oxo. This was proposed to reflect the activated nature of this group, which could thus participate in low-energy radical-type O–O bond formation. Calculations performed using this model for the S₃ state indicated that a structurally similar form would also be stable in the S₄ state, but with a Mn(V) ion. Pushkar et al. additionally identified peroxo isoforms in both the S₃ and the S₄ states using the BP86 [137,138] and B3LYP* [139,140] functionals; the former belongs to the generalized gradient approximation (GGA) of DFT and contains no HF exchange, while the latter is a modified version of the B3LYP functional with 15% HF exchange. The optimized peroxo forms of S₃ and S₄ had the expected O–O bond lengths of ca. 1.4–1.5 Å. Remarkably, peroxo formation in the hypothetical S₄ models was computed to be unfavorable by ca. 19 kcal·mol⁻¹ (BP86 functional) or 9 kcal·mol⁻¹ (B3LYP*), while the peroxo isoforms were less than 5 kcal·mol⁻¹ higher in energy in the case of the S₃ state models.

A possible interpretation of these results is that the computational models of the OEC used in that study do not support O–O bond formation regardless of the S-state assumed, regardless of the functional used. This could indicate potential technical issues with the construction of the models (e.g., aggressive truncation, neglect of second-sphere effects and omission of the redox-active tyrosine), issues with the assumptions regarding the sequence of proton/electron removal during the S_i-state progression, or issues with the reliability of DFT for redox energetics, all of which call for closer scrutiny. Alternatively, the results could be literally interpreted as implying that oxidation of the S₃ to the S₄ state offers no advantage in terms of facilitating formation of the O–O bond. Based on this interpretation, Pushkar et al. suggested that this particular structural type for the S₃ state is predisposed towards O–O bond formation and that a high-energy peroxide isoform of S₃, presumably accessible at physiologic temperatures as a minority species, could be preferentially oxidized by the tyrosyl radical created in the final light-driven electron transfer step of the cycle [49]. This pathway to dioxygen evolution circumvents the creation of a “proper” S₄ state and may represent an evolutionary adaptation that avoids formation of harmful peroxide intermediates [49]. Time-resolved XES studies by the same group did not identify oxidation of the manganese cluster above the all-Mn(IV) oxidation level prior to O–O bond formation, supporting the above scenario [141].

A study by Corry and O’Malley [50] also investigated peroxo formation in the S₃ state and provided a comprehensive report of computed EPR parameters for such models. Starting from the Suga et al. coordinates [46], Corry and O’Malley optimized a series of peroxo and oxo–hydroxo 229-atom models of the S₃ state with the BP86 functional, assuming a high-spin configuration in each model; properties were computed with the hybrid meta-GGA (10% HF exchange) TPSSh functional [142]. Optimized structures of the core region of their models are depicted in Figure 8a.

The model labeled as “oxo–hydroxo-A” in Figure 8a corresponds to the “S₃^A,W” model discussed above and to the “H(open)” model of Isobe et al. Oxo–hydroxo-B is an alternative form that does not contain an intramolecular bond between O6H and O5. These two forms were previously discussed by Krewald et al. [30], who had concluded that the presence or absence of the O6H–O5 hydrogen bond has only a small energetic effect and does not significantly perturb the magnetic and spectroscopic properties of the cluster [30]. The same conclusions are reached by Corry and O’Malley [50]. Note that the O5–O6 distance is ca. 2.4 Å for both conformers. Figure 8a shows that three additional structures were obtained as peroxo models A–C: they all feature a short O5–O6 bond of ca. 1.4 Å and a Mn(III, IV, IV, and III) distribution of oxidation states as clearly identified from manganese spin populations. Peroxo-A and peroxo-B have a fully protonated W2 (H₂O) in a different hydrogen bonding arrangement (attempts to retain one of O5 or O6 protonated in the presence of W2 = OH⁻ resulted in proton transfer to W2), whereas peroxo-C features an overall lower protonation level with W2 = OH⁻. Model peroxo-B from the study of Corry and O’Malley [50] is analogous to model P(open) from the study of Isobe et al. [48] (Figure 7).

Comparison of the optimized structures with the XFEL model of Suga et al. led to the conclusion that only the peroxo forms were compatible with this XFEL model. The comparison with EXAFS distances was less conclusive. Corry and O’Malley subsequently focused on the magnetic and spectroscopic properties of the computational models. They confirmed the much better agreement of oxo–hydroxo compared to the peroxo forms with the properties of the S₃ state component observed by magnetic resonance techniques, but were ultimately in favor of an equilibrium between the oxo–hydroxo and peroxo forms, suggesting an interconversion mechanism depicted schematically in Figure 8b [50]. As in the other studies presented above, the relative energies of the redox isomers were found to be extremely sensitive to the nature of the DFT method, to the point that no safe conclusions could be reached on the basis of computed energetics [50].

6. Evaluation of Early-Onset O–O Bond Formation Models

The representative studies discussed in the preceding section have advanced a range of peroxo models for the S₃ state that are of different quality in terms of computational refinement, with differences in bonding topology and protonation states, and with highly uncertain relative energies compared to alternative redox forms. Nevertheless, they all fit the peroxo description because they contain a well-defined O₂²⁻ moiety interacting in different ways with the Mn₄Ca framework where two Mn ions (Mn1 and Mn4 in all computational models) are reduced to Mn(III) compared to any “canonical” S₃ state formulation that contains four Mn(IV) ions. In the following we take a closer look at the properties of these models in relation to available experimental data.

6.1. Structural Features

It can be stated unequivocally that only peroxo computational models of the S₃ state agree well with the XFEL model of Suga et al. No other type of structure optimized computationally shows this level of agreement, given than no other model can reproduce the peroxo-like O5–O6 distance and the Mn1/Mn4 coordination geometries. On the other hand, peroxo models are incompatible with the XFEL structure proposed by Kern et al. [47], in which O5 and O6 are not formally bonded and the coordination geometries of all manganese ions are consistent with the Mn(IV) oxidation state. Among the computational models of the S₃ state reported in the literature, the one discussed by Pushkar et al. [49] as predisposed to O–O bond formation best approximates the Kern et al. “double-oxo” type of structure [47], without necessarily reproducing all geometric parameters of the latter like the O5–O6 distance. The problem with evaluating computationally derived structures of the OEC against the XFEL crystallographic models cannot be resolved because the available XFEL models are mutually incompatible in essential details. One may assume that the Suga et al. and Kern et al. models represent different components of the S₃ state, the former approximated by a Mn(III)₂Mn(IV)₂ peroxo and the latter by a Mn(IV)₄ double-oxo species. However, this literal reading of the XFEL models seems unjustifiable because the Suga et al. model can be rationalized in terms of sample heterogeneity as proposed above and because it is unlikely that a crystallographic study has almost exclusively captured a form of the OEC that has not been documented spectroscopically.

As described in many studies, oxo–hydroxo computational models for the S₃ state reproduce well the three short Mn–Mn distances of ca. 2.8 Å or less reported by EXAFS, but slightly overestimate the proposed long Mn–Mn distance of 3.3 Å by ca. 0.2 Å. This distance corresponds to Mn1–Mn3. In the peroxo models [50] this is very close to 3.3 Å, however these models feature only two short Mn–Mn distances and an additional, longer one at ca. 2.9–3.0 Å (Mn3–Mn4). None of the models contain four short Mn–Mn distances as suggested by an alternative fit of EXAFS data [53]. No clear difference exists between the oxo–hydroxo and the peroxo models for the Mn–Ca distances. Similar parameters were reported for peroxo models in other studies [48,49,101]. Overall, it appears that the oxo–hydroxo models are in better agreement with EXAFS because the peroxo models have only two as opposed to the three required short Mn–Mn distances, and they also feature a characteristic Mn–Mn distance at ca. 3.0 Å. This distance is absent from the experimental EXAFS fits. As discussed above (see Figure 4), explicit simulations of EXAFS spectra have been presented for oxo–hydroxo models in support of their agreement with experiment [97,98]. To our knowledge this has not yet been done for peroxo models of the S₃ state, but at least from their optimized Mn–Mn distances (two short, one intermediate, and one long) it can be concluded that they do not reproduce the experimental distribution of three short and one long Mn–Mn distances.

6.2. Oxidation States and Spectroscopy

EPR spectroscopic parameters are highly relevant for discussing the local electronic structure of manganese centers given the presence of Mn(III) ions in peroxo models of the S₃ state. Corry and O’Malley addressed this point explicitly with quantum chemical calculations of the magnetic and spectroscopic properties of their optimized models [50]. Among the three peroxo models reported in their study (Figure 8a), only peroxo-A was reported to have the experimentally determined ground spin state of S = 3, whereas both peroxo-B and peroxo-C had ground states of S = 4. In terms of ⁵⁵Mn hyperfine coupling constants (

Table 2. Calculated projected ⁵⁵Mn isotropic hyperfine coupling constants (MHz) for three peroxo models of the S₃ state discussed by Corry and O’Malley [50], compared to experimental values for the S₃ state ordered from high to low in terms of absolute values. Superscripts in parentheses indicate assignments to individual Mn ions.

S3 Model [50]	55Mn |Aiso|
peroxo-A	−130 (Mn4)	83 (Mn1)	−72 (Mn3)	−68 (Mn2)
peroxo-B	−128 (Mn4)	−109 (Mn3)	85 (Mn1)	−58 (Mn2)
peroxo-C	−103 (Mn4)	−83 (Mn3)	−45 (Mn1)	22 (Mn2)
Exp. [68]	−99 (Mn1 or Mn2)	−96 (Mn1 or Mn2)	−26 (Mn3 or Mn4)	≤5 (Mn3 or Mn4)

), peroxo-A and peroxo-B would be disqualified because the computed HFCs are similar for all Mn ions, in disagreement with experiment. Peroxo-C is somewhat better in approximating the pattern of two large and two small HFCs but it is excluded as a candidate for the species observed by EPR because of its spin state of S = 4. Finally, all peroxo models suffer from the fact that they contain electronically dissimilar Mn ions that fall into two distinct pairs, i.e., two isotropic Mn(IV) and two anisotropic Mn(III), a fact that directly contradicts experimental data [68]. Therefore, it can be concluded that the S = 3 component of the S₃ state that was detected by EPR cannot be consistent with any peroxo model. So far only an oxo–hydroxo model like S₃^A,W (Figure 4 and Figure 5, equivalent to H(open) of Figure 7 and the oxo–hydroxo of Figure 8) has been shown to reproduce sufficiently well the properties associated with the experimentally observed S₃ species.

It was suggested instead [50] that a peroxo species might represent a component of the S₃ state as yet unobserved by EPR. In this case the absence of a signal might be attributed to the large zero-field splitting arising from the Mn(III) ions of the peroxo isomer, as opposed to the zero-field splitting of a five-coordinate Mn(IV) ion in a species like S₃^B (Figure 5). The presence of Mn(III) ions in this peroxo form might also explain the NIR absorption in the S₃ state [50]. This hypothesis should be further investigated with explicit calculations, though it is hard to imagine how NIR absorption by a peroxo isoform of the S₃ state could result in the modified S₂Y_Z·′ state observed by EPR (Scheme 1).

X-ray absorption spectroscopy offers additional criteria for evaluation of early-onset O–O bond formation. Here a central problem lies not in the fact that a peroxo species in the S₃ state requires the presence of two Mn(III) ions, but in the fact that the Mn reduction required for peroxo formation in the S₃ state would necessarily lower the overall metal oxidation state level compared to the S₂ state. The Mn K edge would have to shift closer to that of the S₁ state, or even to the most reduced S₀ state in the case of the superoxo isomers described by Isobe et al. [48]. The Mn K edge depends sensitively on the Mn oxidation state and XANES has been interpreted as demonstrating a regular oxidative progression (see Figure 2). Unless the redox state of the Mn ions is not the primary contributor to the S-state dependent changes observed in XANES, it is not obvious how the above expectations relating to peroxo formation in the S₃ state could be compatible with experiment.

In terms of X-ray emission spectroscopy, Schuth et al. [62] presented a comparison against experiment of S₃ minus S₁ Kα difference spectra, obtained from multiple-scattering theory calculations, for various DFT models of the S₃ state (Figure 9). Among the S₃ structural models tested was a structure that contained an O–O bond between atoms O5 and O6 in the form of hydroperoxide, with the two terminal Mn ions in the +III oxidation state (model labeled S₃b in Figure 9). In contrast to the experimentally observed energy downshift of the S₃ compared to the S₁ state, this model showed an energy upshift due to the Mn reduction and hence was incompatible with experiment. A model with terminal water ligand binding (S₃c) was the one that was found to agree best with experiment. Despite the clear conclusions derived from the tested structures, it would be desirable to extend this study to include unprotonated peroxo as well as oxo–hydroxo forms for the S₃ state such as those discussed above, and to refine the approach in order to deal with possible unresolved electronic structure issues implied by the reported presence of unusual intermediate-spin Mn(III) ions. Focusing on Kβ_1,3 spectra as potentially more sensitive for the evaluation of models, as well as refining the level of theory used are also possible targets for future studies.

In conclusion, although it is not possible to exclude the existence of a peroxo species as a high-energy minimally populated S₃ isoform [48,49,50], the above analysis suggests that peroxo models are intrinsically inconsistent with the available EPR/EDNMR, XAS, or XES spectroscopic data on the S₃ state.

6.3. Kinetics of Substrate Exchange

If a peroxo species is a component of the S₃ state either in the sense of a ground-state equilibrium or as a high-energy isomer, then it could be relevant for interpreting substrate exchange kinetics. A critical observation is that the H₂¹⁸O/H₂¹⁶O exchange rates of the two substrate waters—slow-exchanging (W_s) and fast-exchanging (W_f)—are very similar in the S₂ and the S₃ states, which has been interpreted as indicative of a similar chemical nature of the substrate oxygen species in the two states [72,73,74,143,144,145]. According to this argument, O–O bond formation in the S₃ state can be excluded because it would result in drastically reduced substrate exchange rates, in contrast to experiment. Substrate exchange slows down dramatically upon subsequent light-driven formation of the tyrosyl radical, i.e., in the S₃Y_Z· intermediate state [146]. It has been suggested that the above observations are consistent with the oxo–hydroxo model (S₃^A,W) for the S₃ state and that substrate exchange must involve a Mn(III) ion [147]. This can be formed in the Mn(IV)₄ S₃ state by internal electron transfer between Mn(IV) and Y_Z, but this transient reduction of Mn(IV) by the tyrosine residue is not possible in the S₃Y_Z· intermediate where the tyrosine is already oxidized, and hence substrate exchange is arrested [147]. The lack of concrete experimental information on the details of the water exchange mechanism precludes a deeper analysis, but these arguments based on quantum chemical studies [147] appear to fit the experimental observations well. No similar support in the form of explicitly computed water exchange pathways exists for any other hypothetical model of the S₃ state.

Formation of an O–O bond in the S₃ state can probably only be considered in the context of a fast equilibrium with other species, of which an oxo–hydroxo isomer would be dominant. The concept of such an equilibrium has been previously discussed by Renger [45,148] and the reader is referred to his publications for further comments, with the caveat that the argumentation is not informed by current structural and spectroscopic data. Nevertheless, it is worth mentioning an interesting point made by Isobe et al. [48] concerning the idea of label scrambling between W_s and W_f substrates. Specifically, it was proposed that superoxo formation in the S₃ state can be responsible for label scrambling because the identity of the oxygen atoms within the O–O unit can be easily interchanged at the level of the loosely bound superoxo (models S_singlet/S_triplet in that study, see Figure 7) [48]. If such a mechanism is operative then it places restrictions on the relative energy of the superoxo S₃ isoform, which should be sufficiently stable to be relevant for the process but not too stable to lead to complete scrambling inconsistent with the two distinct phases. It does not seem possible at this point to verify whether this suggestion is realistic or indeed whether isotopic scrambling can form part of explaining the experimental observations.

6.4. Computed Energetics of Redox Isomers

In the context of quantum chemical studies of candidate S₃ models, a major part of the argument for or against peroxo species hinges on the computed relative energetics of possible redox isomers; this is precisely where the currently used quantum chemical methods, i.e., various approximate DFT functionals, offer the least reliable results. The strong dependence of computed spin state energetics of transition metal complexes on the nature of a chosen density functional approximation and particularly on the percentage of Hartree–Fock exchange that is incorporated in hybrid functionals is well known. This dependence was identified for the relative energies of the various redox isoforms of the S₃ state in all studies discussed above [48,49,50,51,52]. Isobe et al. [48] reported that the Mn(III)-containing peroxo or superoxo forms ranged from significantly less stable to significantly more stable than Mn(IV)₄ forms of the S₃ state, depending only on small variations of the percentage of HF exchange used in the density functional. Using B3LYP with 10% HF exchange the peroxo/superoxo forms were ca. 10 kcal·mol⁻¹ less stable than their oxo–hydroxo model, while when using the original B3LYP with 20% HF exchange the superoxo and peroxo isomers were more stable by ca. 18 and 7 kcal·mol⁻¹ [48]. Corry and O’Malley reported values obtained with the TPSSh functional; with their optimized models the original definition of the functional (10% HF exchange) suggested that the peroxo forms were more than 30 kcal·mol⁻¹ less stable than the most stable oxo–hydroxo form, while increasing the HF exchange to 30% made them isoenergetic [50]. In view of this enormous variability of results, no conclusions can be safely drawn based on energetics.

Moreover, although extreme sensitivity to HF exchange was documented in all cases, the relative energies of the different redox isomers are not similar among the different studies. This suggests that additional factors are at play: (a) different functionals respond differently to the percentage of HF exchange with respect to the predicted relative stabilities of redox isomers; (b) additional methodological details such as treatment of dispersion effects, relativistic corrections, and basis set convergence might contribute significantly; and (c) the size and definition of the structural model for the OEC, the assumptions that enter its construction and the methods used for refining it and for treating its environment play their own decisive role. The latter is important because it determines whether a computational model can be in principle sufficiently representative of the physical system or not. In conclusion, there are independent sources of uncertainty in these calculations, with the erratic behavior of DFT likely being the central problem.

It should be noted that the amount of HF exchange does not necessarily affect significantly computed relative energies in cases of isomerism that do not involve spin state changes and intramolecular redox transformations; however, it does influence the predicted exchange coupling interactions, spin-dependent spectroscopic properties, and computed redox potentials of manganese complexes [102,149,150,151,152]. Benchmarking DFT against experimental energetics for the type of redox isomerism discussed for the S₃ state seems impossible because it would require well-characterized synthetic oligonuclear transition metal systems that exhibit this type of isomerism with precisely determined structures and relative energies. On the other hand, DFT methods can be benchmarked with respect to spectroscopy using reference sets of synthetic compounds with known structure and spectroscopic parameters. In this sense, the evaluation of possible S₃ models on the basis of spectroscopic properties could be considered more reliable than the use of relative energies. Although DFT methods have and will continue to serve well in the treatment of complex transition metal systems, such as the OEC [153,154,155,156,157], there is no clear path towards consistently accurate results when dealing with redox and spin state energetics of such systems.

Accurate wave function based methods would be highly desirable to tackle the problem of redox isomerism in the S₃ state of the OEC. Multireference methods are appropriate for the description of strongly correlated open-shell transition metal systems, but conventional approaches are limited to systems considerably smaller than the OEC. The density matrix renormalization group (DMRG) [158,159] extends the applicability of such methods and can be used for relative energies and spin state energetics of transition metal systems [160,161]. DMRG-based complete active space self-consistent field (DMRG-CASSCF) calculations have been used [162] to compare the relative stabilities of isomeric forms in the case of a synthetic tetramanganese complex [163] of similar size as typical quantum chemical models of the OEC. The method is being actively developed for exchange-coupled systems [164,165,166,167]. Coupling DMRG-CASSCF with a treatment of dynamic correlation might be possible, such as the N-electron valence state second-order perturbation theory (DMRG-NEVPT2) [168,169] that has already been used in the case of a biomimetic manganese complex [165]. On the other hand, single-reference correlated approaches based on coupled-cluster theory would be equally desirable if the systems are not strongly multiconfigurational and the effects of intracluster magnetic coupling are secondary compared to the energetics of electron redistribution associated with redox isomerism. This situation is not uncommon in transition metal chemistry, and coupled cluster theory at the CCSD(T) level has been known to deliver benchmark-quality results [170,171,172], albeit not without limitations [173]. The cost of conventional coupled-cluster implementations would be prohibitive for realistic models of the OEC, but modern approaches that exploit the locality of electron correlation, such as the domain-based local pair natural orbital (DLPNO) approximation [174,175], can be employed. Ideally, these methods would be combined with a QM/MM approach [176,177,178,179,180] to minimize the size of the OEC subsystem that has to be treated at the coupled-cluster level. It is likely that only the competent application of high-level wave function methods on carefully constructed computational models can clarify the uncertainties surrounding the computed energetics of redox isomers in the S₃ state.

7. Conclusions

The S₃ state of the oxygen-evolving complex and the details of the S₂–S₃ transition continue to challenge experiment and theory. The distinct pieces of structural and spectroscopic data still cannot be combined into a unifying model. The vast majority of observations from EXAFS, X-ray absorption and emission spectroscopies, and EPR/ENDOR studies can be rationalized quite successfully with an oxo–hydroxo type of S₃ structure where all Mn ions are present as octahedral Mn(IV). Recent models proposed from XFEL crystallography complicate this picture because they are not consistent with such an oxo–hydroxo form and, more importantly, they are not mutually compatible. One crystallographic model supports a double-oxo type of structure while the other indicates peroxo formation in the S₃ state with Mn reduction in the S₂–S₃ transition. It is unclear if the double-oxo model is as consistent with spectroscopy as the well-studied oxo–hydroxo models. On the other hand, early-onset O–O bond formation before the final transition of the catalytic cycle has been discussed in the past and has received support from recent computational studies. These suggest that a peroxo isoform of the S₃ state can be part of a complex equilibrium that involves different redox isomers of the cluster or, at least, it can be an unstable but still energetically accessible redox form that is catalytically relevant. In terms of the relative energies of Mn(III)₂Mn(IV)₂–peroxo or Mn(III)₃Mn(IV)–superoxo forms compared to Mn(IV)₄–oxo–hydroxo isomers, the results of computational studies are thoroughly inconclusive. Evaluation of peroxo models nevertheless suggests that their geometric and spectroscopic properties do not agree with the available spectroscopic data. Therefore, a peroxo species is unlikely to represent the most stable form of the OEC in the S₃ state and early-onset ground-state O–O bond formation can be excluded. It is suggested that the peroxo-like XFEL crystallographic model is at least in part the result of superposition of different S_i-state structures. It would be premature to exclude the involvement of a peroxo species as a high-energy isoform of S₃ in the catalytic cycle, but there appears no need to invoke it as a working hypothesis unless experimental data emerges to directly support its presence in a population of the S₃ state. It is also clear that the complex details of the S₂–S₃ transition and the heterogeneous nature of the S₃ state still lack a fully satisfying structural rationalization. They both define a frontier in photosynthesis research that has not been conquered yet.