Article pubs.acs.org/JPCA
Computational Study of H2 and O2 Production from Water Splitting by Small (MO2)n Clusters (M = Ti, Zr, Hf) Zongtang Fang and David A. Dixon* Department of Chemistry, The University of Alabama, Shelby Hall, Box 870336, Tuscaloosa, Alabama 35487-0336, United States S Supporting Information *
ABSTRACT: Coupled cluster [CCSD(T)] theory and density functional theory (DFT) have been used to study the production of H2 and O2 from hydrolysis products generated from H2O addition to (MO2)n (M = Ti, Zr, Hf, n = 1−3) clusters on both the lowest singlet and triplet potential energy surfaces (PESs). H2 production occurs via the formation of an M−H containing intermediate followed by H−H recombination and H2 desorption from MnO2n(OH)2 and MnO2n+2. The hydrogen transfer reactions to form the M−H bond are the rate determining steps and can be considered to be proton coupled, electron transfer (PCET) reactions with one or two electrons being transferred. Oxygen is produced by breaking two weak M−O bonds in an atomic oxygen saturated metal oxide from an M n O2n •O2 intermediate. On the triplet PES, the activation energies for the first and second H transfer to the metal are calculated to be ∼10 to 50 kcal/mol and ∼75 to 90 kcal/mol depending on the size of the clusters and the metal. The barriers on the singlet surface for the first and the second H transfer are predicted to be 110 to 140 kcal/mol, in general larger than the H−O bond dissociation energy. The activation barriers for the step of H−H recombination are 15 to 50 kcal/mol, and the H2 desorption energies are less than 10 kcal/mol on the singlet and triplet PESs. The oxygen desorption energies follow the order Ti < Zr < Hf for the triplets and Ti < Zr ≈ Hf for the singlets. The oxygen desorption energy is approximately independent of the size of the cluster for the same metal. The water splitting reactions prefer to take place on the triplet surface. A low excess potential energy is needed to generate 2H2 and O2 from 2H2O after the endothermicity of the reaction is overcome on the triplet PES.
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INTRODUCTION Since Fujishima and Honda first used TiO2 as the photocatalyst for water splitting to generate H2 and O2 under UV light in 1971,1,2 solar splitting of water with TiO2 has been extensively studied. The other two group 4 transition metal dioxides, zirconia (ZrO2) and hafnia (HfO2), also have been used as photocatalysts for water splitting to generate H2 and O2.3−6 Water splitting into H2 and O2 (2H2O(g) → 2H2(g) + O2(g)) is an endothermic reaction with a reaction enthalpy of 115.6 kcal/mol using the heat of formation of H2O at 298 K (−57.8 ± 0.2 kcal/mol),7 which roughly corresponds to two 500 nm visible photons. Hydrogen evolution from water splitting can be achieved without an external circuit by using TiO2 nanoparticles or TiO2 powder as the photocatalyst under visible light.8−11 In the photocatalytic process, noble metals such as Pt or Ru serve as the catalyst and electric donors such as diethanolamine (DEA) or triethanolamine (TEA) are required to produce the H2. The photogeneration of H2 also can be achieved on a crystalline surface. A Pt-loaded TiO2 hierarchical photonic crystal photocatalyst shows enhanced catalytic activity and can double the hydrogen evolution in comparison with the rate obtained by using nanocrystalline TiO2 due to improved light capture and multiple scattering among segments.12 Although there are © 2013 American Chemical Society
many experiments dealing with the evolution rate and the quantum yield efficiency, the details of the H2 evolution mechanism are not as well-understood. Generally it is believed that H2 production is due to the reduction potential of an excited electron which is sufficient to reduce H+ ions to H2.13 The detailed mechanism including the reaction intermediates and reaction barriers for the photodecomposition of water on crystal TiO2 and TiO2 nanoclusters is still not well-established. To overcome the high overpotential of oxygen evolution from water splitting and improve the efficiency, a photoelectrochemical catalytic approach has been used for water splitting. The presence of an electric field at the interface prevents the recombination of photogenerated electrons and cationic holes.14,15 The mechanism of photoreduction in the water−TiO2 system is still controversial. Early work predicted the formation of several radicals during the reaction. Fujishima and co-workers found that photogenerated holes can produce hydroxyl (•OH) radicals in both the gas phase16 and aqueous environment17,18 on the hydrated TiO2 anode surface. The formation of HO2•, •O2−, and •O33− radical intermediates Received: February 8, 2013 Revised: March 29, 2013 Published: April 1, 2013 3539
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measure of the ability of a surface to bind oxygen.32 Vojovodic and Nørskov33 verified this hypothesis by DFT calculations of the appropriate densities of states. Small TiO2 clusters (Ti2O4) have been used to study34 electrochemical water splitting for one and two water molecules with a combination of DFT at the B3LYP/TZV(d,p) level followed by coupled cluster single and double (CCSD) singlepoint energy calculations. Reactions in solution were modeled by a polarizable continuum model. Proton and electron removal is predicted to be very endothermic in both the gas and aqueous phases. O−O bond formation is predicted to proceed through peroxides and takes place after the removal of two electrons. The mechanism of H2 and O2 evolution using ZrO2 and HfO2 as photocatalysts has not been reported. In our previous work, we predicted that water should readily react with small (MO2)n (M = Ti, Zr, Hf) clusters to form hydroxides.35,36 H2 and O2 evolution would then take place in subsequent steps with breaking of the M−O−H bonds. In the current study, we use electronic structure theory at both the DFT and correlated molecular orbital theory coupled cluster (CCSD(T)) levels to study the H2 and O2 production mechanism of photocatalytic water splitting by (MO2)n (M = Ti, Zr, Hf, n = 1−3) clusters. In our study, we do not employ a separate moiety to produce the H2 as currently practiced and described above. Rather, we focus on the ability of a cluster to split water into both H2 and O2. Both the lowest energy singlet and triplet potential energy surfaces were calculated. Starting from the initial hydrolysis products, the MO−H bond is broken first leading to the formation of a metal hydride before the formation of H2 and then M−O bonds are broken to generate O2. Dehydrogenation and deoxygenation reaction energies and barriers are calculated using the B3LYP functional.37,38 The DFT potential energy surfaces for the monomer and dimer were benchmarked by comparison to the energies calculated at the CCSD(T) level.
were detected with EPR under UV irradiation of hydrated anatase TiO2 in an oxygen environment.19 Salvador and Gutierrez proposed the formation of H2O2 from the coupling of •OH radicals.20,21 On the basis of results from in situ FTIR spectroscopy measurements, Nakato and co-workers22 predicted that O2 evolution is initiated by the formation of a surface peroxo (Ti−O−O−Ti) intermediate on the TiO2 (rutile) surface. In acidic solution, Ti−OOH is formed by protonation of Ti−O−O−Ti by H2O. Without an external electric field, oxygen evolution has only been reported with the assistance of an electron acceptor, such as Ag+ in solution.23−25 Transient absorption spectroscopy has been used to study the kinetics of oxygen evolution where O2 is produced in the aqueous phase using a nanocystalline Pt−TiO2 film under UV irradiation.24 That study predicted that four photogenerated holes are required for 1 mol of oxygen production and that there are three possible unidentified reaction paths for the formation of oxygen. The same spectroscopic method was used to detect the lifetime of photoholes in nitrogen-doped, nanocrystalline TiO2 films.25 Oxygen production requires the lifetime of the photoholes to be at least ∼0.4 s. Computational research on water splitting has been focused on the electrochemical mechanism. The photoelectrochemical oxidation of water on the rutile TiO2 (110) surface was studied by Valdés et al.26 with density functional theory (DFT)27 with the generalized gradient approximation (GGA) RPBE functional. They based their mechanism on four one-electron transfers and predicted the rate limiting step for water splitting to be the formation of an adsorbed hydroxyl group based on thermodynamic correlations. In a neutral environment, an overpotential of at least 0.78 V is needed for both H2 and O2 evolution. O2 evolution was predicted to take place via an intermediate HOO adsorbed on the crystal surface. Part of this group subsequently28 modeled water oxidation on a rutile TiO2 (110) surface by using a (TiO2)26 cluster and found a similar oxygen evolution mechanism.29 Nørskov and co-workers30 reported the same oxygen evolution mechanism on transition metal doped rutile TiO2 (110) surfaces. A lower overpotential for the oxygen evolution reaction was predicted for the doped surface as compared to the undoped surface. Liu and coworkers31 studied oxygen evolution on different TiO2 anatase surfaces in an aqueous environment with DFT with the generalized gradient approximation (GGA) PBE exchangecorrelation functional. They modeled oxygen evolution by adding two H2O molecules to the crystal surface and then removed the four protons step-by-step. After the first H2O decomposed on the crystal surface with formation of a hydroxyl group, a surface bridging Ti−O−O−Ti moiety is formed by loss of the proton from the OH group. The second H2O adsorbs at the same Ti atom and production of the second OH group induces the evolution of O2. In the chemisorption reaction of the second water, the structure of surface bridging O−O changes from peroxide to superoxide. For the overall reaction, the removal of the first proton requires the highest overpotential in comparison to the following steps in their mechanism. A Ti−OH bond is formed instead of a •OH radical, and no adsorbed OOH and HOOH species were identified in the oxygen evolution reaction. They studied the (101), (001), and (102) surfaces and did not find significant differences in terms of the overpotential. Further work on the oxygen evolution reaction led to the proposal that the occupation of the eg orbitals of the active metal in perovskites was a descriptor of the reaction efficiency, as it provides a
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COMPUTATIONAL METHODS Geometry optimization and frequency calculations were performed at the DFT level with the B3LYP37,38 exchangecorrelation functional. This functional was chosen, as it is the same method used for our study of the hydrolysis of (MO2)n (M = Ti, Zr, Hf, n = 1−4) clusters where reasonable results were found in comparison to CCSD(T) calculations.35,36 The DFT optimized DZVP2 based set was used for the reaction of H2O with TiO2 clusters.39 For the reaction of H2O with ZrO2 and HfO2 clusters, the aug-cc-pVDZ basis sets were used for O and H40 and pseudopotential (PP)-based aug-cc-pVDZ-PP basis sets were used for Zr and Hf.41,42 For simplicity, we denote these combined basis sets as aD. Vibrational frequencies were calculated to characterize the stationary points on the potential energy surfaces and to obtain zero-point energy corrections as well as the thermal and free energy corrections at 298 K, the latter values using the normal statistical mechanical expressions.43 The synchoronous transit-guided quasi-Newton (STQN) method was used for the transition state optimizations.44 For the potential energy surfaces for the monomer and the dimer, the B3LYP geometries were used in single-point energy calculations with the coupled cluster [CCSD(T)] theory45−47 with the aD basis set for all atoms.48−50 The open-shell calculations were performed with the R/UCCSD(T) approach where a restricted open shell Hartree−Fock (ROHF) calculation was initially performed and the spin constraint was then relaxed in the coupled cluster calculation.51 3540
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Figure 1. Potential energy surfaces for Ti(OH)4 (1b) → TiO2 (1a) + 2H2 + O2 at 0 K. Relative energies calculated at the CCSD(T)/aD//B3LYP/ DZVP2 (in blue) and B3LYP/DZVP2 (in black) levels in kcal/mol. The O atoms are given in red, Ti atoms in dark blue, and H atoms in gray-white.
The DFT calculations were carried out with the Gaussian 09 program package.52 All CCSD(T) calculations were performed with the MOLPRO 2010.1 program.53 The calculations were performed on local Xeon and Opteron based Penguin Computing clusters, the Xeon based Dell Linux cluster at the University of Alabama, the Opteron and Xeon based Dense Memory Cluster (DMC) and Itanium 2 based SGI Altix systems at the Alabama Supercomputer Center, and the Opteron based HP Linux cluster at the Molecular Science Computing Facility at Pacific Northwest National Laboratory.
Molecular visualization was carried out using the AGUI graphics interface from the AMPAC program package.54
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RESULTS The structures of the optimized intermediates and transition states for M = Ti are shown in Figures 1−5. The total energies, Cartesian coordinates, and pictures of the molecules for the potential energy surfaces (PESs) for the reaction of H2O on M3O6 (M = Zr, Hf) are given as Supporting Information including atom numbering where appropriate. In our previous study of the hydrolysis of M3O6 (M = Zr, Hf),36 we did not 3541
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Figure 2. Potential energy surfaces for Ti2O2(OH)4 (2b) → Ti2O4 (2a) + 2H2 + O2 at 0 K. Relative energies calculated at the CCSD(T)/aD// B3LYP/DZVP2 (in blue) and B3LYP/DZVP2 (in black) levels in kcal/mol.
study the reaction of the addition of a second H2O with the clusters. In the current work, we calculated the reaction of the second H2O addition and the PESs are shown in the Supporting Information. Potential Energy Surfaces. The calculated PESs for H2 and O2 production on the monomer and the dimer of TiO2 clusters at both the CCSD(T) and B3LYP levels are given in Figures 1 and 2. The PESs for MO2 (M = Zr, Hf) and M2O4 (M = Zr, Hf) are shown in the Supporting Information. The PESs for the trimers at the B3LYP level are given in Figures 3−5. In the following sections, the CCSD(T) energy results are used for the discussion of the energetics for the monomer and
dimer reactions. The triplet state is used as a model for the excited state of the cluster, as it is not really possible to study the excited open shell singlet states using current density functional theory approaches. Our prior work on the cluster excitation energies shows that the singlet−triplet splitting is on the order of 0.1 eV.55 This small difference in energy between the first open shell singlet and the triplet state does not change the conclusions. Monomers. The PES for H2 and O2 production for 3TiO2 (1a) starting from the hydrolysis product, 3Ti(OH)4, calculated at the CCSD(T)/aD level is shown in Figure 1. 3Ti(OH)4 can be formed by 1Ti(OH)4 absorbing 84 kcal/mol of energy or by 3542
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Figure 3. Potential energy surfaces for M3O4(OH)4 (3b) → M3O6 (3a) + 2H2 + O2 at 0 K. Relative energies calculated at the B3LYP/DZVP2 (in black) level for M = Ti, the B3LYP/aD (in green) level for M = Zr, and the B3LYP/aD (in purple) level for M = Hf in kcal/mol.
excitation of TiO2 by a visible photon (∼555 nm) with ∼52 kcal/mol of energy followed by the reaction of two H2O molecules. As discussed above, the excited singlet−triplet splitting is small so we approximate the photon absorption energy by the energy needed to generate the triplet. The
reaction starts with an endothermic H migration from a hydroxyl group forming a Ti−H bond with a reaction barrier of 37.4 kcal/mol. The formation of the M−H bond is followed by the recombination of two hydrogens to form H2, one from a Ti−H bond and the other an adjacent H atom in the hydroxyl 3543
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energy. For the formation of the second metal hydride, the barriers are 103.3 and 84.6 kcal/mol for M = Zr and M = Hf, respectively. The barriers for H−H recombination and the H2 desorption energies are comparable to those for 3TiO2. The oxygen desorption energies on 3MO2 are 51.7 and 48.3 kcal/ mol for M = Zr and M = Hf, respectively. The alternative reaction path for the release of O2 before the release of the second H2 from the intermediate 3HMO3(OH) (M = Zr, Hf) is similar to that for TiO2. The reaction barriers for H−H recombination are 39.1 and 44.0 kcal/mol for M = Zr and M = Hf, respectively, slight larger than that for M = Ti. The path proceeding in the order H2 release, O2 release, and H2 release (H2−O2−H2 path) has a higher energy profile than the path discussed above in the order H2 release, H2 release, and O2 release (H2−H2−O2 path) especially for M = Zr, Hf although, for M = Ti, the two paths have more similar energies. For the H2−O2−H2 path, the highest potential energy along the PES is still smaller than or equal to the endothermicity of the reaction 2H2O→ 2H2 + O2, even though it is higher in energy than the H2−H2−O2 path. Dimers. The PESs for H2 and O2 production on Ti2O4 (2a) clusters are shown in Figure 2, and the PESs for the H2−O2− H2 path on Ti2O4 and M2O4 (M = Zr, Hf) are given in the Supporting Information. The H2 production process for the reaction on the dimer is consistent with the reaction on the monomer. For both the triplet and singlet, the O−H bond in M2O2(OH)4 is broken first to form a metal hydride containing species and the reaction is followed by a H−H recombination step and H2 release. After the release of the first H2, the intermediate 3M2O4(OH)2 undergoes a structural transformation with modest energy input and two terminal MO oxygen atoms bond together as shown in 3M2O4(OH)2 (2g) leading to a structure that is favorable for O2 evolution. The process for the release of the second H2 is the same as that for the first one. For O2 formation, an intermediate M2O4•O2 (2n), which contains a five-coordinate metal and an O−O bond, is formed by an O atom transfer to the adjacent metal atom via the path shown for 2l → 2n. The M−O bond in the atomic oxygen saturated intermediate is much weaker than a normal M−O bond,48 so only modest energy input is needed to break the M−O bond to produce O2 and the dimer isomer, M2O4 (C3v, 2o). The ground singlet state isomer 1M2O4 (C2h, 2a) is regenerated by a structural transformation reaction with a small barrier. The barriers for the reactions on 3Ti2O4 for forming two Ti− H bonds are calculated to be 37.9 and 92.0 kcal/mol, comparable to those for 3TiO2. The reaction barriers for the two H−H recombination reactions are 23.4 and 17.6 kcal/mol, slightly smaller than those for 3TiO2. Again, much smaller energies than the two reaction barriers are needed for H2 desorption. The reaction barrier for the formation of the oxygen saturated species is predicted to be 8.1, and 15.2 kcal/ mol is needed to break the weak Ti−O bond in 3Ti2O4•O2 (2n). The isomer relaxation of 1Ti2O4 (C3v, 2o) to the ground singlet state 1Ti2O4 (C2h, 2a) is exothermic with a small barrier. For the reaction on 1Ti2O4, the reaction barriers for hydrogen transfer to the Ti atom are calculated to be 126.4 and 126.9 kcal/mol, much larger than those for 3Ti2O4. The reaction barriers for H−H recombination, the H2 desorption energy, and the O2 desorption energy are comparable with those for 3 Ti2O4. The barrier for the formation of 1Ti2O4•O2 (2n) from 1 Ti2O6 (2l) is 40.9 kcal/mol at the B3LYP/aD level, much larger than that for triplet 2l → 2m.
group. This step is also endothermic with a reaction barrier of 32.3 kcal/mol. The H2 molecule is released from the complex TiO2(OH)2•H2 with a desorption energy of only 2.8 kcal/mol. The process for the production of the second H2 is the same as for the first H2 molecule. The reaction barriers for Ti−H bond formation and H−H recombination are 78.7 and 34.6 kcal/mol, respectively. After the release of two H2 molecules, a triplet oxygen molecule is readily desorbed from the 3TiO2•O2 (1l) species and 1TiO2 is regenerated. The calculated desorption energy of 3O2 is 6.3 kcal/mol. If this reaction were to take place on an excited singlet, then a singlet−triplet crossing would need to occur, which could raise the barrier or decrease the rate. The potential energy surface calculated at the B3LYP/DZVP2 level is in semiquantitative agreement in comparison with the CCSD(T)/aD results with differences of relative energies being less than 5 kcal/mol. The PES for reactions on 1TiO2 at the CCSD(T)/aD level is also shown in Figure 1. The reaction process is similar to that for 3TiO2, and the H2 release follows the same process, Ti−H bond formation, H−H recombination, and H2 desorption. Due to the high exothermicity of the hydrolysis reaction on the singlet cluster, the reaction barrier for the formation of the titanium hydride, 1HTiO(OH)3 (1d) is high, 115.3 kcal/mol, which is larger than the average water H−O bond energy of 110 kcal/mol or the H2 bond energy of 104 kcal/mol.56 This barrier is also much larger than the excitation energy needed to form 3HTiO(OH)3. The barrier for H−H recombination and the H2 desorption energy for the first H2 release are 19.3 and 3.9 kcal/mol, comparable to the values for the triplet surface. For the release of the second H2 from the singlet, the reaction barriers for H transfer to Ti and H−H recombination are 96.7 and 32.7 kcal/mol, respectively, and the H2 desorption energy is 9.1 kcal/mol. The barrier to form the second Ti−H bond on the singlet surface is also higher than that on the triplet surface. Breaking the Ti−O bond in 1TiO2 •O2 (1l) to generate 3TiO2 and 3O2 requires 33.4 kcal/mol if there is no surface crossing to form 1TiO2. The presence of a singlet−triplet surface crossing leads to an exothermic channel to form the 1TiO2. Again, the B3LYP/DZVP2 results for the singlet potential energy surface are similar to those calculated at the CCSD(T)/aD level. An alternative reaction path for the release of O2 and the second H2 is the conversion of 1m → 1a. Oxygen is released first by breaking a Ti−O bond in 3HTiO3(OH) (1i). The O2 desorption energy is 7.5 kcal/mol at the CCSD(T)/aD level. The final step is H2 production with a barrier of 34.6 kcal/mol and a H2 desorption energy of 6.3 kcal/mol on 1TiO2. The processes for H2 and O2 release from the hydrolysis product M(OH)4 (M = Zr, Hf) are the same as those for Ti(OH)4. Consistent with the TiO2 results, the highest reaction barrier takes place in the formation of the metal−hydrogen bond for the release of the second H2 on the triplet surface. For M = Zr, the reaction barriers for the formation of the two Zr− H bonds are 14.4 and 84.5 kcal/mol at the CCSD(T)/aD level. The corresponding energies are 12.1 and 87.9 kcal/mol for M = Hf. The reaction barriers for the two H−H recombination reactions are 44.9 and 27.5 kcal/mol for M = Zr and 50.4 and 30.8 kcal/mol for M = Hf. A much lower energy, generally 2 to 6 kcal/mol, is needed for the desorption of the first and second H2. The energy input to break the M−O bonds are 19.5 and 33.2 for M = Zr and M = Hf respectively. On the singlet cluster, the reaction barrier for the formation of the first M−H bonds are 127.1 and 127.9 kcal/mol for M = Zr and M = Hf, respectively, which are larger than the O−H bond dissociation 3544
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Figure 4. Potential energy surfaces for M3O4(OH)4 (3o) → M3O6 (3a) + 2H2 + O2 at 0 K. Relative energies calculated at the B3LYP/DZVP2 (in black) level for M = Ti, the B3LYP/aD (in green) level for M = Zr, and the B3LYP/aD (in purple) level for M = Hf in kcal/mol.
The reaction mechanisms for Zr2O4 and Hf2O4 are essentially the same as that for Ti2O4. On 3Zr2O4 and 3 Hf2O4, the major energy consuming step is the formation of the second metal hydride. For the reactions on 1Zr2O4 and 1 Hf2O4, both the first and the second H transfers to the metal require significant energy input. The barriers to form 1 HM2O2(OH)3 (2d) are calculated to be 118.4 and 119.9 kcal/mol for M = Zr and M = Hf, both larger than the H−O
bond energy. In comparison with the large barrier for H transfer to the metal, the H−H recombination barriers, the H2 desorption energy, and the O2 desorption energy are much smaller on both the singlet and triplet potential energy surfaces. After formation of HM2O5(OH), the reaction can generate the complex HM2O3(OH)•O2 first via rotation of the O atom adjacent to the M−H bond to bond to the other metal. Then 3 O2 is released by breaking two weak M−O bonds followed by H−H recombination. After the release of the second H2, M2O4 3545
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Figure 5. Potential energy surfaces for M3O4(OH)4 (3aa) → M3O6 (3a) + 2H2 + O2 at 0 K. Relative energies calculated at the B3LYP/DZVP2 (in black) level for M = Ti, the B3LYP/aD (in green) level for M = Zr, and the B3LYP/aD (in purple) level for M = Hf in kcal/mol.
kcal/mol for both the triplet and singlet, ∼10 kcal/mol larger than that from the triplet and singlet HTi2O5(OH). For M = Zr, Hf, on the triplet surface, slightly more energy is needed to regenerate the ground state 1M2O4 for the H2−O2−H2 path than for the H2−H2−O2 path. On the singlet surface for M = Zr, Hf, >30 kcal/mol of additional energy are required to form
(C2h, 2a) is regenerated. For M = Ti, the energy needed to release the second H2 from HM2O5(OH) is >25 kcal/mol energy less than the energy needed to form the complex HM2O3(OH)•O2 for 3O2 release on both the triplet and singlet potential energy surfaces. The reaction barrier for H−H recombination from HTi2O3(OH) are predicted to be ∼30 3546
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Table 1. Calculated Metal Hydrogen Bond Distance in Å at the B3LYP Levela Ti
a
Zr
Hf
moleculeb
singlet
triplet
singlet
triplet
singlet
triplet
HMO(OH)3 (1d) HMO3(OH) (1i) HMO(OH) (1m) HM2O3(OH)3 (2d) HM2O5(OH) (2i) HM3O5(OH)3 (3d) HM3O7(OH) (3i) HM3O5(OH)3 (3q) HM3O7(OH) (3v) HM3O5(OH)3 (3ac) HM3O7(OH) (3ah)
1.686 1.711 1.720 1.699 1.696 1.682 1.680 1.681 1.691 1.706 1.713
1.851 1.724 − 1.900 1.689 2.202 1.679 2.332 1.680 1.975 1.682
1.867 1.873 1.894 1.884 1.878 1.865 1.864 1.868 1.871 1.898 1.882
2.100 1.865 − 2.151 1.874 2.558 1.857 2.122 1.859 2.190 1.859
1.851 1.857 1.864 1.869 1.864 1.849 1.879 1.850 1.851 1.880 1.861
2.088 1.844 − 2.129 1.857 2.441 1.842 2.094 1.843 2.151 1.868
DZVP2 basis set for M = Ti and aD basis set for M = Zr, Hf. bSee Figures 1−5 and Supporting Information for the molecular structures.
desorption energy from the complex of 3Ti3O6•O2 (3n) is calculated to 22.1 kcal/mol. On the singlet potential energy surface, the formation of the first metal hydrogen containing species has large reaction barriers for all three different reactions as shown in Figures 3−5. The barriers for the formation of a second metal hydrogen containing singlet species are predicted to be ∼110 to ∼130 kcal/mol, much larger than on the triplet potential energy surfaces. The reaction barriers and desorption energies for the H2 and O2 release steps are comparable with those on the triplet potential energy surfaces. For M = Zr and Hf, the reaction barriers for forming the metal hydrogen containing species and the H−H recombination reaction as well as the H2 and O2 desorption energies can differ by up to 20 kcal/mol as compared to the reactions with Ti3O6 on the triplet surface. On the singlet surface, those energy differences are less than 5 kcal/ mol. Cluster Geometries and Frequencies. The M−H bond lengths for the metal hydrogen containing intermediates predicted at the B3LYP/DZVP2 level for M = Ti and at the B3LYP/aD level for M = Zr and Hf are given in Table 1 for both singlets and triplets; the corresponding vibrational frequencies are given as Supporting Information. The calculated M−H bond distances for both the triplet and singlet states are similar in HMnO2n+1(OH) (n = 1−3). In the metal hydrogen containing HMnO2n−1(OH)3 (n = 1−3) molecules, the M−H bond distances in the triplet can be longer by up to 0.7 Å than in the singlet depending on the structure. This happens for the first metal hydrogen containing species, where the M−H bond is elongated in comparison with the singlet but not for the second metal hydrogen molecules. The M−H bond distances in the singlet state molecules are predicted to be ∼1.69 to 1.72 Å for Ti, ∼1.86 to 1.90 Å for Zr, and ∼1.85 to 1.88 Å for Hf. The calculated Ti−H bond distances are slightly longer than the Ti−H bond distance of 1.68 Å in TiH4.57 For the HMnO2n−1(OH)3 (n = 1−3) species, the Ti−H bond in the triplet is much longer than in the singlet and is similar to the difference in the Ti−H bond distances in the triplet and singlet states of the H−TiO+ cation.58,59 For the Zr−H and Hf−H bonds, the bond distances are slight shorter than in MH4, which are 1.912 and 1.907 Å for M = Zr and M = Hf respectively.60,61 The structures with long M−H bonds suggest that the excitation is at least partially localized in this region in the triplets. The M−H stretching frequencies in the singlets change up to 50 cm−1 in comparison with those of the corresponding MH4
an oxygen complex compared to H−H recombination from 1 HM2O5(OH). The activation barriers for H−H recombination are predicted to be 30 to 40 kcal/mol for both the triplet and singlet, 10 to 15 kcal/mol larger than the barriers in the second H2 production on the H2−H2−O2 path. Trimers. The PESs for hydrogen and oxygen production on the M3O6 (3a) cluster at the B3LYP/aD level are shown in Figures 3−5. For both the triplet and singlet potential energy surfaces, the reactions can start from three different hydrolysis products, M3O4(OH)4 (3b, 3o, 3aa). All four hydrogen atoms are bonded to a terminal O in M3O4(OH)4 (3b). There are one or two hydrogen atoms bonded to a bridge O in the isomers of 3o and 3aa, respectively. For the reaction shown in Figure 3, the H2 release step is similar to that for the monomers and dimers. After the release of two H2 molecules, the intermediate is M3O8 (3l), in which there is a five-coordinate metal bonded with four bridge O atoms and one terminal one. From this species, one bridge oxygen atom rotates to bond with the terminal oxygen and form a dioxygen complex M3O6•O2 (3n) in which the two oxygens in an O−O bond and M3O6 (3a) are connected by two weak M−O bonds. O2 is released by breaking the two weak M−O bonds. As shown in Figure 4, the two H atoms which are bonded to terminal O atoms are released first after hydrogen transfer to a metal and the reaction is followed by the production of the second H2, which contains the H atom bonded to a bridge O atom. On 3M3O6, after the release of H2 from the complex 3 M3O8•H2 (3x), the oxygen saturated species relaxes to form 3 M3O6•O2 (3n), which is ready for oxygen release. On 1M3O6, a structural transformation step is still needed to form the oxygen complex, 1M3O6•O2 (3n). The same process takes place in the O2 production reactions shown in Figure 5 for water splitting from M3O4(OH)4 (3aa). The H2 production process is similar to the previous reactions. In terms of the energetics, on the triplet potential energy surface starting from the hydrolysis product 3Ti3O4(OH)4 (3b) shown in Figure 3, the barrier for the formation of 3 HTi3O5(OH)3 (3d) is 48.8 kcal/mol, much lower than that for the formation of 3HTi3O7(OH) (3i) which is 97.2 kcal/mol. As shown in Figures 4 and 5, the reaction barrier for the second H transfer is also much larger than the first one. The H−H recombination barriers fall into the range of ∼20 to 35 kcal/ mol, and the H2 desorption energies are predicted to be
