Theoretical study of catalytic mechanism forsingle-site water oxidation processXiangsong Lina,b,1, Xiangqian Hub,1, Javier J. Concepcionc, Zuofeng Chenc, Shubin Liud, Thomas J. Meyerc,2, andWeitao Yangb,2

aHefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei 230026, People’s Republic of China;bDepartment of Chemistry, Duke University, Durham, NC 27708; cDepartment of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill,NC 27599; and dResearch Computing Center, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3420

Edited by Jack Halpern, The University of Chicago, Chicago, IL, and approved March 23, 2012 (received for review January 11, 2012)

Water oxidation is a linchpin in solar fuels formation, and catalysisby single-site ruthenium complexes has generated significant inter-est in this area. Combining several theoretical tools, we have stu-died the entire catalytic cycle of water oxidation for a single-sitecatalyst starting with ½RuIIðtpyÞðbpmÞðOH2Þ�2þ (i.e., ½RuII-OH2�2þ;tpy is 2,2 0∶6 0,2 0 0-terpyridine and bpm is 2,2′-bypyrimidine) as arepresentative example of a new class of single-site catalysts. Theredox potentials and pKa calculations for the first two proton-coupled electron transfers (PCETs) from ½RuII-OH2�2þ to ½RuIV ¼ O�2þand the following electron-transfer process to ½RuV ¼ O�3þ suggestthat these processes can proceed readily in acidic or weakly basicconditions. The subsequent water splitting process involves twowater molecules, ½RuV ¼ O�3þ to generate ½RuIII-OOH�2þ, and H3Oþ

with a low activation barrier (∼10 kcal∕mol). After the key O—Obond forming step in the single-site Ru catalysis, another PECTprocess oxidizes ½RuIII-OOH�2þ to ½RuIV-OO�2þ when the pH is lowerthan 3.7. Two possible forms of ½RuIV-OO�2þ, open and closed, canexist and interconvert with a low activation barrier (<7 kcal∕mol)due to strong spin-orbital coupling effects. In Pathway 1 atpH ¼ 1.0, oxygen release is rate-limiting with an activation barrier∼12 kcal∕mol while the electron-transfer step from ½RuIV-OO�2þ to½RuV −OO�3þ becomes rate-determining at pH ¼ 0 (Pathway 2)with Ce(IV) as oxidant. The results of these theoretical studies withatomistic details have revealed subtle details of reaction mechan-isms at several stages during the catalytic cycle. This understandingis helpful in the design of new catalysts for water oxidation.

catalysis ∣ polypyridyl Ru complexes ∣ quantum mechanics/molecularmechanics

Water oxidation (2H2O → O2 þ 4e− þ 4Hþ) is a key step inboth natural and artificial photosynthesis (1–10). A large

number of studies have been carried out to design new wateroxidation catalysts related to solar fuels (11–19). For example,Meyer et al. have reported single-site polypyridyl ruthenium com-plexes ½RuIIðtpyÞðbpmÞðOH2Þ�2þ (½RuII-OH2�2þ∶tpy ¼ 2; 2 0∶6 0; 2 0 0-terpyridine; bpm ¼ 2; 2 0-bipyrimidine) for water oxida-tion (11). Inspired by this pioneering work, a series of rutheniumcatalysts have been scrutinized to understand the entire catalyticprocesses (17, 18, 20–23). As shown in Fig. 1, ½RuII-OH2�2þ isfirst oxidized to ½RuIV ¼ O�2þ by losing two protons and two elec-trons. Through a simple electron transfer step, ½RuIV ¼ O�2þ isfurther oxidized to ½RuV ¼ O�3þ. The key O—O bond is formedby water molecule attack on ½RuV ¼ O�3þ. It takes two water mo-lecules to generate ½RuIII-OOH�2þ and H3Oþ, and the computedactivation barrier is low (∼10 kcal∕mol) from our previous studies(21). This reaction mechanism of O—O bond formation (i.e.,½RuIII-OOH�2þ) has further helped experimental design byemploying different bases as proton acceptors, including H2PO4

−,H2PO4

2−, and CH3COO−, to increase the rate of the O—O cou-pling step and enhance catalytic efficiency (21). Subsequently,½RuIII-OOH�2þ is oxidized to ½RuIV-OO�2þ by a proton-coupledelectron transfer (PCET) step. Two possible conformations of½RuIV-OO�2þ exist: In the closed conformation, two oxygen atoms

bind to the ruthenium metal center (η2-½RuIV-OO�2þ) while onlyone oxygen atom binds in the open form (η1-½RuIV-OO�2þ).The conformation interconversion between closed and open formsmay hinder O2 release (19). In 0.1 M HNO3, water attack on½RuIV-OO�2þ to release O2 was assumed to be rapid (Pathway 1)(17). In 1.0 M HNO3, ½RuIV-OO�2þ is first oxidized to½RuV-OO�3þ followed by rapid loss of coordinated O2 with wateraddition and proton loss to give ½RuIII-OH�2þ (Pathway 2).Subsequently, another PCET process in Pathway 2 returns½RuIII-OH�2þ to ½RuIV ¼ O�2þ.

Although the catalytic process in Fig. 1 has been explored byseveral experimental and theoretical studies (19, 22–24), thesubtle mechanisms of some key reaction processes still remainenigmatic. For instance, how large are the driving forces of PCETsteps? And how rapid is O2 release? Are there other pathways—adimeric species formed by O—O coupling of two ½RuV ¼ O�3þ athigh concentrations of catalyst followed by further oxidation byCe(IV)?

To answer these questions, it is necessary to conduct theoreti-cal investigations of several reaction steps at the atomistic level.In this paper, we used ab initio quantum mechanics (QM) andhybrid QM/MM (molecular mechanics) simulations. We foundthat the spin states of ruthenium intermediates during the cata-lytic cycle play crucial roles in determining redox potentialvalues and atomistic reaction pathways. The activation barrierof conformation changes between the closed and open formsof ½RuIV-OO�2þ can be lowered to 7 kcal∕mol due to strong spin-orbital coupling effects of ruthenium. To release triplet O2,both ½RuIV-OO�2þ and ½RuV-OO�3þ must reach high spin states;i.e., triplet for ½RuIV-OO�2þ in Pathway 1 and quartet for½RuV-OO�3þ in Pathway 2. As such, our computations show thatthe reaction barrier to release O2 from ½RuIV-OO�2þ is 12 kcal∕mol in Pathway 1 while ½RuV-OO�3þ can rapidly release O2 with-out any activation barrier in Pathway 2. In addition, the dimer-ization of ½RuV ¼ O�3þ to generate ½RuIV-O-O-RuIV�6þ canoccur with a low activation barrier (∼5 kcal∕mol) with the dimerin the singlet spin state.

Results and Discussion½RuII-OH2�2þ (Singlet)/½RuIV ¼ O�2þ (Singlet) Couples. The computedredox potentials and pKa values are shown in Fig. 2 along withsome experimental data in parentheses. Even though the errorsresiding in approximate forms of functionals in density functional

Author contributions: T.J.M. and W.Y. designed research; X.L. and X.H. performedresearch; X.L., X.H., J.J.C., Z.C., and S.L. analyzed data; and X.H., J.J.C., Z.C., S.L., T.J.M.,and W.Y. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1X.L. and X.H. contributed equally to this work2To whom correspondence may be addressed. Email: weitao.yang@duke.edu or tjmeyer@email.unc.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1118344109/-/DCSupplemental.

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theory (DFT) may not reproduce accurate redox potentials andpKa values for ruthenium complexes, we found that a hybrid com-putational protocol can reproduce the correct spin states forruthenium complexes after our extensive tests on functionalsand basis sets (see Tables S1–S3 for complete lists of variousRu species). In this protocol, we employed the B3LYP functionalwith LANL2DZ basis sets to optimize the geometries of ruthe-nium intermediates and MP2 calculations with LANL2DZ toidentify the corresponding spin states. (Note that even MP2/LANL2DZ is too expensive to be applied for geometry optimiza-tions.) All the redox potentials and pKa values are also computedby B3LYP/LANL2DZ with the spin states assigned by MP2/LANL2DZ (some redox potentials were computed by MP2 aswell). This hybrid protocol (see discussions in the Spin-State Iden-tifications Using Different Methods section of SI Text) is used in allof our calculations.

As shown in Fig. 2, when pH > 8.5 (Exp. 9.7), ½RuII-OH2�2þ isfirst deprotonated and then oxidized to ½RuIII-OH�2þ with thecalculated redox potential around 0.6 V (Exp. 0.6–0.8 V). In-creasing the potential to >1.7 V [Exp. 1.2 V (11)] results inoxidation of ½RuII-OH2�2þ to ½RuIII-OH2�3þ. The computed pKavalue suggests that ½RuIII-OH2�3þ is acidic, which is in qualitativeagreement with experimental observations (11, 20, 25). In otherpH-potential domains, both proton transfer and electron trans-fer occur (i.e., PCET) from ½RuII-OH2�2þ to give ½RuIII-OH�2þ.The overall oxidation of ½RuII-OH2�2þ to ½RuIII-OH�2þ is uphilland endothermic with ½RuIII-OH�2þ relatively stable. To reach½RuIV ¼ O�2þ, an additional PCET step occurs by the½RuIII-OH�2þ∕½RuIV ¼ O�2þ couple. ½RuIV-OH2�4þ and ½RuIV-OH�3þ are extremely acidic and unstable in aqueous solution.½RuIII ¼ O�þ and ½RuII ¼ O� cannot be reached due to highpKa values of ½RuIII-OH�2þ and ½RuII-OH�þ.

½RuIV ¼ O�2þ (Singlet)/½RuV ¼ O�3þ (Doublet) Couples. This step is asimple electron transfer process. The redox potential is 1.65 Vcomputed from MP2/LANL2DZ in good agreement with experi-mental observations (19) (1.6–1.8 V). (Note that we observedthat MP2/LANL2DZ calculations usually have lower redox po-tential values than B3LYP/LANL2DZ.) After electron transfer,the bond distance between Ru and O is decreased from 1.807to 1.739 Å (Fig. S1). This shorter Ru-O distance facilitatesconcerted O atom-proton transfer (APT) with O-O bond forma-tion and involvement of two water molecules to produceRuIII-OOH2þ þH3Oþ (21).

Dimerization of ½RuV ¼ O�3þ.To explore a possible reaction pathwayinvolving dimerization of ½RuV ¼ O�3þ at high concentrations of½RuV ¼ O�3þ at low pH, we performed theoretical studies on theputative peroxide-bridged dimer ½RuIV-O-O-RuIV�6þ. Calcula-tions with the implicit solvent model point to mixed triplet-singletspin-state character. Fig. 3 shows the free energy profiles opti-mized by QM/MM-MFEP with explicit water molecules for bothsinglet and triplet spin states when the dimer ½RuIV-O-O-RuIV�6þis broken into two monomers. In the singlet spin state, the barrierto O-O bond fission is ∼20 kcal∕mol. In other words, two ½RuV ¼O�3þ monomers can easily form from the dimer since the activa-tion barrier for dimerization is only 4 kcal∕mol in the singlet spinstate. Note that calculations for the triplet spin state in Fig. 3 givethe opposite result. Even though the energy of singlet spin statesmay be overestimated due to fractional spin errors (26–28), weconclude the dimerization process is likely to proceed in thelow spin state (singlet).

½RuIII-OOH�2þ (Doublet)/½RuIV-OO�2þ (Singlet) Couples.Our computedthermochemical data in Fig. 4 suggest that this is a PCET stepwhen the pH exceeds 3.4. Note that the computed redox potentialfor the ½RuIII-OOH�2þ∕½RuIV-OO�2þ couple is too high [calc.2.6 V vs. exp. 1.4 V (17)]. As shown in Fig. S2, both Ru-O andO—O bonds are shortened after PCEToxidation. The calculatedO—O bond length of 1.339 Å in ½RuIV-OO�2þ points to strongperoxide bonding between the oxygen atoms.

Interconversion of the Singlet and Triplet Spin States of ½RuIV-OO�2þin Pathway 1. Due to the high spin-orbit coupling constant forruthenium (∼1;000 cm−1) (19), the ground electronic spin stateof ½RuIV-OO�2þ is of mixed spin character. For instance, the en-ergy difference between the singlet and triplet spin states of½RuIV-OO�2þ for the closed shell structure can be less than−1.2 kcal∕mol (see Tables S3 and S4 without zero-point energycorrections) from B3LYP/LANL2DZ computations consistentwith mixed spin character. Hence, the interconversion of spin

2Ce4+

Ce4+Ce4+

2Ce3+ + 2H+

Ce3+Ce3+ + H+

O2

H2O

H+

H2O

N

N

N

RuN N

N N

H2O

Ce4+Ce3+

O2 + H+

H2O

Ce4+Ce3+ + H+

[RuII-OH2]2+

[RuIV=O]2+

[RuV=O]3+[RuIII-OOH]2+

[RuIV-OO]2+ 2+

[RuV-OO]3+

[RuIII-OH]2+

Dimerization

[RuIV-O-O-RuIV]6+

Pathway 2

Pathway 1

Fig. 1. Catalytic steps of water oxidation by the single-site catalyst.

Fig. 2. Computed thermochemistry pathways using B3LYP/LANL2DZ from½RuII-OH2�2þ to ½RuIV ¼ O�2þ. The available experimental values are list in par-entheses. NHE (normal hydrogen electrode) is used here (4.24 V).

Fig. 3. Free energy profiles for singlet and triplet spin states when the dimer½RuIV-O-O-RuIV�6þ is broken into two monomers. The QM subsystems arecomputed by B3LYP/LANL2DZ.

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states can influence optimal structures of ½RuIV-OO�2þ. Notethat ½RuIV-OO�2þ has two possible conformations: open (i.e.,only one oxygen atom binding to Ru) and closed (i.e., both oxygenatoms binding to Ru). In addition to our previous studies focusingon the singlet spin state (19), the structural interconversionbetween open and closed structures was scrutinized by usingthe triplet spin state of ½RuIV-OO�2þ. As shown in Fig. S3B,the open structure of ½RuIV-OO�2þ is slightly more stable by2.6 kcal∕mol than the closed one with ½RuIV-OO�2þ in the tripletspin state. More surprisingly, compared to the activation barrierof 14.6 kcal∕mol from the closed structure to the open one forthe singlet spin state (19) (Fig. S3A), the activation barrier is just1.5 kcal∕mol from closed to open structures for the triplet spinstate (Fig. S3B). The significant changes of structures, activationenergies, and spin states indicate that spin flipping may occur in½RuIV-OO�2þ. Fig. 5 illustrates how spin can be flipped during thegeometric change from closed to open forms. The potential en-ergy scan uses the Ru-O1 bond distance as the reaction coordi-nate. When the bond distance between Ru and O1 is stretchedfrom 2.09 Å (the optimal distance for singlet ½RuIV-OO�2þ) to2.5 Å, the energy difference between singlet and triplet spin statesbecomes smaller (see black and red curves in Fig. 5). Eventually,the triplet spin state falls below the singlet at a Ru-O1 bondlength >2.3 Å. This phenomenon supports the conclusion thatthe singlet closed-form of ½RuIV-OO�2þ can be interconvertedto the triplet open-form rapidly with a much lower activation bar-rier (∼7 kcal∕mol in contrast to 14.6 kcal∕mol) without consid-ering spin-orbital coupling effect. This discovery demonstratesthat the conformational change from closed to open form isnot rate-limiting during O2 formation.

O2 Release from the Open Structure of ½RuIV-OO�2þ by Water Attack inPathway 1. O2 is released from ½RuIV-OO�2þ to return to

½RuII-OH2�2þ, which reenters the catalytic cycle for water oxida-tion. As shown in Fig. S4, by scanning the potential energy sur-faces for singlet and triplet spin states with respect to the bonddistance between Ru and the second oxygen atom (i.e., dRu-O2),we believe that the open structure of ½RuIV-OO�2þ at the singletspin state cannot release O2 since the activation barrier is toohigh (>35 kcal∕mol). This is further confirmed by the accurateQM/MM-MFEP simulations shown in Fig. 6. By contrast, forthe triplet spin state, O2 can be released with the low barrierof ∼5 kcal∕mol estimated by the potential energy scan inFig. S4. Based on QM/MM simulations with explicit water mole-cules in Fig. 6 and the optimized structures in Fig. S5, whenone water molecule attacks the transition metal center to releaseO2, the accurate activation barrier is 12 kcal∕mol for the tripletspin state. Therefore, our theoretical studies elucidate that an-other rate-limiting step in water oxidation [besides O—O bondformation (21)] is to release O2 from the open structure of½RuIV-OO�2þ from the triplet spin state. This high spin state isrequired since the ground spin state of O2 in the final productis a triplet.

O2 Release from ½RuV-OO�3þ after ½RuIV-OO�2þ Is Oxidized in Pathway2.At pH ¼ 0, our experiments (11, 17) found that ½RuIV-OO�2þ isoxidized first and then releases O2. The redox potential calcula-tions (Figs. S6 and S7) of closed and open structures of½RuIV-OO�2þ at the singlet spin state suggest the following: (i)both oxygen atoms bind to Ru with the closed structure atpH ¼ 0.0; (ii) this oxidation process involves spin flipping since½RuV-OO�3þ can only be stable in the quartet spin state; (iii)the computed redox potential (E0 ¼ 1.7 V) of the closed formof singlet ½RuIV-OO�2þ and quartet ½RuV-OO�3þ agrees withexperimental observations (1.7 V) (17). Note that the O—O dis-tance is shortened to 1.265 Å after ½RuIV-OO�2þ is oxidized to½RuV −OO�3þ. In this form, no barrier is required to release O2

when one water molecule attacks Ru to form ½RuIII-OH�2þ andrelease a proton. ½RuIII-OH�2þ can be rapidly oxidized to½RuIV-OO�2þ through PCETas shown in Fig. 2. This suggests thatthe electron-transfer process is a rate-limiting step at pH ¼ 0.0rather than the O2 releasing step in Pathway 2.

ConclusionsAlthough water oxidation catalyzed by the single-site Ru catalystis complicated, microscopic details are elucidated clearly by ourtheoretical computations. Even though calculations have asso-ciated errors in pKa and redox potential values, the computedthermochemical pathways for different Ru oxidation states are

Fig. 4. Computed thermochemistry pathways using B3LYP/LANL2DZ of½RuIII-OOH�2þ to ½RuIV-OO�2þ. The available experimental values are listedin parentheses. NHE is used here (4.24 V).

Fig. 5. Potential energy surface of singlet ½RuIV-OO�2þ and the correspond-ing triplet energies with optimal geometries from singlet using B3LYP/LANL2DZ.

Fig. 6. The reaction profile computed by QM/MM-MFEP approach to releaseO2 for the open form of ½RuIV-OO�2þ with both singlet and triplet spin states.The QM subsystems are computed by B3LYP/LANL2DZ.

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still helpful in explaining in qualitative detail how proton-transferand electron-transfer processes occur at the atomistic level. Twopathways at different pH values share the same rate-limiting step[i.e., concerted oxygen atom-proton transfer (APT) to oxidizewater, which was clarified by our previous work (21)]. However,in Pathway 1, O2 release is a key step in determining catalyticrates. This step is also complicated by spin states and conforma-tion changes in ½RuIV-OO�2þ. In Pathway 2, the rate-limiting stepis the oxidation of ½RuIV-OO�2þ to ½RuV-OO�3þ rather than O2

release. Spin-orbital coupling effects are crucial in both pathwaysin bringing the system to a high spin state in order to release tri-plet O2. When the binding ligands are modified, the rate-limitingsteps can be changed as well.

Based on our computations on this heavy transition metal sys-tem, we conclude that several issues need to be addressed beforetheoretical modeling can be helpful in further tuning existing cat-alysts or designing future catalysts: (i) accurate but fast methodsto predict pKa and redox potentials as well as reaction barriers;and (ii) affordable approaches to computing relativistic effects.With the aid of QM/MM-MFEP, we believe that computations

of redox potential (29) and reaction barriers (30) are affordablenow. However, the approximated functionals might impair accu-racy. Further theoretical progress is needed to make computa-tional modeling more accurate.

Materials and MethodsAll QM calculations with IEFPCMwere performed using Gaussian 09 program(31). The QM/MM-MFEP simulations were carried out using our in-house Sig-ma/G03 (30, 32). The B3LYP/LANL2DZ scheme with implicit solvent watermodel (i.e., IEFPCM) was applied for geometries optimizations, potential en-ergy scan, the computations of redox potential and pKa. All the spin states ofruthenium intermediates were identified by MP2/LANL2DZ computations.The QM/MM-MFEP approach with explicit water molecules was employedto obtain the accurate activation barriers of key reactions steps (16, 33–35)(SI Text).

ACKNOWLEDGMENTS. This material is based upon work wholly supported as

part of the UNC EFRC: Solar Fuels, an Energy Frontier Research Center fundedby the US Department of Energy, Office of Science, Office of Basic EnergySciences under Award Number DE-SC0001011.

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