- Email: [email protected]
Understanding the interaction of water with anatase TiO2 (101) surface from density functional theory calculations
Physics Letters A 375 (2011) 2939–2945
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Understanding the interaction of water with anatase TiO2 (101) surface from density functional theory calculations Zongyan Zhao a,b , Zhaosheng Li a,b,c,∗ , Zhigang Zou a,b,∗ a b c
Ecomaterials and Renewable Energy Research Center (ERERC), Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 4 April 2011 Received in revised form 9 June 2011 Accepted 11 June 2011 Available online 14 June 2011 Communicated by R. Wu Keywords: Titanium dioxide surface Water adsorption Density functional theory calculation Surface diffusion
a b s t r a c t The behavior of water molecule on anatase TiO2 (101) surface has been investigated by density functional theory calculations. The primary purpose of this Letter is to clarify the distinctions between molecular adsorption and dissociative adsorption of water on anatase TiO2 (101) surface. By analyzing interaction potential forms and bonding mechanism, it is found that the dipole interaction is the crucial factor for water adsorption on anatase TiO2 (101) surface. The adiabatic potential energy surface calculations indicate that the on-surface diffusion of water molecule is anisotropy: its diffusion energy barrier along [010] direction is smaller than that of along [111]/[111] direction. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The interaction of water with solid surfaces is extremely important research topic for both basic science and applied technology, because water almost exists everywhere and affects everything in ambient environment. And the physical and chemical properties of water on solid surface have a notable impact on their performance. Thus, a fundamental understanding of the interaction of water with solid surface is essential for the progress in many fields [1,2]. Titanium dioxide (TiO2 ), as a representative example of metal oxide, has been widely investigated in the field of surface science [3]. Many of its applications, such as dye sensitized solar cells, photocatalyst, corrosion-protective coating, and gas sensors, are performed in aqueous environment or related to the interaction with water. In particular, Fujishima and Honda [4] discovered it can be used as photocatalyst to split water, thus producing oxygen and/or hydrogen. And then, researchers found it also can be decomposed organic pollutions, and has super-hydrophilic properties under UV-light irradiation. These particular properties, which can effectively solve the energy crisis and environmental pollution, are directly correlated with the interaction between wa-
*
Corresponding authors at: Ecomaterials and Renewable Energy Research Center (ERERC), Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China. Tel.: +86 25 83686603; fax: +86 25 83686632. E-mail addresses: [email protected] (Z. Li), [email protected] (Z. Zou). 0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2011.06.022
ter and TiO2 surfaces. Moreover, water has significant effect on the stability and growth of TiO2 nanoparticles [5–8]. Therefore, the interaction of water with TiO2 attracted broad concern from both fundamental research and industrial development in the past decades. The adsorption of water molecule on TiO2 surface has been extensively investigated by a variety of experimental and theoretical techniques in recent years. But there are some contraries and disputes in the existing literature. Some research groups found that water always molecularly adsorbs on TiO2 surface [9–12]. However, other groups found the opposite results that the dissociative adsorption, “pseudo-dissociative” adsorption, or mixed adsorption is more stable than the molecular adsorption on these surfaces [13–20]. On the imperfect surfaces or high-activity surfaces, the dissociative adsorption is energetically favored [10,21–26]. For the multilayer water adsorption, due to the competition between the interplay of water–water and water–surface, mixed adsorption, various local and/or long-range order structures are formed on the TiO2 surfaces [27–30]. These studies help us to better understand the interaction of water with TiO2 surfaces. However, there are still some unresolved questions in this field. (i) Most published works had only described the adsorption configurations and the corresponding adsorption energy. They did not in-depth discuss the underlying mechanism. (ii) Another important thing is that most of these literatures focused on water adsorbed to rutile TiO2 (110) surface. Only few works are devoted into the exploration of water on anatase TiO2 surfaces. So the knowledge about the
2940
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
interaction of water with anatase TiO2 surfaces is still insufficiency. However, anatase TiO2 has better photocatalytic performance than rutile TiO2 , and it is the preferred phase during the formation of TiO2 nanoparticles [31,32]. (iii) The surface diffusion properties of water on TiO2 surface are still unclear. Thus, it is necessary to in-depth study the interaction of water with anatase TiO2 surfaces, in order to further improve the related investigation. At the atomic-scale level, experimental characterization of the interaction of isolated single water molecule with solid surface is very difficult, while computational simulation has natural advantages in regard to this issue. In order to complement and enhance the comprehend of the interaction of water with TiO2 surfaces, we attempt to adopt the ultrasoft pseudopotential plane wave method based on density functional theory (DFT) framework to systematically investigate the interaction of water with anatase TiO2 (101) surface in this Letter. We chose the anatase TiO2 (101) surface as substrate, because this surface is the dominate surface of anatase phase [32,33]. It is undeniable that the interaction of water with this surface is a key factor that impacts the performance of anatase TiO2 in vast majority circumstances. In this Letter, the adsorption configurations and adsorption energy of water on anatase TiO2 (101) surface were firstly calculated. Then, the underlying mechanism, including interaction potential forms and bonding mechanism, was carefully analyzed in detail. Finally, the surface diffusion behavior of water on this surface was also calculated and analyzed. 2. Computational method and details In this Letter, the density functional theory calculations were performed with Cambridge Serial Total Energy Package (CASTEP) codes [34]. Exchange and correlation effects were described by the Perdew–Burke–Ernzerhof (PBE) of generalized gradient approximation [35]. An energy cutoff of 340 eV was used for expanding the Kohn–Sham wave functions. The Monkhorst–Pack scheme K-points grid sampling was set as 2 × 2 × 1 for the irreducible Brillouin zone. A 64 × 72 × 160 mesh was used for fast Fourier transformation. The minimization algorithm was chosen Broyden–Fletcher– Goldfarb–Shanno (BFGS) scheme [36]. The relaxation run was considered converged when the force on the atomic nuclei was less than 0.03 eV/Å, the stress on the atomic nuclei was less than 0.05 GPa, the displacement of the nuclei was less than 1 × 10−3 Å, and the energy change per atom was less than 1 × 10−5 eV. By the above method, we firstly optimized pure anatase TiO2 structure, and got the bulk lattice parameters as follows: a = b = 3.7748 Å, c = 9.5990 Å, dap = 1.9883 Å, deq = 1.9318 Å, 2θ = 155.403◦ . They were good agreement with experimental values [37]: a = b = 3.7848 Å, c = 9.5124 Å, dap = 1.9799 Å, deq = 1.9338 Å, 2θ = 156.230◦ . These results implied that our calculation methods are reasonable, and the calculated results should be authentic. We utilized a (2 × 3) periodic slab to model the surface structure and properties, which contained four O–Ti–O tri-layers and was separated by a vacuum gap of 20 Å thicknesses. The top two tri-layers were relaxed, while the bottom two tri-layers were fixed to mimic the bulk region. The lengths on [101] and [010] directions of this model are 10.315 and 11.325 Å respectively, which are long enough to avoid the self-interaction of water molecule. The complete dissociation of water (which products are one oxygen atom and two hydrogen atoms) is more difficult than its partial dissociation (which products are one hydroxyl group and one hydrogen atom). And the surface hydroxyl group is a very important active species in the photocatalytic reactions. So, in this Letter, we paid our attention to the partial dissociation of water on TiO2 surface.
3. Results and discussions 3.1. Interaction potential energy At first, we will answer the most basic question: what is the stable adsorption configuration of water on this surface, and why? We placed a water molecule at neighboring 5c-Ti (fivefoldcoordination Ti atom, similarly hereinafter) for molecular adsorption model, and placed an H atom and an OH group at neighboring 2c-O and 5c-Ti sites for dissociative adsorption model. For each 5cTi, two nonequivalent 2c-O sites for H atom are available: the 2c-O directly coordinated to 5c-Ti (intrapair configuration), and the 2c-O indirectly coordinated to 5c-Ti (interpair configuration). Firstly, we set free all the coordinates of water molecule or H + OH fragments, and then obtained the preferred adsorption positions by geometry optimization. Starting from these equilibrium configurations, information about the binding energy of a water molecule and separate H + OH fragments on the surface is obtained from calculations of their adiabatic potential energy surface (PES), whose positions are denoted by the O atom’s coordinates, the PES is defined by fixing the normal coordinate of O atom (for dissociative adsorption the isolated H atom’s normal coordinate surface and its distance from O atom were fixed, too), and relaxing both the other coordinates of water molecule, as well as all coordinates of the top substrate atoms. The results of PES calculations are illustrated in Fig. 1. The height of equilibrium adsorption configurations is 1.138 Å for molecular adsorption, 1.238 Å for intrapair dissociative adsorption and 1.209 Å for interpair dissociative adsorption, respectively. The corresponding adsorption energies (relatively with dry surface’s energy plus isolated water molecule’s energy) are 0.916, 0.622 and 0.5 eV, respectively. Their equilibrium adsorption configurations were respectively displayed in Fig. 1(b)–(d). These results were well consistent with previous theoretical calculations [20]. From the perspective of energy, the molecular adsorption is more stable than both dissociative adsorptions. And from the perspective of thermodynamics, dissociative H + OH fragments very easily recombine to water molecule. That is, the decomposition of water molecule is a reversible process on this surface. On the other hand, the molecular adsorption energy is larger than the hydrogen bond energy between water molecules in ice structure (≈ 0.2–0.3 eV), so it is difficult to form cluster or aggregation for water on this surface at low coverage and low temperatures. Based on these potential energy curves and harmonic approximation, we could predict that the stretching vibration frequency (the vibration along the surface normal direction) of molecular adsorption would be lower than that of dissociative adsorption. This is an approvable result, but we haven’t found any relevant results in the existing literature, probably due to the difficulty to measure such extremely low frequency of these vibration modes. 3.2. Interaction potential forms As a typical many-body quantum problem, to describe the interaction of water with TiO2 surface involves all coordinates, momentum and electrons of all atoms in system, which is the advantage of DFT calculations. However, the DFT calculations only give an overall result of various interactions, leading to the difficulty of understanding the role of each individual interaction. Thus, it is necessary to categorize and simplify the DFT calculation results. Because of the pair potential model which has a simple form and explicit physical meaning is widely concerned, we adopted a combination of variety pair potentials to simplify the calculated results. Our potential function is shown in Eq. (1):
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
2941
(a)
(b)
(c)
(d)
Fig. 1. The interaction potential energy curve of water with anatase TiO2 (101) surface (a), and the segments of equilibrium configuration for each adsorbed form: molecular adsorption (b), intrapair dissociative adsorption (c), interpair dissociative adsorption (d). The red ball represents oxygen atom, the gray ball represents titanium atom, and the blue ball represents hydrogen atom. The black dash line denotes the bond length (the length unit is Å). (For interpretation of colors in this figure, the reader is referred to the web version of this Letter.)
E (r ) = A 1 ·
q1 q2 4πε0 r
C −r + A 2 · be ρ − 6 r
+ A 3 · D e −2a(r −r0 ) − 2e −a(r −r0 ) P1 P2 f (θ, φ) . + A4 · − 3 4πε0 r
(1)
The first term is the Coulomb potential, characterizing the electrostatic interaction. The second term is the Born–Mayer potential, characterizing ionic interaction [38]. The third term is the Morse potential, characterizing the covalent interaction [39]. Water is a polar molecule, and has a certain dipole moment. In the present work, we found that anatase TiO2 (101) surface is formed oxygenrich top layer by surface relaxation (the third oxygen layer is rising above the second titanium layer after relaxation), so this surface is also a polar surface with certain surface dipole moment. Thus, in Eq. (1), we used the fourth term to characterize dipole interaction, which is usually ignored in the classical molecular dynamics (force field MD) simulations. In order to facilitate the fitting of calculated data, we simplify Eq. (1) to Eq. (2):
E (h) =
A h
+ Be
− ρh
−
C
2.5 Å, the energy curve is mutating and the role of dipole interaction is changing. Above this height, dipole interaction is relative large and acts as attraction force. On the contrary, it falls fairly small and acts as repulsion force below this height. In this work, we found below these heights, a great distortion on the surface is induced by water dissociative adsorption. Meanwhile, ionic bonds are formed between H + OH fragments and surface atoms. Therefore, surface dipole moment is accordingly changed, bringing the change of dipole interaction role. By analyzing adsorbed configurations, we found that the molecular plane is nearly parallel to the surface in the entire molecular adsorption process. Whereas in dissociative adsorption process, the dipole plane of H + OH is perpendicular to the surface. It is the distinction that leads to rather weak dipole interaction for molecular adsorption, but strong dipole interaction for dissociative adsorption. Furthermore, near the equilibrium position, the dipole interaction acts as repulsive force, so the energy of molecular adsorption is lower than that of dissociative adsorption. In addition, one could see that the covalent interaction is not zero. This implies that it is also another important interaction form. 3.3. Bonding mechanism
h6
E + D e −2a(h−h0 ) − 2e −a(h−h0 ) + 3 . h
(2)
The fitting results are shown in Fig. 1 and Table 1. The fitting curves are very good in line with calculated data, and all the correlation coefficients are larger than 0.98. For dissociative adsorption, there is a noteworthy feature: at the height of 2.3 or
In general, the interaction of water with TiO2 surface is mainly of local character. Therefore, the analysis of the bonding mechanism should provide at least qualitative insight into the bonding interaction of water in these adsorption forms. In Fig. 2, we display the local partial density of states diagram corresponding to these systems. For the isolated water molecule or H + OH fragments, the
2942
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
Table 1 Fitting results for the data in Fig. 1. M is molecular adsorption, D1 is intrapair dissociative adsorption, D2 is interpair dissociative adsorption. And R is correlation coefficient. Parameters in Eq. (2) A M D1 D2
h 2.3 h 2.4 h 2.5 h 2.6
Å Å Å Å
−0.122 −0.532 1.320 −0.629 1.461
R
B
ρ
C
D
a
h0
1.120 51.260 5.955 24.606 6.078
1.927 15.798 719.424 91.827 421.941
1.509 × 10−8 3.431 × 10−7 3.279 × 10−8 3.127 × 10−8 5.930 × 10−8
1.397 48.035 4.260 × 10−9 24.273 1.304 × 10−8
0.992 0.310 1.350 0.384 1.278
0.993 0.892 0.907 1.206 1.168
valence bands are consisting with the results in literature. When water molecule or H + OH fragments stay at the height of 8 Å from the surface, the interaction is very weak, so the properties of electronic structures are keeping the properties of isolated adsorbate and dry TiO2 (101) surface. At this height, because the distances between H atom and OH group are finite, thus H + OH fragments have similar electronic structure with water. With height decrease, the interaction of water molecule with surface increases. At the equilibrium positions, because the dangling bonds of 5c-Ti and 2c-O are saturated, the corresponding surface states are disappearing. All the valence bands of water molecule are below the Fermi level, owing to the charge transfer achieves to the balance between water molecule and surface. As the water molecule is closer to the surface, its valence bands emerge unoccupied states again, arising from the mutual repulsion between water molecule and TiO2 surface. In the case of dissociative adsorption, the situation is similar with the above discussion. And, there is an obvious state below the valence band, arising from the surface hydroxyl group that is composed by the hydrogen atom and bridge oxygen atom (2c-O). The bonding interaction is mainly due to the hybridization between the surface states and water’s lone-pair states. In molecular adsorption, 1b1 state fully overlaps with Ti-3d, O-2p states, and obvious away from the Fermi lever. Whereas in the case of dissociative adsorption, the 3a1 -like state fully overlaps with Ti-3d, O-2p states, and the 1b1 -like state partially overlaps with surface state that is still near the Fermi level. This means that when water molecule approaches to this surface, molecular adsorption form interplays with surface through 1b1 state; while dissociative adsorption form interplays with surface through 3a1 -like state. Because of the initial 1b1 state is closer to the Fermi level, this interaction will be preferred. In addition, we found that the H atom in OH group is not directly involved in charge transfer and interplays with surface. Based on the above analysis, we believe that for molecular adsorption all atoms of water form relatively stronger covalent bonds with the nearest neighboring surface atoms, respectively. While for dissociative adsorption, H + OH fragments form relatively strong ionic bonds with the nearest neighboring surface atoms, respectively, but still remain a non-bonding H atom at the same time. It is the difference of bonding mechanism that makes water favor molecular adsorption on anatase TiO2 (101) surface. 3.4. Surface diffusion To answer the next question how water molecule diffuses on this surface, we calculated the adiabatic PES again. This time, the PES is defined by relaxing the height of water molecule from surface (for a set of fixed lateral coordinates of water molecule, these coordinates form an equidistant grid with a spacing between the grid points of about 0.5 Å in [101] and [010] directions), as well as all coordinates of the top substrate atoms. As shown in Fig. 3(a), we found the global minimum located at the bridge site between 5c-Ti and 3c-O (denoted “a”), and the global maximum located at atop 3c-O (denoted “b”), which is the
E 2.825 × 10−8 0.003 −13.587 0.002 −19.103
0.990 0.997 0.986 0.981 0.987
significant upward atom in surface relaxation as mentioned above. According to the principle of minimum energy change, we proposed two diffusion pathways (denoted “path 1” and “path 2”) between global minima. On these pathways, the saddle points located at the bridge site and hollow site (denoted “c” and “d”), respectively. We also considered the other two adsorption sites: atop 2c-O and 5c-Ti (denoted “e” and “f”). All these typical adsorption configurations are illustrated in Fig. 3(c). These figures clearly display that the interaction between water and TiO2 (101) surface depends sensitively on the adsorption sites. The sequence of adsorption energies is in line with the temperature program desorption (TPD) experiment data [27]: the desorption temperature of water adsorbed to 5c-Ti sites is larger than that of water adsorbed to 2c-O sites. From these configurations, the adsorption energy is relatively large when the water molecular plane is parallel to surface (for example, in the case of configuration “a” and “f”). On the contrary, the adsorption energy is relatively small when the water molecular plane is perpendicular to surface (for example, in the case of configuration “b”, “c”, “d” and “e”). These results again validate previous conclusion in Section 3.2, that the dipole interaction acts a significant role for the interaction of water with anatase TiO2 (101) surface. Besides the global minima, we did not find the metastable adsorption sites on this surface for water. Thus, water molecule can directly diffuse between the global minima. The binding energy changes and the diffusion barriers for water molecule on-surface hopping from one global minimum to its neighbor global minimum are shown in Fig. 3(b). It can be seen that water diffusion on anatase TiO2 (101) surface is anisotropy: the diffusion energy barrier of water molecule along [010] direction (“path 1”) is smaller than that of along [111]/[111] direction (“path 2”) on this surface. In Ref. [12], the authors used STM to observe the mobility of water molecule on anatase TiO2 (101) surface. From their result (Fig. 2(c) in Ref. [12]), one can see that the mobile probability along [010] direction is larger than that of along [111]/[111] direction. Our result is very well agreement with the experimental observation, and can clearly explain its underlying mechanism. 4. Conclusions In summary, in the present work in this Letter, we have solved the questions that were remained by the previous works. Because of the distinctions of interaction potential forms and bonding mechanism, water tends to adsorb on anatase TiO2 (101) surface by molecular adsorption. The preferred adsorption site is bridge site between 5c-Ti and 3c-O sites, which adsorption energy is about 0.916 eV, resulting in difficult formation of cluster or aggregation at low coverage and low temperatures. For the interaction water with this surface, the role of dipole interaction is so important that should not be ignored. Meanwhile, the dipole interaction exhibits different performance forms at different height region. On this surface, water molecule on-surface diffusion is anisotropy: its diffusion energy barrier along [010] direction is smaller than that of along [111]/[111] direction.
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
2943
(a)
(b)
(c) Fig. 2. The partial and local density of state of various adsorption conformations at variety height from surface, compared with that of the isolated adsorbate and dry TiO2 (101) surface: (a) molecular adsorption; (b) intrapair dissociative adsorption; (c) interpair dissociative adsorption. The zero references are the Fermi energy level. The atom labels are shown in Fig. 1.
2944
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
(a)
(b)
(c)
Fig. 3. (a) The contour map of adiabatic PES for molecular adsorption of water on anatase TiO2 (101) surface. (b) Potential energy profile for the proposed diffusion pathways. (c) Adsorption configurations on some typical sites shown in PES map (side and top views). And the adsorption potential energies are given below.
Acknowledgements
The authors acknowledge the financial support from the National Basic Research Program of China (973 Program, Grant Nos. 2007CB613301 and 2007CB613305), China–Japan cooperation project of science and technology (2009DFA61090), the National Natural Science Foundation of China (50732004 and 21073090),
and the Jiangsu Provincial Science and Technology Research Program (BK2008028 and BE2009140). References [1] P.A. Thiel, T.E. Madey, Surf. Sci. Rep. 7 (1987) 211. [2] M.A. Henderson, Surf. Sci. Rep. 46 (2002) 1. [3] U. Diebold, Surf. Sci. Rep. 48 (2003) 53.
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
[4] A. Fujishima, K. Honda, Nature 238 (1972) 37. [5] C. Arrouvel, M. Digne, M. Breysse, H. Toulhoat, P. Raybaud, J. Catal. 222 (2004) 152. [6] G. Li, L. Li, J. Boerio-Goates, B.F. Woodfield, J. Am. Chem. Soc. 127 (2005) 8659. [7] A.A. Levchenko, G. Li, J. Boerio-Goates, B.F. Woodfield, A. Navrotsky, Chem. Mater. 18 (2006) 6324. [8] J. Boerio-Goates, G. Li, L. Li, T.F. Walker, T. Parry, B.F. Woodfield, Nano Lett. 6 (2006) 750. [9] E.V. Stefanovich, T.N. Truong, Chem. Phys. Lett. 299 (1999) 623. [10] I.M. Brookes, C.A. Muryn, G. Thornton, Phys. Rev. Lett. 87 (2001) 266103. [11] L.A. Harris, A.A. Quong, Phys. Rev. Lett. 93 (2004) 086105. [12] Y. He, A. Tilocca, O. Dulub, A. Selloni, U. Diebold, Nat. Mater. 8 (2009) 585. [13] P.J.D. Lindan, N.M. Harrison, J.M. Holender, M.J. Gillan, Chem. Phys. Lett. 261 (1996) 246. [14] T. Bredow, K. Jug, Surf. Sci. 327 (1995) 398. [15] J. Goniakowski, M.J. Gillan, Surf. Sci. 350 (1996) 145. [16] J. Ahdjoudj, C. Minot, Surf. Sci. 402 (1997) 104. [17] P.J.D. Lindan, N.M. Harrison, M.J. Gillan, Phys. Rev. Lett. 80 (1998) 762. [18] S. Wendt, J. Matthiesen, R. Schaub, E.K. Vestergaard, E. Laegsgaard, F. Besenbacher, B. Hammer, Phys. Rev. Lett. 96 (2006) 066107. [19] H. Perron, J. Vandenborre, C. Domain, R. Drot, J. Roques, E. Simoni, J.J. Ehrhardt, H. Catalette, Surf. Sci. 601 (2007) 518. [20] A. Vittadini, A. Selloni, F.P. Rotzinger, M. Gratzel, Phys. Rev. Lett. 81 (1998) 2954. [21] C. Di Valentin, A. Tilocca, A. Selloni, T.J. Beck, A. Klust, M. Batzill, Y. Losovyj, U. Diebold, J. Am. Chem. Soc. 127 (2005) 9895.
2945
[22] O. Bikondoa, C.L. Pang, R. Ithnin, C.A. Muryn, H. Onishi, G. Thornton, Nat. Mater. 5 (2006) 189. [23] A. Ignatchenko, D.G. Nealon, R. Dushane, K. Humphries, J. Mol. Catal. A: Chem. 256 (2006) 57. [24] Y. Du, N.A. Deskins, Z. Zhang, Z. Dohnalek, M. Dupuis, I. Lyubinetsky, Phys. Rev. Lett. 102 (2009) 096102. [25] Y. He, W.-K. Li, X.-Q. Gong, O. Dulub, A. Selloni, U. Diebold, J. Phys. Chem. C 113 (2009) 10329. [26] P.M. Kowalski, B. Meyer, D. Marx, Phys. Rev. B 79 (2009) 115410. [27] G.S. Herman, Z. Dohnalek, N. Ruzycki, U. Diebold, J. Phys. Chem. B 107 (2003) 2788. [28] C. Zhang, P.J.D. Lindan, J. Chem. Phys. 118 (2003) 4620. [29] A. Tilocca, A. Selloni, Langmuir 20 (2004) 8379. [30] A.V. Bandura, J.D. Kubicki, J.O. Sofo, J. Phys. Chem. B 112 (2008) 11616. [31] H.Z. Zhang, J.F. Banfield, J. Mater. Chem. 8 (1998) 2073. [32] M. Lazzeri, A. Vittadini, A. Selloni, Phys. Rev. B 63 (2001) 155409. [33] Z. Zhao, Z. Li, Z. Zou, J. Phys.: Condens. Matter 22 (2010) 175008. [34] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, M.C. Payne, Z. Kristallogr. 220 (2005) 567. [35] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [36] B.G. Pfrommer, M. Câté, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997) 233. [37] J.K. Burdett, T. Hughbanks, G.J. Miller, J.W. Richardson, J.V. Smith, J. Am. Chem. Soc. 109 (1987) 3639. [38] M. Born, J.E. Mayer, Z. Phys. A 75 (1932) 1. [39] P.M. Morse, Phys. Rev. 34 (1929) 57.
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Understanding the interaction of water with anatase TiO2 (101) surface from density functional theory calculations Zongyan Zhao a,b , Zhaosheng Li a,b,c,∗ , Zhigang Zou a,b,∗ a b c
Ecomaterials and Renewable Energy Research Center (ERERC), Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 4 April 2011 Received in revised form 9 June 2011 Accepted 11 June 2011 Available online 14 June 2011 Communicated by R. Wu Keywords: Titanium dioxide surface Water adsorption Density functional theory calculation Surface diffusion
a b s t r a c t The behavior of water molecule on anatase TiO2 (101) surface has been investigated by density functional theory calculations. The primary purpose of this Letter is to clarify the distinctions between molecular adsorption and dissociative adsorption of water on anatase TiO2 (101) surface. By analyzing interaction potential forms and bonding mechanism, it is found that the dipole interaction is the crucial factor for water adsorption on anatase TiO2 (101) surface. The adiabatic potential energy surface calculations indicate that the on-surface diffusion of water molecule is anisotropy: its diffusion energy barrier along [010] direction is smaller than that of along [111]/[111] direction. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The interaction of water with solid surfaces is extremely important research topic for both basic science and applied technology, because water almost exists everywhere and affects everything in ambient environment. And the physical and chemical properties of water on solid surface have a notable impact on their performance. Thus, a fundamental understanding of the interaction of water with solid surface is essential for the progress in many fields [1,2]. Titanium dioxide (TiO2 ), as a representative example of metal oxide, has been widely investigated in the field of surface science [3]. Many of its applications, such as dye sensitized solar cells, photocatalyst, corrosion-protective coating, and gas sensors, are performed in aqueous environment or related to the interaction with water. In particular, Fujishima and Honda [4] discovered it can be used as photocatalyst to split water, thus producing oxygen and/or hydrogen. And then, researchers found it also can be decomposed organic pollutions, and has super-hydrophilic properties under UV-light irradiation. These particular properties, which can effectively solve the energy crisis and environmental pollution, are directly correlated with the interaction between wa-
*
Corresponding authors at: Ecomaterials and Renewable Energy Research Center (ERERC), Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China. Tel.: +86 25 83686603; fax: +86 25 83686632. E-mail addresses: [email protected] (Z. Li), [email protected] (Z. Zou). 0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2011.06.022
ter and TiO2 surfaces. Moreover, water has significant effect on the stability and growth of TiO2 nanoparticles [5–8]. Therefore, the interaction of water with TiO2 attracted broad concern from both fundamental research and industrial development in the past decades. The adsorption of water molecule on TiO2 surface has been extensively investigated by a variety of experimental and theoretical techniques in recent years. But there are some contraries and disputes in the existing literature. Some research groups found that water always molecularly adsorbs on TiO2 surface [9–12]. However, other groups found the opposite results that the dissociative adsorption, “pseudo-dissociative” adsorption, or mixed adsorption is more stable than the molecular adsorption on these surfaces [13–20]. On the imperfect surfaces or high-activity surfaces, the dissociative adsorption is energetically favored [10,21–26]. For the multilayer water adsorption, due to the competition between the interplay of water–water and water–surface, mixed adsorption, various local and/or long-range order structures are formed on the TiO2 surfaces [27–30]. These studies help us to better understand the interaction of water with TiO2 surfaces. However, there are still some unresolved questions in this field. (i) Most published works had only described the adsorption configurations and the corresponding adsorption energy. They did not in-depth discuss the underlying mechanism. (ii) Another important thing is that most of these literatures focused on water adsorbed to rutile TiO2 (110) surface. Only few works are devoted into the exploration of water on anatase TiO2 surfaces. So the knowledge about the
2940
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
interaction of water with anatase TiO2 surfaces is still insufficiency. However, anatase TiO2 has better photocatalytic performance than rutile TiO2 , and it is the preferred phase during the formation of TiO2 nanoparticles [31,32]. (iii) The surface diffusion properties of water on TiO2 surface are still unclear. Thus, it is necessary to in-depth study the interaction of water with anatase TiO2 surfaces, in order to further improve the related investigation. At the atomic-scale level, experimental characterization of the interaction of isolated single water molecule with solid surface is very difficult, while computational simulation has natural advantages in regard to this issue. In order to complement and enhance the comprehend of the interaction of water with TiO2 surfaces, we attempt to adopt the ultrasoft pseudopotential plane wave method based on density functional theory (DFT) framework to systematically investigate the interaction of water with anatase TiO2 (101) surface in this Letter. We chose the anatase TiO2 (101) surface as substrate, because this surface is the dominate surface of anatase phase [32,33]. It is undeniable that the interaction of water with this surface is a key factor that impacts the performance of anatase TiO2 in vast majority circumstances. In this Letter, the adsorption configurations and adsorption energy of water on anatase TiO2 (101) surface were firstly calculated. Then, the underlying mechanism, including interaction potential forms and bonding mechanism, was carefully analyzed in detail. Finally, the surface diffusion behavior of water on this surface was also calculated and analyzed. 2. Computational method and details In this Letter, the density functional theory calculations were performed with Cambridge Serial Total Energy Package (CASTEP) codes [34]. Exchange and correlation effects were described by the Perdew–Burke–Ernzerhof (PBE) of generalized gradient approximation [35]. An energy cutoff of 340 eV was used for expanding the Kohn–Sham wave functions. The Monkhorst–Pack scheme K-points grid sampling was set as 2 × 2 × 1 for the irreducible Brillouin zone. A 64 × 72 × 160 mesh was used for fast Fourier transformation. The minimization algorithm was chosen Broyden–Fletcher– Goldfarb–Shanno (BFGS) scheme [36]. The relaxation run was considered converged when the force on the atomic nuclei was less than 0.03 eV/Å, the stress on the atomic nuclei was less than 0.05 GPa, the displacement of the nuclei was less than 1 × 10−3 Å, and the energy change per atom was less than 1 × 10−5 eV. By the above method, we firstly optimized pure anatase TiO2 structure, and got the bulk lattice parameters as follows: a = b = 3.7748 Å, c = 9.5990 Å, dap = 1.9883 Å, deq = 1.9318 Å, 2θ = 155.403◦ . They were good agreement with experimental values [37]: a = b = 3.7848 Å, c = 9.5124 Å, dap = 1.9799 Å, deq = 1.9338 Å, 2θ = 156.230◦ . These results implied that our calculation methods are reasonable, and the calculated results should be authentic. We utilized a (2 × 3) periodic slab to model the surface structure and properties, which contained four O–Ti–O tri-layers and was separated by a vacuum gap of 20 Å thicknesses. The top two tri-layers were relaxed, while the bottom two tri-layers were fixed to mimic the bulk region. The lengths on [101] and [010] directions of this model are 10.315 and 11.325 Å respectively, which are long enough to avoid the self-interaction of water molecule. The complete dissociation of water (which products are one oxygen atom and two hydrogen atoms) is more difficult than its partial dissociation (which products are one hydroxyl group and one hydrogen atom). And the surface hydroxyl group is a very important active species in the photocatalytic reactions. So, in this Letter, we paid our attention to the partial dissociation of water on TiO2 surface.
3. Results and discussions 3.1. Interaction potential energy At first, we will answer the most basic question: what is the stable adsorption configuration of water on this surface, and why? We placed a water molecule at neighboring 5c-Ti (fivefoldcoordination Ti atom, similarly hereinafter) for molecular adsorption model, and placed an H atom and an OH group at neighboring 2c-O and 5c-Ti sites for dissociative adsorption model. For each 5cTi, two nonequivalent 2c-O sites for H atom are available: the 2c-O directly coordinated to 5c-Ti (intrapair configuration), and the 2c-O indirectly coordinated to 5c-Ti (interpair configuration). Firstly, we set free all the coordinates of water molecule or H + OH fragments, and then obtained the preferred adsorption positions by geometry optimization. Starting from these equilibrium configurations, information about the binding energy of a water molecule and separate H + OH fragments on the surface is obtained from calculations of their adiabatic potential energy surface (PES), whose positions are denoted by the O atom’s coordinates, the PES is defined by fixing the normal coordinate of O atom (for dissociative adsorption the isolated H atom’s normal coordinate surface and its distance from O atom were fixed, too), and relaxing both the other coordinates of water molecule, as well as all coordinates of the top substrate atoms. The results of PES calculations are illustrated in Fig. 1. The height of equilibrium adsorption configurations is 1.138 Å for molecular adsorption, 1.238 Å for intrapair dissociative adsorption and 1.209 Å for interpair dissociative adsorption, respectively. The corresponding adsorption energies (relatively with dry surface’s energy plus isolated water molecule’s energy) are 0.916, 0.622 and 0.5 eV, respectively. Their equilibrium adsorption configurations were respectively displayed in Fig. 1(b)–(d). These results were well consistent with previous theoretical calculations [20]. From the perspective of energy, the molecular adsorption is more stable than both dissociative adsorptions. And from the perspective of thermodynamics, dissociative H + OH fragments very easily recombine to water molecule. That is, the decomposition of water molecule is a reversible process on this surface. On the other hand, the molecular adsorption energy is larger than the hydrogen bond energy between water molecules in ice structure (≈ 0.2–0.3 eV), so it is difficult to form cluster or aggregation for water on this surface at low coverage and low temperatures. Based on these potential energy curves and harmonic approximation, we could predict that the stretching vibration frequency (the vibration along the surface normal direction) of molecular adsorption would be lower than that of dissociative adsorption. This is an approvable result, but we haven’t found any relevant results in the existing literature, probably due to the difficulty to measure such extremely low frequency of these vibration modes. 3.2. Interaction potential forms As a typical many-body quantum problem, to describe the interaction of water with TiO2 surface involves all coordinates, momentum and electrons of all atoms in system, which is the advantage of DFT calculations. However, the DFT calculations only give an overall result of various interactions, leading to the difficulty of understanding the role of each individual interaction. Thus, it is necessary to categorize and simplify the DFT calculation results. Because of the pair potential model which has a simple form and explicit physical meaning is widely concerned, we adopted a combination of variety pair potentials to simplify the calculated results. Our potential function is shown in Eq. (1):
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
2941
(a)
(b)
(c)
(d)
Fig. 1. The interaction potential energy curve of water with anatase TiO2 (101) surface (a), and the segments of equilibrium configuration for each adsorbed form: molecular adsorption (b), intrapair dissociative adsorption (c), interpair dissociative adsorption (d). The red ball represents oxygen atom, the gray ball represents titanium atom, and the blue ball represents hydrogen atom. The black dash line denotes the bond length (the length unit is Å). (For interpretation of colors in this figure, the reader is referred to the web version of this Letter.)
E (r ) = A 1 ·
q1 q2 4πε0 r
C −r + A 2 · be ρ − 6 r
+ A 3 · D e −2a(r −r0 ) − 2e −a(r −r0 ) P1 P2 f (θ, φ) . + A4 · − 3 4πε0 r
(1)
The first term is the Coulomb potential, characterizing the electrostatic interaction. The second term is the Born–Mayer potential, characterizing ionic interaction [38]. The third term is the Morse potential, characterizing the covalent interaction [39]. Water is a polar molecule, and has a certain dipole moment. In the present work, we found that anatase TiO2 (101) surface is formed oxygenrich top layer by surface relaxation (the third oxygen layer is rising above the second titanium layer after relaxation), so this surface is also a polar surface with certain surface dipole moment. Thus, in Eq. (1), we used the fourth term to characterize dipole interaction, which is usually ignored in the classical molecular dynamics (force field MD) simulations. In order to facilitate the fitting of calculated data, we simplify Eq. (1) to Eq. (2):
E (h) =
A h
+ Be
− ρh
−
C
2.5 Å, the energy curve is mutating and the role of dipole interaction is changing. Above this height, dipole interaction is relative large and acts as attraction force. On the contrary, it falls fairly small and acts as repulsion force below this height. In this work, we found below these heights, a great distortion on the surface is induced by water dissociative adsorption. Meanwhile, ionic bonds are formed between H + OH fragments and surface atoms. Therefore, surface dipole moment is accordingly changed, bringing the change of dipole interaction role. By analyzing adsorbed configurations, we found that the molecular plane is nearly parallel to the surface in the entire molecular adsorption process. Whereas in dissociative adsorption process, the dipole plane of H + OH is perpendicular to the surface. It is the distinction that leads to rather weak dipole interaction for molecular adsorption, but strong dipole interaction for dissociative adsorption. Furthermore, near the equilibrium position, the dipole interaction acts as repulsive force, so the energy of molecular adsorption is lower than that of dissociative adsorption. In addition, one could see that the covalent interaction is not zero. This implies that it is also another important interaction form. 3.3. Bonding mechanism
h6
E + D e −2a(h−h0 ) − 2e −a(h−h0 ) + 3 . h
(2)
The fitting results are shown in Fig. 1 and Table 1. The fitting curves are very good in line with calculated data, and all the correlation coefficients are larger than 0.98. For dissociative adsorption, there is a noteworthy feature: at the height of 2.3 or
In general, the interaction of water with TiO2 surface is mainly of local character. Therefore, the analysis of the bonding mechanism should provide at least qualitative insight into the bonding interaction of water in these adsorption forms. In Fig. 2, we display the local partial density of states diagram corresponding to these systems. For the isolated water molecule or H + OH fragments, the
2942
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
Table 1 Fitting results for the data in Fig. 1. M is molecular adsorption, D1 is intrapair dissociative adsorption, D2 is interpair dissociative adsorption. And R is correlation coefficient. Parameters in Eq. (2) A M D1 D2
h 2.3 h 2.4 h 2.5 h 2.6
Å Å Å Å
−0.122 −0.532 1.320 −0.629 1.461
R
B
ρ
C
D
a
h0
1.120 51.260 5.955 24.606 6.078
1.927 15.798 719.424 91.827 421.941
1.509 × 10−8 3.431 × 10−7 3.279 × 10−8 3.127 × 10−8 5.930 × 10−8
1.397 48.035 4.260 × 10−9 24.273 1.304 × 10−8
0.992 0.310 1.350 0.384 1.278
0.993 0.892 0.907 1.206 1.168
valence bands are consisting with the results in literature. When water molecule or H + OH fragments stay at the height of 8 Å from the surface, the interaction is very weak, so the properties of electronic structures are keeping the properties of isolated adsorbate and dry TiO2 (101) surface. At this height, because the distances between H atom and OH group are finite, thus H + OH fragments have similar electronic structure with water. With height decrease, the interaction of water molecule with surface increases. At the equilibrium positions, because the dangling bonds of 5c-Ti and 2c-O are saturated, the corresponding surface states are disappearing. All the valence bands of water molecule are below the Fermi level, owing to the charge transfer achieves to the balance between water molecule and surface. As the water molecule is closer to the surface, its valence bands emerge unoccupied states again, arising from the mutual repulsion between water molecule and TiO2 surface. In the case of dissociative adsorption, the situation is similar with the above discussion. And, there is an obvious state below the valence band, arising from the surface hydroxyl group that is composed by the hydrogen atom and bridge oxygen atom (2c-O). The bonding interaction is mainly due to the hybridization between the surface states and water’s lone-pair states. In molecular adsorption, 1b1 state fully overlaps with Ti-3d, O-2p states, and obvious away from the Fermi lever. Whereas in the case of dissociative adsorption, the 3a1 -like state fully overlaps with Ti-3d, O-2p states, and the 1b1 -like state partially overlaps with surface state that is still near the Fermi level. This means that when water molecule approaches to this surface, molecular adsorption form interplays with surface through 1b1 state; while dissociative adsorption form interplays with surface through 3a1 -like state. Because of the initial 1b1 state is closer to the Fermi level, this interaction will be preferred. In addition, we found that the H atom in OH group is not directly involved in charge transfer and interplays with surface. Based on the above analysis, we believe that for molecular adsorption all atoms of water form relatively stronger covalent bonds with the nearest neighboring surface atoms, respectively. While for dissociative adsorption, H + OH fragments form relatively strong ionic bonds with the nearest neighboring surface atoms, respectively, but still remain a non-bonding H atom at the same time. It is the difference of bonding mechanism that makes water favor molecular adsorption on anatase TiO2 (101) surface. 3.4. Surface diffusion To answer the next question how water molecule diffuses on this surface, we calculated the adiabatic PES again. This time, the PES is defined by relaxing the height of water molecule from surface (for a set of fixed lateral coordinates of water molecule, these coordinates form an equidistant grid with a spacing between the grid points of about 0.5 Å in [101] and [010] directions), as well as all coordinates of the top substrate atoms. As shown in Fig. 3(a), we found the global minimum located at the bridge site between 5c-Ti and 3c-O (denoted “a”), and the global maximum located at atop 3c-O (denoted “b”), which is the
E 2.825 × 10−8 0.003 −13.587 0.002 −19.103
0.990 0.997 0.986 0.981 0.987
significant upward atom in surface relaxation as mentioned above. According to the principle of minimum energy change, we proposed two diffusion pathways (denoted “path 1” and “path 2”) between global minima. On these pathways, the saddle points located at the bridge site and hollow site (denoted “c” and “d”), respectively. We also considered the other two adsorption sites: atop 2c-O and 5c-Ti (denoted “e” and “f”). All these typical adsorption configurations are illustrated in Fig. 3(c). These figures clearly display that the interaction between water and TiO2 (101) surface depends sensitively on the adsorption sites. The sequence of adsorption energies is in line with the temperature program desorption (TPD) experiment data [27]: the desorption temperature of water adsorbed to 5c-Ti sites is larger than that of water adsorbed to 2c-O sites. From these configurations, the adsorption energy is relatively large when the water molecular plane is parallel to surface (for example, in the case of configuration “a” and “f”). On the contrary, the adsorption energy is relatively small when the water molecular plane is perpendicular to surface (for example, in the case of configuration “b”, “c”, “d” and “e”). These results again validate previous conclusion in Section 3.2, that the dipole interaction acts a significant role for the interaction of water with anatase TiO2 (101) surface. Besides the global minima, we did not find the metastable adsorption sites on this surface for water. Thus, water molecule can directly diffuse between the global minima. The binding energy changes and the diffusion barriers for water molecule on-surface hopping from one global minimum to its neighbor global minimum are shown in Fig. 3(b). It can be seen that water diffusion on anatase TiO2 (101) surface is anisotropy: the diffusion energy barrier of water molecule along [010] direction (“path 1”) is smaller than that of along [111]/[111] direction (“path 2”) on this surface. In Ref. [12], the authors used STM to observe the mobility of water molecule on anatase TiO2 (101) surface. From their result (Fig. 2(c) in Ref. [12]), one can see that the mobile probability along [010] direction is larger than that of along [111]/[111] direction. Our result is very well agreement with the experimental observation, and can clearly explain its underlying mechanism. 4. Conclusions In summary, in the present work in this Letter, we have solved the questions that were remained by the previous works. Because of the distinctions of interaction potential forms and bonding mechanism, water tends to adsorb on anatase TiO2 (101) surface by molecular adsorption. The preferred adsorption site is bridge site between 5c-Ti and 3c-O sites, which adsorption energy is about 0.916 eV, resulting in difficult formation of cluster or aggregation at low coverage and low temperatures. For the interaction water with this surface, the role of dipole interaction is so important that should not be ignored. Meanwhile, the dipole interaction exhibits different performance forms at different height region. On this surface, water molecule on-surface diffusion is anisotropy: its diffusion energy barrier along [010] direction is smaller than that of along [111]/[111] direction.
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
2943
(a)
(b)
(c) Fig. 2. The partial and local density of state of various adsorption conformations at variety height from surface, compared with that of the isolated adsorbate and dry TiO2 (101) surface: (a) molecular adsorption; (b) intrapair dissociative adsorption; (c) interpair dissociative adsorption. The zero references are the Fermi energy level. The atom labels are shown in Fig. 1.
2944
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
(a)
(b)
(c)
Fig. 3. (a) The contour map of adiabatic PES for molecular adsorption of water on anatase TiO2 (101) surface. (b) Potential energy profile for the proposed diffusion pathways. (c) Adsorption configurations on some typical sites shown in PES map (side and top views). And the adsorption potential energies are given below.
Acknowledgements
The authors acknowledge the financial support from the National Basic Research Program of China (973 Program, Grant Nos. 2007CB613301 and 2007CB613305), China–Japan cooperation project of science and technology (2009DFA61090), the National Natural Science Foundation of China (50732004 and 21073090),
and the Jiangsu Provincial Science and Technology Research Program (BK2008028 and BE2009140). References [1] P.A. Thiel, T.E. Madey, Surf. Sci. Rep. 7 (1987) 211. [2] M.A. Henderson, Surf. Sci. Rep. 46 (2002) 1. [3] U. Diebold, Surf. Sci. Rep. 48 (2003) 53.
Z. Zhao et al. / Physics Letters A 375 (2011) 2939–2945
[4] A. Fujishima, K. Honda, Nature 238 (1972) 37. [5] C. Arrouvel, M. Digne, M. Breysse, H. Toulhoat, P. Raybaud, J. Catal. 222 (2004) 152. [6] G. Li, L. Li, J. Boerio-Goates, B.F. Woodfield, J. Am. Chem. Soc. 127 (2005) 8659. [7] A.A. Levchenko, G. Li, J. Boerio-Goates, B.F. Woodfield, A. Navrotsky, Chem. Mater. 18 (2006) 6324. [8] J. Boerio-Goates, G. Li, L. Li, T.F. Walker, T. Parry, B.F. Woodfield, Nano Lett. 6 (2006) 750. [9] E.V. Stefanovich, T.N. Truong, Chem. Phys. Lett. 299 (1999) 623. [10] I.M. Brookes, C.A. Muryn, G. Thornton, Phys. Rev. Lett. 87 (2001) 266103. [11] L.A. Harris, A.A. Quong, Phys. Rev. Lett. 93 (2004) 086105. [12] Y. He, A. Tilocca, O. Dulub, A. Selloni, U. Diebold, Nat. Mater. 8 (2009) 585. [13] P.J.D. Lindan, N.M. Harrison, J.M. Holender, M.J. Gillan, Chem. Phys. Lett. 261 (1996) 246. [14] T. Bredow, K. Jug, Surf. Sci. 327 (1995) 398. [15] J. Goniakowski, M.J. Gillan, Surf. Sci. 350 (1996) 145. [16] J. Ahdjoudj, C. Minot, Surf. Sci. 402 (1997) 104. [17] P.J.D. Lindan, N.M. Harrison, M.J. Gillan, Phys. Rev. Lett. 80 (1998) 762. [18] S. Wendt, J. Matthiesen, R. Schaub, E.K. Vestergaard, E. Laegsgaard, F. Besenbacher, B. Hammer, Phys. Rev. Lett. 96 (2006) 066107. [19] H. Perron, J. Vandenborre, C. Domain, R. Drot, J. Roques, E. Simoni, J.J. Ehrhardt, H. Catalette, Surf. Sci. 601 (2007) 518. [20] A. Vittadini, A. Selloni, F.P. Rotzinger, M. Gratzel, Phys. Rev. Lett. 81 (1998) 2954. [21] C. Di Valentin, A. Tilocca, A. Selloni, T.J. Beck, A. Klust, M. Batzill, Y. Losovyj, U. Diebold, J. Am. Chem. Soc. 127 (2005) 9895.
2945
[22] O. Bikondoa, C.L. Pang, R. Ithnin, C.A. Muryn, H. Onishi, G. Thornton, Nat. Mater. 5 (2006) 189. [23] A. Ignatchenko, D.G. Nealon, R. Dushane, K. Humphries, J. Mol. Catal. A: Chem. 256 (2006) 57. [24] Y. Du, N.A. Deskins, Z. Zhang, Z. Dohnalek, M. Dupuis, I. Lyubinetsky, Phys. Rev. Lett. 102 (2009) 096102. [25] Y. He, W.-K. Li, X.-Q. Gong, O. Dulub, A. Selloni, U. Diebold, J. Phys. Chem. C 113 (2009) 10329. [26] P.M. Kowalski, B. Meyer, D. Marx, Phys. Rev. B 79 (2009) 115410. [27] G.S. Herman, Z. Dohnalek, N. Ruzycki, U. Diebold, J. Phys. Chem. B 107 (2003) 2788. [28] C. Zhang, P.J.D. Lindan, J. Chem. Phys. 118 (2003) 4620. [29] A. Tilocca, A. Selloni, Langmuir 20 (2004) 8379. [30] A.V. Bandura, J.D. Kubicki, J.O. Sofo, J. Phys. Chem. B 112 (2008) 11616. [31] H.Z. Zhang, J.F. Banfield, J. Mater. Chem. 8 (1998) 2073. [32] M. Lazzeri, A. Vittadini, A. Selloni, Phys. Rev. B 63 (2001) 155409. [33] Z. Zhao, Z. Li, Z. Zou, J. Phys.: Condens. Matter 22 (2010) 175008. [34] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, M.C. Payne, Z. Kristallogr. 220 (2005) 567. [35] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [36] B.G. Pfrommer, M. Câté, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997) 233. [37] J.K. Burdett, T. Hughbanks, G.J. Miller, J.W. Richardson, J.V. Smith, J. Am. Chem. Soc. 109 (1987) 3639. [38] M. Born, J.E. Mayer, Z. Phys. A 75 (1932) 1. [39] P.M. Morse, Phys. Rev. 34 (1929) 57.