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Dec 30, 2015 - calculations to investigate how chemical equilibria can be described in the S3 state of the oxygen-evolving complex in photosystem II...
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Chemical Equilibrium Models for the S3 State of the Oxygen-Evolving Complex of Photosystem II Hiroshi Isobe,*,†,‡ Mitsuo Shoji,§ Jian-Ren Shen,† and Kizashi Yamaguchi‡,∥ †

Photosynthesis Research Center, Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan ‡ The Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan § Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan ∥ Institute for NanoScience Design, Osaka University, Toyonaka, Osaka 560-0043, Japan S Supporting Information *

ABSTRACT: We have performed hybrid density functional theory (DFT) calculations to investigate how chemical equilibria can be described in the S3 state of the oxygen-evolving complex in photosystem II. For a chosen 340-atom model, 1 stable and 11 metastable intermediates have been identified within the range of 13 kcal mol−1 that differ in protonation, charge, spin, and conformational states. The results imply that reversible interconversion of these intermediates gives rise to dynamic equilibria that involve processes with relocations of protons and electrons residing in the Mn4CaO5 cluster, as well as bound water ligands, with concomitant large changes in the cluster geometry. Such proton tautomerism and redox isomerism are responsible for reversible activation/deactivation processes of substrate oxygen species, through which Mn−O and O−O bonds are transiently ruptured and formed. These results may allow for a tentative interpretation of kinetic data on substrate water exchange on the order of seconds at room temperature, as measured by time-resolved mass spectrometry. The reliability of the hybrid DFT method for the multielectron redox reaction in such an intricate system is also addressed.

1. INTRODUCTION Oxygenic photosynthesis in plants, algae, and cyanobacteria is one of the fundamental processes for the maintenance of life in the biosphere. It uses a unique pigment−protein complex called photosystem II (PSII) to capture the energy from sunlight by splitting water into oxygen, protons, and electrons (2H2O → O2 + 4H+ + 4e−); the latter two products are used to drive the synthesis of ATP and NADPH, which are the sources of the energy and electrons required to convert carbon dioxide into carbohydrates.1 The remarkable catalytic efficiency of the lightdriven water oxidation is possible owing to the evolutionary invention of the oxygen-evolving complex (OEC) embedded in PSII. The catalytic cycle by OEC involves five different redox states denoted by Si (i = 0−4), which couples the one-electron photochemistry at the P680 reaction center with the fourelectron oxidation of two substrate water molecules bound closely to the inorganic Mn4CaO5 cluster within the OEC.2,3 In the past few years, there have been significant refinements of the X-ray diffraction structures of PSII in the dark stable S1 state.4 At the same time, significant advancements in a variety of spectroscopic techniques,3b,c,5−8 as well as numerous efforts using theoretical calculations,9 have provided various lines of information on the geometric and electronic structures of the Mn4CaO5 cluster in each S state, which are very important to © XXXX American Chemical Society

understand how the OEC performs catalytic function. For example, Figure 1 displays the recently suggested structures of the Mn4CaO5 core in the S3 state by an electron paramagnetic resonance (EPR)/density functional theory (DFT) study.10 Despite extensive studies, however, there is still ambiguity regarding the substrate binding sites and the mechanism of O− O bond formation,3 and two competing possibilities have been proposed based on different experimental and computational evidence.11,12 A common feature is the formation of a highvalent metal site, MnV or MnIV, which makes a bound substrate oxygen species highly electrophilic in an oxo or oxyl radical form. In the acid−base mechanism, the highly polarized oxo group by the MnV ion is regarded as an ideal target for nucleophilic attack by a terminal water molecule bound within the coordination sphere of the Ca2+ ion.3a,11 An alternative mechanism involves the oxyl radical formed at the MnIV site, which couples with a nearby Mn-bridging oxo group.12 A time-resolved mass spectrometry experiment can be used to determine the rate of substrate water exchange by Special Issue: Small Molecule Activation: From Biological Principles to Energy Applications Part 3 Received: October 27, 2015

A

DOI: 10.1021/acs.inorgchem.5b02471 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 1. Open- and closed-cubane structures in the S3 state, as suggested by a recent EPR/DFT study,10 which are both in the all-MnIV oxidation state with S = 3.

quantifying the degree of incorporation of 18O from isotopically labeled water (H218O) into dioxygen product.11a,13 This technique provides valuable information on the interactions of substrate water molecules with the catalytic site throughout the S-state cycle. Such measurements resolved only one slowly exchanging water in the S0 and S1 states, with a rate that dropped substantially from ∼10 to ∼0.02 s−1 upon the S0 → S1 transition (at 10 °C, pH 6.8).13d In the S2 and S3 states, two kinetic phases were resolved; the first one was decelerated gradually as the OEC advances to the higher S state (∼120 s−1 for S2 and ∼40 s−1 for S3), while the slow one, in turn, increased significantly to ∼2 s−1 upon the S1 → S2 transition but remained almost unchanged for the subsequent S2 → S3 transition.13d These puzzling kinetic patterns imply that the water exchange mechanism may be complex, in particular for the slow water exchange. Siegbahn attempted to resolve this difficult problem with DFT calculations and suggested a probable mechanism for the fast- and slow-exchange kinetics within the framework of the oxo−oxyl radical coupling mechanism, in which two substrate oxygen species are assigned to a bridging μ-oxo group (O5) and a terminal oxygen ligand (Win) at the MnD site;12e for the labeling of Mn atoms and ligands, see Figure 1. The results showed that the slow water exchange in the S1 and S2 states might represent the net result of complex, multistep processes via the exchange of two hydroxides at the MnB center with an oxidation state of III.12e This means that the rate of 18O isotope exchange determined by the mass spectrometry cannot be used as a direct measure of the substrate binding affinity at the catalytic metal site. Siegbahn also addressed the water exchange in the S3 state by invoking an equilibrium mediated by the redox-active tyrosine residue Tyr161 (YZ), S3YZ (normal S3 state) ↔ S2YZ• (proton-depleted S2 state), and suggested that water exchange might occur in the S2YZ• state in a manner similar to the one in the S2 state. A recent hybrid quantum mechanical/molecular mechanical (QM/MM) study, however, indicated that the reverse reaction S3YZ → S2YZ• requires a prohibitively high activation barrier of about 35 kcal mol−1.14 This finding naturally raises a question: how can chemical equilibria be described in the normal S3 state? To answer this question, we have investigated the geometric and electronic structures and relative energies of low-lying intermediates in the S3 state by means of dispersion-corrected hybrid DFT calculations. As will be demonstrated below, our calculations predict that the dynamic aspects of the S3 state on the order of seconds at room temperature can be described by the interplay of multiple states

that are chemically reversible via proton tautomerism and redox isomerism. This picture resembles closely the “multiple S3 state” model suggested by Renger.15 We also address whether the hybrid DFT method can provide reasonable results for the redox reaction in such an intricate system as the OEC.

2. COMPUTATIONAL DETAILS The computational procedure in the present study is the same as the one previously described.16 The initial structure for QM calculations was taken from the X-ray structure of PSII (PDB ID: 3ARC, monomer A).4a The QM model consisted of 340 atoms (Figure S1), including the inorganic Mn4CaO5 cluster, 20 crystallographic water molecules plus one extra water molecule (labeled Win), one chloride ion (Cl−), and the following amino acid residues in the first and second coordination spheres: Asp61, Tyr161 (YZ), Gln165, Ser169, Asp170, Asn181, Phe182 (backbone only), Val185, Glu189, His190, Asn298, Lys317, His332, Glu333, His337, Asp342, Ala344, Glu354, and Arg357. All calculations were carried out with Gaussian 09.17 Geometry optimizations were performed with the hybrid B3LYP functional18 using a set of extensive basis sets that consists of LANL0819a for Ca, LANL2TZ(f)19a for Mn, 6-311+G(d,p)19b for aqua/hydroxo/oxo ligands, crystallographic water molecules, and a Cl− ion, and D95V19c for amino acid residues. Empirical dispersion corrections were done for energies and gradients using the D3 version of Grimme’s empirical dispersion with the Becke−Johnson damping function.20 The atomic positions of the backbone as well as entire Gln165 and Asn298 residues at the periphery of the model were fixed to their X-ray structure coordinates during geometry optimization. The polarizable continuum model was used for each optimized geometry to account for the polarization effect by the surrounding protein environment.21 The dielectric constant of 5.7 (corresponding to chlorobenzene) was employed to include an implicit contribution from the low polarizability of the protein interior. We further applied different percentages of the nonlocal Hartree−Fock (HF) exchange in the B3LYP functional (10 and 15% in addition to the standard 20%) to eliminate the uncertainty of parameters defining the hybrid functional. The energies for the nonstandard HF percentages (10 and 15%) were evaluated by single-point calculations with B3LYP(20%)-D3 dispersion corrections included.

3. RESULTS AND DISCUSSION There are a large number of possible states in the OEC if all combinations of the charge and spin states of the Mn4CaO5 core and the protonation states of water-derived, terminal ligands bound to Ca and MnA/MnD ions are explicitly considered. Thus, the specifications of these states are required. We follow the previously employed notations:16 the oxidation state in parentheses (MnA, MnB, MnC, MnD), the spin state in braces 2Stotal+1{MnA, MnB, MnC, MnD···L} (L is a redox-active B

DOI: 10.1021/acs.inorgchem.5b02471 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 1. Chemical Forms and Relative Energies of Low-Lying Intermediates for Proton Tautomerism Calculated with Three Different Percentages of the HF Exchange in the B3LYP Functionala relative energiesb substrates

notation

protonation

charge

aqua−oxo hydoxo−oxo

A(closed) H(open) H(closed) Hbridged(closed) O(closed) Obridged(closed)

[HO−, HO−, H2O, H2O] [H2O, HO−, H2O, HO−] [H2O, HO−, H2O, HO−] [H2O, HO−, H2O, HO−] [H2O, H2O, H2O, O2−] [H2O, H2O, H2O, O2−]

(4444) (4444) (4444) (4444) (4444) (4444)

oxo−oxo a

spin

HF 10%

HF 15%

HF 20%

{↓↑↑↑} 7 {↓↑↑↑} 7 {↓↑↑↑} 7 {↓↑↑↑} 13 {↑↑↑↑} 13 {↑↑↑↑}

10.1 0.0 9.2 2.7 4.2 4.0

10.4 0.0 9.3 3.1 4.2 4.3

10.7 0.0 9.5 3.4 4.3 4.6

7

Geometry optimizations were performed at the B3LYP(20%)-D3 level. bRelative energies with reference to H(open) are given in kcal mol−1.

Table 2. Chemical Forms and Relative Energies of Low-Lying Intermediates for Redox Isomerism Calculated with Three Different Percentages of the HF Exchange in the B3LYP Functionala relative energiesb substrates

notation

oxyl−oxo

O*(open) O*(closed) P(open) P(closed) Ssinglet Striplet

peroxo superoxo a

protonation [H2O, [H2O, [H2O, [H2O, [H2O, [H2O,

H2O, H2O, H2O, H2O, H2O, H2O,

H2O, H2O, H2O, H2O, H2O, H2O,

charge O•−] O•−] O22−] O22−] O2•−] O2•−]

(3444) (4443) (3443) (3443) (3343) (3343)

spin

HF 10%

HF 15%

HF 20%

{↑↑↑↑···↓} 13 {↑↑↑↑···↓} 7 {↑↑↑↓} 7 {↑↑↑↓} 1 {↓↑↓↑···↓} 3 {↓↑↓↑···↑}

1.6 12.8 8.9 9.7 7.8 10.2

−0.4 11.2 0.9 1.0 −4.7 −2.9

−2.8 9.0 −7.3 −7.9 −17.6 −16.2

13

Geometry optimizations were performed at the B3LYP(20%)-D3 level. bRelative energies with reference to H(open) are given in kcal mol−1.

Figure 2. Energy diagrams and geometric parameters for proton tautomerism in the closed conformation at the B3LYP(10%)//B3LYP(20%) level. The relative energies with reference to H(open) are given in kilocalories per mole; interatomic distances are given in angstroms.

mol−1 in this study), as reported by the EPR/DFT study.10 This means that the OEC may be predominantly on the open conformation of the hydroxo intermediate with (4444) 7{↓↑↑ ↑} after the system reaches equilibrium.22 Starting from the above two hydroxides, low-lying intermediates were generated with the following strategy. In the first step, we investigated possible protonation equilibria by relocating protons on water-derived, terminal ligands (W1,

ligand), and the protonation state in brackets [W1, W2, W3, Win]. Besides these multiple protonation and redox states, two quite different topologies of the Mn4CaO5 cluster, called open and closed cubanes, are suggested to be involved in the S3 state, as shown in Figure 1. When [H2O, HO−, H2O, HO−] (4444) 7 {↓↑↑↑} was employed, our calculations reproduced the overall topologies and oxidation and spin states of these structures, as well as a large energy separation in favor of the former (9.2 kcal C

DOI: 10.1021/acs.inorgchem.5b02471 Inorg. Chem. XXXX, XXX, XXX−XXX

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proximity. After proton transfer, the bridged water W5 may change its orientation and form a hydrogen bond with the backbone carbonyl of Asp170, so that W3 can instead become a hydrogen-bond donor to the oxo ligand, as shown by the process Obridged(closed) → O(closed) in Figure 2. Unlike the closed form, the open form of the hydroxide, H(open) [H2O, HO−, H2O, HO−] (4444) 7{↓↑↑↑}, is unable to conduct a rapid hydoxo ↔ oxo interconversion in the absence of a hydrogen-bonded connection between two distant hydoxo ligands at MnA and MnD. The QM/MM study, however, suggested that H(open) can convert into H(closed) by triggering a proton migration from HO−(Win) at MnD to a nearby central μ-oxo bridge (O5) followed by a single displacement reaction between nascent μ-hydoxo (O5) and terminal oxo (Win) groups at the MnB center.14 As shown in the next section, interconversion between open- and closed-cubane topologies is also possible for the oxo/oxyl species through redox-induced structural changes. 3.2. Redox Isomerism. The most remarkable finding in our study is that at relatively high temperatures (room temperature) the Mn ions in the Mn4CaO5 core may exchange electrons with bound oxygen ligands, accompanied by large structural changes. This can be achieved by initial oxidation of a terminal oxo (Win) or a bridging μ-oxo (O5) group by the MnDIV ion in O(closed), as shown by a dashed arrow in Figure 2, leading to an oxyl radical (O•−) species O*(closed) [H2O, H2O, H2O, O•−] (4443) 13{↑↑↑↑···↓}, with a ligand-based radical being effectively delocalized over the two oxo units at the Win (−0.23) and O5 (−0.31) positions (Table S4). This oxygen activation process is endothermic by 8.6 kcal mol−1. Likewise, the open-cubane isomer of the oxyl species O*(open) [H2O, H2O, H2O, O•−] (3444) 13{↑↑↑↑···↓} could be located, only 1.6 kcal mol−1 higher in energy than H(open), by a formal migration of a proton, although the direct conversion of H(open) into O*(open) may be difficult. Interestingly, the closed (open) form of the oxyl species O*(closed) [O*(open)] possesses a charge distribution (4443) [(3444)], which is favored in the open (closed) conformation in the S2 state.24,25 This reversed charge state originates from coordination of a terminal oxo/oxyl ligand to the originally vacant MnA (MnD) site. A comparison of the optimized geometries of O(closed) and O*(closed), as illustrated in Figure 2, reveals that the oxygen activation process is coupled with elongation of the MnD−O5 bond from 1.869 to 2.126 Å due to the Jahn−Teller effect on the reduced MnDIII ion. Access to this activated state is sufficient to induce sequential reductions of the Mn4 core

W2, and Win) and allowing associated reorganizations of water molecules in the vicinity of the Mn4CaO5 cluster; this search was performed with the spin configuration 7{↓↑↑↑}. Finding a global minimum in the large cluster is, in general, a very difficult task and requires an exhaustive exploration of possible local minima. Parts of our efforts are given in Figure S2. Subsequently, we relocated electrons residing in the Mn4CaO5 core to study possible redox equilibria and coupled structural changes of the inorganic cluster itself. The Mn4CaO5 core contains four redox-active Mn centers and hence possesses eight different broken-symmetry (BS) configurations. If ligandcentered oxidation happens, the spin structure of the OEC can be characterized by a total number of 16 BS solutions. We carried out geometry optimizations for all BS configurations to find out the lowest-spin configuration. Four types of hydrogenbonding patterns of water molecules near the Mn4CaO5 core were then applied to each optimized structure with the lowestspin configuration to investigate possible local minima, as summarized in Table S1 and Figure S3. Of all data, we selected important low-lying intermediates with an adiabatic excitation energy of less than 13 kcal mol−1 with respect to the open form of the hydroxide. For simplicity, various species are labeled by the acronym of the chemical form of Win: A stands for Win = H2O (aqua), H for Win = HO− (hydroxo), O for Win = O2− (oxo), O* for Win = O•− (oxyl), P for Win = O22− (peroxo), and S for Win = O2•− (superoxo). In addition, we specify in parentheses the topology of the Mn4CaO5 cluster: “open” for the open cubane and “closed” for the closed cubane. The chemical forms and their relative energies are summarized in Tables 1 and 2. In the following, these results are discussed in separate sections (3.1 and 3.2), in which all energetic results are given at the B3LYP(10%) level because only the low HF percentage (10%) provides an overall energy landscape that matches the current consensus that Mncentered oxidation occurs during the S2 → S3 transition.10 Finally, in section 3.3, we compare energy profiles obtained by three different HF percentages in the B3LYP functional (10, 15, and 20%) and propose chemical equilibrium models for the S3 state. 3.1. Proton Tautomerism. We first consider inner-sphere proton relocations that would occur in the closed from of the hydroxide, H(closed) [H2O, HO−, H2O, HO−] (4444) 7{↓↑↑ ↑}. Figure 2 shows energy profiles at the B3LYP(10%) level, alongside B3LYP(20%)-optimized geometries. In this form, a HO− ligand (W2) trans to a μ-oxo bridge (O4) of the MnA dihydroxide is expected to be more basic than HO−(Win) trans to H2O(W1) and can accept a proton from HO−(Win) in a cis position, leading to a protonation state [H2O, H2O, H2O, O2−], i.e., formation of a terminal oxo group at the Win position as a component at equilibrium, MnA(OH)2 ↔ MnA(H2O)(O).23 This structural isomerism actually consists of several steps, as indicated in Figure 2. The first step is breakage of a hydrogen bond between W5 and the backbone carbonyl oxygen of Asp170 that allows W5 to participate in the formation of a hydrogen-bonded water bridge between W2 and Win, as shown by a structure Hbridged(closed) in Figure 2. This reorganization process is exothermic by 6.5 kcal mol−1. A water triangle so formed between HO−(Win) and HO−(W2) via W5 is suited for sequential proton migrations via a hydrogen-bond network, thereby generating an oxo species Obridged(closed) that lies 1.4 kcal mol−1 above Hbridged(closed). This proton transfer may be accompanied by a change in the spin configuration of the Mn4 cluster from 7{↓↑↑↑} to 13{↑↑↑↑} because of their energetic

(4444) ↔ (4443)/(3444) ↔ (3443) ↔ (3343)

(1)

with complementary oxidations of the substrate O atoms (Win and O5) (O2 − ···O2 −) ↔ (O•− ···O2 − ↔ O2 − ···O•−) ↔ (O2 2 −) ↔ (O2•−)

(2)

which results in transient Mn−O bond dissociation and O−O bond formation in the S3 state. These correlated oxidation and structural changes are depicted in Figure 3. Radical character did not appear on the tyrosine residue Tyr161 (YZ) during the chemical transformations (Table S4), even when the hydrogenbonding patterns near YZ and MnA were changed (Table S1 and Figure S3). The scans of potential energy surfaces clarify that the redox-induced structural changes are kinetically facile with a maximal barrier of about 10 kcal mol−1 once two D

DOI: 10.1021/acs.inorgchem.5b02471 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 4 shows more detailed energy diagrams at the B3LYP(10%) level including vertical energy levels of excited spin configurations; the corresponding B3LYP(20%) results are indicated in Figure S5, and Tables S5−S10 collect all vertical excitation energy gaps at the B3LYP(20%) and BLYP(10%) levels. We can see from Figure 4 that the spin state also varies along the structural changes. In the activated oxyl−oxo form O*(closed) (O•−···O2− ↔ O2−···O•−), there are 16 different spin configurations that are sparsely distributed up to 27.5 kcal mol−1 (Table S6). Among these, two nearby configurations, 13 {↑↑↑↑···↓} and 7{↑↑↓↑···↓}, lie markedly low in energy, with the former being only 0.21 kcal mol−1 below the latter. Both of them have a characteristic alternating spin arrangement (↑↓↑ /↑) along MnAIV···(Oin···O5)···MnDIII/MnCIV. This arrangement is, however, an unfavorable situation for O···O radical coupling because transfer of an up-spin electron from O2−(Win) to MnAIV that satisfies Hund’s rule on MnA results in two unpaired electrons with parallel spins on O•−(Win) and O•−(O5), which prevents subsequent pairing for bond formation. Nevertheless, an O−O bond can be formally made if O2−(Win) donates its down-spin electron to MnAIV at the expense of attaining maximum stabilization by parallel spins on MnAIII, as shown by eq 3, in which ↑IS means SMn = 1, and asterisks represent either ↑ or ↓. (4443){ ↑ ***... ↓ }[O*(closed)] → (3443){ ↑IS ***}[Pexcited (closed)]

(3) −1

This reaction is endothermic by 7.6 kcal mol , leading to a highly unstable peroxo structure Pexcited(closed). If, on the other hand, the spins of unpaired electrons on MnAIV and (Oin···O5) are parallel, O−O bond formation becomes very facile because electron transfer conforms to Hund’s rule on MnA, as given by eq 4. (4443){ ↑ ***... ↑ }[O*(closed)] → (3443){ ↑ ***}[P(closed)]

(4)

The half of 16 spin configurations of O*(closed) satisfies the spin alignment requirement for O···O coupling in eq 4 and is correlated to 8 configurations of a low-lying peroxo intermediate P(closed) with a favorable high-spin MnAIII site (SMn = 2). This is a downhill energetic process by 3.1 kcal mol−1. The rest of the half obeys eq 3 and is related to 8 configurations of the high-lying peroxide Pexcited(closed) containing an unfavorable intermediate-spin MnAIII ion (SMn = 1). Thus, O−O bond formation in the S3 state can be described as the interplay between at least two spin configurations to enable facile interchange of electron pairs between a terminal oxo/oxyl and a bridging oxo/oxyl. Such a covalent bond formation necessitates a coupled O···O stretching motion because of large vertical energy gaps between the lowest and allowed configurations at the equilibrium geometry of O*(closed) (>7.6 kcal mol−1). This type of mechanism is most relevant to the one suggested by Siegbahn.12 In the peroxo intermediate P(closed), MnAIII···O and MnDIII···O bonds are almost broken with distances of 2.023 and 2.279 Å, and the peroxo ligand binds to the MnBIV site in a bent end-on manner with a MnBIV−O distance of 1.874 Å and a MnBIV−O−O angle of 111.8°. Unlike the oxyl species O*(closed), P(closed) involves 8 spin configurations that are densely populated to within only 2.1 kcal mol−1 (Table S8),

Figure 3. Redox-induced structural changes of the Mn4 core and two substrate oxygen species. MnIV ions are colored purple, MnIII ions orange, O atoms red, and H atoms white; interatomic distances are given in angstroms.

substrate oxygen species have been activated (Figure S4); however, several steps may be severely inhibited at very low temperatures. E

DOI: 10.1021/acs.inorgchem.5b02471 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 4. Energy diagrams for redox isomerism at the B3LYP(10%)//B3LYP(20%) level. The relative energies with reference to H(open) are given in kilocalories per mole; for the vertical energy gaps of all excited configurations, see Tables S5−S10.

thereby acquiring a high degree of electronic flexibility. The peroxide may undergo a further electron shift from the peroxo ligand to MnBIV concurrently with dissociation of the MnBIV−O bond, generating an superoxo species that lies somewhat (1.1 kcal mol−1) below P(closed). In the superoxo intermediate, the O2•− ligand is weakly trapped by three Mn ions. According to the orientation of O2•−, a change in the spin state may be induced thermally because of nonnegligible magnetic interaction between the Mn4 core and O2•−. A side-on triangular conformation with two MnBIII···O distances of about 2.7−2.8 Å and two MnBIII···O−O angles of about 74−78° favors a triplet configuration Striplet 3{↓↑↓↑···↑}, as depicted in Figure 3. However, asymmetric distortion of the isosceles triangle toward an angular end-on geometry with MnBIII···O distances of 2.430 and 3.025 Å and MnBIII···O−O angles of 51.4 and 103.5° in turn places a singlet configuration Ssinglet 1{↓↑↓↑···↓} below Striplet by 2.4 kcal mol−1, as shown in a rectangular box in Figure 4. The MnBIII site of the singlet superoxo intermediate Ssinglet (3343) 1{↓↑↓↑···↓} is susceptible to radical attack by O2•−, transferring a single electron to O2•−. Upon this recombination, the superoxide bifurcates to yield two isomeric peroxides, P(open) and P(closed), depending on whether the distal oxygen atom of the resulting MnBIV−O22− moiety coordinates to MnDIII or MnAIII. P(open) and P(closed) share common charge and spin structures, (3443) 7{↑↑↑↓}, although their geometric topologies are very different. P(open) may be transformed into an oxyl species O*(open) (3444) 13{↑↑↑↑ ···↓}, an isomeric pair of O*(closed) (4443) 13{↑↑↑↑···↓}, through an electron shift from the peroxo bond to MnDIII

coupled with O−O bond dissociation and MnDIV−O bond formation. This electron-transfer-coupled bond reorganization involves the interplay of at least two spin configurations that behave differently and cross along the O−O bond dissociation: one is associated with a low-lying configuration of P(open) that leads to a high-lying configuration of O*(open) {***↑···↑}, and the other is associated with a configuration for an excited peroxide Pexcited(open) containing an unfavorable SMn = 1 site that is correlated with a low-lying configuration of O*(open) {***↑···↓}, as shown in Figure 4 [vertical energy levels of Pexcited(open) are not shown for clarity]. This process is downhill with 7.3 kcal mol−1. 3.3. Chemical Equilibrium Models. To gain insight into 18 O-labeled water exchange, we have thoroughly explored lowlying intermediates within the range of 13 kcal mol−1. Our calculations identify 1 stable and dominant intermediate H(open) [H2O, HO−, H2O, HO−] (4444) 7{↓↑↑↑} and 11 metastable states, which would interconvert reversibly and reach dynamic equilibria at room temperature. The relative stability of the open- and closed-cubane isomers for the hydroxide depends significantly on the clustering structure of water molecules near the MnA ion. Hbridged(closed) that adopts a bridged W2−W5−Win triangular conformation is closest in energy to H(open) (only 2.7 kcal mol−1 difference), while H(closed) with a nonbridged water cluster is relatively high [9.2 kcal mol−1 above H(open)]. The conformational diversity of the water cluster in the front of the MnA site of the closed cubane may have implications in the mechanism of substrate water exchange as discussed later because this site is solventaccessible via several water-inlet channels across the thylakoid F

DOI: 10.1021/acs.inorgchem.5b02471 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 5. Energy diagrams for proton tautomerism and redox isomerism in the S3 state by B3LYP(10%)//B3LYP(20%) (blue), B3LYP(15%)// B3LYP(20%) (green), and B3LYP(20%)//B3LYP(20%) (red). The relative energies with reference to H(open) are given in kilocalories per mole.

membrane.4,26 An unexpected finding is that the Mn4CaO5 cluster may start to shuttle electrons between metal centers and substrate oxygen species at elevated temperature, thereby inducing large structural changes. To eliminate a bias due to the use of a single density functional and comprehend the whole reaction process, we display in Figure 5 energy diagrams for proton tautomerism and redox isomerism in the S3 state calculated with three different percentages of the HF exchange (10, 15, and 20%). The results clearly show that the chemical equilibria for redox isomerism are strongly influenced by the amount of HF exchange, while there is no significant shift in the equilibria for proton tautomerism that occur in the all-MnIV oxidation state (4444). Increasing the HF percentage systematically drives the equilibrium to the state with more reduced Mn ions (by about 2−7 kcal mol−1 per one-electron reduction for each 5% increase). In fact, as shown by red lines in Figure 5, the standard B3LYP functional with the 20% HF exchange predicts

a smaller endothermicity for the initial coupling of electron transfer and substrate activation (4.5 kcal mol−1 vs 8.6 kcal mol−1 by HF 10%) and a larger exothermicity for the subsequent O···O radical coupling (16.9 kcal mol−1 vs 3.1 kcal mol−1), and an even stronger driving force (26.6 kcal mol−1 vs 5.0 kcal mol−1) is provided for formation of the superoxide Ssinglet/Striplet 1(3){↓↑↓↑···↓(↑)}, with the most reduced state (3343) corresponding to the S0 state. Although early parallel polarization EPR signals were explained by a S = 1 spin state,27a recent highly resolved EPR spectra were all indicative of a S = 3 spin system for the S3 state.10,27b,c Without convincing experimental evidence for the existence of a lowlying triplet state, this functional seems to overestimate the stability of the reduced state relative to the oxidized state, leading to accumulated errors on the superoxo species. This finding cautions against the thoughtless use of the popular B3LYP functional for the multielectron redox reaction within the OEC. The HF 15% functional, also called B3LYP*, is G

DOI: 10.1021/acs.inorgchem.5b02471 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

does not seem to be a convenient mechanism for water exchange in the open conformation. Our scenario is that the slow substrate water exchange may be associated with label scrambling such as occurs in the loosely bound superoxo complex Ssinglet/Striplet, in which two O atoms (originally labeled W in and O5) are interchangeable. Complete isotopic scrambling implies that the apparent 18O exchange behaviors of two substrate O atoms should ideally be identical, which is, however, inconsistent with two distinct phases observed by the experiments.13 The contradiction dismisses the HF 15% picture, in which the superoxo species is still stable compared with the deactivated species. In the other extreme case with very low HF percentages (