Computational Study of the Hydrolysis Reactions of the Ground and

ARTICLE pubs.acs.org/JPCC

Computational Study of the Hydrolysis Reactions of the Ground and First Excited Triplet States of Small TiO2 Nanoclusters Tsang-Hsiu Wang, Zongtang Fang, Natalie W. Gist, Shenggang Li, and David A. Dixon* Department of Chemistry, The University of Alabama, Shelby Hall, Box 870336, Tuscaloosa, Alabama 35487-0336, United States

James L. Gole Schools of Physics and Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, United States

bS Supporting Information ABSTRACT: Density functional theory and coupled cluster theory are used to study the hydrolysis reactions of (TiO2)n (n = 1
4) nanoclusters to provide insight into H2O activation on TiO2. The singlet
triplet energy gaps of (TiO2)n are predicted to lie between 30 and 65 kcal/mol, depending on the cluster size and structure, consistent with our previous studies. The excitation energies for the various hydroxides, TinO2n
m(OH)2m (n = 1
4, 1 e m e n) are predicted to be, in general, higher than those for (TiO2)n. The partial charge on Ti increases as the Ti dO bonds are replaced with the Ti
OH bonds. The TidO and Ti
O frequencies in the triplet state of (TiO2)n and TinO2n
m(OH)2m are, in general, lower than those in the singlet state. The first H2O adsorption (physisorption) energies for these TiO2 nanoclusters are predicted to be
10 to
35 kcal/mol for the singlet states and
10 to
50 kcal/mol for the triplet states. These physisorption energies depend on the cluster size and the site of adsorption, consistent with existing experimental studies. In general, H2O prefers to physisorb on the Ti site with one TidO bond and two Ti
O bonds and at the Ti site with no TidO bond and three Ti
O bonds. The first hydrolysis (dissociative chemisorption) reaction energies of the TiO2 nanoclusters are predicted to be
20 to
70 kcal/mol for the singlet states and
15 to
80 kcal/mol for the triplet states. Both singlet and triplet potential energy surfaces for the hydrolysis are calculated. Our calculations show that H2O readily reacts with both the singlet and the triplet states of the TiO2 nanoclusters to form the hydroxides with reaction barriers of 5
16 kcal/mol for the singlet states and 5
26 kcal/mol for the triplet states for the first hydrolysis steps, which are, in general, less than the H2O complexation energies. Because H2O splitting to form H2 and O2 is a strongly endothermic process by ∼116 kcal/mol, photocatalytic processes are necessary only in the subsequent steps.

’ INTRODUCTION The photocatalytic splitting of H2O into H2 and O2 using TiO2 has been an active research area since the work of Fujishima and Honda,1,2 where H2 and O2 are produced from H2O on TiO2 surfaces under UV irradiation. There is an extensive effort to elucidate the mechanism of this photocatalytic process and improve the photocatalytic efficiency of TiO2.3
7 TiO2 is also used as a photocatalyst for environmental cleanup, including the destruction of organic compounds in wastewater.8 The reaction enthalpy at 298 K for H2O splitting (2H2O f 2H2 þ O2) is 115.6 kcal/mol, calculated from the experimental heat of formation of H2O at 298 K (
57.8 ( 0.2 kcal/mol),9 which corresponds approximately to the energy of two 500 nm photons. There have been numerous experimental studies on the interaction of H2O with TiO2 surfaces. Henderson used temperature-programmed desorption to study the adsorption of H2O on TiO2(110).10,11 TiO2(110) was found to be active for H2O dissociation at defect sites, including steps. The Ti
OH2 bond distance between the adsorbed H2O and TiO2(110) was r 2011 American Chemical Society

measured to be 2.21 ( 0.02 Å using scanned-energy mode photoelectron diffraction.12 Henrich and co-workers used ultraviolet photoelectron spectroscopy to study the interaction of H2O with the TiO2 surface and found that the OH groups were formed upon H2O adsorption on TiO2 (rutile, 110) at 300 K;13 similar results were observed by other groups.14 It was proposed that an adsorbed H2O molecule reacts with an O atom on the TiO2 surface to form two OH groups. The adsorption of H2O was found to occur below 160 K with the formation of OH groups above 200 K. The interaction of H2O with single-crystal TiO2 surfaces as well as powdered TiO2 has been studied. Somorjai and co-workers15 observed the dissociative adsorption of H2O on TiO2 (rutile, 100) and suggested that Ti3þ defect sites were required for the dissociative adsorption. Thornton and coworkers made the conclusion from their photoemission16 and Received: November 18, 2010 Revised: April 10, 2011 Published: April 25, 2011 9344

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The Journal of Physical Chemistry C scanning tunneling microscopy (STM) experiments17 that H2O dissociates on TiO2(100) and that Ti3þ sites are not required for H2O dissociation. Experimental adsorption (physisorption) energies range from
14 to
24 kcal/mol.18 Engel and co-workers studied the physisorption of H2O on TiO2 (rutile, 110) using modulated molecular beam scattering, and the physisorption energy was determined to be
17 to
24 kcal/mol.19 Sato and co-workers reported the production of H2 after the adsorption of H2O on TiO2.20,21 In addition, Schrauzer and co-workers used powdered TiO2 (anatase) as the photocatalyst and exposed it to H2O vapor under UV irradiation, leading to the production of O2 and H2.22 However, despite numerous experimental studies, the actual mechanism for water splitting, especially photocatalytic splitting, is still not clear. There have also been extensive computational studies on the interaction of H2O with TiO2 clusters and surfaces. Ferris and Wang studied the adsorption of H2O on TiO2 clusters serving as models for the (110) and (100) surfaces at the HF/3-21G* level.23 They predicted the H2O physisorption energies to be
42.5 and
36.0 kcal/mol for the (110) and (100) model clusters, respectively. The dissociative chemisorption energies of H2O were predicted to be
14 and
21 kcal/mol on model (110) and (100) clusters, respectively. Minot and co-workers used the periodic Hartree
Fock (HF) method and predicted a more negative dissociative adsorption energy of
121.2 kcal/mol for the (110) surface with a physisorption energy of
74.6 kcal/mol.24
26 Their prediction of a more negative dissociative adsorption energy than the physisorption energy is in contrast to the results of Ferris and Wang. Semiempirical molecular orbital SINDO1 calculations also predict more negative dissociative absorption energies than physisorption energies.27 Bredow and co-workers used the SINDO1 method to study H2O adsorption on cluster models of TiO2 ((rutile, 110) and (anatase, 001)) surfaces.28 They found that H2O prefers to adsorb at the five-coordinated Ti4þ sites on the model (rutile, 110) surface. The physisorption and dissociative adsorption energies were predicted to be
29.9 and
41.9 kcal/ mol, respectively, on the model rutile surface. Adsorption energies at the O defect sites on the model rutile surface were predicted to be more exothermic than those on the defect-free sites. At the MSINDO level, the H2O physisorption energy on TiO2(110) was predicted to be
28 kcal/mol.29 Periodic DFT calculations with the BP86 functional predicted the physisorption and dissociative adsorption energies to be
31 and
37 kcal/mol, respectively, after extrapolation to the zero coverage limit.30 Using an embedded cluster model, Stefanovich and Truong found an opposite trend.31 They predicted the physisorption energy to be
34 to
37 kcal/mol at the B3LYP and MP2 levels and the dissociative chemisorption energies to be
18 to
23 kcal/mol. More recently, the physisorption energy of H2O on TiO2(110) was predicted to be about
10 kcal/mol with a Ti
OH2 bond distance of 2.32 Å at the density functional theory (DFT) level using a revised PBE functional.32 These authors reported that their calculations were consistent with the experiments performed below 160 K, where only physisorption was observed. The barrier heights for H2O dissociation on TiO2(110) were predicted to be 5
10 kcal/mol. At the PW91 level, the Ti
OH2 bond distance and the adsorption energy were predicted to be 2.29 Å and
16 kcal/mol, respectively.33 The physisorption energy of H2O was predicted to be
20 to
25 kcal/mol at the PW91 level depending on the surface coverage.34 The physisorption energy of H2O on TiO2(110) was predicted at the PW91 level to be
18 to
25 kcal/mol with

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Ti
OH2 bond distances of 2.19
2.28 Å depending on the adsorption site and surface coverage.35 On the basis of combined experimental and computational studies with STM and periodic DFT calculations using a revised PBE functional, it was concluded that bridging O vacancy sites on TiO2 (rutile, 110) were responsible for H2O splitting by hydrogen transfer to an oxygen atom, leading to the formation of two OH groups.36,37 Onal and co-workers used the Ti2O9H10 cluster to model TiO2 (anatase, 101) and predicted the physisorption energy of H2O to be
25 to
29 kcal/mol at the B3LYP/6-31G** level.38 We previously predicted the ground state of Ti2O4 to be 1Ag (C2h, 2a), with two low-energy isomers, 1A1 (C2v, 2h) and 1A1 (C3v, 2k).39 The ground state of Ti3O6 was predicted to be 1A0 (Cs, 3a), with two low-energy isomers, 1A (C2, 4a) and 1A0 (Cs, 5a). The ground state of Ti4O8 was predicted to be 1A1 (C2v, 6a) with two low-energy isomers, 1Ag (C2h, 7a) and 1A1 (C2v, 8a). (The labeling corresponds to that in the figures discussed below.) The singlet
triplet energy gap was predicted to be 2.24 eV at the CCSD(T)/aD//B3LYP/aD level for the monomer, 2
3 eV for the dimers, 2.5
3 eV for the trimers, and 2
3.5 eV for the tetramers. In the current study, we use electronic structure theory at the DFT40 level to study the hydrolysis reactions of (TiO2)n (n = 1
4) nanoclusters. Reactions with up to four H2O molecules were studied. Both the singlet and the triplet potential energy surfaces were calculated. Physisorption energies, hydrolysis reaction energies (dissociative chemisorption energies), and reaction barriers were calculated using the B3LYP functional41,42 and the DZVP2 basis set. The DFT potential energy surface for the singlet for the monomer was benchmarked by comparing with those calculated at the coupled cluster theory [CCSD(T)] level with a large basis set and including core
valence and scalar relativistic corrections.

’ COMPUTATIONAL METHODS The DFT calculations were carried out with the B3LYP41,42 and/or the BP8643,44 exchange-correlation functionals with the DFT optimized DZVP2 based set.45 These functionals were chosen based on our previous work on the TiO2 nanoclusters.39 As discussed below for the reaction of H2O with TiO2, there is a good agreement between the B3LYP and the CCSD(T) results for the relative energies at the stationary points on the potential energy surface. However, B3LYP is subject to artificial symmetry breaking for some of the triplet states, leading to energy lowerings of 1
3 kcal/mol. The BP86 functional is less prone to artificial symmetry breaking.39 Thus, we used both functionals by combining the symmetry-constrained B3LYP energies and the BP86 zero-point energies. Vibrational frequencies were calculated to characterize the stationary points located on the potential energy surface and to obtain the 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.46 For transition-state optimizations, the synchoronous transit-guided quasi-Newton (STQN) method was usually employed.47 The DFT calculations were carried out with the Gaussian09 program package.48 For the singlet potential energy surface for the monomer, the B3LYP/DZVP2 geometries were used in single-point energy calculations with the coupled cluster [CCSD(T)] theory.49
51 The CCSD(T) calculations were performed at the second-order Douglas
Kroll
Hess (DKH) level52
54 with the all-electron augcc-pVTZ-DK basis set for O55 and the aug-cc-pwCVTZ-DK basis set for Ti;56 these basis sets will be collectively denoted as awCVTZ-DK. 9345

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The Journal of Physical Chemistry C

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Figure 1. Potential energy surface for TiO2 þ 2H2O f Ti(OH)4 at 0 K (O in red, Ti in blue, and H in gray). Relative energies calculated at the CCSD(T)-DK/awCVTZ-DK//B3LYP/DZVP2 (in blue) and B3LYP/DZVP2 (in black) levels in kcal/mol.

The 3s23p2 electrons on Ti were correlated in these calculations as they are close in energy to the 3s2 electrons on O. All CCSD(T) calculations were performed with the MOLPRO 2010.1 program.57 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 Opeteron 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.58

’ RESULTS Cluster Geometries. The optimized molecular structures for the (TiO2)n (n = 1
4) clusters are given in the Supporting Information. They are consistent with our previous results.39 The optimized structures of the hydroxides, hydrates, and transition states on the singlet potential energy surfaces for the hydrolysis reactions of the (TiO2)n nanoclusters are shown in Figures 1
8. Those on the triplet potential energy surfaces, as well as the raw energies, Cartesian coordinates, harmonic frequencies, and larger pictures of these molecules are given in the Supporting Information. The atomic numbering is also given in the Supporting Information. Singlet States. TiO(OH)2 (1d) is predicted to have Cs symmetry, with two slightly different Ti
OH bond distances, 1.851 and 1.840 Å. The Ti
OH bond distances in Ti(OH)4 (1g) are predicted to be shorter than those in TiO(OH)2 (1d) by 0.02
0.03 Å. The Ti
OH bond distances in Ti2O2(OH)4 (2g) are predicted to be 1.825 and 1.812 Å. The calculated Ti
OH

bond distances in Ti3O3(OH)6 and Ti4O4(OH)4 are between 1.8 and 2.0 Å depending on their structures. Triplet States. TiO(OH)2 (1d) is predicted to also have Cs symmetry, and the Ti
OH bond distances are shorter than those in the singlet state by 0.03
0.04 Å. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of 1Ti(OH)4 (1g) are both degenerate, so the triplet state undergoes a Jahn
Teller distortion. There are two long Ti
OH bonds of 2.037 Å with Ti2O4 (2a) > Ti2O4 (2h) > TiO2 (1a). For the different Ti sites of the same cluster structure, a lower reaction barrier can generally be correlated with a higher FA of the site, for example, for Ti3O6 (3a), Ti3O6 (4a), and Ti4O8 (8a). There are also exceptions to this correlation. For Ti4O8 (6a) and Ti4O8 (7a), the Ti site with the higher FA has a higher reaction barrier. The reaction barrier follows the order of TiO2 (1a) < Ti2O4 (2k) < Ti2O4 (2h) < Ti2O4 (2a), whereas the FA follows the order of Ti2O4 (2k) > Ti2O4 (2a) > Ti2O4 (2h) > TiO2 (1a). Thus, the correlations between the FAs and the adsorption energies (physisorption or chemisorption) as well as the reaction barriers are only qualitative. This indicates that the adsorption energies and the reaction barriers depend on other factors than the Lewis acidity of the Ti site, such as the local structure the Ti site and the O site to which the H atom is transferred.

’ CONCLUSIONS Density functional theory (DFT) and coupled cluster [CCSD(T)] theory have been used to study the hydrolysis reactions of the (TiO2)n (n = 1
4) nanoclusters. The shifts of the TidO frequencies upon hydrolysis depend on the cluster size and structure and the hydrolysis site. The TidO frequencies in the triplet states of the TiO2 nanoclusters and their hydrates are, in general, lower than those in the singlet states. The first H2O adsorption energies for the singlet and triplet states of the TiO2 nanoclusters are predicted to be exothermic by
10 to
50 kcal/ mol depending on the cluster size and structure as well as the hydrolysis site. These results are consistent with previous experimental and computational studies. For some clusters, the first H2O adsorption energies for the triplet states of these clusters are 9358

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The Journal of Physical Chemistry C predicted to be more exothermic than those for the singlet states by up to 22 kcal/mol. For Ti3O6 (4a) and Ti3O6 (5a), H2O prefers to adsorb on the Ti site with a TidO bond. For Ti3O6 (3a) and the tetramers, H2O prefers to adsorb on the Ti site with only bridge Ti
O bonds. The reaction energies for the first hydrolysis step (dissociative adsorption) of the TiO2 nanoclusters are, in general, predicted to be highly exothermic and decrease with increasing cluster size with a significant dependence on the absorption site. The potential energy surfaces for the hydrolysis reactions of both the singlet and the triplet (TiO2)n (n = 1
4) nanoclusters have been studied. The reaction is initiated by the formation of a Lewis acid
base complex (physisorption), followed by hydrogen transfer from H2O to a terminal dO or bridge
O atom, leading to the formation of the Ti
OH bonds (dissociative adsorption). For the singlet states, the reaction barriers for the first H2O addition are 6 to 17 kcal/mol depending on the cluster size, structure, and adsorption site. The second hydrolysis step follows a similar reaction path with comparable or higher reaction barriers. The third hydrolysis step for the trimers and tetramers has reaction barriers of 2
24 kcal/mol. The fourth hydrolysis step for the tetramers has reaction barriers of 4
18 kcal/mol. The potential energy surfaces for the triplet states show similar trends as those for the singlet states. Our results show that H2O can be readily split on the TiO2 nanoclusters to form OH groups on the Ti sites. The hydrolysis reactions of the TiO2 nanoclusters are highly exothermic with fairly small reaction barriers; thus, the energy of a visible photon is not required for the hydrolysis steps. However, the H2Osplitting reaction to form H2 and O2 (2H2O f 2H2 þ O2) is itself endothermic by ∼116 kcal/mol. Approximately two 500 nm photons are needed to overcome the above endothermic H2O-splitting reaction. When using TiO2 as the photocatalyst and assuming that the hydrolysis of TiO2 in the singlet state takes place before the formation of H2 and O2, significantly more energy from light than 116 kcal/mol would be required to generate 2 mol of H2O molecules due to the high exothermicities of the hydrolysis reactions. However, if TiO2 is first photoexcited to an excited state and is then followed by the hydrolysis of this excited state and the formation of H2 and O2, the photoenergy required for the overall H2O-splitting reaction can be expected to be much less, assuming that this excited state has a lower hydrolysis reaction energy as compared with the ground-state singlet, as found for the triplet excited states in this study.

’ ASSOCIATED CONTENT

bS

Supporting Information. Figures of the optimized molecular structures and relative energies of (TiO2)n (n = 1
4), atomic spin density for the triplet states of (TiO2)n (n = 1
4), molecular structures of the triplet states, molecular structures of the (TiO2)nF
anions, and combined singlet and triplet energy diagrams. Tables of CCSD(T) energies and T1 diagnostics, physisorption enthalpies at 0 K, enthalpies at 0 and 298 K, 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.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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’ ACKNOWLEDGMENT This work was supported by the National Science Foundation (CTS-0608896), through the NIRT program, and by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, U.S. Department of Energy (DOE), under Grant No. DE-FG02-03ER15481 (catalysis center program). D.A.D. also thanks the Robert Ramsay Chair Fund of The University of Alabama for support. ’ REFERENCES (1) Fujishima, A.; Honda, K. Nature 1972, 238, 37. (2) Fujishima, A.; Honda, K. Chem. Soc. Jpn. 1971, 44, 1148. (3) Bard, A. J. J. Phys. Chem. 1982, 86, 172. (4) Bard, A. J. J. Photochem. 1979, 10, 59. (5) Henderson, M. A. Surf. Sci. Rep. 2002, 46, 1. (6) Kalyanasundaram, K.; Gratzel, M.; Pelizzetti, E. Coord. Chem. Rev. 1986, 69, 57. (7) Osterloh, F. E. Chem. Mater. 2008, 20, 35. (8) Linsebigler, A. L.; Lu, G.; Yates, J. T. Chem. Rev. 1995, 95, 735. (9) Chase, M. W., Jr. J. Phys. Chem. Ref. Data 1998, Mono. 9, Suppl. 1, NIST-JANAF Thermochemical Table, 4th ed. (10) (a) Henderson, M. A. Langumir 1996, 12, 5093. (b) Henderson, M. A. Surf. Sci. 1996, 355, 151. (c) Henderson, M. A. Langmuir 2005, 21, 3443. (11) (a) Henderson, M. A. Mater. Res. Soc. Symp. Proc. 1995, 357, 91. (b) Henderson, M. A. Surf. Sci. 1994, 319, 315. (c) Henderson, M. A. Langmuir 1996, 12, 5093. (12) Allegretti, F.; O’Brien, S.; Polcik, M.; Sayago, D. I.; Woodruff, D. P. Phys. Rev. Lett. 2005, 95, 226104. (13) Henrich, V. E.; Dresselhaus, G.; Ziger, H. J. Solid State Commun. 1977, 24, 623. (14) Kurtz, R. L.; Stockbauer, R.; Madey, T. E.; Roman, E.; de Segovia, J. L. Surf. Sci. 1989, 218, 178. (15) Lo, W. J.; Chung, Y. W.; Somorjai, G. A. Surf. Sci. 1978, 71, 199. (16) (a) Muryn, C. A.; Tirvengadum, G.; Crouch, J. J.; Warburton, D. R.; Raiker, G. N.; Thornton, G.; Law, D. S. L. J. Phys.: Condens. Matter 1989, 1, SB127. (b) Muryn, C. A.; Hardman, P. J.; Coruch, J. J.; Raiker, G. N.; Thornton, G.; Law, D. S. L. Surf. Sci. 1991, 747, 251. (c) Thornton, G. Springer Ser. Surf. Sci. 1993, 33, 115. (17) (a) Murray, P. W.; Leibsle, F. M.; Muryn, C. A.; Fisher, H. J.; Flipse, C. F. J.; Thornton, G. Phys. Rev. Lett. 1994, 72, 689. (b) Murray, P. W.; Leibsle, F. M.; Muryn, C. A.; Fisher, H. J.; Flipse, C. F. J.; Thornton, G. Surf. Sci. 1994, 321, 217. (18) (a) Hugenschmidt, M. B.; Gamble, L.; Campbell, C. T. Surf. Sci. 1994, 302, 329. (b) Henderson, M. A. Surf. Sci. 1996, 355, 151. (19) Brinkely, T.; Dietrich, M.; Engel, T.; Farrall, P.; Gantner, G.; Schafer, A.; Szuchmzcher, A. Surf. Sci. 1998, 395, 292. (20) Sato, S.; White, J. M. J. Am. Chem. Soc. 1980, 102, 7206. (21) Sato, S.; White, J. M. J. Phys. Chem. 1981, 85, 592. (22) Schrauzer, G. N.; Guth, T. D. J. Am. Chem. Soc. 1977, 99, 7189. (23) Ferris, K. F.; Wang, L.-Q. J. Vac. Sci. Technol., A 1998, 16, 956. (24) Fahmi, A.; Minot, C. Surf. Sci. 1994, 304, 343. (25) Ahdjoudj, J.; Minot, C. Surf. Sci. 1998, 402, 104. (26) Ahdjoudj, J.; Markovits, A.; Minot, C. Surf. Sci. 1996, 365, 649. (27) (a) Nalewajski, R. F.; Koester, A. M.; Bredow, T.; Jug, K. J. Mol. Catal. 1993, 82, 407. (b) Bredow, T.; Jug, K. Surf. Sci. 1995, 327, 398. (28) Bredow, T.; Jug, K. Surf. Sci. 1995, 327, 398. (29) Jug, K.; Nair, N. N.; Bredow, T. Surf. Sci. 2005, 590, 9. (30) (a) Goniakowski, J.; Gillan, M. J. Surf. Sci. 1996, 350, 145. (b) Lindan, P. J. D.; Harrison, N. M.; Holender, J. M.; Gillan, M. J. Chem. Phys. Lett. 1996, 261, 246. (31) Stefanovich, E. V.; Troung, T. N. Chem. Phys. Lett. 1999, 299, 623. (32) (a) Zhang, C.; Lindan, P. J. D. J. Chem. Phys. 2003, 118, 4620. (b) Zhang, C.; Lindan, P. J. D. J. Chem. Phys. 2004, 121, 3811. (c) Lindan, P. J. D.; Zhang, C. Phys. Rev. B 2005, 72, 075439. 9359

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