Structural models of the biological oxygen-evolving complex : achievements , insights , and challenges for biomimicry

The oxygen-evolving complex (OEC) in Photosystem II (PS-II) of oxygenic photosynthesis catalyzes the oxidation of water into dioxygen, protons and electrons, a reaction that underpins solar to chemical energy conversion in the biosphere. The inorganic core of the OEC is an oxo-bridged cluster that comprises four Mn and one Ca ions, Mn4CaO5. Deciphering the structure of this cluster and its immediate environment has been the aim of intense experimental efforts that span decades of research. The constantly improving structural definition of the OEC in the last fifteen years has offered opportunities to better understand its properties and function; it has also provided ever clearer and more well-defined targets for biomimetic synthetic chemistry. Here we present a critical overview of the most recent advances in molecular structural models of the OEC, focusing mostly on successful research efforts reported after the availability of atomically resolved crystallographic models of PS-II. We delineate the properties that have been targeted in biomimetic studies and analyze which structural aspects have by now been reproduced in synthetic systems. In combination with in-depth theoretical studies, the availability of novel synthetic structural analogues has led to considerable insight into structure–property correlations despite the lack of catalytic activity. Nevertheless, there are important features of the OEC that remain inaccessible to synthetic chemistry. Principal among them are the unique type of restricted structural flexibility and the highly structured and stable ligand sphere which enable the tightly controlled interplay of geometry, spin state and reactivity that is the hallmark of the OEC.


Introduction
][24][25][26][27][28][29][30] The OEC contains a Mn 4 CaO 5 cluster, 31,32 often discussed in terms of a Mn 3 CaO 4 unit connected with a dangling fourth manganese via one of the unit's oxo bridges and an additional bis-μ-oxo bridge (Fig. 1a).The metal ions are coordinated to mostly carboxylate ligands (side chains of aspartate and glutamate residues), one histidine, and four water molecules or water-derived ligands.4][35][36][37][38] Driven by photoinduced charge separation at the reaction center chlorophylls of PS-II, the OEC cycles from the S 0 state with individual manganese oxidation states of Mn(III) 3 Mn(IV), via a series of metal-centered oxidation to the all-Mn(IV) S 3 state; the fourth oxidation, which may or may not be metal-centered, leads to a transient S 4 state that evolves O 2 and resets the catalyst to S 0 .
Even the above cursory structural description of the OEC is in fact the combined product of enormous research efforts pursued internationally over many years.For example, although various structural elements of the OEC were known for a long time and techniques ranging from EXAFS to EPR spectroscopy provided important information about the possible arrangements of the metal ions, the first crystallographic model of PS-II only appeared in 2001. 39During the 1980s and 1990s the elemental composition and the fact that the manganese ions should be close enough and magnetically interact-ing, and hence at least partially connected in an uncertain topology by an uncertain number of oxygen and/or carboxylate bridges pretty much summarized the available information about the structure of the OEC.During this time hypotheses regarding the structure of the OEC were stimulated by molecules that were synthesized and structurally characterized, i.e. the availability of any given connectivity pattern would inspire speculation about whether this pattern might mimic the OEC.This period of time for synthetic inorganic chemistry was characterized by the absence of specific targeted structural motifs: the topology of the OEC core was unknown so there was no directed effort towards a synthetic structural goal.By surveying the literature of that period one would be excused to form the impression that any molecule that contained more than one Mn could be considered a potential mimic of the OEC.Regarding the suggestions about the structure of the OEC itself, the absence of concrete structural data behind the ideas circulated at the time led Wieghardt to characterize the then available models as "an aesthetically pleasing combination of experimental facts, thoughtful deduction, and a lot of imagination". 40mportant and beautiful chemistry resulted this way nevertheless, vastly enriching the library of manganese complexes, especially of oligonuclear compounds.Early synthetic endeavors encompassed oxo-bridged mixed-valent dimeric manganese complexes, and gradually extended to achieve successful preparation and characterization of manganese complexes of varying nuclearity, composition and architecture.Manganese complexes of this time and the insights gained from them have been extensively reviewed. 7,10,40,43,44The main focus of the present review will instead be on more recent achievements and on synthetic efforts that were expressly guided by a structure-oriented biomimetic approach inspired by modern knowledge on the topology of the OEC.
The protein crystallography era was inaugurated in 2001 by the first X-ray diffraction model of PS-II. 39This low-resolution model (3.8 Å) could not offer an atomistic model of the inorganic core, but for the first time it looked like the structure of the OEC was within reach.An important milestone was reached in 2004 with the 3.5 Å resolution model of Ferreira et al., 45 known more colloquially as the "London model".This offered the first, incomplete yet daringly specific suggestion about the topology of the inorganic core, proposing the presence of a Mn 3 CaO 4 cubane subunit with a fourth Mn ion attached to one of the four O bridges of the cube (Fig. 2a).6][57][58][59][60][61][62][63][64] The first atomicresolution (1.9 Å) model of the OEC was reported in 2011 by Umena et al. 41 This model established the contemporary view of the inorganic core with the five oxo bridges and altered connectivity compared to the original Ferreira et al. model (Fig. 2b).Still, a 1.95 Å resolution model that is free from radiation-damage [64][65][66][67] and can be safely attributed to predominantly 42,68,69 the S 1 state of the OEC was only reported in 2015. 70g. 1 (a) The manganese-calcium cluster of the oxygen-evolving complex and its protein environment. 41See Fig. 2b for a schematic diagram and labelling of the inorganic core.(b) The cycle of S i states with structural, individual Mn oxidation states, and total spin state assignments. 42g. 2 Schematic connectivity diagram of the London model for the OEC core (a) 45 and of the current model for the Mn 4 CaO 5 cluster (b). 41,70nspired by the 2011 crystallographic model, 41 a staggering volume of subsequent experimental and theoretical studies (too many to recount here) began to refine it and address additional structural and electronic aspects of the OEC in various S i states.A landmark achievement in structural insight was the structural interpretation in 2012 of the two well-known distinct EPR signals of the S 2 state (a multiline signal at g ≈ 2 arising from a spin S = 1/2 state and a signal at g ≥ 4.1 arising from an S = 5/2 state) in terms of valence isomeric forms of the inorganic core that differ in their oxo-bridge connectivity. 71][101][102][103] A point that is important to clarify from the outset because it is highly relevant for the present review concerns the precise bonding topology in the inorganic core.The description of the cluster in terms of a "3 + 1" model for the arrangement of Mn ions (a topology already included in the multitude of possible interpretations of EXAFS data for a long time 55 ) is intimately connected with the analysis of the S 2 state multiline EPR signal by Britt and coworkers. 104The seemingly analogous description of the cluster in terms of a cuboidal oxo-bridged Mn 3 Ca unit plus a "dangler" Mn ion reflects the original London model of the inorganic core (Fig. 2a), but strictly speaking this terminology is not entirely appropriate for current models of the OEC-at least not for the connectivity in the lower S i states.In other words, the (still valid in most cases) 105,106 "trimer-monomer" description of the magnetic topology of the OEC and the "cubane-dangler" description of the geometric structure are neither synonymous nor equally applicable.Besides, it is already obvious from the core models shown in Fig. 1b that the inorganic core in general does not contain a "proper", fully bonded Mn 3 CaO 4 cubane in most of the observable states.This point will prove important in the discussion of current synthetic models.
It is useful to keep the above evolution of structural ideas and models in mind when reviewing the efforts of synthetic chemists to create structural analogues of the OEC, because for a long time these efforts were inspired by models that eventually proved to be inaccurate or of only indirect relevance to the current detailed view of the OEC.Pecoraro and Hsieh appropriately remarked on this point: "at times, it seems as if nothing in photosynthetic research stands the test of time…". 9n the present review we wish to provide a critical perspective on the recent evolution in the geometry, electronic structure and associated properties of synthetic systems from recent progress towards improved structural mimics of the OEC.At this point in time there is no convergence of structural analogy and water-oxidizing ability in synthetic models.This means that existing Mn complexes that have been implicated in oxygen evolution do not, in general, resemble the OEC in terms of geometric structure.1][112] Given that such non-biomimetic manganese-based systems and their chemistry have been extensively reviewed in recent literature, [18][19][20][21][113][114][115][116] we will not discuss them here. Similarl, we will not address heterogeneous systems, 17,[117][118][119][120][121] although it should be recognized that specific structural motifs related to the OEC can be present in Mn or Mn/Ca oxides.17,122 Our point of departure is a series of synthetic tetramanganese clusters.From the first generation of oxo-bridged tetramanganese clusters the presentation of systems proceeds to oxomanganese cubanes incorporating calcium and the description of structures where a fifth ion is attached to the Mn 3 Ca unit.Through experimental characterization and the significant input of theoretical chemistry many of these structural analogues of the OEC have already contributed significant insights into the properties of the biological system.

Targeted structural features
Before we proceed it is useful to highlight a few salient properties of the OEC that serve as individual or combined targets for structural biomimetic chemistry.These include: • The stoichiometry of four manganese and one calcium ions.
• Incorporation of Ca 2+ within an oxo-bridged metal framework.
• A Mn 3 CaO 4 substructure that may or may not be present as a fully bonded unit in some of the S i states depending on the Mn oxidation states.
• A fourth Mn ion ("dangler Mn") external to the above cuboidal unit, connected with it via oxo bridges.
• Almost exclusively carboxylate and water-derived ligands.
• In addition to the above structural features, a model should contain the physiologically relevant oxidation states of Mn ions (exclusively III and IV) 42 and the ligand framework would ideally support access to multiple oxidation states.
All of the above structural features have important implications for the electronic structure of the cluster, its magnetic and spectroscopic properties, and ultimately for its catalytic function, although the latter cannot be meaningfully considered in isolation from the protein matrix of the OEC and the rest of the PS-II machinery.

Tetramanganese complexes
First we would like to present a few tetranuclear Mn complexes that have been historically important in biomimetic synthetic chemistry, even though most of them would not be recognized today as direct mimics of the OEC.A variety of systems with metal oxidation states ranging from Mn(II) 4 to Mn(IV) 4 pervade the literature of tetranuclear manganese chemistry.Reviews on tetranuclear Mn-oxo clusters provide a classification in terms of commonly observed and structurally distinct patterns shown in Fig. 3. 7,10,123 One of the earliest models with a tetramanganese motif was the Mn(IV) 4 O 6 4+ adamantane stabilized by three chelating 1,4,7-triazacyclononane ligands (Fig. 4a). 124The complex by Wieghardt and co-workers shows weak ferromagnetic interaction between Mn ions that changes to weak antiferromagnetic upon protonation, as observed by Hagen et al. 125 Similar adamantane-shaped tetranuclear complexes were reported by Armstrong and co-workers. 126 Mn 4 (µ 3 -O) 4 cubane core has been one of the early suggestions for the OEC structure in different S i states of the catalytic cycle. 128,1291][132] Magnetochemistry revealed a high-spin (S = 9/2) ground state with well separated excited states resulting from antiferromagnetic interaction between the unique Mn(IV) and the three ferromagnetically coupled Mn(III) ions, [132][133][134] while the near-parallel alignment of the three Jahn-Teller axes of the Mn(III) ions leads to high magnetic anisotropy. 133,134Lowtemperature X-band EPR spectra showed two sets of signals, a broad peak at g ≈ 6 and another well resolved 16-line signal with 55 Mn hyperfine structure centered at g ≈ 2, reminiscent of the two EPR signals in the S 2 state of the OEC. 131,135ver the following years analogous compounds with varying terminal ligands (Cl − , pyridines, acetylacetonates, dibenzoylmethane, etc.) and the anionic µ 3 -X positions ( 7][138][139][140][141][142][143] Some of them, for example a compound reported by Wang et al., were also shown to mimic the S 1 to S 2 oxidation step. 142][146] Despite being a mixed valent species, the compound Mn 4 O 4 L 6 , (L = Ph 2 PO 2 − ), showed almost equivalent Mn-O bond lengths, which was attributed to valence delocalization at elevated temperature (298 K).Lowering the temperature to 150 K led to a small differentiation of Mn-O bonds 147 and the bond length inequivalence was also shown to depend on the ligand L. 148,149 The crystal structure of the singly oxidized product of the complex [Mn 4 O 4 ] 7+ demonstrates a trigonal distortion compared to the tetragonal symmetry of the parent complex, i.e.
[Mn 4 O 4 ] 6+ . 150In this oxidized form the Mn(III)Mn(IV) 3 valence distribution was assigned to the manganese ions, although no significant axial tetragonal distortion is observed for Mn(III).A similar Mn 4 O 4 cubane with two Mn(III) and two Mn(IV) was prepared by Kanady et al. 151 An exciting feature of the Dismukes cubane is that it can undergo photo-rearrangement to yield O 2 and a diarylphosphinate ligand and ultimately decays to a butterfly-shaped product (Fig. 5).The idea of a reversible cubane/ butterfly rearrangement was actually one of the early proposed mechanisms for the catalytic cycle of the OEC and the butterfly-shaped structure was one of the suggested structural models for the lower S i states. 129,152][155] Another example of the butterfly type of complex is the series   oxidation states from Mn(II) 2 Mn(III) 2 to Mn(III) 4 , which contains a non-planar Mn 4 unit, with two Mn atoms forming a central Mn 2 O 2 diamond core and the other two Mn ions being ligated to the oxo bridges (Fig. 6). 156,157The presence of two types of Mn-Mn distance in the OEC inferred from EXAFS, at ca. 2.7 Å and 3.3 Å, 40 is fulfilled by the butterfly-shaped complex that contains two different Mn-Mn distances of 2.85 Å and 3.30 Å.9][160][161][162][163][164] It should be noted that without the presence of at least one Mn(IV) such complexes do not correspond to any one of the physiological states of the OEC.
The "dimer of dimers" geometry has been another possible model of the OEC discussed on the basis of EXAFS data. 56,57his motif was influential and enjoyed popularity for a long time, until the 3 + 1 arrangement of the Mn ions began receiving stronger support. 39,104The archetypal form (Fig. 3) involves two Mn 2 O 2 rings bridged by an oxo, which would justify the presence of both short and long Mn-Mn distances as deduced from EXAFS measurements of the OEC.6][167][168][169] These are discussed in the comprehensive review by Mukhopadhyay and Armstrong. 7Fig.7a shows an example of this type of core, in this case a complex by Chen et al. 169 that features two μ-O bridged Mn(IV) 2 O 2 units with each Mn coordinating a terpyridine ligand.
A closely related type of topology is that of three joined bisμ-oxo units.The example of the Mn(IV) 4 compound reported by Philouze et al., 170 shown in Fig. 7b, utilizes bipyridine ligands and comprises a chain of bis-μ-oxo units with Mn-Mn distances ca.2.75 Å. Antiferromagnetic coupling between the Mn ions leads to a diamagnetic (S = 0) ground state.This complex gained high relevance to the OEC because under γ-ray irradiation at cryogenic temperatures it is reduced to the Mn(IV) 3 Mn(III) form that shows an 18-line X-band EPR signal similar to the multiline signal of the S 2 state of the OEC. 167ence the compound serves as a spectroscopic mimic for understanding the S 2 state EPR multiline signal in the OEC 135 and has been successfully employed in the evaluation of quantum chemical methods that were developed to target the spin states and EPR parameters of oligonuclear manganese systems. 171ll of the complexes described above are characterized by a high degree of symmetry and the presence of predominantly N-donor ligands, whereas the core of the OEC is in fact asymmetric and ligated by carboxylates and only one N-donor.In the following we describe how the efforts to introduce calcium to the cluster led to more diverse structures and eventually to the synthesis of carboxylate-bridged Mn 3 CaO 4 cubanes.

Manganese-calcium cubanes
The calcium ion is indispensable for water oxidation in the OEC and specifically for advancement to the S 3 state of the catalytic cycle. 172Its close association with the Mn ions first became apparent from EXAFS, which suggested a Mn-Ca distance of 3.4 Å. 173 Gerey et al. have very recently compiled a comprehensive review of manganese-calcium heterometallic compounds; 14 here we focus on selected examples.A tetramanganese structure attached to Ca was reported by Jerzykiewicz et al., 174 but the first high-valent Ca-incorporating oxomanganese cubane was prepared by Christou and co-workers-albeit as a substructure of a higher nuclearity complex.The structure consists of a Mn 13 Ca 2 core held together by bridging oxo, hydroxo and methoxy ions and showed a Mn-Ca distance of ca.3.5 Å (Fig. 8a). 175,176The whole structure can be visualized as a combination of four subunits, two of which are Mn 3 CaO 4 cubanes attached by Mn-O linkages to two other Mn 3 O 4 .Thus, a portion of the compound, the Mn 3 CaO 4 cubane subunit linked to a fourth manganese center via an oxo bridge, resembles the OEC.
Chen et al. reported a family of heteronuclear Mn(IV)Caoxido complexes with carboxylate ligands which contain fused manganese/calcium cuboidal moieties and water molecules on Ca 2+ similar to the OEC of PSII. 177The complex contains three [Mn 2 Ca 2 O 4 ] distorted cubanes sharing a trigonal bipyramidal [Ca 2 O 3 ] central motif (Fig. 8b).Christou's group also reported the synthesis, structure and physical properties of a diamagnetic Mn(III) 4 Ca complex possessing the correct 4 : 1 Mn : Ca ratio, but apart from the stoichiometry the complex can hardly be regarded as a structural mimic of the OEC. 178Other Mn/Ca complexes with exact Mn 4 Ca stoichiometry that are not topological analogues of the OEC were reported by Powell and co-workers, but in lower Mn oxidation states. 179he first distinct cuboidal Mn(IV) 3 CaO 4 unit was synthesized by Agapie and co-workers (Fig. 9). 1511][182] In all compounds the approximately octahedral environment of Mn ions is stabilized by coordination of three alkoxide groups and three pyridine groups attached to an appropriately designed 1,3,5-triarylbenzene spacer.In the lanthanoid series, the crystal structure of Dy 3+ -substituted cubane also shows two water molecules coordinated to Dy 3+ , reminiscent of the two Ca-bound water molecules in the OEC (Fig. 1a and 2b). 1824][185][186][187][188][189][190][191][192][193] Although an architecture containing a Mn 3 CaO 4 cubane attached to another manganese ion was discussed already (Fig. 8), these complexes had overall much higher nuclearity than the biological cluster.Similarly, an example of incorporated cubane attached to another metal comes from Chen et al. (Fig. 10). 194nstead of calcium the complex incorporates strontium and the fifth ion, in this case another strontium, does not adopt the same connectivity mode as in the OEC, being rather a component of the second, similar cubane.The core of the complex is composed of two Mn(IV) 3 SrO 4 units connected by one µ 2 -oxo and two µ 4 -oxo moieties (Fig. 10).
A complex with a unique dangling Ca 2+ ion attached to a distinct Mn 3 Ca cubane was first reported by Mukherjee et al. (Fig. 11). 195The complex is composed of an asymmetric Mn(IV) 3 CaO 4 core where the metal ions are bridged exclusively by carboxylate/carboxylic acid ligands.The external seven-coordinate Ca 2+ is connected to one of the oxo bridges and to six carboxylates, three of which bridge it to Mn ions of the cubane.Dominant ferromagnetic coupling results in a highspin, S = 9/2 ground state.The magnetic and spectroscopic (EPR) properties of this molecule have been carefully characterized, 195 and thus the complex served as an invaluable reference in quantum chemical analysis of the electronic properties of manganese-calcium cubanes. 196gapie and co-workers described a rational way to increase the basicity of µ 3 -oxo ligands by modulating ligand scaffolds and desymmetrizing the Mn 3 CaO 4 cluster. 181In this way they could obtain a Ag-Mn 3 CaO 4 complex, where the dangling Ag + is linked to the cubane via a µ 4 -oxo, a µ 2 -alkoxide, and a pyridine (Fig. 12). 181Thus, the synthesis of [Mn(IV) 3 CaAgO 4 ] from [Mn(IV) 3 CaO 4 ] provided an example of a systematic approach for the synthesis of the asymmetric pentanuclear core structure of the OEC.
The latest addition in this series came from Zhang's laboratory; it contains a manganese ion attached to a Mn 3 CaO 4    cubane complexes and represents currently the closest mimic of the OEC. 197This is the first complex to contain a manganese ion attached to the Mn 3 CaO 4 cuboidal unit, thus correctly reproducing the metal stoichiometry of the biological cluster (Fig. 13).Importantly, it was synthesized with a Mn(III) 2 Mn(IV) 2 oxidation state distribution that mirrors that of the S 1 state of the OEC and exhibits similar redox properties as the OEC, being able to span several oxidation states.This is a key feature that differentiates this complex from the other cubaneincorporating complexes.Access to multiple oxidation states had previously been demonstrated with a pentanuclear manganese helicate complex, which however does not progress beyond Mn(III) 5 within its original ligand framework. 198,199In the one electron oxidized state, the complex by Zhang et al.
shows two simultaneous EPR signals, a major one at g ≈ 4.9 and a secondary multiline signal at g ≈ 2, which are reminiscent of the two signals in the S 2 state of the OEC. 197he limits of structural analogies should also be recognized so that future challenges can be defined: comparison of the core in Fig. 13 with that in Fig. 2 shows that this synthetic model still does not exactly reproduce the stoichiometry and the connectivity of the OEC.Thus, similarities in observable properties should not be automatically assumed to have the same structural origin.Nevertheless, this complex satisfies many of the target points listed in the previous section and represents the current pinnacle of structural biomimicry.

Discussion of specific examples
In the preceding section we traced, in an inevitably selective manner, the historical development of structural models for the OEC.Here we will discuss in greater depth selected models that incorporate Mn 3 CaO 4 cubane units and discuss the insights obtained from them so far in terms of correlating structure and composition with observed properties.

Mn 3 CaO 4 and Mn 3 CaO 4 -Ca complexes
We discuss these complexes from the Agapie and Christou groups together because despite the fundamentally different ligand framework, the electronic structure and properties of the inorganic core are similar and are principally defined by the three Mn ions of the Mn 3 CaO 4 cubane.
The average Mn-Mn, Mn-Ca and Mn-µ 3 -O distances in the [Mn 3 CaO 4 ] 6+ core of the complex by Kanady et al. (Fig. 9) as obtained from X-ray diffraction data are 2.834 Å, 3.231 Å and 1.872 Å, consistent with the presence of three Mn(IV) ions. 151omparison of these distances with experimental data (EXAFSderived distances and crystallography) on the S 1 state of the OEC reveals that the corresponding distances are longer in the natural system.The shorter Mn-Ca distances in the synthetic complex compared to the S 1 state of the OEC presumably stem from the constraints imposed by the bridging acetate ligands.However, unlike Mn(IV) ions in the synthetic cubane, the presence of Jahn-Teller distorted Mn(III) in the S 1 state of OEC can also be the source of this difference. 14In the S 2 state of the OEC, the cluster exists in two interconvertible forms, the open cubane form with the Mn(III) located at the Mn1 site within the Mn 3 Ca unit, and the closed cubane form with a dangling Mn(III) and a "genuine" Mn 3 (IV)CaO 4 cubane. 71These two valence isomers can be oxidised to the all-Mn(IV) S 3 state, 82 subject to appropriate ligand binding and deprotonation. 74ence, the comparison of the synthetic Mn(IV) 3 CaO 4 core with the OEC only finds relevance in the closed-cubane form of the OEC in the S 2 and S 3 states.
The asymmetric cubane bound to an external Ca ion, [Mn(IV) 3 Ca 2 O 4 (O 2 CBu t ) 8 (Bu t CO 2 H) 4 ], reported by Mukherjee et al. 195 (Fig. 11) mirrors the OEC with respect to the peripheral carboxylate ligands and obviously the Mn 3 CaO 4 subunit, which as noted above is relevant for the closed cubane forms of the S 2 and S 3 states of the OEC.The attachment of the external Ca causes a lowering of the threefold symmetry of the [Mn 3 CaO 4 ] cubane, leading to variance in the Mn-Mn separation and slight changes in the Mn-Ca distances.Whilst the complex by Kanady et al. 151 features almost equivalent Mn-Mn distances of ca.2.83 Å, here the Mn-Mn distances within the cube are 2.74 Å and 2.86 Å, 195 highly reminiscent of the 2.73 Å and 2.82 Å Mn-Mn distances in 2 : 1 ratio suggested from EXAFS on the S 2 state of the OEC. 200The Mn-Ca separation of 3.39-3.45Å within the cubane is similar to the distances (3.3-3.4Å) in the crystallographic model of the S 1 state of the OEC and the EXAFS-deduced average distance (ca.3.4 Å). 63,70 Mn-µ 3,4 -oxo bond lengths are also comparable to those in the OEC.
A DFT study on the Mn 3 CaO 4 complex of Kanady et al. 151 revealed small splitting between high spin and low spin states of the complex, consistent with small values (≤8.0 cm −1 ) of the pairwise exchange coupling constants (Table 1). 196The weak ferromagnetic interaction of manganese spins indeed leads to closely spaced states in the spin ladder with a total high-spin (S = 9/2) ground state.As discussed earlier, the closed cubane form of the OEC in the S 2 and S 3 states adopts the same valence state distribution and geometry.However, despite little differences in the Mn-Mn distances in the synthetic system compared to the OEC, the synthetic model shows much weaker magnetic coupling between manganese ion pairs com-Fig.13 The Mn 3 CaO 4 -Mn complex of Zhang et al., 197 with schematic depiction of the inorganic core in analogy to Fig. 2.
pared to the OEC in either the S 2 or the S 3 closed cubane states (intra-cubane J values for the latter are reported to be up to 36 cm −1 ). 71,82The presence of an external dangling Mn ion in the OEC obviously acts as a major source of this distinction, as can be understood from the study of magnetic interactions in oxo-bridge protonated species. 1965][206][207][208] The constrained Mn(IV)-O-Mn(IV) bond angle also disfavors the overlap of metal-ligand orbitals resulting in the damping of superexchange.This is reflected in the large positive value of the exchange coupling constants in the native OEC.However, the overall ferromagnetic coupling between the manganese sites leading to a S = 9/2 ground state in the synthetic cubane is consistent with the highspin situation within the closed-cubane core of the OEC in the S 2 and S 3 states. 71,82he structural asymmetry induced by the external calcium ion in the complex of Mukherjee et al. has a strong effect on magnetic properties.Magnetic susceptibility data suggests strong ferromagnetic coupling among the manganese ions resulting a S = 9/2 spin ground state.The pairwise exchange coupling constants obtained both from fitting of the data and from theoretical calculations on the crystallographic model correspond to two moderately strong ferromagnetic and a weaker antiferromagnetic interaction (Table 1).
Both complexes serve to demonstrate that the Mn(IV) 3 CaO 4 cube is an intrinsically high-spin unit.Christou and coworkers related the sign of J values to the Mn-O-Mn bond angles. 195s shown by Krewald et al., 196 the effect of the angle on superexchange can be visualized using the concept of corresponding orbitals 209 between pairs of Mn ions.Although this is normally applied to dimeric systems, a pictorial view of the magnetic orbital interactions in the cubanes can be obtained by diamagnetic substitution, where one of the three Mn ions is replaced by the diamagnetic Ge 4+ .This allows the corresponding orbital analysis to be carried out for the two remaining Mn centers as in the case of a simple dimer, and hence to obtain orbital pairs such as those shown in Fig. 14.This analysis showed that the Mn-O-Mn angles within the cubane are such that the overlap between the magnetic orbitals is minimal, explaining the dominant ferromagnetic coupling.
The magnetic coupling situation in these complexes can be described by "spin maps", which indicate the ground state spin resulting from possible combinations of the three pairwise exchange coupling constants.Fig. 15 shows an example for a system of three coupled local S = 3/2 spins corresponding to three Mn(IV) ions.The two complexes discussed here fall into the S = 9/2 areas of the spin maps, although in one case (Mn 3 CaO 4 cubane by Kanady et al.) all J couplings are weakly ferromagnetic and in the other (Mn 3 CaO 4 -Ca complex by Mukherjee et al.) there are two strong ferromagnetic and one   weak antiferromagnetic coupling constants.In either case, for a complex of this type to fall outside the S = 9/2 region of the map would require significant asymmetry and hence structural distortions to an extent that in practice would probably mean disruption of the cubane framework.
A relevant point here is that reduction of the cubane to produce a mixed valence Mn(III)Mn(IV) 2 complex, which introduces axial Jahn-Teller elongation at the Mn(III) site, was suggested to be insufficient to open up the structure like in the S 2 state of the OEC. 196This strongly suggests that the opening of the rigid framework of the cubane towards a more OEC-like topology is non trivial and depends on a number of factors beyond the Mn oxidation states.
The theoretical study further found the bulky t Bu group in the case of the Mn 3 CaO 4 -Ca complex to be relevant for the magnetic topology of the complex, 196 because in models where the t Bu group was replaced by a methyl group, all three exchange coupling constants were predicted to be positive.The strong coupling sets the first excited S = 7/2 spin state much higher (57 cm −1 and 68 cm −1 from experimental fitting and computation respectively) above the S = 9/2 ground spin state, which is similar to the situation in the closed-cubane core of the OEC in the S 2 and S 3 states. 71,82he Mn 3 CaO 4 -Ca complex was also studied by EPR and ENDOR spectroscopies.Complicated hyperfine splitting is seen, as in other oligonuclear Mn(IV) containing complexes. 14,105To get a clear picture of the hyperfine splitting due to the three Mn nuclei, obscured in the inhomogeneously broadened EPR line, the 55 Mn ENDOR spectrum was collected.Very low values for the anisotropic component of the hyperfine coupling constant were observed, which match well to other octahedral Mn(IV) systems, including the late S i states of the OEC. 82,105Experimental values of the isotropic hyperfine coupling constants are in agreement with computed values 195,196 and are very similar for all Mn(IV) ions, with only small deviations consistent with the structural asymmetry of the cubane caused by the external Ca (Table 2).

Substituted Mn 3 AO 4 cubanes
The role of calcium in the OEC has been a question of perennial interest that, in the absence of detailed understanding of the catalytic mechanism, remains without a convincing answer.Using their Mn 3 CaO 4 cubane complexes as a platform, Agapie and coworkers contributed important results from synthetic models as they developed and studied a series of calcium-substituted Mn 3 AO 4 complexes (A = Mn 3+ , Sr 2+ , Zn 2+ , Sc 3+ , Y 3+ , Gd 3+ , Ln 3+ ).
In all cubanes where Ca has been substituted with another cation, apart from the scandium complex Mn(III)Mn(IV) 2 ScO 4 , the manganese ions remain as Mn(IV), consistent with Mn-O bond distances of 1.821-1.913Å.The Mn(III) center in the scandium complex shows an axial elongation in metal-ligand bond lengths (2.134-2.142Å) and the reduced Gd 3+ complex with Mn(IV) 2 Mn(III) composition also displays an axial elongation with Mn(III)-O distances of 2.169 and 2.163 Å, both cases typical of an axial Jahn-Teller distortion due to population of a metal-ligand σ-antibonding orbital of metal d z 2 origin. 182The zinc complex shows similar structure as that of the Ca 2+ and Sr 2+ complexes but due to its smaller ionic radius the zinc center cannot bind solvent molecules.The symmetry of the complex has been systematically lowered by substituting the THF ligand with [ON 4 O] 2− , which results in a broader range of Mn(IV)-Ca and Mn(IV)-Mn(IV) distances. 181heoretical studies 210 on these models similarly suggest that the Mn 3 O 4 subunits of the Mn 3 AO 4 series in both the oxidized and reduced forms show very limited variation, in contrast to the A-Mn and A-O distances which essentially reflect the differences in ionic radii of the cations A n+ .The geometries of the oxidized and reduced form also differ only in the Jahn-Teller elongation of the Mn(III) associated axis, while the others remain almost the same.This implies a predominantly ionic interaction between the redox-inactive A n+ metal and the Mn 3 O 4 framework.
Of relevance at this point is a Ca XAS study that detected significant change in the Ca K-pre-edge XAS data from Mn(IV) 3 to Mn(IV) 2 Mn(III), which was related to the lengthening of the Mn(III)-O bonds. 211The longer bonds around the Jahn-Teller distorted Mn(III) ion in the reduced system imparts small changes in the Ca-bound bond distances and bond angles, which presumably lower the Ca 3d-2p mixing as reflected in ca.23% lower pre-edge intensity.In terms of reactivity, the manganese-only cubane Mn 4 O 4 was shown to be more reactive towards ligand exchange than the CaMn 3 O 4 and ScMn 3 O 4 complexes.This enhanced activity can be attributed to the presence of two Mn(III) sites in the Mn 4 O 4 cubane, which imparts lability related to the presence of two Jahn-Teller axes.In the other two compounds all manganese ions are Mn(IV). 44imilarly, Mn(III) 2 Mn(IV) 2 O 4 is more reactive in oxygen atom transfer compared with Mn(IV) 3 CaO 4 because this requires dissociation of an acetate ligand that renders a Mn ion five-coordinate, a situation that is possible for Mn(III) but unfavorable for Mn(IV). 212Similar conclusions regarding the higher reactivity of the all-Mn cubane versus the Mn 3 CaO 4 one were reached from computational studies that investigated hypothetical water oxidation pathways. 213he original Mn 3 CaO 4 compound shows quasireversible reduction to Mn(IV) 2 Mn(III)CaO 4 at −940 mV versus Fc/Fc + in DMA, whereas the all-Mn cubane shows a quasireversible reduction at −700 mV in similar conditions.These data suggest that the presence of redox-inactive Ca may facilitate the formation of species with higher oxidation states at lower potential.However, this comparison is not entirely convincing because different redox couples are involved, i.e.Mn(IV) Mn(III) 3 O 4 /Mn(IV) 2 Mn(III) 2 O 4 in case of the all-manganese cubane, and Mn(IV) 2 Mn(III)CaO 4 /Mn(IV) 3 CaO 4 for the calciumcontaining cubane.The reduction potentials of the Ca and Sr complexes are practically the same, whereas the reduction potential of the Zn complex is more positive (E 1/2 = −630 mV), despite having the same total charge as that of the Ca and Sr complex.Similarly, despite the same charge, the reduction potentials of Sc and Y complexes differ by ca.200 mV.The fact that the Ca and Sr compounds have the same redox potential has an obvious relevance for the OEC, which can function catalytically only with these two cations. 44 major outcome of the studies by the Agapie group was the identification of a linear correlation between the Lewis acidity of the redox-inactive cations (measured in terms of the pK a of their aquo complexes) and the reduction potential of the clusters (Fig. 16a).This points to a role of the redox-inactive metal cation in fine-tuning the redox potential of the OEC in biological water oxidation.The positive shift in redox potential with increasing Lewis acidity is interpreted as the increased electronwithdrawing effect upon the µ 3 -oxo ligands, which stabilizes the more reduced manganese oxidation state.On the other hand, increased number of oxo ligands per redox active metal site helps to stabilize higher oxidation states by providing an electron-rich environment.180,214 Additionally, in case of the Ln 3+ cubanes the reduction potential is reduced with increase in the ionic radii and subsequent decrease in the Lewis acidity.182 A recent computational study reproduced the correlation between Lewis acidity and reduction potential.210 However, no such correlation was found for models of the OEC in the S 1 -S 2 (Fig. 16b) and S 2 À S 2 Y • Z transitions.The theoretical analysis of the Mn 3 AO 4 series of compounds and their comparison with the biological cluster reveals that the geometric relaxation energy for the cubane models upon ionization hardly varies across the series of A n+ cations, whereas their vertical ionization energies vary systematically with the pK a values of the aquo-A n+ cations.By contrast the OEC, modeled with the same range of A n+ cations, shows a completely non-systematic variation in geometric relaxation energy from S 1 to S 2 or from S 2 À S 2 Y • Z , while the change in vertical ionization energy depends entirely on the charge of A n+ and not on the Lewis acidity (Fig. 17).
These results illustrate that the flexible core and first coordination sphere of the OEC can adopt a multitude of closely related geometries, for example by rearranging the hydrogen-bonding network of residues with structural waters, and/or adopting alternative orientations of water, amino acid side chains, etc. when exposed to structural perturbations induced by redox-inactive metal substitution.By contrast, the structurally rigid synthetic models show a markedly different response as a result of the structurally rigid hexadentate ligand scaffold, enabling "second-order correlations" to emerge.
In turn, this suggests that the attribution to the Ca 2+ ion of a role as regulator of redox potential in the OEC is not straightforward.Other ideas have been advanced in this respect, for example in water delivery to the active site, 72 in O 2 release, 215 and in fine-tuning the hydrogen bonding network that affects the properties of the redox-active tyrosine and its tyrosyl radical form. 81 3 CaO 4 -Mn complex An impressive step in the evolution of structural models of the OEC is the asymmetric complex [Mn 4 CaO 4 (Bu t CO 2 ) 8 (Bu t CO 2 H) 2 ( py)] (Bu t : tert-butyl; py: pyridine) (Fig. 13), by Zhang and co-workers.197 The structural similarity between this complex and the OEC is portrayed through similar metalmetal and metal-ligand distances.All metal ions are pairwise connected by a bridging oxo group as well as a bridging car-   boxylate group, which matches the pattern in the biological system.Bond-valence sum analysis of the complex suggested a Mn1(III)-Mn2(IV)-Mn3(IV)-Mn4(III) valence distribution, in complete analogy with the OEC in its dark-stable S 1 state.Mn-Mn distances also agree well with recent EXAFS 36,63 and XFEL data on the OEC.70 Nevertheless, this complex is still not a precise mimic of the OEC.70 A comparison of Fig. 2 and 13 reveals very clearly that the complex is instead an accurate synthetic realization of the Ferreira et al. model of the OEC.45 Like the older crystallographic model, the complex lacks the additional oxo bridge (O4 in the core of the OEC as depicted in Fig. 1 and 2) between the dangling Mn4 and the Mn3 ion; in the synthetic model this is substituted by a bridging carboxylate group.Furthermore, the bonds between the µ 4 -oxo and the associated metal ions are significantly shorter in the synthetic complex (1.85, 1.85 and 2.28 Å) relative to corresponding bond lengths in the S 1 state of the OEC (2.3, 2.2 and 2.7 Å) 70 despite the same oxidation states of the Mn ions.In addition, the number of peripheral carboxylate bridges is six in the synthetic complex compared to ten in the OEC.14 The distance between the terminal Mn ions, Mn1 and Mn4, is also significantly shorter in the model (3.59 Å) compared to the native OEC (4.89-4.97Å). 216 All of the above are different manifestations of a fundamental characteristic the distinguishes the synthetic model from the OEC: the fact that it is highly compact as a result of a rigid Mn 3 CaO 4 cubane subunit, a part of the structure that is not formally present as a distinct structural unit in the S 1 state of the OEC.Another difference is that the Jahn-Teller axes of the terminal Mn(III) ions are found to be oriented in a mutually perpendicular fashion, in contrast to the collinear orientation of Jahn-Teller axes in the S 1 state of the OEC.Finally, we note the absence of any water or water derived ligands at the Ca and any of the Mn ions.However, exchangeable ligands at these sites do allow for the possibility of water coordination under appropriate conditions.
7][218] Computed exchange coupling constants from broken-symmetry DFT indicate that the ground spin state of the complex is S = 1, with low lying spin states within the range of 10 cm −1 . 217,218This is in contrast to the S = 0 ground spin state of the OEC. 42This difference can be correlated with the much stronger antiferromagnetic coupling between the Mn3-Mn4 couple in the OEC, induced by the presence of the additional oxo bridge.The computational studies showed that the complex can access total oxidation states that correspond to the S 0 -S 3 states of the OEC in terms of Mn oxidation states, Mn(III) 3 Mn(IV) to Mn(IV) 4 , with limited structural rearrangements.
More fascinating than geometric aspects are the various physicochemical properties of the complex that resemble those of the OEC much closer than any previous structural model.One of them is its electrochemical behavior.In its neutral form it resembles the S 1 state of the OEC by requiring ca. 1 eV for one-electron oxidation.Most interestingly, the cyclic voltammogram of the complex in a mixture of organic solvents shows that the system can accumulate oxidation equivalents in a way similar to the OEC: reversible transitions were noted between oxidations states that might correspond to the S 0 -S 3 states of the OEC.This type of extended redox behavior was not present in earlier Mn 3 CaO 4 cubane complexes that did not contain the dangling Mn, which suggests that -in addition to the role of the ligands in potentially supporting a range of oxidation states-the fourth Mn playing an important role in controlling the redox behavior of the cluster.
The EPR results on the complex are particularly intriguing.A solution of the complex in its neutral form exhibits only a broad parallel mode EPR signal like that in the S 1 state of OEC, however the effective g value of 12 in the synthetic complex is significantly different from the g ≈ 4.9 in the OEC.These differences likely stem from the distinctly different orientations of the Jahn-Teller axes of the Mn(III) ions in the two systems (perpendicular in the model and collinear in the OEC) which would result in the local d tensors contributing differently to the total D value of the system.The most striking aspect however is the simultaneous appearance of g ≈ 4.9 and g ≈ 2 EPR signals in the one-electron oxidized form, reminiscent of the S 2 state of the native enzyme (Fig. 18). 71To obtain the EPR spectrum on the oxidized state of the complex, Zhang et al. employed [Fe(Phen) 3 ] 3+ as a chemical oxidant with a redox potential +1.1 V versus NHE.They observed two signals in perpendicular mode, a multiline signal centered at g ≈ 2 with a width of ca.1600 G and more than 20 hyperfine peaks, and a signal centered at g ≈ 4.9, with a width of ca.500 G without resolved hyperfine structure.Both EPR signals exhibit a linear Curie behavior suggesting that they are both ground-state signals.Such characteristic signals had never been observed before in other synthetic structural models of the OEC. 219hang et al. could detect subtle structural differences, particularly in the Mn1-Mn4 and Ca-O4 distances between two monomers in the crystallographic unit cell of the neutral state.They assumed that the structural difference, possibly amplified during solvation or S 1 to S 2 state change, could affect the exchange coupling between Mn ions leading to two different spin states, which might explain the simultaneous appearance of two signals.The apparent similarities of the EPR of the oxidized form with the S 2 state of the OEC, led also to the suggestion that the structural interpretation of the EPR of the OEC described by Pantazis et al. 71 might also be valid here, i.e. that the two signals could arise by valence isomers of the oxidized synthetic complex. 217However, this hypothesis is not consistent with the experimental data.In stark contrast to the OEC, the two EPR signals of the oxidized synthetic model are noninterconvertible, suggesting that they are unlikely to arise from valence isomers as in the S 2 state of the OEC.Given the rigid structural framework of the synthetic complex there is no need for extensive structural reorganization and hence electron hopping between Mn ions in the singly oxidized state of the complex should be more facile compared to the OEC instead of prohibited.This is a strong argument against the valence isomer hypothesis and indicates that the spectroscopic similarities with the S 2 state of the OEC are superficial.This was recently confirmed with density functional theory and multireference wave function calculations by Paul et al., 218 who established that only one valence isomer is energetically accessible in the structurally intact one-electron oxidized form of the complex.This has a valence distribution that resembles the high-spin closed cubane form of the S 2 state of the OEC, with the Mn(III) at the "dangler" position.It displays an S = 5/2 ground state and can readily explain the g = 4.9 signal.However, alternative valence isomers that might give rise to an S = 1/2 ground state are significantly higher in energy. 218hese results demonstrate that despite geometric similarities the synthetic model does not mimic the valence isomerism of the OEC and suggest that the multiline EPR signal in the singly oxidized form may originate from an as yet unidentified rearrangement product.
A particularly interesting question is of course whether this complex can evolve oxygen by oxidizing water as a molecular catalyst.This is not clear from the available experimental data, but the answer is likely negative.Electrochemistry suggests that oxidation past the S 3 state, i.e. to the equivalent of an oxygen-evolving S 4 state, is irreversible.Consistent with this observation, Paul et al. showed that oxidation of the all-Mn(IV) S 3 state would be ligand-centered. 218Besides, there are no water-derived ligands in the as-isolated complex that could serve as substrates.Indeed, a recent computational study 220 suggested that a mechanism for water oxidation is conceivable only after extensive substitution of existing ligands by water molecules.It is unclear whether such a process should be expected to precipitate the chemically more plausible decomposition of the high-valent manganese cluster rather than enable catalytic water oxidation with an otherwise intact inorganic core.

Conclusions and perspectives
In this review we aimed to trace broadly, albeit selectively, the historical development of structural models for the oxygen-evolving complex and to highlight major achievements and insights.We singled out as three important milestones in this route the Mn 3 CaO 4 cubane complex and related substituted systems by the Agapie group, 151 the Mn 3 CaO 4 -Ca cubane complex by the Christou group, 195 and the most recently reported Mn 3 CaO 4 -Mn cubane complex by the Zhang group. 197Although the structural parameters of the cubane units are very similar, these complexes define a series of increasing asymmetry induced by the presence of an external Ca 2+ cation and a dangling redox-active manganese.They also define a series of increasing complexity in terms of behavior, with the Zhang complex displaying remarkable aspects of redox accumulation and spectroscopic properties.
Obtaining insights from the synthetic models has often been inseparable from a theoretical analysis of their properties and has relied to a large extent on deciphering the fundamental electronic structure basis of geometry-property correlations using modern quantum chemistry that focuses on spectroscopic properties.These cubane-incorporating complexes have already served as sources of insight in this respect, in themselves and in comparison to models of the OEC, as showcased by numerous studies on magnetism, spectroscopy, and redox behavior.
However, we would also like to delineate some remaining challenges.Despite the enormous progress in ligand design, in controlling the meal stoichiometry and in incorporating asymmetry into the inorganic core, the precise stoichiometry (Mn 4 CaO 5 ) and connectivity of the OEC (Fig. 1 and 2) have not been reproduced.Without exception, all models mimic the "closed cubane" forms of the OEC (or the older "London" model of the OEC).This motif first appears in a component of the S 2 state but is not formally present in S 0 and S 1 , or in one component of the S 3 state. 82It is not considered likely to be involved in O-O bond formation according to existing mechanistic hypotheses, 84 however closed cubane species were recently shown to be intimately involved in advancement to the S 3 state, 74 so this structural motif is certainly of high relevance to modeling the OEC.On the other hand, the rigidity of the cubane core itself in the synthetic models stands in contrast to the flexibility shown by the OEC.The exact Mn 4 CaO 5 stoichiometry with the correct bridging modes, a more open connectivity pattern, and a potentially more flexible/bistable core constitute therefore part of future biomimetic challenges.To these, one might add the finer structure-based control of local and total spin, a crucial aspect of the OEC. 78eyond these points, synthetic models that attempt to mimic the structure are still short of mimicking functionality, although it should be recognized that the structural determinants of function for the OEC itself remain ill-defined.Catalytic progression is tightly dependent on coupling, perhaps entirely, of substrate deprotonations with metal-centered oxidations preceding O-O bond formation.The function of the OEC depends critically on the protein matrix and on the tight control of water access, which allow the high-valent Mn cluster to perform water oxidation chemistry without damage and side reactions.Thus, eliciting function from geometric structure represents an entirely different level of challenge and would require exquisite architectural control of the second coordination sphere.For structural biomimetic chemistry the OEC still represents a peak to be conquered, not simply in terms of precisely reproducing the core topology and supporting ligand sphere in its stable states but also in targeting intermediates that might appear in the later catalytic stages, whose structural complexity has only very recently began to be fully appreciated. 6,74

Fig. 5
Fig. 5 Photoinduced opening of the Dismukes cubane to a butterfly core.

Fig. 6
Fig. 6 Butterfly type complex by Vincent et al. 156

Fig. 8
Fig. 8 Cores of polynuclear complexes by Mishra et al. 175 (a) and by Chen et al. 177 (b) containing Mn 3 Ca cubanes as integrated substructures (ligands omitted for clarity).

Fig. 10
Fig.10Core of the Mn 6 Sr 2 complex by Chen et al.194

Fig. 14
Fig.14Selected corresponding orbital pairs between pairs of Mn ions, computed by the diamagnetic substitution approach; the green sphere indicates the manganese ion replaced by Ge 4+ in each case.

Fig. 15
Fig.15Spin maps indicating the ground spin state obtained by combinations of the three pairwise exchange coupling constants in a system of three local spins S = 3/2 (adapted with permission from Krewald et al.196Copyright 2013 American Chemical Society).

Fig. 16 (
Fig. 16 (a) Correlation between the experimental reduction potential E 1/2 (eV) and the literature-known pK a values of the aquo-cations A n+ in the Mn 3 AO 4 cubane models. 180,182(b) Correlation of computed vertical ionization energies and pK a values of aquo-A n+ cations for the S 1 -S 2 transitions of the OEC 210 (adapted from ref. 210 with permission from the PCCP Owner Societies).

Fig. 17
Fig. 17Vertical ionization energies (eV, green) and geometry relaxation energies (eV, orange) for the systems studied here.Top to bottom: synthetic cubane models, OEC S 1 -S 2 transition, OEC S 2 À S 2 Y • Z transition (adapted from ref. 210 with permission from the PCCP Owner Societies).
Fig. 17Vertical ionization energies (eV, green) and geometry relaxation energies (eV, orange) for the systems studied here.Top to bottom: synthetic cubane models, OEC S 1 -S 2 transition, OEC S 2 À S 2 Y • Z transition (adapted from ref. 210 with permission from the PCCP Owner Societies).

Table 1
Comparison of exchange coupling constants (cm −1 ) for the Mn 3 CaO 4 cubane complex of Kanady et al. (computed values), the Mn 3 CaO 4 -Ca complex of Mukherjee et al. (experimental and computed values), and the closed cubane S 2 and S 3 forms of the OEC (computed values)

Table 2
55mparison of55Mn isotropic hyperfine coupling constants (MHz, absolute values) for the Mn 3 CaO 4 -Ca complex of Mukherjee et al. (experimental and computed values), and for the closed cubane S 2 and S 3 forms of the OEC (computed values)