Computational Study of Molecular Hydrogen Adsorption over Small

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A: Molecular Structure, Quantum Chemistry, and General Theory

Computational Study of Molecular Hydrogen Adsorption over Small (MO) Nanoclusters (M = Ti, Zr, Hf, n = 1 to 4 ) 2

n

Zongtang Fang, Monica Vasiliu, Kirk A. Peterson, and David A Dixon J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b12634 • Publication Date (Web): 10 Apr 2018 Downloaded from http://pubs.acs.org on April 10, 2018

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The Journal of Physical Chemistry

Computational Study of Molecular Hydrogen Adsorption over Small (MO2)n Nanoclusters (M = Ti, Zr, Hf, n = 1 to 4 ) Zongtang Fang,a Monica Vasiliu,a Kirk A. Peterson, b and David A. Dixon a,*,† a

Department of Chemistry and Biochemistry, The University of Alabama, Shelby Hall, Box

870336, Tuscaloosa, AL 35487-0336 b

Department of Chemistry, Washington State University, Pullman WA 99164-4630 USA

Abstract Hydrogen adsorption on small group 4 metal oxide clusters for both the singlet and the first excited triplet states have been investigated by density functional theory and correlated molecular orbital theory at the coupled cluster CCSD(T) level. The reaction starts with hydrogen physisorption on a metal center followed by formation of metal hydride/hydroxides due to splitting H2 into H- and H+. The hydrogen physisorption energies are predicted to be -1 to -8 kcal/mol for the singlet and -1 to -26 kcal/mol for the triplet respectively. The formation of metal hydride/hydroxides does not involve redox processes. Chemisorption leading to formation of metal hydride/hydroxides is exothermic by -10 to -50 kcal/mol for the singlet, and exothermic by up to -60 kcal/mol for the triplet. The predicted energy barriers are less than 20 kcal/mol. Formation of metal dihydroxides from the metal hydride/hydroxides is generally endothermic for the monomer and dimer and is exothermic for the trimer and tetramer. Formation of the dihydroxide is a proton coupled electron transfer (PCET) process. The singlet energy barriers for the H-→ H+ transfer process are predicted to be 35 to 60 kcal/mol, in comparison to triplet energy barriers of less than 15 kcal/mol for the H·→ H+ transfer process. For trimers and tetramers, there exist two different pathways; the first is a direct pathway with PCET to a

†

Email: [email protected] 1 ACS Paragon Plus Environment

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terminal oxygen and the second is a two-step pathway with initial formation of a bridge OH group followed by a proton transfer to generate a terminal OH group. For the singlet, the twostep pathway is preferred for M = Ti and the direct pathway is more favorable for M = Zr and Hf. The two-step pathway is always preferred for the triplet as one-electron transfer is always more likely than two-electron transfer in the direct pathway.

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Introduction Metal oxides have a broad range of uses including catalysts,1 gas sensors,2,3,4 and gas storage. 5 , 6 , 7 Nano-manganese oxide, 8 mesoporus nickel, and magnesium oxide 9 have been studied for hydrogen storage. Group 4 metal oxides are well established for the generation of hydrogen in a photoelectrochemical cell,10,11,12 and play an important role in gas absorption13 and hydrogen storage. 14 , 15 , 16 Thus, it is important to understand the interactions between hydrogen and Group 4 metal oxides to determine their potential capability for hydrogen storage. Hydrogen adsorption on the rutile TiO2 (110) crystal surface has been experimentally investigated using helium atom scattering (HAS)17. Ti-H and O-H bonds were observed to form on the crystal surface. Scanning tunneling microscopy (STM) combined with density functional theory (DFT) calculations were used to study the diffusion of H2 on bridge-bonded oxygen sites on the rutile TiO2 (110) surface.18 There is an initial diffusion of localized charge and repulsive OH-OH repulsions lead to an increase in the diffusion barrier. In addition, hydrogen adsorption on Ru/ZrO2 was studied by Fourier transform infrared spectroscopy (FTIR).19 The metal hydride was not observed and water species were formed after the introduction of hydrogen on the ZrO2 crystal surface. Another study of hydrogen adsorption on a pure ZrO2 crystal surface by FTIR showed the formation of both Zr-H and O-H species through the heterolytic dissociation of H2.20 Theoretical methods have been used to study H2 adsorption on various Group 4 metal oxide crystal surfaces. A recent study of hydrogen adsorption on anatase TiO2 (101) and rutile (110) surfaces at the DFT/PW91 level predicted that the H2 binding energy on the anatase surface is 0.2 to 0.3 eV smaller than on rutile.21 Hydrogen transfer into the bulk is more favorable than diffusion on the surface or desorption of an H2 molecule. A DFT study of H2 on TiO2 nanotubes predicted that the formation of Ti-H species occurs only at high hydrogen coverage. 22 3 ACS Paragon Plus Environment


Adsorption of hydrogen on an amorphous hafnia crystal surface23 was studied at the DFT level using the hybrid PBE0-TC-LRC functional.24 Dissociation of H2 with formation of an OH group is predicted to be more thermodynamically favorable than physisorption. DFT with the PBE functional was used to model the interaction of H2 with a layer of MO2 (M = Zr and Hf ) deposited on a Ge (100) surface. Depending on the layer geometry, hydrogen can form either an M-H bond or an O-H bond.25 The adsorption energy is predicted to slightly more exothermic for M = Hf than for M = Zr. Both physisorption and dissociative chemisorption of H2 on (ZrO2)n ( n = 1 to 6 ) clusters has been studied with the B3LYP functional.26 A dissociative chemisorption pathway with formation of an M-H bond and an O-H bond was predicted. In addition, a study on the hydrogenation of (TiO2)n (n = 1 to 10) clusters with the B3LYP functional predicted a reduction of the titanium sites with the formation of two OH groups on the clusters. 27 The reverse process, loss of H2 from MxOy cluster for M = Ti, Zr, and Hf generated by addition of H2O to (MO2)n for n =1 to 4 has also been studied.28 Although adsorption of H2 on small TiO2 and ZrO2 nanoclusters has been studied with DFT, the corresponding hafnia clusters have not been studied and there are no available studies using correlated molecular orbital methods at the CCSD(T) level which can provide accurate adsorption energies. MO2 (M = Ti, Zr, Hf) materials are useful photocatalysts, for example water splitting, so it is important to study the interaction between H2 and electronically excited MO2 clusters as well to provide further insight into the mechanism of the catalytic reactions. There are no available computational studies of the excited state reactions either. We have studied the molecular structures and energetics of small group 4 metal oxide clusters29, 30 as well as their reactions with H2O28,31,32 with both coupled cluster CCSD(T) theory and density functional


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theory. In the current work, we use the same approach to study hydrogen adsorption on those group 4 metal oxide clusters for both the singlet and the first excited triplet states. Computational Methods Geometry optimizations for the species on the potential energy surface have been performed with the B3LYP33,34 exchange correlation functionals at the DFT level. Geometries of the ground state and the first excited state clusters without hydrogen were taken from our previous work.28,29,30,31,32,32 For the reactions on TiO2 clusters, the DFT optimized DZVP2 based set was used for the DFT calculations.35 For the reactions on ZrO2 and HfO2 clusters, the aug-ccpVDZ basis sets36 for O and H and PP-based aug-cc-pVDZ-PP basis sets37,38 for the metal were used for the DFT calculations. We denote these combined correlation-consistent basis sets as aD. The B3LYP functional and the choice of basis sets were selected based on our previous work on the study on the molecular structures of Group 4 metal oxide (MO) nanoclusters as well as the hydrolysis reactions of those MO nanoclusters.28,29,30,31,32,32

The calculated vibrational

frequencies of the global minimum on the potential energy surface are employed to obtain the zero-point energy corrections (ZPEs) and the thermal corrections at 298 K, which were calculated by using the normal statistical mechanical expressions.39 The potential energy surfaces are calculated for the ground state as well as the first excited state of the triplet state. The synchronous transit-guided quasi-Newton (STQN) method was used to search for the transition states.40 The DFT calculations were carried out with the Gaussian 09 program package.41 The optimized geometries for the monomers and dimers were used in single point energy calculations at the coupled cluster [CCSD(T)] level42, 43, 44, 45 with the sequence of correlationconsistent basis sets aX (X = D, T, and Q).36,37,38, 46 The electronic energies of the open-shell species are calculated at the R/UCCSD(T) level where a restricted open shell Hartree-Fock 5 ACS Paragon Plus Environment


(ROHF) calculation was initially performed and the spin constraint was then relaxed in the coupled cluster calculation.47,48,49 These CCSD(T) energies were extrapolated to the complete basis set (CBS) limit using a mixed Gaussian/exponential formula. 50 For the trimers and tetramers, the optimized singlet geometries are used for the singe point calculations at the CCSD(T) level with the aD and aT basis sets and the triplet geometries were used for calculations at the R/UCCSD(T) level with the aD basis set. The open-shell CCSD(T) calculations for the open shell triplets are very expensive as an open shell calculation is effectively double the number of orbitals for the singlet and CCSD(T) scales as ~ N7. For example, there are 766 basis functions for the aT basis set for the tetramer + H2. For the singlet, the difference between using the aD and aT basis sets is small, usually less than 2 kcal/mol and the aT values are close to the CBS limit values as shown below and in the Supporting Information (SI). There is a larger basis set dependence for the triplet than for the singlet due in part to the basis set dependence for the initial excitation of the cluster as shown in the SI. All CCSD(T) calculations were performed with the MOLPRO 2012.1 program.51,52 The calculations were performed on the 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 done using the AGUI graphics program from the AMPAC program package.53 Results and Discussions Potential Energy Surfaces The CCSD(T) potential energy surface (PES) for hydrogen adsorption on both the singlet and triplet MO2 nanoclusters are shown in Figures 1 to 4. The less 6 ACS Paragon Plus Environment

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exothermic and/or endothermic pathways to form either metal hydride/hydroxide species or metal dihydroxides as well as the DFT results are shown in the SI. For the trimer and tetramers, we studied hydrogen adsorption on both a metal having an M=O bond and a metal bonded to all bridge oxygen atoms. Monomers The potential energy surfaces for the formation of metal hydride/hydroxide species for the monomers at the CCSD(T)/CBS level are shown in Figure 1. The adsorption reaction starts with formation of a physisorption complex. This is followed by a hydride (H-) transfer to the metal and a proton transfer to a terminal =O leading to the formation of a M-H hydridic bond and an O-H bond simultaneously, corresponding to the chemisorption process. On the singlet PES, the hydrogen physisorption energies are calculated to be only -5 to -7 kcal/mol at the CCSD(T)/CBS level. The formation of the metal hydride/hydroxide is more exothermic than the physisorption step with chemisorption energies of -34.0, -36.9, and -48.9 kcal/mol for M = Ti, Zr, and Hf respectively at the same level. The reaction energy barriers from the physisorbed complex for the formation of a metal hydride and metal hydroxide (splitting the H2 into H- and H+) are less than 8 kcal/mol, following the order of Ti > Zr > Hf. As the transition states are below or slightly above the reactant asymptote, hydrogen should readily dissociate on the monomer clusters without little or no energy input. For the triplet, the interaction between hydrogen and the cluster is still weak and the physisorption energy is close to that for the corresponding singlet. The energy barriers for the proton transfer for the triplet range from 7 to 17 kcal/mol, slightly larger than for the singlet. The formation of 3HMO(OH) (1d) is also exothermic with reaction energies less than -25 kcal/mol for the three metals.



Figure 1. Potential energy surfaces for H2 + MO2 → HMO(OH) (M = Ti, Zr, Hf) for both the ground state singlet and the first excited triplet MO2 clusters at the CCSD(T)/CBS level at 0 K. Relative energies are shown in black for M = Ti, red for M =Zr, and purple for M = Hf. The O atoms are given in red, metal atoms in dark blue and H atoms in gray-white.

Can the metal hydride/hydroxide HMO(OH) (1d) proceed further to form M(OH)2(1f)? The results for the formation of M(OH)2(1f) are shown in the SI. For the singlet, the pathway to generate 1M(OH)2(1f) via a H-→H+ transfer to the remaining =O atom in 1HMO(OH)(1d) is an 8 ACS Paragon Plus Environment

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endothermic process with endothermicities of 20.1, 20.2, and 4.9 kcal/mol for M = Ti, Zr, and Hf respectively at the CCSD(T)/CBS level. This process corresponds to a proton coupled electron transfer (PCET). The energy barriers range from ~ 30 to 50 kcal/mol following the order Ti > Zr > Hf. Thus, the second step to form M(OH)2 would not happen on the singlet clusters without significant energy input. In contrast, the reaction for formation of 3M(OH)2 (1f) from 3HMO(OH) (1d) is an exothermic process via a H·→H+ transfer with exothermicities of ca -40 to -60 kcal/mol; the reaction energies for three metals again follow the order of Ti > Zr > Hf. The formation of 3M(OH)2 (1f) is also a PCET reaction. The activation energies are 9.5, 2.5, and 3.2 kcal/mol for M = Ti, Zr and Hf respectively. In addition, 3Ti(OH)2 is 17.7 kcal/mol more stable than 1Ti(OH)2, whereas, 3M(OH)2 is less stable in energy than 1M(OH)2 for M = Zr and Hf. The triplet-singlet gaps are 0.3 kcal/mol for M = Zr and 20.7 kcal/mol for M = Hf. As shown in in the SI, Ti(OH)2 has a triplet ground state, consistent with what has been predicted for TiF2. 54 The singlet-triplet splitting is very small for Zr(OH)2 with the singlet favored over the triplet, in contrast to ZrF2 which has the triplet slightly lower than the singlet. For Hf(OH)2, the singlet is clearly the ground state just as found for HfF2. The triplet ground state for Ti(OH)2 means that a singlet-triplet crossing could occur and the reaction from 11d to 3

1f is endothermic by only by 2.4 kcal/mol. However, there will still be a substantial energy

barrier >40 kcal/mol. The effects of spin-orbit (SO) coupling on the first addition of H2 to HfO2 were calculated with the DIRAC program 55 using the Dirac-Hartree-Fock (DHF) method as the difference between a calculation with the full 4-component Dirac-Coulomb-Gaunt Hamiltonian and one with Dyall's spin-free Hamiltonian, 56 both with a finite-nucleus model.

The

uncontracted cc-pVDZ basis set of Dyall was used for Hf,57 and the uncontracted aug-cc-pVDZ 9 ACS Paragon Plus Environment


sets were used for H and O.36 The singlet and triplet states were obtained in separate DHF calculations. The calculations for the triplet states involved the average-of-configuration (AOC) DHF method with 2 electrons in 4 open-shell spinors. The ground states for the triplets were subsequently resolved from the AOC-DHF wavefunctions through complete open-shell configuration interaction (COSCI) calculations. The effects of spin orbit splitting on the singlettriplet are very small: -0.11 kcal/mol or HfO2, 0.08 kcal/mol for the HfO2-H2 adduct, 0.15 kcal/mol for the first hydrogen transfer transition state, and 0.05 kcal/mol for HHf(O)OH product. The spin orbit effects are thus less than 0.3 kcal/mol for the various energy differences on the PES for H2 addition to HfO2 and these are less than the accuracy of the calculations. Thus spin orbit effects can be considered to be negligible and were not calculated for the remaining species. Attempts to calculate the various spin-orbit corrections at the density functional theory level were unsuccessful. Dimers Hydrogen addition on the M2O4 (2a) clusters is shown in Figure 2 for the formation of the metal hydride/hydroxide species. The PES’s for the formation of the metal dihydroxides are shown in the SI. The physisorption step again involves weak binding interactions for the singlet dimers and the physisorption energies are predicted to be comparable to those for the singlet monomers. The chemisorption mechanism is similar to that for the monomers for the formation of the metal hydride/hydroxide species. The dissociative chemisorption energies for the formation of 1HM2O3(OH) (2d) are less exothermic than for the monomers. Again, the exothermicities for the three metals follow the order of Ti < Zr < Hf. The energy barriers are less than 10 kcal/mol and the transition states are below the reactant asymptote for M = Hf and slightly above the reactant asymptote for M = Ti and Zr. For the triplet dimer, the hydrogen physisorption energies are more exothermic than for the singlet and the energy barriers are 10 ACS Paragon Plus Environment

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comparable to the singlet. The formation of 3HM2O3(OH) (2d) via the addition of a hydrogen molecule to 3M2O4 (2a) is also more exothermic than for the singlet ground state. The reaction energies for the triplet dimer also follow the order of Ti < Zr < Hf.

Figure 2. Potential energy surfaces for H2 + M2O4 → HM2O3(OH) (M = Ti, Zr, Hf) for both the ground state singlet and the first excited triplet M2O4 clusters at the CCSD(T)/CBS level at 0 K. See Figure 1 caption for description of colors.



The formation of singlet metal dihydroxides via H- → H+ transfer to the remaining terminal oxygen in1HM2O3(OH) (2d) for the 1M2O4(2a) dimers is generally an endothermic process with the exception of M = Ti and the results are shown in the SI. The process 1

HTi2O3(OH) (2d) →

1

Ti2O2(OH)2 (2f) is slightly exothermic by -3.6 kcal/mol at the

CCSD(T)/CBS level. In contrast, the corresponding process is endothermic by 13.0 and 8.4 kcal/mol for M = Zr and Hf respectively. The energy barriers are predicted to be ~ 39 kcal/mol for M = Ti and ~ 50 kcal/mol for M = Zr and Hf, consistent with the reaction energies. The formation of 3M2O2(OH)2(2f) from 3HM2O3(OH) (2d) similarly involves H·→H+ transfer to the terminal oxygen atom for the triplet monomers. The exothermicities are ca. -40 to -60 kcal/mol and follow the order Ti > Zr > Hf. The relative stabilities of the M2O2(OH)2 (2f) are generally consistent with the mono metal dihydroxides discussed above and the triplet-singlet gaps are predicted to be smaller.

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Ti2O2(OH)2 is 3 kcal/mol more stable than 1TiO2(OH)2, so a singlet-

triplet crossing could occur for Ti leading to the triplet albeit with a substantial energy barrier. Trimers The potential energy surfaces for the trimers are shown in Figure 3. We studied hydrogen addition to the metal bound to all bridge -O atoms and to the metal having a M=O bond. For M = Ti, the most stable chemisorbed product is the metal hydride/hydroxide HTi3O5(OH) (3d) generated by hydrogen adsorption on the metal bonded to all bridge oxygen atoms (Figure 3a). The corresponding physisorption for the triplet is significantly larger than for the singlet and the phsysorption to chemisorption process is endothermic for the triplet. The energy barriers are slightly larger than for the monomer and dimer for M = Ti. The step to form the metal dihydroxide is shown in the SI. Consistent with the monomer and dimer, the formation of titanium dihydroxide 1Ti3O4(OH)2 (3n) from 1HTi3O5(OH) (3d) is an endothermic process. On the triplet PES, the step 3HTi3O5(OH) (3d) → 3Ti3O4(OH)2 (3n) is 12 ACS Paragon Plus Environment

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exothermic. 3Ti3O4(OH)2 (3n) with two OH bridge groups is more stable than 1Ti3O4(OH)2 with an adiabatic triplet-singlet energy gap of 15.1 kcal/mol. Again, a singlet-triplet crossing could occur from 13d to form 33n. A different physisorption mode with hydrogen addition to a metal bonded to a terminal oxygen atom leads to the formation a different metal hydride/hydroxide, HTi3O5(OH) (3g) and a different metal dihydroxide, Ti3O4(OH)2 (3l). These reactions proceed by H-→H+ transfer for the singlet and H·→H+ transfer for the triplet as shown in the SI. For the singlet, the physisorption energy and chemisorption energy are less exothermic than for the addition to the metal bonded to all bridge oxygen atoms for the singlet. The metal hydride/hydroxide

1

HTi3O5(OH) (3g) can proceed to form the metal

dihydroxide 1Ti3O5(OH)2 (3i) by H-→H+ transfer by two different pathways. One pathway is H→H+ transfer from the metal to the adjacent =O atom. We label this as the direct pathway. The other pathway includes two steps with an initial H-→H+ transfer to an adjacent bridge oxygen bonded to the two active metals followed by proton transfer from the bridge to the terminal oxygen. We label this as the two-step pathway. The energy barrier for the direct pathway is 6 kcal/mol larger than for the two-step pathway. 1

The formation of 1Ti3O4(OH)2 (3l) from

HTi3O5(OH) (3g) is slightly endothermic by 2 kcal/mol with a global minimum energy barrier

of 48 kcal/mol at the CCSD(T)/aT level. On the triplet PES, the physisorption energy, chemisorption energy, and the energy barrier for the formation of the metal hydride/hydroxide are comparable to those for the singlet. In contrast, the process 3HTi3O5(OH) (3g) → 3Ti3O4(OH)2 (3l) is exothermic by -53 kcal/mol at the CCSD(T)/aD level. Again, the energy barrier for the H·→H+ transfer to an adjacent bridge oxygen is predicted to be 28 kcal/mol lower than that for the direct formation of 3Ti3O4(OH)2 (3l) 13 ACS Paragon Plus Environment


via H-→H+ transfer to a terminal oxygen atom. 3Ti3O4(OH)2 (3j) with a bridge OH and a terminal OH is 12 kcal/mol more stable than 1Ti3O4(OH)2 (3j) at the CCSD(T)/aD level. 3Ti3O4(OH)2 (3l) with two terminal OH groups on different Ti is 2 kcal/mol more stable than the corresponding singlet at the CCSD(T)/aD level. 3Ti3O4(OH)2 (3l) is slightly more stable than 3Ti3O4(OH)2 (3j). Again, the triplets would have to be formed by a spin crossing.


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Figure 3. Potential energy surfaces for H2 + Ti3O6 → HTi3O5(OH) and H2 + M3O6 → M3O4(OH)2 (M = Zr, Hf) for the ground state singlet and the first excited state triplet cluster at 0 K. Relative energies are calculated at the CCSD(T)/aD and /aT level for the singlet and the R/UCCSD(T)/aD level for the triplet. Relative energies are in black for aD and red for aT. O atoms in red, Ti atoms in dark blue, Zr atoms in light blue, Hf atoms in blue, and H atoms in gray-white. 16 ACS Paragon Plus Environment

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Hydrogen adsorption on Zr3O6 or Hf3O6 differs from that for M = Ti with the metal dihydroxide 1M3O4(OH)2 (3l) being the most stable product. The calculated PES’s are shown in Figures 3b and 3c. The reaction begins with hydrogen physisorption on a metal bonded to a terminal oxygen atom with a weak binding energy. Formation of 1HM3O5(OH) (3g) is exothermic by -25 kcal/mol with an energy barrier of 11 kcal/mol for Zr with corresponding values of -38 kcal/mol and 5 kcal/mol for M = Hf; this barrier for Hf is the smallest of the three metals.

1

M3O4(OH)2 (3l) for Zr and Hf can be produced by a H- → H+ transfer to the adjacent

terminal oxygen following a direct pathway similar to that for M = Ti discussed above with an energy barrier of 61 kcal/mol or by a two-step pathway with a H- → H+ transfer to an adjacent bridge oxygen followed by proton transfer from the bridge oxygen to the terminal oxygen with a comparable barrier. The energy barrier for the proton transfer step is predicted to be only 12 kcal/mol. On the triplet PES, the formation of 3HM3O5(OH) (3g) is slightly more exothermic than for the singlet. The generation of 3M3O4(OH)2 (3l) proceeds preferably via a two-step pathway. The reaction energy barrier for the two-step pathway is predicted to be 10 and 5 kcal/mol lower than that for the direct pathway for Zr and Hf. The second transfer step has a 24 and 12 kcal/mol larger energy barrier than the initial H· → H+ transfer step for Zr and Hf. 3Zr3O4(OH)2 (3l) is 6.5 kcal/mol higher in energy than 1Zr3O4(OH)2 (3l) in contrast to the result for M = Ti for 3i. 3

Hf3O4(OH)2 (3l) is less stable than 1Hf3O4(OH)2 (3l) with a singlet triplet gap of 22 kcal/mol at

the CCSD(T)/aD level. Triplet 3j for Hf is predicted to be slightly more stable than singlet 3j by less than 1 kcal/mol so an intersystem crossing may occur. The reaction for hydrogen addition to the metal bonded to all bridge oxygen with formation of metal hydride/hydroxide HM3O5(OH) (3d) for M = Zr and Hf is similar to the process of 3a → 3d for M = Ti. The results are shown in 17 ACS Paragon Plus Environment


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the SI. The reaction energy barriers and chemisorption energies are comparable to that for M = Ti for both the singlet and triplet. The reaction barrier for the formation of metal hydride 1

HM3O5(OH) (3d) is 7 and 10 kcal/mol larger than the formation of 1HM3O5(OH) (3g) (Figure

3c). Tetramers We also studied hydrogen adsorption on both the Ti bonded to all bridge oxygen atoms and the Ti having a Ti=O bond. Physisorption on the Ti bonded to all bridge oxygen atoms is more exothermic and the results are shown in the SI. The mechanism for the formation of HTi4O7(OH) (4d) is consistent with those of the smaller clusters. The energetics for the triplet are similar to those for the singlet. The further step to produce titanium dihydroxide 1Ti4O6(OH)2 (4n) from 1HTi4O7(OH) (4d) via a H-→H+ transfer is an endothermic process. The PES for the formation of the most stable product for hydrogen adsorption on the Ti4O8 cluster is 1Ti4O6(OH)2 (4l) is shown in Figure 4a. Again, H2 first physisorbs on the metal bonded to a terminal oxygen followed by proton and H- transfer to the adjacent terminal oxygen and the active metal respectively leading to the formation of

1

HTi4O7(OH) (4g). The

chemisorption energies for the singlet and the triplet are slightly exothermic and are less exothermic than hydrogen addition on the Ti bonded to all bridge atoms. The energy barriers for the formation of HTi4O7(OH) (4g) are comparable for the singlet and triplet, and are also comparable to the energy barrier for the formation of HTi4O7(OH) (4d) via a different hydrogen adsorption mode. The formation of Ti4O6(OH)2 (4l) from HTi4O7(OH) (4g) follows a two-step pathway, which is similar to that for the trimer. The reaction takes place via H-→H+ transfer to the adjacent bridge oxygen which is bonded to another Ti having a Ti=O double bond leading to the formation of Ti4O6(OH)2 (4j). Ti4O6(OH)2 (4l) is generated via proton transfer from a bridge 18 ACS Paragon Plus Environment

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Figure 4. Potential energy surfaces for H2 + Ti4O8 → HTi4O7(OH) (M = Ti) and H2 + M4O8 → M4O6(OH) 2 (M = Zr, Hf) for both the ground state singlet and the first excited triplet M4O8 clusters at 0 K. See Figure 3 caption for labelling of colors. 21 ACS Paragon Plus Environment


oxygen atom to the remaining terminal oxygen atom. On the singlet PES, the largest energy barrier is predicted for H-→H+ transfer for the formation of Ti4O6(OH)2 (4j). This energy barrier is much smaller for the triplet proceeding by a H·→H+ transfer process. The energy barrier for proton transfer is much lower for the singlet than for the triplet. An alternative direct pathway for the formation of Ti4O6(OH)2 (4l) is by H-→H+ transfer to the remaining terminal oxygen atom in HTi4O7(OH) (4g) is shown in the SI. The H-→H+ transfer energy barrier for this pathway is larger than the two-step pathway for the singlet and the triplet. The PES’s for hydrogen adsorption on a M4O8 cluster with formation of the most stable product M4O6(OH)2 (4l) for M = Zr and Hf are shown in Figures 4b and 4c, respectively, and the other pathways are shown in the SI. The pathway for the formation of 1HM4O7(OH) (4g) for M = Zr and Hf is consistent with that for Ti4O8 with more exothermic reaction energies and smaller energy barriers. In general, the reaction on the Hf4O8 cluster has more exothermic physisorption and chemisorption energies than on the Zr4O8 cluster. The energy barriers for the Hf4O8 cluster are also smaller than for Zr4O8 except for the proton transfer step, where the energy barriers are comparable. The direct pathway is preferred over the two-step pathway for the formation of 1

M4O6(OH)2(4l) from 1HM4O7(OH) (4g). The reaction for the triplet still prefers the two-step

pathway. Physisorption and Chemisorption Energies The calculated physisorption and chemisorption energies for the formation of metal hydride/hydroxides at 298 K at the CCSD(T) level are summarized in Table 1. For the singlet, the physisorption energies are generally less than -9 kcal/mol and hydrogen physisorption on the monomers and dimers is slightly more exothermic than on the trimers and tetramers. For H2 physisorption on M3O6 and M4O8 clusters, the addition to the metal bonded to all bridge oxygen atoms is slightly more exothermic than the addition to 22 ACS Paragon Plus Environment

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Table 1. Calculated Reaction Energy Barriers from the Reactant Complexes (∆H‡298K, kcal/mol), Physisorption and Dissociative Chemisorption Enthalpies (∆Had,298K, kcal/mol) at 298K in kcal/mol at the CCSD(T) Level.a Ti Molecule 1

∆H‡298K

Zr

∆Had,298K

∆Had,298K

Phys

Chem

∆H‡298K

Hf

∆Had,298K

∆Had,298K

Phys

Chem

∆H‡298K

∆Had,298K

∆Had,298K

Phys

Chem

MO2(1a)+H2 →1HMO(OH)(1d)

6.8

-7.6

-35.3

5.8

-5.7

-38.1

1.6

-8.3

-50.2

1

M2O4(2a)+H2 →1HM2O3(OH) (2d)

10.9

-7.1

-23.6

7.2

-4.8

-32.8

2.8

-6.3

-44.0

1

M3O6(3a)+H2 →1HM3O5(OH) (3d)

19.2

-7.1

-14.7

16.7

-4.4

-14.9

15.4

-5.5

-19.7

M3O6(3a)+H2 →1HM3O5(OH) (3g)

15.8

-3.0

-12.9

10.0

-1.5

-25.9

4.2

-2.9

-38.9

M4O8(4a) +H2 →1HM4O7(OH) (4d)

16.8

-5.0

-8.2

13.5

-4.1

-9.5

12.4

-5.2

-13.9

17.7

-1.0

-3.6

10.3

-1.1

-20.7

4.1

-1.8

-32.9

MO2(1a)+H2 →3HMO(OH)(1d)

6.7

-3.9

-25.8

15.5

-1.0

-17.6

15.1

-0.5

-20.3

3

M2O4(2a)+H2 →3HM2O3(OH) (2d)

7.9

-4.3

-25.4

6.8

-25.7

-54.9

2.6

-21.3

-62.4

3

3

21.4

-17.3

-8.9

19.6

-17.0

-6.6

18.7

-13.7

-3.3

M3O6(3a)+H2 →3HM3O5(OH) (3g)

12.3

-6.2

-18.2

2.6

-2.2

-37.4

1.4

-11.9

-49.7

M4O8(4a)+H2 →3HM4O7(OH) (4d)

16.7

-4.8

-4.0

18.8

-21.5

-29.0

3.6

-16.3

-38.7

3

M4O8(4a) +H2 →3HM4O7(OH) (4g)

17.1

-1.8

-15.6

3.6

-12.0

-38.9

5.6

-7.5

-46.0

a

The energies are calculated at the CCSD(T)/CBS level for the monomers and dimers. For the trimers and tetramers, the energies are

1 1

1

M4O8(4a) +H2 →1HM4O7(OH) (4g) 3

M3O6(3a)+H2 → HM3O5(OH) (3d)

3 3

at the CCSD(T)/aT level for the singlet and the CCSD(T)/aD level for the triplet.



the metal having a terminal oxygen. Those physisorption energies differ by 4 kcal/mol. The predicted energy barriers are less than 20 kcal/mol following the order of Ti > Zr > Hf. For the 1

Hf3O6 and 1Hf4O8 clusters, different hydrogen physisorption modes result in significantly

different energy barriers for the formation of metal hydride/hydroxides and the energy difference is more than 10 kcal/mol. For M = Ti, the energy barriers differ by 3.5 kcal/mol for hydrogen transfer to two different metals. This difference is up to 6.7 kcal/mol for M = Zr. Chemisorption for the formation of metal hydride/hydroxides are exothermic by -10 to -50 kcal/mol and the reaction energies follows the order of Ti < Zr < Hf for the same size clusters. For the 1Ti3O6 and 1

Ti4O8 clusters, the formation of the metal hydride/hydroxide with an OH group in the terminal

position is slightly less exothermic than formation of the metal hydride/hydroxide with the OH group in the bridge. However, the metal hydride/hydroxide with one OH in the terminal is more stable than the other for M = Zr and Hf. For the triplets, a broader energy range of -1 to -26 kcal/mol is predicted for hydrogen physisorption on the MO2 clusters. The energy barriers are predicted to be 1 to 20 kcal/mol and do not follow a specific order for the three metals. The chemisorption energies are comparable to those for the singlet. Differing from the singlet, the triplet metal hydride/hydroxide with one OH in the terminal position is always more stable than the structure with one OH in the bridge for the trimer and the tetramer for all three metals. The relative energies for these two different metal hydride/hydroxides are predicted to be 10 to 45 kcal/mol, depending on the size of cluster and the metal. Formation of Metal Dihydroxides from Metal Hydride/Hydroxides The CCSD(T) reaction energies and the energy barriers for the formation of metal dihydroxides from metal hydride/hydroxides for the monomers and tetramers at 298 K are shown in Table 2. The 24 ACS Paragon Plus Environment

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Table 2. CCSD(T) Reaction Energies (∆Hrxn) and Reaction Energy Barriers (∆H‡) for the Formation of Metal Dihydroxide from the Metal Hydride/Hydroxide at 298K in kcal/mol. a Ti

Molecule

Zr

Hf

∆H‡

∆Hrxn

∆H‡

∆Hrxn

∆H‡

∆Hrxn

1

HMO(OH)(1d)→1M(OH)2(1f)

41.6

20.5

46.4

20.4

37.9

5.2

1

HM2O3(OH) (2d)→1M(OH)2(2f)

38.3

-3.0

50.8

13.5

52.4

9.1

1

HM3O5(OH) (3g)→ 1M3O4(OH)2 (3l)

48.2 b

2.7

62.6 c

-2.0

65.1 c

-19.3

1

HM3O5(OH) (3g)→ 1M3O4(OH)2 (3j)

48.2

13.9

63.0

31.8

65.5

36.7

1

HM4O7(OH) (4g)→ 1M4O6(OH)2 (4l)

47.0 b

-46.0

59.2 c

-33.5

59.0 c

-39.1

1

HM4O7(OH) (4g)→ 1M4O6(OH)2 (4j)

47.0

-27.4

64.4

2.3

69.2

5.2

3

HMO(OH)(1d)→3M(OH)2(1f)

9.3

-61.7

2.1

-53.1

2.8

-43.6

3

HM2O3(OH) (2d)→ M(OH)2(2f)

15.5

-64.7

15.1

-49.8

16.8

-43.9

3

HM3O5(OH) (3g)→ 3M3O4(OH)2 (3l)

36.7 d

-52.8

29.9 d

-46.7

25.9 d

-35.7

3

HM3O5(OH) (3g)→ 3M3O4(OH)2 (3j)

11.9

-51.2

5.1

-19.9

14.2

-4.8

3

HM4O7(OH) (4g)→ 3M4O6(OH)2 (4l)

44.2 d

-78.7

14.1 d

-80.7

10.3d

-81.9

3

HM4O7(OH) (4g)→ 3M4O6(OH)2 (4j)

8.5

-58.9

7.0

-43.2

8.4

-34.2

a

3

The energies are calculated at the CCSD(T)/CBS level for the monomers and dimers. For the

trimers and tetramers, the energies are at the CCSD(T)/aT level for the singlet and the CCSD(T)/aD level for the triplet. b

The formation of singlet 3l or 4l is through a two-step pathway and the rate limiting step is the

H- → H+ transfer. The direct pathway energy barriers are 53.6 and 53.9 kcal/mol for the formation of 3l and 4l respectively for M = Ti. c

The formation of singlet 3l or 4l is through a direct pathway.

d

The formation of triplet 3l or 4l is through a two-step pathway and the rate determining step is

the proton transfer from a bridge to a terminal oxygen. The energy barriers for direct H- → H+ transfer to form triplet 3l are 39.5, 15.0, and 20.3 kcal/mol for M = Ti, Zr, and Hf. The energy barrier for direct H- → H+ transfer to form triplet 4l are 50.3, 24.7, and 27.9 kcal/mol for M = Ti, Zr, and Hf respectively. 25 ACS Paragon Plus Environment


transformation from the singlet metal hydride/hydroxide to the metal dihydroxide is generally an endothermic process for the monomer and dimer and an exothermic process for the trimer and tetramer except for Ti2O4 and Ti3O6 clusters. The step of 2d → 2f for Ti2O4 is slightly exothermic by -3.0 kcal/mol and the process of 3g → 3l is slightly endothermic by 2.7 kcal/mol. The formation of the most stable product for the tetramer is more exothermic than for the trimer. The energy barriers range from 35 to 60 kcal/mol, depending on the cluster and the metal. For the trimer and tetramer, the energy barrier for H+ transfer (3g → 3j and 4g → 4j) is much larger than proton transfer from a bridge oxygen to a terminal oxygen (3j→ 3l and 4j → 4l) (Table 2 and Figures 3 and 4). For the H+ transfer step, a hydride is transformed to a proton and two metal are reduced to the +III oxidation state from the +IV oxidation state. However, there is no redox involved in the proton transfer step to form 3l or 4l. Clearly, the reduction process results in a large reaction energy barrier and is the rate limiting step for the formation of the metal dihydroxides 3j or 4j. In addition, comparable energy barriers between the direct and the twostep pathways are predicted for the Zr3O6 and Hf3O6 clusters. The energy barriers for the direct pathway to form 4l are 5 and 10 kcal/mol less than the two step pathway for Zr4O8 and Hf4O8 clusters respectively. In contrast, the two-step pathway is preferred for both the Ti3O6 and Ti4O8 clusters. For the triplet, the metal dihydroxides are more stable than the metal hydride/hydroxides for all three metals and the relative energies are predicted to be -35 to -80 kcal/mol. Thus, formation of the metal dihydroxides from metal hydride/hydroxides is a highly exothermic step for the triplet. This process for the tetramer is predicted to be -20 to -40 kcal/mol more exothermic than for the other clusters. For the monomer and dimer, the energy barriers for Htransfer for the triplets are generally less than 15 kcal/mol and are less than those for the singlets. 26 ACS Paragon Plus Environment

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For the trimer and tetramer, a two-step pathway is preferred and the rate-limiting step is in the second step of proton transfer instead of the initial H+ transfer. The proton transfer energy barriers follow the order of Ti > Zr > Hf. The energy barriers for the formation of tri- and tetrametal dihydroxides are also smaller than the singlet. To understand the difference of the energy barriers for the two-step pathway to form the metal dihydroxides between the singlet and triplet, we take the Ti3O6 cluster as an example for a detailed analysis. The results are shown in Figure 5. As described above, the energy barrier for the H-→H+ step for the singlet is 36 kcal/mol larger than the corresponding step for the triplet resulting in the formation of an OH group (SI). The spin densities for this triplet transition state (SI) show that the spin generally localizes on the active metal and the hydrogen being transferred, which is different from the spin densities for the triplet reactant. Thus, the formation of 3Ti3O4(OH)2 (3j) most likely begins with an intermolecular spin transfer from the terminal oxygen and the metal bonded to all bridge oxygen atoms to the active metal and the hydrogen bonded to that in 3HTi3O5(OH) (3g). Then a proton coupled one-electron transfer step (H· → H+) occurs since the transferring hydrogen in the transition state species can be regarded a hydrogen atom (radical).58 In contrast, the formation of 1Ti3O4(OH)2 (3j) on the singlet PES is a proton coupled two-electron transfer step, where the H- is oxidized to H+ by losing two electrons. Simultaneously, two active metal centers are reduced to the +III oxidation state. The two electron transfer process (H- → H+) on the singlet PES costs more energy than the one electron transfer on the triplet PES. This is similar to the proton coupled electron reactions for the formation of M-H bond from the metal dihydroxides found in our previous work.28 In the second proton transfer step (3j → 3l), there is no reduction involved for the singlet and this is not a PCET process. For the triplet, the location of the spin changes from two active metals to one metal. 27 ACS Paragon Plus Environment


Figure 5. Detailed reaction pathway analysis for the formation of metal dihydroxide Ti3O4(OH)2 (3l) from the metal hydride/hydroxide HTi3O5(OH) (3g). The α spin densities are shown for the triplet (translucent grey). The β spin densities are negligible.


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This inter-molecular spin transfer for the triplet requires energy in addition to that for proton transfer, which is the only energy cost to form 3l from 3j for the singlet. So, the energy barrier is higher for the triplet than the singlet for 3j → 3l. In contrast, in the direct pathway to form 3HTi3O4(OH)2 (3l), the spin in the transition state species 3TS (3i) does not localize on the hydrogen atom being transferred to the remaining terminal oxygen atom (SI). The direct pathway is actually a proton coupled two-electron transfer (H- → H+), which has a 28 kcal/mol larger energy barrier than the two-step pathway. The energy barriers for the two pathways for the singlet differ only by 5.6 kcal/mol as both of them involve redox processes. The small energy difference is in part due to the geometry of the cluster causing different behaviors of the oxygen atoms for H- → H+ transfer. The chemistry behind the energy barrier difference between the singlet and triplet for the two-step pathway is similar for Zr3O6 and Hf3O6 clusters as well as the other size clusters. For the trimers and tetramers, a two-step pathway is always preferred for the triplet as one-electron transfer is energetically more favorable than the two-electron transfer in the direct pathway. The pathway preference for the singlet is dependent on the metal. Usually a two-step pathway is preferred for M = Ti, and a direct pathway is favored for M = Zr and Hf. Our predicted small H2 physisorption energies on small TiO2 clusters are close to the calculated H2 adsorption on TiO2 nanotubes.59 These authors reported a physisorption energy of 2.3 kcal/mol with H2 weakly bonded to a Ti atom instead of an O atom. The hydrogen physisorption energies on small (MO2)n (n = 1 to 4) clusters are close to that on (MO2)n·O2 clusters, which are predicted to be less than -10 kcal/mol.28 A theoretical study on the hydrogenation of (TiO2)n (n = 1 to 10) clusters has been performed with the B3LYP functional using the 6-31+G* basis set for O and H and the LANLD2Z pseudopotential for Ti.27 The prior 29 ACS Paragon Plus Environment


DFT values are consistent with our higher level predicted physisorption energies. A similar reaction sequence with the formation of a Ti-H bond followed by a proton transfer to form a metal hydroxide (this was called a dihydroxy compound in the prior work) has been studied.27 The DFT energy barriers are generally consistent between our values and their work. In our work, we also studied additional pathways to obtain a more detailed mechanism for hydrogen adsorption on TiO2 clusters. For example, we studied the reaction pathway to generate the most stable titanium dihydroxide product 1Ti4O6(OH)2 (4l) with two OH groups in the terminal position, which was not been examined previously. They27 also predicted that the triplet metal dihydroxides are more stable than the singlet for the monomer to trimer and the singlet metal dihydroxide is more stable for the tetramer. Our CCSD(T) singlet-triplet gaps for the Ti4O6(OH)2 (4l) are 10 kcal/mol larger than their B3LYP value. Our chemisorption energies for the formation of singlet titanium hydride/hydroxides are less than -35 kcal/mol, which is less than the calculated exothermicity of the formation of a Ti-H and an O-H from a two-fold oxygen on TiO2 anatase (100) and (001) surfaces.60 In that study, periodic DFT with the PW91 functional gave dissociative chemisorption energies of -40 to -50 kcal/mol on the anatase (100) and (001) surfaces. The chemisorption energy difference between the small TiO2 clusters and crystal anatase surface suggests that there are different behaviors for the metal as well as for the oxygen to split hydrogen, in part due to the different coordination environments. A study61 on a different product for two OH groups on the TiO2 anatase surface using the same calculation method gave chemisorption energies of -23 to -43 kcal/mol, depending on the type of oxygen atom. In contrast, our calculated energies for the formation of titanium dihydroxides are -10 to -50 kcal/mol (1a→1f, 2a→2f, 3a→3l, and 4a→4l in Tables 1 and 2 for M = Ti), which are comparable to the results on the TiO2 anatase surface. 30 ACS Paragon Plus Environment

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Geometries The calculated M-H Bond distances at the B3LYP level are shown in the SI. The H in M-H bonds can be regarded as hydric except for the 3HTi4O7(OH) (4g) in which the H behaves as a hydrogen atom58 due to the longer bond distance. The Ti-H bond distance in 3

HTi4O7(OH) (4g) is 0.32 Å longer than the Ti-H bond length in 1HTi4O7(OH) (4g). Generally,

the Ti-H hydridic bond distances in different size clusters are consistent with the difference less than 0.04 Å. This bond difference is also small for M = Zr and Hf. The M-H bond distance follows the order of Ti < Zr ≈ Hf. A previous study on H2 adsorption on the TiO2 anatase (100) surface with the PW91 functional predicted Ti-H bond distance ranging from 1.73 to 1.78 Å dependent on the relaxation degree during optimization.60 In comparison, our predicted Ti-H bond distances for the singlet are from 1.69 to 1.72 Å, which are slightly shorter than those on TiO2 anatase (100) surface.60 In that study, the calculated Ti-H bond distances on the TiO2 anatase (001) surface are between 1.77 to 1.82 Å, which are also longer than our values for the clusters. The calculated Zr-H bond distances are consistent with the previous study on the HZrO(OH), HZr2O3(OH), and HZr4O7(OH) species using the B3LYP functional. 26 Spin Densities The spin densities for the triplet metal hydride/hydroxides and metal dihydroxides are shown in the SI. Little, if any, spin polarization was observed. The spin densities are generally consistent for all three metals. For the monomer and dimer, the spin is localized on the terminal oxygen and the metal bonded to the terminal oxygen in the metal hydride/hydroxide species, 3HMO(OH) (1d) and 3HM2O3(OH) (2d). For the metal dihydroxides 3

MO(OH)2 (1f) and 3M2O2(OH)2 (2f), the spin localizes only on the metals. The spin is localized

on a terminal oxygen and the metal bonded to that terminal oxygen in 3HM3O5(OH) (3d). In 3

HM3O5(OH) (3g), the spin is localized on the terminal oxygen and the metal bonded to all 31 ACS Paragon Plus Environment


bridge oxygen atoms. For 3M3O4(OH)2 (3j), the spin is localized on the metal bonded to an OH group and the metal bonded to all bridge oxygen atoms. In contrast, the spin is localized on the metal bonded with all bridge oxygen atoms in 3M3O4(OH)2 (3l). For the tetramer, 3HTi4O7(OH) (4g) is the only compound which has the spin on the hydrogen bonded to a metal. The remaining spin is on one metal bonded to all bridge oxygen atoms. In 3HM4O7(OH) (4g) (M = Zr, Hf), the terminal oxygen is an open shell instead of the hydrogen bonded to the metal. Similarly, one terminal oxygen and the metal bonded to all bridge oxygen atoms have the two unpaired electrons in 3HM4O7(OH) (4d) for all three metals. In the metal dihydroxides 3M4O6(OH) 2 (4j and 4l), the spin delocalizes on the two metals not bonded to an OH group. Conclusions Density functional theory and correlated molecular orbital theory at the coupled cluster CCSD(T) level have been used to study H2 adsorption on group 4 metal oxide clusters for both the singlet and the first excited triplet states. The exothermic hydrogen physisorption energies for the singlet are predicted to be generally less than -10 kcal/mol. A broader range of -1 to -26 kcal/mol is predicted for the triplet. Hydrogen addition to the metal bonded to all bridge oxygen atoms is slightly more exothermic than is addition to the metal having a terminal oxygen for the trimers and tetramers. The predicted energy barriers for the formation of a metal hydride/hydroxide are less than 20 kcal/mol. The energy barriers follow the order of Ti > Zr > Hf for the singlet and do not follow a specific order for the triplet. Chemisorption for the formation of metal hydride/hydroxides is exothermic by -10 to -50 kcal/mol for the singlet and the exothermicities are as large as -60 kcal/mol for the triplet. The metal hydride/hydroxides with a single terminal OH group can undergo a further reaction to form metal dihydroxides with two OH groups. This step is generally endothermic for 32 ACS Paragon Plus Environment

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the monomer and dimers and is exothermic for the trimers and tetramers. The singlet-triplet gaps for the metal dihydroxides are dependent on the size of the cluster and the metal. The formation of metal dihydroxides is a PCET process. For the singlet, two electrons are transferred with redox involved, a H-→ H+ transfer process. In contrast, only one electron is transferred in most cases for the triplet, which can be described as a H·→ H+ transfer process with a much smaller energy barrier than for the singlet. The singlet energy barriers for the H-→ H+ transfer process are predicted to be 35 to 60 kcal/mol, depending on the cluster and the metal. The triplet energy barriers for the H·→ H+ transfer process are less than 15 kcal/mol. For the monomers and dimers, the formation of metal dihydroxides is through a PCET to the terminal oxygen atom for both singlets and triplets. For the trimer and tetramers, there are two possible pathways for both singlets and triplets including a direct pathway with PCET to a terminal oxygen and a two-step pathway with the formation of a bridge OH group first followed by a proton transfer. A two-step pathway is always preferred for the triplet as one-electron transfer is more likely than two-electron transfer in a direct pathway. The rate limiting step for the triplet is the second step of proton transfer. For the singlet, a two-step pathway is preferred for M = Ti and a direct pathway is more favorable for M = Zr and Hf. Generally, formation of metal hydride/hydroxides is preferred for the monomers and dimers. For the trimer and tetramer, formation of metal dihydroxides is more exothermic than formation of metal hydride/hydroxides.

For H2 adsorption on TiO2 crystal surfaces, the

preference for the formation of either a M-H and an OH group or two OH group is dependent on the surface as well as the oxygen site.60,61 H atom migration into the bulk is predicted to be a kinetically favorable pathway on the anatase TiO2 (101) surface.61 In our cluster study, we do not find H transfer into the cluster to be an energetically favorable process. Thus, hydrogen 33 ACS Paragon Plus Environment


adsorption reactions on both the clusters and crystals can differ due to the varying structural environments. Acknowledgments This work was supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, U.S. Department of Energy (DOE) under the DOE BES Catalysis Center Program by a subcontract from Pacific Northwest National Laboratory (KC0301050-47319). DAD also thanks the Robert Ramsay Chair Fund of The University of Alabama for support. Supporting Information. Complete author lists for References 41, 51, and 55. Figures: The PES’s with the B3LYP functional and the PES’s for the other reaction pathways; Spin densities for the metal hydride/hydroxides, metal dihydroxides as well as the transition state species. Tables: Singlet triplet relative energies for metal dihydroxides; Calculated M-H bond distances and vibrational frequencies; B3LYP results for the physisorption energies, chemisorption energies as well as the energy barriers for the formation of both metal hydride/hydroxides and metal dihydroxides; Zero-point energies and total electronic energies at both the B3LYP and CCSD(T) levels, and Cartesian coordinates for all reactants, transition states, and products. This material is available free of charge via the internet at http://pubs.acs.org. References 1

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Computational Study of Molecular Hydrogen Adsorption over Small

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