Interplay between protonation and Jahn–Teller effects in a manganese vanadium cubane water oxidation catalyst Open Access

Photochemically driven water splitting (2H₂O $→hν$ O₂ + 2H₂) is a promising technique to produce clean, renewable energy and thus has sparked a lot of research.^1,2 In particular, the oxidation half-reaction (2H₂O → O₂ + 4H⁺ + 4e⁻) is generally regarded as one of the most challenging steps, requiring specialized water oxidation catalysts (WOCs) that support multiple oxidation states and proton-coupled electron transfer steps and are sufficiently stable under various conditions, ideally based on abundant metals.^3–6 The structure of the oxygen-evolving complex of Photosystem II—which contains a Mn₄CaO₅ cluster surrounded by amino acids—has inspired a class of artificial WOCs based on a Mn₄O₄ cubane core that can be stabilized with organic ligands and/or polyoxometalates (POMs).^7–10 One of these compounds, [(Mn₄O₄) (V₄O₁₃) (OAc)₃]³⁻ [called MnV WOC henceforth and depicted in Fig. 1(a)],⁹ showed very promising activity—a turn-over frequency of 3.6 s⁻¹ and turn-over number of 12 000¹¹—but degraded within a few hours.

This MnV WOC was extensively studied in the last few years by some of us, placing emphasis on its redox potentials,¹² catalytic activation,¹³ molecular structure,¹⁴ IR and UV/Vis absorption spectroscopy,¹⁵ all the way toward its actual water oxidation catalysis steps¹⁶ and corresponding regeneration and degradation mechanisms.¹⁷ During our work, it was also highlighted that various protonation states are involved in its chemistry, most importantly during the activation of the catalyst¹³ (when acetate is replaced by water/hydroxyl ligands) and during the proton-coupled electron transfer steps of the water/hydroxyl/oxyl ligands during the catalytic cycle¹⁶ [see Fig. 1(a)]. Most recently, we also realized¹⁷ that under certain conditions, the cubane O atoms can be protonated and that this could potentially lead to an irreversible opening of the cubane structure and, therefore, degradation of the catalyst.¹⁸ 

Protonation of POM clusters has been the subject of many studies in the last decades, including a large body of computational work, mostly employing density functional theory (DFT).^19–24 Earlier works explaining that many POMs made from V, Mo, and W show consistent behavior have been nicely summarized in a review from 2012.²⁴ Generally, the ordering of the oxygen sites with respect to basicity is the following for the mentioned metals: terminal sites (M = O) are least favorable, followed by bridging sites (M–O–M or OM₃), followed by internal sites, although the latter are often absent or inaccessible to protons. Typical factors that affect POM protonation energies of oxygen sites are the number and type of metal atoms directly bonded to the oxygen, the total charge and size of the cluster (i.e., the surface charge density), and the relevant M–O–M bonding angle (where smaller angles increase basicity).²³ A more recent DFT study identified the location and effect of protonation of the hetero-nuclear complexes [M₄(H₂O)₂(P₂W₁₅O₅₆)₂]¹⁶⁻ (M = Mn, Co),²⁵ where the mixed-metal sites M–O–W were found to be by far the most basic ones. Interestingly, the authors showed that an inspection of the molecule’s electrostatic potential and the O atoms’ partial charges is not helpful to identify the most basic sites—only the direct computation of relative energies (through geometry optimization) appeared to be reliable.

Given that protonation appears to be of critical importance in the chemistry of the MnV WOC, it seems expedient to investigate in detail its various protonation sites. Such an investigation is complicated due to several factors. First, the MnV WOC is a hetero-metallic cluster with many nonequivalent oxygen sites, including terminal, μ₂-bridging, μ₃-bridging, and internal sites [see Fig. 1(b)]. Second, the MnV WOC can be found in multiple different oxidation states, ranging from Mn$4IV$ to Mn$4III$⁠. Finally, if at least one Mn^III atom is present, then there are multiple possible orientations and locations of the corresponding Jahn–Teller axes.^14,16 Jahn–Teller distortions tend to lower the molecular symmetry, which in turn removes the equivalence between the oxygen sites, producing a very large search space for the best protonation sites. Experimentally, only a pH-dependent absorption spectrum⁹ that shows a significant reduction in low-energy absorption associated¹⁵ with d → d transitions located on the cubane is available and could provide a hint about preferred protonation sites.

Therefore, the aim of the present work is to explore computationally the basicity of the different O atoms of the MnV WOC. Besides the peculiarities attached to the investigated MnV WOC, we hope to obtain a better understanding of the basicity of redox-flexible hetero-nuclear metal oxide clusters in general—e.g., of the effect of Jahn–Teller axes on basicity and of the effect of protonation on geometry and electronic structure.

The rest of the paper is organized as follows. In Sec. II, we explain the nomenclature employed to refer to each of the relevant structures, followed by the computational details. The results and discussion in Sec. III are organized according to the different oxidation states of the MnV WOC. Finally, we compare our findings to the experimental spectrum and provide some general conclusions.

In the present work, we investigate the protonation behavior of the system in the form [(Mn₄O₄)(V₄O₁₃)(OAc)₃]³⁻, which actually constitutes the precatalyst for the water oxidation reaction.¹³ We make this choice because we are interested in obtaining general insights into the protonation of mixed Mn–V clusters, so the simpler and more symmetric precatalyst serves our purposes better than the activated catalyst ([(Mn₄O₄)(V₄O₁₃)(OAc)₂(H₂O)(OH)]³⁻). As in our previous studies,^14,16,17 we consider the five oxidation states from Mn$4IV$ to Mn$4III$⁠, which have been linked previously to the S₋₁ to S₃ states of the Kok cycle.²⁶ Henceforth, these oxidation states are labeled from “Mn4444” to “Mn3333.” We note that the precatalyst as obtained by synthesis⁹ has a Mn$2III$Mn$2IV$ oxidation state, which is labeled as “Mn3344.” Other oxidation states of the precatalyst can be produced by electrochemical methods^9,15 (see Refs. 12 and 13 for a discussion of their redox potentials), but they have not been used in actual catalysis because catalyst activation involves the exchange of one acetate by water or hydroxide.

A Mn^IV atom in the MnV WOC has a d³ configuration and, therefore, it exhibits mostly undistorted octahedral coordination. In contrast, a Mn^III atom has a d⁴ high-spin configuration, which leads to a strongly distorted octahedral coordination sphere with two trans-standing bonds being significantly elongated (the JT axis) and the four other bonds being compressed, compared to Mn^IV. As discussed thoroughly elsewhere,¹⁴ the positions and orientations of the JT axes follow several rules: (i) JT axes are less favorable at the apical Mn atom (the one bonded to all three acetates); (ii) JT axes crossing at the same O atom are less favorable than JT axes that avoid each other; and (iii) JT axes involving a vanadate O atom are unfavorable. These rules determine which JT arrangements constitute stable minima of the different oxidation states, and in this case, they lead to 12 structures (1, 2, 3, 4, and 2 minima for Mn4444, Mn3444, Mn3344, Mn3334, and Mn3333, respectively).

The MnV WOC has a total of 23 O atoms—13 on the vanadate, 4 in the cubane, and 6 in the three acetates. As shown in Fig. 1(b), there are eight different O sites for which we employ the labels used for the atom types in the previously published force field.¹² There are two kinds of terminal O atoms related to the V=O groups of the vanadate (1 atom labeled OA, 3 atoms labeled OC). Additionally, the vanadate has two kinds of μ₂-bridging O atoms, 3 atoms in V–O–V bridges (OB) and 6 atoms in V–O–Mn bridges (OE). In the cubane, we find 4 atoms that are μ₃ bridges (OMn₃), where 1 atom is inside the vanadate cage (OJ), and 3 atoms, located between the acetates, are accessible (OL). Finally, the acetates have two kinds of O atoms (both C–O–Mn bridges), 3 atoms closer to the vanadate (OO), and 3 atoms attached to the apical Mn atom at the bottom (OP).

The Mn4444 oxidation state is free of JT distortions and thus adopts C_3v symmetry, making O atoms with the same label (OA, OB, …) symmetry-equivalent. However, in the other oxidation states (Mn3444, …), the appearance of the JT axes breaks the symmetry of the molecule and formally introduces additional symmetry-inequivalent O sites. JT arrangements that retain a mirror plane (C_s symmetry) thus have 15 distinguishable O sites. If the JT axes lift all symmetry (C₁), then all 23 O sites become distinguishable. Therefore, the 12 stable structures of the MnV WOC¹⁴ exhibit a total of 198 distinguishable O sites (8 for Mn4444, 30 for Mn3444, 53 for Mn3344, 69 for Mn3334, and 38 for Mn3333); see Table S1 in the supplementary material. Symmetry equivalent JT arrangements in C_3v are summarized in Table S2.

The main goal of this work is the identification of the most likely protonation sites of the MnV WOC in its different oxidation states and JT arrangements and the subsequent characterization of the most favorable protonated structures. To this end, we prepared initial geometries for each of the 198 protonated structures (as discussed in Sec. II A) by combining the previously reported stable structures¹⁴ with H atoms at the relevant positions. Each structure was subsequently optimized, and a frequency calculation was carried out in order to confirm the minima and obtain the relevant free energies. The optimized Cartesian coordinates for protonated and unprotonated structures are provided in separate supplementary material. For each optimization, we analyzed whether bond lengths and Mulliken charges change significantly in order to identify cases where the JT axes relocate or reorient during the optimization. As our level of theory is slightly different from the previous work on the MnV WOC,¹⁴ we also recomputed the geometries and energies of the unprotonated structures (i.e., the 12 stable structures of the oxidation states Mn4444 to Mn3333) at the same level of theory. Figure S1 additionally provides molecular orbital depictions of the twenty Mn d orbitals (α spin) for an exemplary subset of oxidation and protonation states. Finally, for the Mn3344 geometries, we computed excited states with time-dependent DFT (TDDFT) in order to compare the molecule’s absorption spectra with and without protonation to the available experimental⁹ pH-dependent absorption spectrum.

All optimizations and frequency calculations were carried out with ORCA 4.2.1.^27,28 An ORCA input file is provided in the supplementary material, which also provides the charges and multiplicities for the different oxidation and protonation states. We employed unrestricted Kohn–Sham theory to describe the high-spin state of the compound. This approach was previously used¹⁴ and provides sufficiently accurate results, even though some oxidation states experimentally are found to be antiferromagnetically coupled.⁹ We employed the BP86 exchange-correlation functional,^29,30 which is reported to work well for the geometries of Mn complexes.^31,32 Scalar relativistic effects were described through the zeroth order regular approximation (ZORA),^33–35 using the ZORA-def2-SVP^35,36 basis set for all atoms. Furthermore, we used the D3 dispersion correction³⁷ and the conductor-like polarizable continuum model (C-PCM)³⁸ with the Gaussian charge scheme³⁹ and a van-der-Waals-like cavity to describe the solution in acetonitrile. We note that the usage of (implicit) solvent models in computations of POMs is of critical importance because POM calculations in vacuum can lead to very unreliable results.²⁴ The calculations were sped up by using the resolution of identity (RI-J) technique with the def2/J basis set.⁴⁰ As shown in Tables S3–S6, a comparison of results obtained with other exchange-correlation functionals and with larger basis sets evidences that the relative energies carry an uncertainty of about 2–3 kcal/mol, where the errors tend to be larger for lower oxidation states (e.g., Mn3333) than for higher ones (e.g., Mn4444).

Absorption spectra were computed with the help of TDDFT calculations, also performed with ORCA 4.2.1.^27,28 We used the Tamm–Damcoff approximation⁴¹ to compute 100 roots so that we cover absorption wavelengths up to about 300 nm. As exchange and correlation effects are more critical for excited-state calculations than for ground state optimizations, the hybrid CAM-B3LYP functional⁴² was employed in this endeavor. The larger ZORA-TZVP basis set^35,36 was used for Mn, V, and O atoms. The calculations were accelerated with the RIJCOSX technique.⁴³ The obtained vertical excitation energies and oscillator strengths were converted into spectra by convolution with Gaussian line shape functions with a full width at half-maximum of 0.25 eV.

For all the considered oxidation states, we show in Fig. 2 the calculated relative free energies for each protonated O atom of each JT isomer. Corresponding Mn–O bond lengths and JT arrangements are in Tables S7–S10 and corresponding free energies are in Tables S11–S15. In our analysis, we are mostly interested in the relative free energy of the protonated species depending on the protonation site as well as the position of that protonation site relative to the JT axes. Therefore, we distinguish between three different relative protonation positions, as sketched at the top of Fig. 2. An “on-axis” position corresponds to one of the two O atoms involved in a JT axis (i.e., one of the two O atoms with exceptionally long distances to Mn^III). An “orthogonal” position is one of the four other O atoms surrounding a Mn^III atom. Finally, a “remote” position is one that is at least three bonds away from any Mn^III atom; this also includes O atoms on the vanadate ligand and those in Mn4444 structures. All the similar O sites (terminal, bridges, cubane, and acetate) are grouped together and indicated by braces in panel a.

The relative energies of the eight distinguishable protonation sites of the Mn4444 oxidation state (Table S11) are plotted in Fig. 2(a). As in this oxidation state, there are no Mn^III atoms and, therefore, no JT axes; all protonation sites correspond to remote sites (black lines). We see that the different protonation sites lead to strongly varying energies. According to the employed BP86 functional, the least favorable sites are the apical cubane O atom OJ, at a relative free energy of 27 kcal/mol, followed by the acetate O atoms OO and OP, with energies of 18 and 19 kcal/mol, respectively. Lower energies are predicted for the cubane sites OL (10 kcal/mol) and the bridges OB (7 kcal/mol) and OE (2.5 kcal/mol). The most favorable protonation sites are the vanadate terminal O atoms OA (1.4 kcal/mol) and OC (0 kcal/mol). Recalling that our estimated free energies have an uncertainty of about 3 kcal/mol (Tables S3–S6), we conclude that OC, OA, and OE are the dominant protonation sites for Mn4444.

Table S7 lists the average bond lengths of the 12 coordination axes of the Mn atoms and how they change upon protonation. On average, all Mn coordination axes slightly contract (0.01–0.02 Å) upon protonation, regardless of where the proton is attached—even protonation at the OA site leads to a contraction of the bond lengths in the cubane unit. Furthermore, protonation leads to some localized changes in bond length, e.g., protonation of an acetate at OO or OP leads to a moderate elongation of the corresponding Mn–O bond (by 0.05–0.06 Å). Overall, protonation of the Mn4444 structure has only a little effect on the bond lengths.

The vibrational frequencies of the O–H stretch mode related to the attached proton are given in Table S11. Interestingly, the vibrational frequencies correlate almost linearly with the relative free energy of the respective geometry (Fig. S2). The highest frequency is found for OC protonation (0 kcal/mol and 3670 cm⁻¹), whereas the lowest one is found for OJ protonation (27 kcal/mol and 3520 cm⁻¹). The proton being nestled in between the V and O atoms, feeling electrostatic attraction and repulsion, respectively, leads to a reduction of the vibrational frequency. In the case of Mn3444 (see below), especially for 4z44, we could also observe such a linear behavior. Yet, the O–H frequency of OJ deviates significantly, being ∼500 cm⁻¹ lower than the others. With further reduction of the Mn atoms, the observed linearity between frequency and relative energies vanishes (Fig. S2).

In Table S11, we also collect the distance between OJ and the apical V atom (the one bonded to OA). For Mn4444, this distance is about 3 Å for either the unprotonated or protonated molecule. The only exception is protonation at the OJ site, which slightly extends the vanadate cage, leading to an increased OJ–V distance of 3.2 Å.

Finally, Table S11 additionally provides information on the protonation free energies, indicating the likelihood of the complex absorbing a proton from the solution. For the Mn4444 oxidation state, these energies are positive or only slightly negative, indicating that only a small fraction of molecules will be protonated in solution even at a rather low pH.

Some of these results, regarding the energetic ordering and structural changes of protonated Mn4444, are somewhat surprising. According to the literature,^23–25 in POMs, the terminal sites (M = O) are typically not good protonation sites if the metal atoms are prone to forming terminal double bonds (those include V, W, and Mo).^44,45 In such POMs—e.g., the MnV WOC—the bridging sites (M–O–M, μ₂ or μ₃) are preferred as protonation sites. However, the MnV WOC in the oxidation state Mn4444 clearly shows a preference for terminal sites. Heterometallic bridges (Mn–O–V, labeled as OE) might be competitive with terminal sites because they are easier to protonate than other bridging sites, an aspect that is in line with the literature.²⁴ The other bridging O atoms are progressively worse protonation sites, in the order V–O–V, Mn₃O (μ₃), and Mn–O–C (acetate). Noticeably, this finding is consistent in the other oxidation states (see below), except that the protonation on-axis will progressively become more stable.

Intriguingly, the energetic ordering of the protonation sites does not seem to be directly related to the properties of the unprotonated species. For example, population analysis or electrostatic potentials are sometimes used in older works as a proxy for predicting the basicity of different sites in POMs.^19,46 The Mulliken charges of unprotonated Mn4444 are in Table S16. The most negative O atom—presumably the most basic site—is OJ, which is clearly the worst protonation site according to the relative free energies. The least negative O atoms are the acetate OO and OP sites, but they are the second-worst protonation sites. By contrast, the preferred protonation sites, OE, OA, or OC, have intermediate Mulliken charges. We thus agree with some other works^22,25 that the partial charges of O atoms cannot be used to accurately predict favorable protonation sites. While the energetic ordering of the protonation sites appears to be rather non-intuitive in general, some aspects seem more obvious. The very unfavorable energy of protonation at the OJ site can be explained by the strong steric hindrance of bringing a proton inside the vanadate cage. A clear sign of such steric effects is provided by the OJ–V distance (Table S11), which is significantly longer for protonating OJ than for any other protonation site. This shows that the vanadate cage needs to be deformed to enable the housing of the proton, making this process energetically demanding. We note that OJ is the only protonation site that is sterically hindered in the MnV WOC.

It also appears that the structural changes (bond lengths) upon protonation are indicative of a general charge redistribution in the system. As shown in Table S7, the entire molecule seems to contract systematically (by 0.01–0.02 Å) upon protonation, rather independent of where the proton is added. We assume that this is an effect of reducing the overall charge of the molecule and allowing the electrons to delocalize over a slightly larger volume. This reduces overall electron–electron repulsion and allows the molecule to contract slightly.

Figure 2(b) shows the relative free energies of protonation of the catalyst in the oxidation state Mn3444. Unprotonated, this oxidation state exhibits two (meta-)stable JT arrangements: One in which the JT axis extends from OJ to one of the three OO atoms [see Fig. 1(b)], which was labeled in Ref. 14 as 4z44. In the other, the JT axis stretches from one of the OL atoms through the apical Mn atom to the trans-standing OP atom, which was labeled¹⁴ as z444. This z444 arrangement is about 10 kcal/mol less stable than 4z44. Based on these facts, four protonation sites—OJ, OL, OO, OP—can in principle be protonated in an on-axis fashion. Alternatively, the sites OJ, OL, OP, and OE might be protonated in an orthogonal position.

In Fig. 2(b), one can see that the reduction of one Mn atom does not strongly change the relative ordering of the protonation sites. The most favorable sites are still OC, OA, and OE; the lowest minima corresponding to these protonation sites show up at relative free energies of 0–4 kcal/mol. The sites OB and OL appear at intermediate energies (lowest conformers at 7 or 5 kcal/mol, respectively). The sites OJ (16 kcal/mol), OO (12 kcal/mol), and OP (17 kcal/mol) are only found at high relative energies. For protonation of the vanadate (OA, OC, OB, and OE), we note that the various minima are clustered in two sets separated by about 10 kcal/mol. The low-energy set corresponds to protonation of the more stable 4z44 JT arrangement, whereas the high-energy set arises from protonation of z444. In the protonation of the cubane or the acetates (OJ, OL, OO, OP), these two sets are not discernible anymore, as the interaction of JT axes with the proton leads to notable energy shifts.

We note that Table S11 indicates a systematic decrease in the protonation free energies relative to Mn4444. This can be traced to the increased negative charge of the reduced Mn3444 species.

We also note that the results of the “remote” protonation sites (black lines) of Mn3444 agree very well with the ones of Mn4444, as indicated by the dotted lines in Fig. 2(b). On the contrary, some O sites exhibit very different protonation energies when in an “orthogonal” (red) or “on-axis” (blue) position. For example, in the case of Mn4444, protonating OJ requires 27 kcal/mol (relative to the most easily protonated site), while in Mn3444 it requires only 16 kcal/mol if OJ is located on-axis. Similarly, on-axis protonation of OL and OO requires less energy than remote protonating of the same site.

At this point, one should note that during some of the optimizations, the JT arrangement changed (Tables S7–S10). For the Mn3444 oxidation state (Table S7), this occurred in four cases when the initial JT arrangement was z444—the least stable JT arrangement for that oxidation state. These cases are depicted schematically in Fig. 3. In panel (a), the JT axis is initially located on the apical Mn atom (bottom left), but protonation of the remote OJ site seems to favor a JT axis through one of the three other Mn atoms so that on-axis protonation can be achieved. In panel (b), protonation of the (initially orthogonal) OL site leads to a change in the orientation of the JT axis on the apical Mn atom, again to achieve on-axis protonation. Panels (c) and (d) show similar JT arrangement changes upon protonation of the OO and OP, corresponding to the acetate O atoms, to form on-axis protonation geometries. Moreover, in panels (a) and (c), a “jump” of the JT axis can be observed, accompanied by an electron transfer originating from the apical Mn atom.

The results of the Mn3444 oxidation state are very helpful in understanding the interaction between the JT effects of the MnV WOC and its protonation. First, as one could have expected, protonation of the vanadate ligand does not notably interact with the JT axes. Hence, the relative energies of the vanadate protonation sites (OA, OC, OB, OE) are nearly identical to the Mn4444 oxidation state, and the relative energies of the JT arrangements (z444, 4z44) are nearly identical to the unprotonated Mn3444 oxidation state. This is presumably because the vanadate protonation sites are too far away from the cubane to interact with the extra electron density of the Mn^III atoms. Second, the protonation of a cubane or acetate site is strongly affected by the position of the JT axis relative to the proton. As is clearly visible from our results, an O atom located directly on a JT axis (i.e., an atom that belongs to an elongated Mn–O bond) is much more basic than the same atom in the absence of the JT axis. The same is true, but to a lesser extent, for O atoms that are orthogonal to a JT axis, i.e., bonded to a Mn^III atom but not by an elongated bond. This stabilization of protonation sites via JT axes can be explained by the larger electron density of the O atoms due to the occupied $dz2$ orbital of the neighboring Mn atom. Note, however, that Mulliken charges do not properly capture the effective charges (see Table S17), as discussed earlier.

The molecular orbital energies in Fig. S1 show nicely how the electronic structure of the MnV WOC is affected by reduction and protonation. In Mn4444, the HOMO–LUMO gap is about 1.6 eV, but reduction of one of the Mn atoms decreases that to 1.1 eV. Protonation at OJ (on-axis) further decreases the gap to 0.8 eV, whereas protonation at OB (remote) only slightly increases it to 1.2 eV. On-axis protonation also leads to an overall stabilization of all orbital energies, explaining why such protonation configurations are more favorable.

The relative free energies of the Mn3344 oxidation state are shown in Fig. 2(c). Unprotonated, this oxidation state exhibits three stable minima, with two JT axes crossing at OJ (labeled 44xy), with one JT axis through the apical Mn atom and both axes parallel (zz44), or with one JT axis through the apical Mn atom and both axes skew-aligned (yz44).¹⁴ With two JT axes, protonation sites formally could be “double on-axis,” “double-orthogonal,” or even “simultaneously on-axis and orthogonal” (classified under “on-axis”).

As shown in Fig. 2(c), the protonation site preference in the Mn3344 oxidation state is different than in the Mn3444 and Mn4444 oxidation states. The preferred site for Mn3344 is clearly OL (cubane O atoms located between the acetates), which provides the lowest relative free energy (0 kcal/mol). The runners-up are structures with protonation at OC and OE positions (about 4 kcal/mol), which are the preferred sites for the Mn3444 and Mn4444 oxidation states. At higher relative free energies, we find OA (8 kcal/mol), OB (10 kcal/mol), OJ (10 kcal/mol), and eventually the acetate sites OO (18 kcal/mol) and OP (19 kcal/mol).

As discussed for Mn3444, there seems to be a strong effect of the JT axis proximity to the protonation site on the relative protonation energies. As shown in Fig. 2(c), the relative energies of remote sites (black lines) are nearly unchanged when compared to the relative energies of the Mn4444 oxidation state (dotted lines). Stated differently, when looking only at the remote sites, the preference for protonation does not depend on the overall oxidation state. However, the picture changes dramatically when protonating in orthogonal (red lines) or, particularly, on-axis positions (blue lines). For OJ and OL, the relative free energies are strongly reduced compared to Mn4444 (dotted lines). In addition, for the acetate sites OO and OP, protonation requires less energy for on-axis positions than for remote positions. This strong stabilization of on-axis protonation sites leads to a switch in the preferred protonation site for the Mn3344 oxidation state.

The stabilization of on-site protonation changes the preference of the protonation sites and also the favored JT arrangement. Tables S7 and S8 illustrate how, during some of the optimizations, the initial JT arrangement was not preserved; in most cases, the JT arrangement changed in such a way to achieve on-axis protonation, similar to what was observed for Mn3444. This phenomenon is particularly pronounced when considering the protonation of the Mn cubane. Except for protonations that already show an initial on-axis geometry, cubane protonation leads to a shift of the JT axis toward an on-axis orientation. In the few other cases, a JT switch preserved a remote protonation, e.g., protonation of the OA vanadate site, but switched to a more favorable JT arrangement—in agreement with the rules laid out in Ref. 14. We also observed two cases where protonation led to a rare compressed octahedral coordination of Mn^III instead of the typical elongated octahedral coordination. In these latter compressed octahedral coordination cases, inspection of the orbitals showed that protonation seemingly changed the ordering of the $dz2$ and $dx2−y2$ orbitals of the affected Mn atom. In general, protonation of the cubane and acetate sites (OJ, OL, OO, and OP) seems to have the greatest chance of modifying the JT arrangement, in line with the large stabilization offered by on-axis protonation.

The Mn3334 oxidation state’s protonation energies are shown in Fig. 2(d). Unprotonated, this oxidation state has four stable minima within 3 kcal/mol.¹⁴ In all minima, there are two JT axes from OJ to one of the OO sites, and the different minima differ only in the third JT axis. The two most stable structures have the third JT axis on the apical Mn atom in two possible orientations that do not affect energy (labeled z4xy and y4xy). The third minimum features one JT axis pointing to a vanadate OE (4yxy), and the fourth one exhibits all three JT axes between OJ and OO (4zxy).¹⁴ These minima provide opportunities for double or triple on-axis protonation of OJ, while OL could be protonated in an “on-axis plus doubly orthogonal” fashion.

For the Mn3334 oxidation state, Fig. 2(d) shows that the preferred protonation site is clearly OL. The next favorite site is, surprisingly, OA, at about 6 kcal/mol, surpassing the previously preferred sites OC and OE. The other protonation sites are predicted at higher energies: OC (9 kcal/mol), OJ (9 kcal/mol), OE (10 kcal/mol), and OB (14 kcal/mol). The acetate sites OO and OP are very unfavorable, requiring energies of about 20 kcal/mol. Therefore, the reduction of the complex by one electron again changes the order of protonation sites.

One of the reasons for this change is the strong stabilization of the OJ and OL protonation sites by the JT axes. The most stable structure features a protonated OL atom stabilized by three nearby JT axes; it is classified as singly on-axis and doubly orthogonal. This structure is depicted in Fig. 4(a). The proximity to three Mn^III atoms in the cubane provides the high electron density required to stabilize the proton. Another case of strong stabilization of a protonation site is the OJ site when it is located on-axis for all three JT axes. As indicated in Fig. 4(b), in this constellation, the O atom OJ and the proton could be thought of as a hydroxyl ion trapped in a cage consisting of the vanadate and the remainder of the cubane. Whereas JT axes provide a strong boost in basicity for the OL and OJ sites, OO and OP sites (on the acetate) and OE sites (on the vanadate) become only slightly more basic when located on a JT axis.

Tables S8 (bottom) and S9, as well as Tables S13 and S14, provide some additional details on the effects of protonation on the Mn3334 oxidation state. Protonation of the OA site produced only one optimized minimum—independent of the initial geometry—that exhibits the 4zxy JT arrangement with all three JT axes pointing toward the OJ atom. Interestingly, this triple JT axis crossing was previously reported to be energetically unfavorable,¹⁴ but protonation of OA seems to stabilize it. Inspection reveals that the OJ atom is actually transferred to the vanadate—the distance between OJ and the apical V atom is compressed to only 1.85 Å, and the apical V atom adopts a trigonal bipyramidal coordination sphere with five nearly equal V–O distances [Fig. 4(c)]. In this geometry (similar to panel b), the cubane is arguably broken, leaving a Mn₄O₃ moiety similar to several structures reported by different groups.^47–49 Some of the OB-protonated structures show similar behavior—switching to the 4zxy JT arrangement and migration of OJ to the vanadate [Fig. 4(d)].

After the protonation of OC, in some cases, we observe an electron transfer from Mn to V, forming a formal Mn3344 (44xy) structure and reducing the V atom near the protonated OC site to V^IV. In this structure, the distance between OJ and the reduced V atom gets rather short (2.2 Å), although it does not form a five-coordinated V atom (this would require a MnO₂V four-membered ring) as seen in OA protonation. Instead, the V^IV adopts trigonal pyramidal coordination [see Fig. 4(e)].

Finally, the bond lengths in Tables S8 (bottom) and S9 indicate that protonation in an OO position can lead to the dissociation of the affected acetate ligand (actually acetic acid) in the case of y4xy. This only happens if two JT axes point toward the same acetate, already providing elongated bonds and easing the dissociation. As shown in Fig. 4(f), the dissociated ligand stays near the complex (in the example, the acetate is rotating, leading to a hydrogen bond to the vanadate ligand with a bond length of 1.55 Å). We assume that an explicit description of the solvent would be required to properly simulate the separation between the acetic acid leaving group and the complex.

In addition to the previously noted observations, we identified two instances similar to Mn3344, where protonation led to a rearrangement of the $dz2$ and $dx2−y2$ ordering, resulting in a compressed octahedral coordination.

Finally, the relative free energies of the protonated Mn3333 structure are shown in Fig. 2(e). There exist two unprotonated stable JT arrangements,¹⁴ either with three JT axes meeting at OJ and another JT axis at the apical Mn (zzxy) or with two JT axes meeting at OJ, the apical Mn axis, and an axis to the vanadate (zyxy). As can be appreciated in the figure panel, this oxidation state behaves similarly to Mn3334, exhibiting essentially the same ordering of protonation sites: OL < OA ∼ OE < OC ∼ OJ < OB < OO ∼ OP. On-axis protonation of OJ and OL is strongly stabilized. Similar to Mn3334, the optimizations involved many alterations of the JT axes. Every protonation of the cubane O atoms, or OP, led to the formation of an on-axis protonation structure.

Even though the energies are consistent with those predicted for the Mn3334 oxidation state, here we observe additional features. As shown in Table S10, for two OL-protonated structures, we find an apical Mn atom where all three coordination axes are stretched, differing from the elongated or compressed octahedral coordination that is otherwise found in the MnV WOC. Inspection of the spin populations and occupied orbitals confirms that in this structure, the apical Mn atom is Mn^II. The population of both the $dz2$ and $dx2−y2$ orbitals leads to the above-mentioned stretching in all directions. Therefore, protonation can enable the intramolecular disproportionation of the MnV WOC to a Mn^IIMn$2III$Mn^IV oxidation state, which emphasizes the flexibility of the redox states of the Mn₄O₄ cubane cluster. In addition to Mn–Mn disproportionation, for some Mn3333 structures, we have observed electron transfer from Mn to V, similar to some examples of Mn3334 discussed earlier.

As expected, the protonation free energies (Tables S10 and S11) of the Mn3333 oxidation state are the most negative. Comparing all oxidation states, the protonation free energies clearly correlate with the overall amount of negative charge of the molecule.

Based on the observations made across the different oxidation states, we can summarize a set of heuristic protonation rules for the present MnV WOC, some of which should be generalizable to other heterometallic polyoxometalates.

• The protonation of acetate ligands consistently shows unfavorable energetics. This implies that ligands with low basicity (or, conversely, ligands whose conjugated acid is rather strongly acidic) are generally unlikely protonation sites. However, if they are actually protonated, they might be decent leaving groups [see, e.g., Fig. 4(f)].

• In the MnV WOC and other POMs with polyvalent metal atoms, intramolecular charge transfer and JT axis reorientation can stabilize a proton at certain O sites.

• O atoms coordinating Mn^III tend to be more basic than O atoms coordinating Mn^IV atoms (or more generally, O atoms coordinating metals in lower oxidation states are more basic).

• Moreover, O atoms located on a JT axis are more basic than other O atoms coordinated to the same metal atom.

• POM cubane structures generally become more basic upon reduction. This can lead to a switch in protonation preference relative to other parts of the molecule (here, relative to the vanadate).

Figure 5 provides a graphical overview of how the oxidation state governs the preferred protonation sites. The figure also summarizes the observed chemical consequences of the protonation, especially at low oxidation states. In general, when the system is reduced, the entire molecule, but particularly the cubane, becomes more susceptible to protonation. The system experiences chemical effects, including degradation through dissociation, electron transfers, and cubane opening.

The experimental observation of the preferred protonation sites in the MnV WOC is very challenging due to fast proton exchange dynamics and the fact that protons are not readily visible in x-ray structures.¹³ Hence, one way to validate some of our results, i.e., the different protonated structures and their relative free energies, is to compare them with the available experimental pH-dependent absorption spectrum of the Mn3344 oxidation state of the MnV WOC.⁹ We note that this validation is limited by the narrow wavelength range available in the spectrum (600–900 nm), but we are not aware of other experimental data that would allow the investigation of the protonation behavior of the MnV WOC.

We simulated the absorption spectra of all protonated Mn3344 structures (as given in Tables S7 and S8). The spectra are shown in Fig. 6(a), grouped by protonation site. For each protonation site, the spectrum of the most stable structure is drawn with a solid line. The spectra of less stable structures are drawn with semi-transparent lines, as these will contribute less to the overall absorption spectrum. Note that the transparency scale is applied independently for each protonation site—a global transparency scale would produce only a single solid line (for the most favorable protonation site) and many transparent lines, hampering clarity. The relative free energies between the protonation sites are indicated in brackets on the right of Fig. 6(a). As discussed earlier, for Mn3344, the most favorable site is OL, which has a relative free energy of 0 kcal/mol, and protonating other sites requires at least 4 kcal/mol more. A consequence of using individual transparency scales is that transparent lines of a favorable protonation site (e.g., transparent lines of OL) can correspond to lower free energies than solid lines of unfavorable protonation sites (e.g., solid lines for OP). This is on purpose because we would like to focus our discussion on the most likely spectral shape arising from the protonation of the different sites so that we can later infer the protonation site from the observed spectrum.

The spectra can be divided into three main regions¹⁵ based on the predominant excitation characters. At wavelengths shorter than about 350 nm, various local and charge transfer transitions localized on the vanadate, acetates, and cubane overlap with each other, as given in Figs. S3–S10 (see excitations $>3.5$ eV). This spectral congestion of the short-wavelength region makes it hard to rationalize the spectral changes upon protonation and, therefore, to use this region as an indicator for the preferred protonation site. Above 350 nm, nearly all transitions are predominantly local d → d transitions within the Mn atoms (Figs. S3–S10; pay attention to states below 3.5 eV). The most interesting spectral region is above 600 nm (⁠$<2$ eV), which is exclusively due to one local excitation per Mn^III atom involving the occupied $dz2$ orbitals that produce the JT deformations. Please refer to Fig. S1 to see how the reduction of a Mn^IV atom leads to a strongly reduced HOMO–LUMO gap, which gives rise to the absorption above 600 nm.

Based on the spectra shown in Fig. 6(a), it is possible to estimate how the absorption spectrum would change upon protonation of a specific site, in particular in the Mn^III region above 600 nm. To this end, we compare the spectra of the lowest-energy structures for each protonation site (solid colored lines) with the spectrum of the unprotonated compound (dotted lines). We see that protonation of the acetate ligands at site OP leads to a strong reduction of absorption above 600 nm due to a decrease in oscillator strength and a blueshift of the relevant absorptions. Instead, if protonation occurs on OO, the band at 800 nm is slightly weakened, and another band at 600 nm arises. Protonation directly at the cubane OL atoms leads to a significant reduction in the intensity of the 800 nm band and a blueshift to about 700 nm. On the contrary, protonation at OJ does not change the low-energy band significantly. Protonation of the bridges OE and OB splits the low-energy absorption band. By contrast, a proton added at the terminal site OC leads to a remarkable broad absorption at 800–1200 nm, whereas protonation at OA does not affect the absorption spectrum strongly. For the higher-energy part of the spectrum, we see that the 400–500 nm band is almost unaffected by protonation, except if protonation occurs on the cubane (OL and OJ). In the latter case, this band increases significantly in intensity (compare the dotted lines against the solid lines). Below 350 nm, the maximum at 330 nm of the unprotonated complex shifts to shorter wavelengths upon protonation, regardless of the position the proton is attached to.

The overall influence of protonation on the absorption spectrum is depicted in Fig. 6(b), where we plot the Boltzmann-averaged sum of all absorption spectra in panel a. The resulting spectrum, mostly due to structures protonated at OL, is shown as a black line. The gray line is the spectrum of the unprotonated compound¹⁵ at the same level of theory. One can see that upon protonation, the band at 800 nm of the unprotonated spectrum weakens and splits into two components: the stronger blueshifts and the weaker redshifts. On the contrary, the band at 450 nm remains at the same energy but significantly increases in intensity.

Our simulated spectra of unprotonated and protonated MnV WOC can be compared to the experimental pH-dependent absorption spectra recorded⁹ in DMSO upon the addition of five aliquots of 10 mM para-toluene sulfonic acid, as shown in Fig. 6(c). The spectra show an isosbestic point at 667 nm, indicating that the pH-dependent spectra are the result of the superposition of only two spectra. This makes it likely that only one single protonation step (Mn3344³⁻ ⇌ HMn3344²⁻) is involved in the experiment in the measured pH range. At longer wavelengths, especially in the 750–900 nm region, absorption is reduced by acid addition, showing that in this region, the protonated MnV WOC absorbs less than the unprotonated one. The opposite is true at wavelengths below 667 nm. These findings agree qualitatively with our computed absorption spectra.

Based on our calculations and the shape of the absorption spectra in Fig. 6, we can identify two main mechanisms by which the spectrum is affected through protonation. First, on-axis protonation—the predominant type of protonation for Mn3344—significantly lowers the energy of the involved $dz2$ orbital, which blueshifts the corresponding transitions. Second, protonation can induce changes in the relative stability of the JT isomers and, therefore, lead to a switch, e.g., from “44xy” to “zz44” or “xz44” structures. We observe such switches for the most relevant OL protonation site, which indicates that this might be the main mechanism for the pH dependence of the absorption spectrum of the MnV WOC in the Mn3344 oxidation state. Further possible mechanisms that might contribute at lower oxidation states are switches from occupied $dz2$ to occupied $dx2−y2$ orbitals due to protonation and migration of the OJ atom from the cubane to the vanadate, although the involved structures have relatively high energy.

In this work, we investigated the protonation behavior of the manganese-oxo vanadate water oxidation catalyst [(Mn₄O₄) (V₄O₁₃) (OAc)₃]³⁻ by examining the basicity of different O atoms. For that purpose, we considered five oxidation states from Mn$4IV$ (“Mn4444”) to Mn$4III$ (“Mn3333”). Due to mixed-valence and Jahn–Teller orientational isomerism, these five oxidation states have 12 different stable structures,¹⁴ which were all considered in the present work. A total of 198 symmetry-inequivalent protonated structures were optimized by DFT calculations. We identified the most likely protonation sites based on the relative free energies of the optimized structures, finding that for high oxidation states, protonation on the vanadate dominates, whereas for lower oxidation states, the protons attach to the Mn₄O₄ cubane. This change of preference is caused by a strong increase in the basicity of O atoms upon the reduction of the coordinated Mn atom. In other words, O atoms partaking in JT axes are very basic—significantly more than O atoms orthogonal to or remote from the JT axes. Our analysis allowed us to derive a set of five heuristic rules that provide comprehensive insight into the protonation behavior not only of this MnV WOC but possibly other similar polyoxometalates.

Besides the relative free energies of the different protonated structures, we also investigated what possible effects protonation can have on the MnV WOC. We found that, particularly at low oxidation states, protonation can induce the relocation of the JT axes, charge transfer (from Mn to Mn, or possibly from Mn to V), ligand dissociation (of acetates), or the opening of the cubane structure. Moreover, protonation affects the electronic structure and, therefore, the UV/Vis absorption spectrum of the compound. We calculated the corresponding spectral shifts for the Mn$2III$Mn$2IV$ oxidation state, for which experimental pH-dependent spectra are available.⁹ Overall, we obtained a qualitatively good agreement with the experiment in that protonation reduces absorption at long wavelengths (local excitations of Mn^III atoms). Two main mechanisms for how the spectra are affected by protonation have been identified. First, protonation can affect which of the Mn atoms are in oxidation state III and which are in oxidation state IV, which in turn affects the ligand field of the available Mn^III atoms. Second, protonation near the Mn^III atoms affects the energies and shapes of the Mn d orbitals, leading to shifts in excitation energies and intensities.

This study deepens our understanding of polyoxometalates, underscoring the significant impact of Jahn–Teller distortions on protonation behavior. As a result, we anticipate that this research will help not only enhance the efficiency of WOCs but also pave the way for targeted exploration into new and improved catalysts. The current work is also interesting to predict possible hydrogen bonding sites of the WOC, as, e.g., one can expect that in protic solvents, the most easily protonated O atoms form hydrogen bonds most readily.

Overview of the symmetry of protonation sites and JT axes; molecular orbitals; ORCA input file; benchmarks of the DFT level of theory; bond lengths and JT configurations of all geometries; free energies, O–H frequencies, and OJ–V distances; Mulliken charges; correlation plots of protonation free energy and O–H frequencies; and transition analysis of excited states.

This research was funded in whole or in part by the Austrian Science Fund (FWF) [grant DOI 10.55776/I6116] and the Deutsche Forschungsgemeinschaft (DFG) [TRR234 “CataLight,” Project No. 364549901, subproject C3]. For open access purposes, the authors have applied a CC-BY public copyright license to any author accepted manuscript version arising from this submission. The authors acknowledge the Vienna Scientific Cluster for the generous allocation of computational resources, the University of Vienna for continuous support, and Dr. Ludwig Schwiedrzik for preliminary work.

The authors have no conflicts to disclose.

Simon Tippner: Data curation (equal); Formal analysis (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Patrick Lechner: Data curation (equal); Formal analysis (equal); Validation (equal); Writing – original draft (equal). Leticia González: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal). Sebastian Mai: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Methodology (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.