Simulation of the isotropic EXAFS spectra for the S₂ and S₃ structures of the oxygen evolving complex in photosystem II

Significance

A few years ago, spectroscopy confirmed almost every detail of the previous density functional theory (DFT)-suggested structure for the S₂ state of photosynthesis. Earlier this year, the 2-y-old DFT structure for the S₃ state was also confirmed in detail, which means that there is now an answer to what happens in the important S₂–S₃ transition, and there is an opportunity to discuss and evaluate the predictions for this transition made by extended X-ray adsorption fine structure (EXAFS) over the past decades. The present analysis also shows that the EXAFS spectra are consistent with the suggested DFT structures within normal DFT errors. Importantly, there are no major structural changes in this transition.

Abstract

Most of the main features of water oxidation in photosystem II are now well understood, including the mechanism for O–O bond formation. For the intermediate S₂ and S₃ structures there is also nearly complete agreement between quantum chemical modeling and experiments. Given the present high degree of consensus for these structures, it is of high interest to go back to previous suggestions concerning what happens in the S₂–S₃ transition. Analyses of extended X-ray adsorption fine structure (EXAFS) experiments have indicated relatively large structural changes in this transition, with changes of distances sometimes larger than 0.3 Å and a change of topology. In contrast, our previous density functional theory (DFT)(B3LYP) calculations on a cluster model showed very small changes, less than 0.1 Å. It is here found that the DFT structures are also consistent with the EXAFS spectra for the S₂ and S₃ states within normal errors of DFT. The analysis suggests that there are severe problems in interpreting EXAFS spectra for these complicated systems.

The knowledge of the different steps of water oxidation in photosystem II has increased rapidly the past years. After the first low-resolution X-ray structures appeared ∼10 y ago (1–3), quantum chemical studies using density functional theory (DFT) have played a major role for obtaining a mechanistic understanding. First, an O–O bond formation mechanism was suggested in 2006 (4) in which a terminally bound oxyl radical in the center of the oxygen evolving complex (OEC) was attacked by a manganese-bridging oxo group. Second, an improved structure was suggested in which, most importantly, the outer manganese was placed differently from where it was placed in the previous X-ray structures (5). This position led to an open space in the center of the OEC, which is critical for allowing the low-barrier O–O bond formation suggested earlier (4).

In 2011, a major experimental breakthrough occurred when the first high-resolution X-ray structure at 1.9 Å was presented by Umena et al. (6), which essentially confirmed the quantum chemical structure of the OEC. The main difference was that Asp170 was found to bind in a bridging mode between the terminal manganese and calcium instead of only terminally to the manganese as in the quantum chemical structure. The rest of the structure is very similar, including the critical positions of the outer manganese and the oxo groups, and the ligand connections. A minor problem with the X-ray structure is that it is most probably reduced by X-ray radiation (7–9), indicating that it is unlikely to be in the S₁ state as claimed. More recently, spectroscopic studies have played a major role by confirming the most important aspects of the quantum chemical suggestions. On the basis of the new X-ray structure and old DFT(B3LYP) structure (5), using electron paramagnetic resonance (EPR), electron nuclear double resonance (ENDOR), and DFT, a detailed structure of the OEC in the S₂ state was reached (10) that agrees almost perfectly with a structure obtained independently by a DFT(B3LYP) energy minimization (11, 12) (Fig. 1). The positions of the oxo groups and the protonation states, including which ligands are water and which are hydroxides, agree, along with which manganese are Mn(III) and which are Mn(IV) at that stage. Also, the DFT(B3LYP) structure from 2009, before the high-resolution structure, is very similar (13). Two years ago, the substrate oxygen positions were suggested for S₂ using a W-band ¹⁷O ELDOR-detected NMR spectroscopy (14). The position for the slowly exchanging substrate agrees with the one suggested by the DFT studies (4, 11–13), but there is still a minor possible disagreement for the fast-exchanging substrate. Very recently, a combined experimental and theoretical study by Cox et al. (15) used EPR and ⁵⁵Mn–EDNMR spectra to suggest an S₃ structure almost identical to the structure suggested by DFT(B3LYP) 2 y ago (16) (Fig. 2), and again very similar to the one from 2009 (13). It was claimed that only this structural model fits the measured spectra.

Fig. 1.

(Left) Previously DFT(B3LYP)-optimized structure for the S₂ state (11, 12). (Right) Structure suggested after a spectroscopic analysis (10).

Fig. 2.

(Left) Previously DFT(B3LYP)-optimized structure for the S₃ state (12, 16). (Right) Structure suggested after a spectroscopic analysis (15).

Even though the major features of water oxidation can now be claimed to be reasonably well understood, additional studies are required to sort out details of the mechanism. A puzzling observation stems from previous extended X-ray adsorption fine structure (EXAFS) studies of the S₂–S₃ transition. In the EXAFS studies by Yachandra and coworkers (17–19), three short distances of 2.7–2.8 Å were found in S₂. In another EXAFS study by Dau and coworkers (20), only two short Mn–Mn distances of 2.7 Å were suggested. Instead, two of the Mn–Mn distances were proposed to be longer than 3.0 Å. For the S₂–S₃ transition, the discrepancies were even more marked. In the studies by Yachandra and coworkers (17–19), it was concluded that there is a lengthening of one of the 2.7–2.8 Å distances to 3.00 Å. In the study by Dau and coworkers (20) it was instead suggested that there is a shortening of one of the distances, which was >3.0 Å, down to 2.7 Å, indicating a formation of an additional Mn–Mn bis-μ-oxo bridge in S₃. Perhaps the most noteworthy of the differences of the suggested S₃ distances is the one that is 2.80 Å in the Dau and coworkers (20) study, and as long as 3.0 Å in the Yachandra et al. study (17). The suggestions from both these studies give larger deviations to the DFT/spectroscopy structure than are expected from DFT, greater than 0.1 Å on some distances and a topology change. The two different EXAFS interpretations led to different proposals for the water oxidation mechanism. It should in this context be mentioned that for S₂ the raw data from the two groups are the same but not for S₃. In the present work, the EXAFS information from Dau and coworkers (20) has been used. Recently, after the theoretical and spectroscopic consensus structure of S₂ had appeared, a reanalysis of the EXAFS spectra was made by the group of Yachandra and coworkers (21); for the S₂ structure, they now find full agreement between the EXAFS analysis and the DFT/spectroscopic structure in Fig. 1. For the S₃ structure, two alternatives were given, one with essentially four equivalent distances and one where one distance is longer.

It is not straightforward to compare DFT and EXAFS data, because the latter are very sensitive to the metal–ligand distances (with an accuracy of 0.01–0.02 Å), whereas DFT calculations often give ∼0.05 Å too-long metal–O bonds and even larger deviations in the metal–metal distances. Therefore, an EXAFS spectrum calculated directly on a DFT structure will be poor, and a direct comparison of DFT and EXAFS distances will also show extensive deviations. Instead, it is better to perform a combined EXAFS/DFT refinement of the EXAFS spectrum, in which the EXAFS raw data (not only the EXAFS distances) are used as a restraint in the DFT geometry optimization (22–24). Thereby, DFT will determine the general structure of the complex, whereas the EXAFS data will determine the detailed distances involving the metals. Such calculations are presented in this study for the S₂ and S₃ states, for a large DFT model used previously (11, 12), and also for a much smaller model. The results are compared with the two different experimental EXAFS analyses. The main purpose of the present study is to investigate whether the discrepancies to experiments for the computational model, concerning the structural changes in S₂ to S₃, really indicate significant differences in the structures or if they are mainly due to minor differences in bond lengths and technical differences in how the spectra are analyzed. The present study agrees with earlier ones (25, 26) in that a major problem of interpreting EXAFS spectra of complicated molecules is that it is possible to fit several different structures to the same spectrum.

It should finally be emphasized that a comparison with other theoretical and experimental work is not part of the purpose of the present paper, which is instead focused on EXAFS results. However, other theoretical work on water oxidation in photosystem II has been discussed in detail in recent reviews (12, 27, 28).

Methods and Models

In previous studies where the present starting structures were obtained, the DFT method used was the hybrid functional B3LYP (29) with the lacvp* basis set. For the present EXAFS refinement analysis, the nonhybrid functional BP86 (30) has been used instead for technical reasons. The structures were therefore first reoptimized with this functional using a def2-SV(P) basis set. BP86 is known to give structures of similar quality as B3LYP, and the structural changes were indeed small. It has previously been emphasized that for the present system, B3LYP gives much better energetics than BP86 (31). However, the comparison made concerned relative energies for different structures, whereas in the present study the energy differences entering the fitting procedure concern points in the same local minima. Because the equilibrium geometries are very similar using B3LYP and BP86, these energy differences should also be very similar. The cluster-type modeling of the active site was used (28). The details, which are the same as used in previous studies (12), are described in SI Appendix.

The DFT/EXAFS refinements were performed with the ComQum-EXAFS software (23, 24). This method is a combination of QM geometry optimization and an EXAFS structure refinement, and is the same used in previous studies (22–24). Technical details are provided in SI Appendix.

Results

The results from the present optimizations and refinements for the S₂ and S₃ states are given in Table 1, where the results from the experimental EXAFS analyses are also shown. For the S₃ states, results for two topologically different structures are given (Fig. 3), the first ones for the energetically optimal structure with the central oxo group closer to the outer manganese Mn4, and the second for a local minimum where this oxo group is closer to Mn1. These two types of structures have been known to be nearly degenerate (“outer” oxo preferred) for the S₂ state (13), and recently they have been shown to correspond to the two states observed by EPR (32). The refined S₃ spectrum for the outer oxo position is shown in Fig. 4 together with the one for the S₂ state. The refined spectra are superimposed in SI Appendix, Fig. S2. The spectrum for the “inner” oxo position is shown in SI Appendix, Fig. S3. The optimized distances for the S₂ state from the previous study (12) using the large model were Mn1–Mn2 = 2.83 Å, Mn2–Mn3 = 2.80 Å, Mn3–Mn4 = 2.74 Å, and Mn1–Mn3 = 3.46 Å. These results were obtained using B3LYP with the lacvp* basis set. For the present study, a reoptimization using BP86 was done. The differences to the B3LYP results are very small (0.01–0.04 Å), with the BP86 results being Mn1–Mn2 = 2.87 Å, Mn2–Mn3 = 2.81 Å, Mn3–Mn4 = 2.77 Å, and Mn1–Mn3 = 3.44 Å. The calculated results compare very well with the EXAFS analysis by Yachandra and coworkers (17), where the distances were suggested to be two of 2.73 Å, one of 2.82 Å, and one of 3.30 Å. It should be noted that the EXAFS analysis could not distinguish between the different Mn–Mn distances. In the more recent study, the results of the analysis are similar with three distances of 2.7 Å and one with 3.2 Å (21). As usual, the DFT(B3LYP) distances are somewhat long. In contrast, the EXAFS analysis by Dau and coworkers (20) suggests one distance of 2.69 Å, one of 2.74 Å and two distances larger than 3.0 Å. From the nearly perfect agreement between the general DFT structure and recent results of EPR and ENDOR spectroscopy for the S₂ state (10), it must be concluded that the assignment by Dau and coworkers of only two short Mn–Mn distances is unlikely to be correct.

Table 1.

Mn–Mn distances obtained for S₂ and S₃ using different methods and models

Method	Mn1–Mn2	Mn2–Mn3	Mn3–Mn4	Mn1–Mn3	Ref.
S2
EXAFS	2.82	2.73	2.73	3.30	(17)
EXAFS	2.70	2.70	2.70	3.20	(21)
EXAFS	2.69	2.74	>3.0	>3.0	(20)
B3LYP	2.83	2.80	2.74	3.46	(12)
BP86	2.87	2.81	2.77	3.44
Refined†	2.83	2.74	2.68	3.62
Truncated, refined‡	2.74	2.83	2.69	3.60
S3
EXAFS	2.73	2.80	3.00	3.30	(17)
EXAFS	2.70	2.70	3.2 (2.8)	2.80	(21)
EXAFS	2.73	2.73	2.77	>3.0	(20)
Outer oxo
B3LYP	2.84	2.81	2.76	3.55	(12)
BP86	2.88	2.82	2.79	3.53
Refined§	2.74	2.73	2.81	3.78
Truncated, refined¶	2.72	2.79	2.79	3.80
Inner oxo
B3LYP	2.75	2.78	3.18	2.89
BP86	2.78	2.80	3.19	2.92
Refined#	2.72	2.75	3.15	2.81

^†χ² = 337; ^‡χ² = 169; ^§χ² = 174; ^¶χ² = 73; and ^#χ² = 169.

Fig. 3.

The two topologically different S₃ states discussed in the text, the outer oxo position (Left) and the inner one (Right).

Fig. 4.

(Upper) Refined EXAFS spectrum for the S₂ state. (Lower) S₃ state, for the case with the central oxo close to the outer manganese Mn4, the outer oxo position. Experimental spectra are in red.

The DFT/EXAFS refinement leads to the expected shortening of the three short Mn–Mn distances. The refined results are Mn1–Mn2 = 2.83 Å, Mn2–Mn3 = 2.74 Å, Mn3–Mn4 = 2.68 Å, and Mn1–Mn3 = 3.62 Å. The three short distances are now in even better agreement with the analysis by Yachandra et al. For the long Mn–Mn distance, the refined distance is slightly longer than the experimental one, but this cannot be regarded as a serious difference because this distance is extremely sensitive to details in the models used in the calculations.

Turning to the results for the S₃ state, the B3LYP distances for the energetically optimal outer position of the oxo group are Mn1–Mn2 = 2.84 Å, Mn2–Mn3 = 2.81 Å, Mn3–Mn4 = 2.76 Å, and Mn1–Mn3 = 3.55 Å. The differences to the short S₂ distances are +0.01 Å, +0.01 Å, and +0.02 Å, respectively. The similarity of these Mn–Mn distances to the ones for the S₂ state is surprising from two aspects. First, both EXAFS studies suggest much larger changes of these Mn–Mn distances. Second, because Mn1 is oxidized from Mn(III) to Mn(IV) in this transition, there is a loss of a Jahn–Teller axis, which leads to a significant shortening of a Mn–O bond along this axis by as much as 0.6 Å, from 2.4 to 1.8 Å, though this does not seem to affect the Mn–Mn distances. The reoptimized BP86 distances show the same tendency with Mn1–Mn2 = 2.88 Å, Mn2–Mn3 = 2.82 Å, Mn3–Mn4 = 2.79 Å, and Mn1–Mn3 = 3.53 Å. The differences to the short S₂ distances are +0.01 Å, +0.01 Å, and +0.02 Å, respectively, the same differences as for B3LYP. The DFT/EXAFS refinement changes the picture somewhat, with distances of Mn1–Mn2 = 2.74 Å, Mn2–Mn3 = 2.73 Å, Mn3–Mn4 = 2.81 Å, and Mn1–Mn3 = 3.78 Å, leading to differences for the short distances of −0.09 Å, −0.01 Å, and +0.13 Å, respectively, compared with the S₂ distances, instead indicating two notable changes of the short Mn–Mn distances. An even larger difference is found for the long distance after the refinement, from 3.62 to 3.78 Å. However, in this context the long distance is much more sensitive to details of the structures.

The EXAFS analysis by Yachandra and coworkers (17) led to suggested distances for the S₃ state of 2.73 Å, 2.80 Å, 3.00 Å, and 3.30 Å. There is one rather large difference to the DFT(B3LYP) results and this is the 3.00 Å distance, which is only 2.81 Å using DFT/EXAFS. As mentioned previously, DFT(B3LYP) normally overestimates distances, so this would be a surprising difference. In the EXAFS analysis by Dau and coworkers, the suggested distances are two of 2.73 Å, one of 2.77 Å, and one larger than 3.00 Å. Notably, the longest of the short distances is only 2.77 Å in comparison with 3.00 Å in the analysis by Yachandra et al. However, the results of the Dau and coworkers analysis are well in line with the DFT results. Again, the EXAFS raw data from the two experimental studies is different for the S₃ state, and the raw data from Dau and coworkers was used here. In the recent reanalysis by the Yachandra group, two alternatives were given, one where all four distances are short, and one where one distance is longer (21). For the first of these suggestions there is thus a discrepancy to the present analysis; in the second one there is a discrepancy concerning which distance is the long one (see below).

From the above, it can be concluded that the agreement between the DFT(B3LYP) and EXAFS results are quite good compared with the Yachandra and coworkers (17) analysis for the S₂ state. For the S₃ state, the agreement is quite good compared with the Dau and coworkers analysis. For the earlier analysis of Yachandra and coworkers (17), the agreement is not as good. In the more recent reanalysis, there are still disagreements (see below) (21). Because the two EXAFS analyses differ substantially to each other for each state, the discrepancies between the results of DFT(B3LYP) and EXAFS become more pronounced when the changes of the distances between S₂ and S₃ are compared. The DFT changes of the short Mn–Mn distances are very small, as noted previously. However, it is interesting that the DFT/EXAFS refinement led to somewhat larger changes of +0.13 and −0.09 Å for two distances. The refined results therefore agree better qualitatively with the interpretations of the EXAFS studies, indicating some structural changes in this transition. A conclusion that appears clear is that DFT (B3LYP or BP86) by itself is not accurate enough for predicting the detailed changes in the distances (see below). Two of the distances (Mn1–Mn2 and Mn2–Mn3 in the cube) show the same type of shortening of the (short) distances after refinement as in the case of the S₂ state, which is in line with previous experience. However, the third distance (Mn3–Mn4) to the outside manganese shows an unexpected lengthening, which may be a sign of a slightly worse description by DFT(B3LYP) for the S₃ state. Errors of 0.1 Å are not unusual for DFT-optimized geometries. The typical accuracy of DFT calculations for metal–ligand distances is ∼0.06 Å, whereas the accuracy of DFT(B3LYP) is lower for nonbonded distances such as Mn–Mn and Mn–Ca (probably 0.1–0.2 Å).

Even though the two experimental EXAFS analyses agree that there should be a significant structural change in the S₂–S₃ transition, the details of this change, and the consequences of it, are quite different in the two studies. The earlier analysis by Yachandra and coworkers (17) gave one change of more than 0.2 Å (or one of 0.2 and one of 0.1 Å). This change, supported by results of earlier and later XANES spectra (33), led to the conclusion that an oxygen rather than a manganese is oxidized in this transition, which strongly affected the suggested O–O bond formation mechanism (34, 35). The conclusion from the XANES spectra has been questioned experimentally (36), and also recently on the basis of DFT model calculations (37). The Dau and coworkers results, however, gave one change from a distance larger than 3.0 Å down to 2.77 Å; this led to a suggested structural change in this transition with a formation of an additional Mn–Mn bis-μ-oxo bridge in S₃ (38). With the present knowledge, both from model calculations and spectroscopy experiments, none of these suggestions are likely to be correct. One conclusion that can be drawn is that it appears to be very difficult to obtain detailed structural information from EXAFS spectra, even if these are accurately measured, of such a complicated multimetal complex like the OEC, without detailed information from similar model complexes where the structures are known. Such information is presently missing.

There are two different alternatives to explain the changes of the short Mn–Mn distances that are implicated by the DFT/EXAFS refinement, assuming that it is reliable. These changes could stem from either a minor error in DFT or something missing in the chemical model used. Even before the recent spectroscopic verification of also the S₃ state (15) (when the present study was performed), the first possibility appeared to be by far the most likely explanation. One interesting aspect is that in this transition a strong hydrogen bond is introduced from the substrate hydroxyl group bound to Mn1 and an oxo group bridging Mn3–Mn4. The hydrogen bond is very short, only 1.49 Å, and a lengthening effect on the Mn3–Mn4 bond could have been expected, but the DFT(B3LYP)-optimized structure shows only a small lengthening of +0.02 Å; the EXAFS refinement indicates that it should be larger with +0.13 Å. The actual error for the DFT bond distances implied by the refinement is +0.06 Å for one distance and −0.05 Å for the other. DFT errors like these cannot be excluded. At the same time, Mn1 is oxidized, which could implicate a shortening of the Mn1–Mn2 bond distance. Instead, DFT surprisingly shows a small increase by 0.01 Å. The EXAFS refinement shows the expected trend with a shortening of −0.09 Å with individual errors of +0.00 Å and +0.10 Å. Again, a DFT error of this size cannot be excluded.

The second alternative to explain the effects on the distances from the DFT/EXAFS refinement would be some sort of error in the model used for the DFT calculations. Because there is a very large degree of consensus between computational modeling and spectroscopic experiments concerning both the S₂ (10) and the S₃ structure (15), an error of this type appears highly unlikely. Another question in that case is what type of defect this could be. An effect from the surrounding, not included in the DFT model, can most likely be ruled out on the basis of previous experience. Inside the model, a protonation of one of the μ-oxo bonds between Mn3 and Mn4 could explain the lengthening of this bond distance, but could hardly explain the shortening of the Mn1–Mn2 bond. A protonation of an oxo bond in the S₂ state is unlikely on the basis of the present knowledge of this state. In the S₂–S₃ transition, a water binds to the OEC and a proton from that water could, in principle, protonate one of the oxo bonds, but this would require a lack of proton release in this transition. However, there is convincing experimental evidence that a proton release does occur (38). A protonation of a μ–oxo bond in the S₂–S₃ transition would furthermore complicate O–O bond formation substantially. In all known mechanisms for O–O bond formation, natural or biomimetic, an oxygen radical is critically needed. At the stage the oxygen radical is formed, the presence of another protonated group than a substrate should therefore preferably be avoided, because that group could be deprotonated instead.

Another alternative to the present optimal S₃ structure could have been the one where the central oxo group is close to Mn1 (Fig. 3); this has been suggested in one of the alternatives in the recent reanalysis of the EXAFS spectra (21), but this analysis used a definition of the outer structure with a 5-coordinated Mn4 (present numbering) in contrast to the structure here. Also, it can now be added that the inner structure was ruled out by the recent spectroscopic analysis (15). The B3LYP distances (Table 1) with the energetically less optimal inner position for the oxo group are Mn1–Mn2 = 2.75 Å, Mn2–Mn3 = 2.78 Å, Mn3–Mn4 = 3.18 Å, and Mn1–Mn3 = 2.89 Å. Because EXAFS cannot identify which Mn–Mn distance is which, a comparison with the S₂ distances should be made with a rearrangement of the assignments for the bonds. The differences to the short S₂ distances are then +0.01 Å, −0.02 Å, and +0.06 Å, respectively. These changes are again, like for the outer model, smaller than the suggestions made by EXAFS. For the refined distances the corresponding differences are +0.04 Å, +0.01 Å, and −0.02 Å, which thus show even smaller differences to the ones in the S₂ state; this is different from the case of the “outer” oxo where the refined distance changes showed a better correspondence with EXAFS. However, the results for the outer and inner structures show too-small differences between each other to allow any conclusion of which structure should be best, on the basis of the EXAFS analysis. Energetically, the outer minimum is preferred with a margin of 4.9 kcal/mol at the B3LYP level. In line with the excellent agreement obtained so far between the DFT results and spectroscopic experiments, the suggestion based solely on the calculations would therefore be that the outer minimum is the actually preferred one; e.g., it has in this context been shown that the correct order, with a reasonable energy separation, compared with experiments, is obtained by DFT for the corresponding states in S₂ (13, 32). At the BP86 level, the preference for the outer minimum is even larger by another 5 kcal/mol. As discussed, the choice between these minima does not have any major effects on the actual O–O bond formation mechanism (13). The refined spectrum for the inner oxo position is shown in SI Appendix, Fig. S3.

Another comment can be made concerning the present EXAFS analysis. Both the experimental EXAFS spectra show large differences between the S₂ and S₃ states, which was the reason for suggesting a much larger structural change than found both here and in the recent EPR spectroscopic analysis. However, the present analysis shows that it is indeed possible to obtain different EXAFS spectra for two structures with highly similar Mn–Mn distances (Fig. 4).

A remaining question is whether the DFT/EXAFS refined distances would have significant effects on the energetics, and thereby the mechanism. To test this possibility, the S₂ and S₃ structures were reoptimized, keeping the short Mn–Mn distances fixed to the values obtained after the refinement; by definition, this is less optimal energetically for DFT, but the difference for S₂ is small, with an energy increase of only 1.3 kcal/mol. The same small difference of 1.3 kcal/mol is found for the inner minimum of S₃. For the outer minimum of S₃, the effect is slightly larger with 2.2 kcal/mol. In line with previous experience, the other detailed differences in the geometries do not matter much. Previously, it has been shown that the choice of basis set for the geometry optimization does not have significant effects on the energetics, even though this could change the distances by even more than the difference between the optimal and refined structures discussed here (39). Finally, the energies were calculated with fixed distances from the different EXAFS studies (17, 20, 21). Again the energy differences to the optimized structures are small, in the range 1–2 kcal/mol. The exceptions are when EXAFS has suggested only two, rather than three, short distances, where the energy difference goes up to 10 kcal/mol. For the most recent EXAFS study, the energy differences are also somewhat larger with 4–5 kcal/mol for the outer oxo structures. It is not possible to draw any conclusion from these values, except that the energies are insensitive to the details of the Mn–Mn distances, and these details do not affect the mechanism.

Results for a truncated model (Methods and Models) are also shown in Table 1. In general, the full and the truncated structures are similar. Concerning the changes of the distances from S₂ to S₃, the truncated model gives a shortening (after refinement) of −0.04 Å for Mn2–Mn3, whereas the full model gives −0.01 Å. The lengthening of the distance to the outer manganese (Mn3–Mn4) is also similar in the two models with +0.10 and +0.13 Å, respectively.

Conclusions

In the present study, a DFT/EXAFS refinement procedure has been applied to DFT structures for the S₂ and S₃ states, previously presented (12). Previous experimental spectroscopic studies have confirmed the details of the DFT(B3LYP) structure for the S₂ state (10) (Fig. 1). Very recently (after the present study was made), a similar confirmation also exists for the S₃ state (15) (Fig. 2). The oxidation states of the four manganese atoms, the ligation of the amino acids, the identification of oxo, hydroxide, and water ligands have for both states been confirmed by the experiments. Also, the mechanism for O–O bond formation has been essentially confirmed by experiments (14). With this background it was now of high interest to go back to the analysis of the EXAFS spectra. Over many years, EXAFS studies have been made on the OEC, mainly by two groups reaching rather different conclusions. However, both groups have agreed that there should be a significant structural change in the S₂–S₃ transition, because the EXAFS spectra for the two states are different. However, the details of this change have been suggested to be quite different. In one of the studies, a major lengthening of one Mn–Mn distance by more than +0.2 Å was suggested (17–19), whereas in the other one a major shortening of one distance by at least −0.2 Å was instead suggested (20). In contrast, the DFT(B3LYP) optimizations showed only limited changes of the Mn–Mn distances in this transition (12). The main purpose of the present study was therefore to investigate whether the DFT structures could be considered consistent with the EXAFS spectra. The conclusion from the study is that the DFT structures could be well-fitted to match the spectra keeping the same topological structures and with only minor distortions, within the normal errors of DFT; this also means that it is indeed possible to obtain EXAFS spectra that agree very well with those obtained experimentally, even from structures of the S₂ and S₃ states that are highly similar.

The DFT/EXAFS refinement modified the previous DFT(B3LYP) results somewhat. Instead of the small changes in the S₂–S₃ transition obtained previously, one Mn–Mn distance was suggested to increase by +0.13 Å, whereas another decreased by −0.09 Å. The most likely explanation for this correction is minor errors in DFT. Errors in metal–metal distances of this magnitude have been noticed several times before, and the energetic consequence of these errors is minor. Defects in the chemical model used are considered much less likely, in particular after the recent spectroscopic verification of also the S₃ state; this provides further support for the previously suggested O–O bond formation mechanism, with an attack by an oxyl radical, bound to Mn1, on a μ-oxo-ligand bound between Mn3 and Mn4 (4, 12, 13).