Stress Relief and Reactivity Loss of Hydrated Anatase (001) Surface

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Stress Relief and Reactivity Loss of Hydrated Anatase (001) Surface Eugenio Vitale, Giuseppe Zollo, Lorenzo Agosta, Fabrizio Gala, Erik G Brandt, and Alexander Lyubartsev J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05646 • Publication Date (Web): 06 Sep 2018 Downloaded from http://pubs.acs.org on September 6, 2018

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The Journal of Physical Chemistry

Stress relief and reactivity loss of hydrated Anatase (001) surface Eugenio Vitale,∗,† Giuseppe Zollo,∗,† Lorenzo Agosta,‡ Fabrizio Gala,† Erik G. Brandt,‡ and Alexander Lyubartsev‡ †Dipartimento di Scienze di Base e Applicate per l’Ingegneria, University of Rome “La Sapienza”, Via A. Scarpa 14–16, 00161 Rome, Italy ‡Department of Materials and Environmental Chemistry, Stockholm university, 2014 Arrhenius Laboratory, Svante Arrhenius v¨ag 16C, Stockholm, Sweden E-mail: [email protected]; [email protected] Phone: +39 (0) 6 49766947. Fax: +39 (0) 6 44240183

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Abstract Dissociative and molecular water adsorption on the anatase (001) surface is studied in the context of state of the art Density Functional Theory in large supercells suited for adsorption studies at various water coverage ratios. At low coverage values below 1/4 ML, water adsorption remains dissociative and a network of hydrogen bonds between the so formed hydroxyl groups favors the formation of a ridge surface structure. The hydroxyl patterned (4x4) surface thus undergo a (2x4) reconstruction that causes the relief of the large tensile stress measured in the unreconstructed surface along the direction orthogonal to the ridge. This phenomenology is accompanied by the loss of reactivity of the reconstructed surface with respect to the dissociative water adsorption that becomes molecular above 1/4 ML. We show, also, that the molecular adsorption on the terrace is weaker than the one on the ridge. The present water reconstruction model is discussed and compared to the well known ADM model of the reconstructed anatase (001) surface in dry environment.

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1

Introduction

The fundamental physical and chemical surface properties of Titanium Dioxide (TiO2 ) have been studied extensively for years. 1,2 TiO2 is a versatile material, which has a central role in many environment- and energy-related applications, such as the photo-decomposition of organic pollutants, solar cells, and solar-hydrogen production. 3,4 Most technological applications of this material are carried out in aqueous environment. Thus, in order to gain a better understanding of TiO2 -based devices, it is important to obtain a detailed comprehension of the atomic scale mechanisms of processes occurring at the T iO2 -water interface. 5–7 Titanium Dioxide is a polymorph crystal that shows three different crystalline phases. The metastable anatase form is known to be photocatalytically more active than the rutile phase, which is the macroscopic ground state. 8 Further, the thermodynamically most stable anatase surface, that has been widely studied in water environment, 7,9,10 is the (101) 11,12 but there is evidence that the minoritary (001) surface is more reactive than its most stable counterpart. 13,14 Indeed, during the last years the anatase (001) surface of TiO2 has received major attention due to its high photocatalytic reactivity and the fact that procedures of synthesis have been devised to obtain stable TiO2 particles with minority facets. 15–17 For this reason, many studies of TiO2 (001) surface with water adsorption have been accomplished theoretically and experimentally and many structural and electronic outcomes have been gained by their results. 6,18 In particular, while the bare (unreconstructed) TiO2 (001) surface has been predicted as a dissociative reactive surface for water absorption and, therefore, a good candidate to obtain photo-reactive water splitting for energetic purposes, the experimental results are rather controversial and do not confirm such predictions. 19–21 Moreover there are evidences that in vacuum the TiO2 (001) surface shows a (1x4) reconstruction that has been explained with the so called ADM model. 22 According to the ADM model, a TiO2 ad-molecule is employed to obtain the (1x4) surface reconstruction. However some discrepancies with the experimental results have emerged concerning the properties of the ADM reconstructed surface, especially regarding its reactivity: indeed while the ADM sur3



face is still reactive on the ridge sites, experiments show the inertness of the TiO2 (001) surface in water. This circumstance has been further investigated showing that an oxidized model could explain the inertness of this surface and that only reduced TiO2 (001) surface shows some reacivity. 23 Recently it has been argued, using large supercells in the context of atomistic modelling based on the density functional theory (DFT) 24,25 that reactivity loss on ADM reconstructed (001) surface, that is related to the strain relaxation, might be enhanced on the ADM ridge by the presence of defects such as oxygen ad-atoms and vacancies, Ti interstitials and water ad-molecules. 26 However, regarding the behavior of TiO2 (001) surface in water environment, it has been argued that water patterned TiO2 (001) surface might compete with the ADM models from the stability point of view; 21,27–29 according to the recent literature, various hypotheses have been raised concerning the water patterning of TiO2 (001) surface, namely (1x3) 27 or (1x4) reconstruction. 29 All these studies have not reached conclusive statements concerning the reconstruction of TiO2 (001) surface in water and on the strain relaxation that should be presumably the cause of the unexpected lack of reactivity found in experiments. Therefore in this article we report a systematic study on the TiO2 anatase (001) surface reconstruction in water and on its reactivity loss related to the surface stress reduction. The present study has been performed in the context of DFT with a (4x4) supercell. The supercell here considered is larger than the ones employed in the previous studies and thus is more suitable to evidence the full hydration path at various water coverage values.

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Computational Details

Calculations were performed using the plane wave pseudopotential approach within DFT theory implemented in the Quantum ESPRESSO (QE) package. 30 The generalized gradient approximation for the exchange-correlation functional was applied using the Perdew-BurkeErnzerhof (PBE) 31 functional. According to the theoretical review of Titania-water interac-

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tion by Sun et al. 6 and the tests on various different DFT functionals reported by Santra and co-workers, 32 PBE is the approximation that performs best (with respect to other, commonly used GGA exchange-correlation functionals) for the TiO2 -water system. Electron-core interactions of both oxygen and titanium are described by Ultrasoft pseudopotentials. 33 Valence states include 6 electrons for O in the 2s and 2p shells, and 12 electrons for Ti in the 3s, 3p, 3d, and 4s states. The energy cutoff values have been set at 60 Ry and 600 Ry for the wave functions and the electron density respectively. The energy threshold for self-consistency has been set at 10−8 Ry. Lastly, the Monkhorst-Pack scheme 34 is employed for k-point sampling of the Brillouin zone with a uniform mesh of 4 x 4 x 4 for bulk T iO2 , as determined by the total energy convergence test. The ground state configurations have been found relaxing at T = 0K by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) 35 algorithm, the forces being calculated with Hellmann-Feynman scheme. Each configuration was optimized until the largest component of the ionic forces was lower than 10−4 Ry/bohr and the total energy change for ionic minimization was lower than 10−8 Ry. Further, an atom-pairwise dispersioncorrected term is included in the present study through the DFT-D2 method by Grimme. 36 Generally speaking, the inclusion of a dispersion energy term should always improve the energetics because it is well known that the medium-long range interaction are neglected in standard DFT. Previous studies state how this correction generally leads to a slight shortening of the lattice constants 37,38 that, however, are still in the range of the GGA-DFT results. On the other hand and more importantly, it has been shown how dispersion influences the adsorption geometries and the binding energies of the water on TiO2 anatase (001) surface described by a GGA density functional. 39 Hence, Grimme-D2 correction is strongly recommended in order to obtain an accurate description of the weak interactions taking place at the TiO2 surface with the adsorbate. We will also discuss in the end of this manuscript how the dispersion energy is needed also to obtain a reliable prediction of the adsorption and the surface energy. The structural properties of the optimized bulk anatase TiO2 (see Fig. 1(a)), obtained

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Figure 1: a) Unit cell of TiO2 bulk; b) DOS and PDOS of TiO2 bulk. E=0 eV represents the Fermi energy level. with the described scheme and parameters, are reported in Table 1 together with the same properties obtained in previous studies. The energy gap value obtained with the present scheme is also compared with previous results and the experimental value. Concerning the electronic properties, we outline the importance of the outer O2p orbitals that almost fill the valence band (VB) whereas the 3d orbitals of Ti are mainly located in the conduction band (CB). The electronic properties (such as the band gap value) are greatly affected by the well known self-interaction problem of DFT, especially in transition metals like Ti, because of an inaccurate description of the electrons localization of d-shell elements.

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Table 1: Anatase bulk data from the present work compared to some theoretical and experimental data from the previous literature. The experimental band gap value (3.21 eV) was obtained from reflectance experiments. 41 Acronyms used are: PW (Plane-Wave basis set), PBE (Perdew-Burke-Ernzerhof functional), vdW (van der Waals dispersive term), sp (spin polarized), U (Hubbard term, in eV). Ref.

DFT scheme

a [˚ A]

c [˚ A]

Ti-Oeq [˚ A]

Ti-Oax [˚ A]

α [ deg ]

Gap [eV]

Experim. 40 This work

PW-PBE+D2

2016 38

PW-sp-PBE+D2 +U=4.2 PW-sp-PBE +D2

2010 42

PW-PBE

3.782 3.777 (−0.13%) 3.809 (+0.71%) 3.834 (+1.36%) 3.775 (−0.19%)

9.502 9.697 (+2.05%) 9.641 (+1.46%) 9.632 (+1.36%) 9.599 (+1.02%)

1.932 1.935 (+0.15%) 1.950 (+0.92%) 1.960 (+1.41%) 1.932 (−0.01%)

1.979 2.005 (+1.31%) 2.003 (+1.22%) 2.002 (+1.15%) 1.988 (+0.46%)

156.30 154.99 (−0.84%) 156.20 (−0.06%) 156.00 (−0.17%) 155.40 (−0.58%)

3.21 41 2.00 (−37.69%) 2.00 (−37.69%) 2.00 (−37.69%) 2.13 (−33.64%)

A workable approach to improve localization is the DFT+U scheme where the so-called Hubbard term is included to force the orbital occupancy to integer values. 21 In the case of bulk TiO2 that is an n-type semiconductor, the data reported in Tab.1 show quite clearly that the structural properties are sufficiently well described by the PBE+vdW DFT scheme. In the present case, however, since the electronic properties are, in principles, important to define the surface reactivity and the Hubbard term affects the electronic structure of the studied system, the potential influence of the Hubbard term cannot be totally ignored and should be evaluated. Therefore, some test calculations have been performed with U = 4.1 eV (see below) showing that the main results we draw concerning stress and surface reactivity are not affected by the inclusion of the Hubbard term. Moreover, a recent theoretical work by Selcuk and Selloni, 28 including the Hubbard term, shows that excess electrons are delocalized well below the (001) anatase surface and therefore water adsorption should be just slightly affected by the self-interaction problem. For all these reason, the the Hubbard term has been excluded from our scheme. The anatase (001) surface has been modeled through a slab geometry. The anatase bulk crystal was cleaved to expose the (001) surface. This configuration, the so called ”bulktruncated” structure, presents two surfaces made of rows of under-coordinated atoms along

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the [100] direction (Fig. 2) formed by sequences of five-fold titanium atoms (Ti5c ) and two-fold oxygen atoms (O2c ). Such under-coordinated atomic rows are the origin of the large surface energy and the larger reactivity of (001) surface with respect to other anatase surfaces. Different number of layers for this specific (001) surface have been already studied

Figure 2: Side view of the bulk-truncated configuration of the anatase (001) surface before relaxation. Red: oxygen; Grey: titanium. by other theoretical works. 26,28,38,43 Indeed, the local reorganization of the under-coordinated atoms causes a strong perturbation, which can spread into the slab along many atomic layers. Lopez et al. 44 have shown that a four layers slab is sufficient to reproduce reliably the (001) surface. In the same work it was indicated that the vacuum space should be larger than 14 ˚ A. Hence, a four layers slab is considered in the present study with a vacuum of nearly ∼40 ˚ A along the orthogonal direction to the slab surface. The vacuum region and the supercell are large enough to allow a direct comparison with MD simulations of (001) surface in bulk water 45 and to avoid spurious interactions between the periodic replicas of the system in the adjacent supercells. Moreover, the bottom layer is kept fixed at its bulk configuration position in order to reproduce the bulk behavior. Of course water is adsorbed only on the upper surface. A large surface area is preferred in order to evaluate different water coverages with a 8


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significant number of adsorption sites. For the first time, up to the authors knowledge, a (4x4) area of anatase (001) surface is considered in a systematic study of different hydrated configurations by DFT static calculations. First, the interaction between the replicas of the adsorbed water molecules is decreased by such a large surface. Second, previous works have argued that the reactivity of the anatase (001) surface might be related to the supercell size; for instance Sumita et al 46 suggested in their conclusions the evaluation of a (4x4) supercell as a further step to improve the knowledge on the properties of the anatase (001) surface. Given the large size of the slab system along all the three directions (15.10 x 15.10 x 50 ˚ A3 ), the k point mesh has been reduced to the Γ point only. The artificial electric field across the slab generated by periodic boundary conditions (PBC) is handled by a self-consistent dipole correction scheme 47 applied along the [001] direction.

3

Results

Before starting to elucidate the properties of the hydration pathways on the anatase (001) surface, it is worth to point out some aspects that are related to this tricky system. Conflicting structural properties have been reported for the anatase (001) surface with either a mirror symmetry along the [100] direction 43,48 (Fig. 3a), as in the bulk anatase crystal, or (and this is the most frequent case) an asymmetric surface with a broken mirror symmetry along [100]. 49 In this last case, the [100] surface rows are made of alternating long and short surf Ti5c -O2c bonds and both the surface angle α(T i5c −O2c −T i5c ) and the distance between the two

top-most layers (Fig. 3b) are reduced with respect to the symmetric surface. Actually, structural relaxation of the slab system have evidenced the occurrence of both the reported cases, depending on the relaxation parameters and conditions. However the case resembling the bulk structure is a symmetric surface configuration where the system may be easily trapped in. This circumstance occurs quite often if no constraints to the atoms are applied during the relaxation whereas the ground state configuration (i.e. the one with broken symmetry)

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occurs more easily when the bottom layer is kept fixed, as in the present case. A small perturbation of this symmetric configuration allows to get the ground state one in a second relaxation run, also without atomic constraints.

Figure 3: a) symmetric configuration; b) ground state configuration A valid parameter used for the analysis and comparison of the last two resulting surface configurations is the so called surface formation energy (γ). This parameter is also related to the TiO2 anatase (001) surface reactivity that, according to the recent literature, is affected by the stress relief and the stability properties of the surface. In the present case we have reformulated the surface energy definition taking into account that the atoms of the bottom layer are kept fixed to their bulk positions whereas the upper layer is relaxed to either the symmetric or the ground state configurations. Thus, first of all we have calculated the (γf ) surface energy obtained from the slab geometry with fixed top and bottom layers according to the known formula f Eslab = 2γf A + nT iO2 ET iO2

(1)

f is the total energy of the slab with fixed top and bottom layers, A is the surface where Eslab

area of one side of the slab, nT iO2 is the number of TiO2 bulk units included in the slab and ET iO2 is the total energy of one TiO2 bulk unit. Then, the upper surface energy of either

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the symmetric or the ground state configurations is obtained as follows:

Eslab = (γ + γf )A + nT iO2 ET iO2

(2)

that casts into:

γ=

f Eslab − nT iO2 ET iO2 2Eslab − Eslab − nT iO2 ET iO2 − γf = . A 2A

(3)

Using Eq. 3 we obtain γsym =1.228 J/m2 and γgs =1.107 J/m2 , respectively, for the symmetric and the ground state configurations. The optimized ground state structural values here obtained are listed in Table 2 together with the ones from previous theoretical works. Table 2: Surface and energy parameters of different theoretical works on (001) surface of the anatase phase. Acronyms used are: Nl (Number of layers), l (long), s (short), PW (Plane-Wave basis set), LO (Localized basis set), PBE (Perdew-Burke-Ernzerhof functional), vdW (van der Waals dispersive term), sp (spin polarized), U (Hubbard term, in eV), PAW (Projected augmented-wave), PW1PW (Hybrid DFT method), PBE0 (Hybrid functional). Ref.

DFT scheme

(Area)xNl

γ [J/m2 ]

(Ti5c -O2c )l [˚ A]

(Ti5c -O2c )s [˚ A]

αsurf [◦ ]

This work 2016 38

PW-PBE+D2 PW-sp-PBE+D2 +U=4.2 PW-sp-PBE +D2 PW-PBE PAW-PBE +U=4.0 LO-PW1PW PW-PBE LO-PBE0 PW-PBE PW-PBE

(4x4)x4 (2x2)x5

1.107 1.169

2.215 2.217

1.743 1.767

144.9 145.7

(2x2)x5 (3x3)x4 (3x3)x5

0.977 1.057 1.009

2.191 2.180

1.768 1.770

145.8 150.8 146.0

(1x1)xn (2x2)x4 (2x2)x6 (1x1)x6 (1x1)x4

1.362 0.977 1.270 0.900 0.900

2.233 2.245 2.218 2.200

1.742 1.713 1.750 1.760

144.9 146.0

2014 50 2014 49 2014 43 2012 51 2011 52 2008 53 2001 11

It is evident how the hybrid functionals show surface energies larger than the average. Moreover, the ground state surface energy value of the present work is larger than the other PBE calculations due to the short range dispersion term included in our calculations: in the surface energy formula, indeed, the bulk energy subtracted contains a negative dispersion term (see Eq. 11 of the original article from S. Grimme 36 ) accounting for the medium/long range 11



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interaction with the bulk material that is cut away from the slab. It can be seen, also, that the usage of the Hubbard term does not guarantee the agreement with the results found with the hybrid functionals. In any case, our data are close to the most recent ones obtained with the dispersion term and the LDA+U scheme by Lopez et al. 38

3.1

Adsorption of an isolated water molecule

As shown in Fig. 4, the water molecule exhibits a dissociative adsorption as a result of its interaction with the under-coordinated surface atoms. Indeed, the oxygen atom of water moves closer to the Ti5c atom and breaks the Ti5c -O2c surface bond. This leads to the simultaneous formation of two hydroxyl groups on the clean surface, one from the water molecule and the other one from the O2c and the dissociated proton. The two hydroxyl groups are connected by a strong hydrogen bond. Identical results were obtained starting from various different initial position of the H2 O molecule and resulting in the same final configuration and energy. Dissociative water adsorption on anatase (001) was already studied in several theoretical works 12,46,48,54 and the results of the present study are qualitatively consistent with them. However, the larger surface of the slab geometry here employed is better suited for a reliable representation of the isolated water in the relaxation process. As also highlighted by Sumita et al., 46 (3x3) wide supercells appear rather small because, along [100], two out of three Ti5c atoms are involved in dissociative water adsorption. This leaves only one Ti5c free site along the same row, a rather short distance to avoid spurious interactions between the images in the PBC context. The average water adsorption energy, calculated as,

Ea =

Ewet − Edry − nH2 O EH2 O nH2 O

(4)

where Ewet represents the total energy of the slab+water system, Edry the total energy of the bare slab, EH2 O the total energy of the single water molecule and nH2 O the number of water

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Figure 4: Dissociative adsorption configuration and relative bond lengths along [010] before/after the reaction. molecules, gives EaH2 O = −2.32 eV . We outline that the same calculation performed with the H2 O Hubbard term in the context of DFT+U gives Ea,DF T +U ≈ −2.09eV , 228 meV larger than

the bare PBE+vdW result, not really a negligible difference. However by comparing the dissociative adsorption energy of two water molecules, calculated with either the DFT+U or the bare PBE+vdW schemes (see below), with the ones reported for the isolated water, we soon discover that the stability hierarchy is negligibly affected by the usage of the Hubbard term in the present system. In any case, due to the large surface employed, the reported dissociative adsorption energy value can be considered, up to the authors knowledge, as the most accurate and reliable value of the dissociative adsorption energy of an isolated water molecule on the anatase (001) clean surface appeared so far. The value here reported is larger than the ones from previous studies and is close to the one reported for dissociative water adsorption on the ridge of (1x4) reconstructed anatase (001) surface calculated in a (4x8) surface supercell (Eads = −2.33eV ). 26 The dissociative adsorption is accompanied by a marked surface relaxation that, of course, implies a change of the surface energy. The energy of the wet surface γwet can be obtained from the one of the ground state dry surface and the water adsorption energy as 55 :

γwet = γgs + nH2 O

13

Eads A


(5)


H2 O and gives γwet = 0.944 J/m2 with a marked reduction with respect to the dry surface.

Hence, the dissociative adsorption of water implies a stabilization of the surface (as already evidenced in the literature 55 ) with the two hydroxyl groups that cause a stress relief of the dry surface, and indirectly stabilizes all the other atoms of the [100] row. In Fig. 4 it can be appreciated how the water dissociation, with the consequent surface hydroxilation, causes the reduction of the Ti5c -O2c bonds asymmetry, typical of the highly stressed ground state surface. Then the mirror plane symmetry of the bulk-truncated surface is approached with stronger Ti5c -O2c bonds.

3.2

Hydration pathway

Starting from the ground state configuration of the isolated water molecule adsorbed on the (001) surface, we have constructed, one brick at a time, the hydration pathway of the first water layer. Taking into account the supercell periodicity, the isolated water molecule case corresponds, actually, to a coverage ratio θ =

1 , 16

i.e. one molecule out of a total of

16 Ti adsorption sites. The first step was to examine a coverage of θ = 18 . Also in this case, as in the isolated water one, we have considered different starting configurations with the second water molecule placed on different sites of the (001) surface. Interestingly we obtain that water adsorption is molecular on the same [100] row of the first dissociated water molecule, while it is still dissociative elsewhere as chematically drawn in Fig. 5. Some of the configuration tested are reported in Fig. 6(a)-(c). Dissociative adsorption energies at the various sites are listed in Table 3 and evidence that the closer the second adsorption site is to the first one, the stronger is the adsorption. The molecular adsorption (Fig. 6(c)) is, of course, weaker than the dissociative ones (Figs. 6(a)-(b)). The ground state configuration is the one with the two water molecules dissociated in opposite directions (i.e. with the two hydroxyl groups along [100] in opposite directions) at two adjacent adsorption sites along the [010] direction. This configuration is stabilized also by the two hydrogen bonds between the hydroxyl groups at adjacent sites (see Fig. 14


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Figure 5: Adsorption map of the second water molecule: the green area indicates molecular adsorption, the yellow one dissociative adsorption 6(a)). The same ground state configuration has been evaluated in the context of the DFT-U 2H2 O approach. The adsorption energy obtained is Ea,DF T +U = −2.28 eV , about 213 meV larger

than the PBE result. Hence, if we consider the difference between the average adsorption energy of two and one water molecules obtained either with the PBE-vdW or the DFT+U schemes we see that they are quite close (they differ by just about 15 meV ) which means that the stability hierarchy is not affected by the usage of the Hubbard term. Therefore it is likely that the Hubbard term causes only a total energy shift at different water coverages by δE ∼0.22 eV. Then, as mentioned in the Sect. 2, an accurate description of the Ti d-shells is not necessary for our purpose and, from this point forward, we consider only the PBE+vdW scheme to study the hydration pathway.

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Table 3: Average adsorption energy values per water molecule and surface energies for all the tested configurations at different water coverages. Coverage θ=

1 16

ML

θ=

1 8

ML

θ=

3 16

ML

θ=

1 4

ML

θ=

5 16

ML

Configuration Average Adsorption Energy per molecule Surface Energy eV ( mJ2 ) Fig. 4 Fig. 6(a)-I,II Fig. 6(b)-I,II Fig. 6(c) Fig. 6(d) Fig. 6(e) Fig. 6(f) Fig. 6(g) Fig. 6(h) Fig. 6(i) Fig. 10(a) Fig. 10(b) Fig. 10(c)

-2.32 -2.49 -2.40,-2.34 -1.43 -2.52 -2.45 -1.84 -2.60 -2.51 -1.99 -2.22 -2.22 -2.17

0.944 0.757 0.757, 0.778 0.906 0.577 0.592 0.720 0.376 0.401 0.547 0.328 0.328 0.357

The adsorption energy of the last added nth water molecule,

Ea,n = nEanH2 O − (n − 1)Ea(n−1)H2 O

gives Ea,2 = −2.66 eV , markedly lower than the isolated water molecule due to the formation of the hydrogen bonds. The stabilizing effect of the hydrogen bonds can be quantified by calculating the total binding energy:

nH2 O H2 O EbnH2 O = Ewet − nEwet + (n − 1)Edry

and the binding energy of the last added molecule (n−1)H2 O

nH2 O Eb,n = Ewet − Ewet

(n−1)H2 O

H2 O − Ewet + Edry = EbnH2 O − Eb

that, in the case of n = 2 coincide and give Eb2H2 O = Eb,2 = −0.345 eV ; this value reflects

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both the hydrogen bond energy and the distortion energy 56 of the hydroxyl groups toward adjacent dissociated water along the [010] direction. The same scenario occurs when a third water molecule is added to the two waters ground state configuration. We have sampled three different initial positions and the most favored one is found to be again with the third dissociated water next to the previous two along [010], as evidenced from Fig. 6(d) (see the adsorption energy data in Table 3). Further, an hydrogen bond network forms between the dissociated waters that are oriented in opposite alternating directions and linked to the adjacent one by a hydrogen bond. We see, using the data of Table 3, that the total binding energy of this configuration is Eb3H2 O = −0.59 eV while the adsorption and the binding energies of the third water molecule are respectively Ea,3 = −2.57 eV and Eb,3 = −0.25 eV . The larger value of the binding energy with respect to the two waters case is due to the formation of just one extra hydrogen bond. Lastly we have added a fourth water molecule to the previously described ground state composed of three dissociated waters. As expected, we have obtained dissociative adsorption only along the [100] row where previous dissociated waters are absent. All the other sites revealed molecular adsorption. Once again, the ground state adsorption configuration is the one with the fourth molecule at the adjacent site to the already dissociated molecule (see Fig. 6(g)) with the hydroxyl groups oriented along opposite alternating directions. Therefore a H bond network forms that stabilizes the ground state configuration. Because the surface supercell is (4x4), the 8 hydroxyl groups made of the H2 O dissociated waters and four surface oxygen atoms, placed along the same [010] row form a ridge along the [010] direction similarly to one of the well known ADM model. In the present case, however, the advantage is that, in water environment, no mass transport is required except for the spontaneous water adsorption. We notice from Table 3 that the average adsorption energy is smaller then the one with three waters. Accordingly, we observe that the total binding energy is Eb4H2 O = −1.13 eV that is quite lower than the one for three molecules. Lastly the adsorption and the binding energies of the fourth water molecule are respectively Ea,4 = −2.85 eV and Eb,4 = −0.54 eV

17



Figure 6: Configurations of water adsorption onto T iO2 with 2 ≤ nH2 O ≤ 4. The arrows represent the orientations of the hydroxyl group along [100] that determines the topology of the hydrogen bond network along [010].

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reflecting the strong binding of the forth water that completes and stabilizes the ridge forming two extra hydrogen bonds with the adjacent sites. This water induced reconstruction has a surface periodicity of (2x4) due to the network of hydrogen bonds connecting adjacent hydroxyl groups along [010]. We have also found another ridge configuration with a (1x4) surface reconstruction where all the water molecules are dissociated along the same direction (see Fig. 6(h)). While still forming a ridge, this configuration, however, is larger in energy by nearly 100 meV per water molecule. Lastly, as expected, water is adsorbed molecularly along the [100] rows where a dissociative adsorption has already occurred (Fig.6(i)). As a further stage beyond the dissociative hydration pathway, we have added a fifth water molecule at different initial sites, either on the terrace or on the ridge. In all these cases, a molecular adsorption occurred on the water reconstructed surface (see Table 3). Accordingly the total adsorption energies rise to larger values. This effect will be extensively discussed in the next section in terms of the relation with the surface stress relief.

3.3

Reactivity loss and stress relief

The previously described hydration pathway, that results in the (2x4) reconstruction and in the ridge formation, is characterized by a marked stress relief and is accompanied by a large decrease of the surface energy (Eq. 3) as reported in Table 3. The energy of the (2x4) water reconstructed surface, indeed, is reduced to approximately one third of the dry ground state one, as shown in Fig. 7 where the energetically most favored values of Table 3 are drawn. According to that, we have focussed our attention to the stress along the [100] direction calculating the xˆxˆ component of the stress tensor, gxˆxˆ , and keeping in mind that the ground state dry surface is remarkably stressed along [100] with gxˆxˆ = -29.99 kbar. We outline that the stress obtained is nearly hydrostatic for each of the structures considered. Fig. 8 shows the xˆxˆ component of the stress tensor throughout all the different optimizations steps ranging from one to five water molecules (the insets are the optimized final configurations): an evident tensile stress decrease occurs in correspondence of each disso19



Figure 7: Adsorption and surface energies of the ground state configurations at various water coverage. For each coverage value the configuration with the lowest average adsorption energy per water molecule is considered (see Table 3). Red represents the calculated adsorption energy per water molecule (left y axis) and blue the surface energy (right y axis). ciative adsorption step. For better clarity, all the diagonal elements of the stress tensor are reported in Table 4 for the bulk anatase, the ground state surface configurations and the water reconstructed surface. The optimized bulk structure does not exhibit any stress whereas, as mentioned before, the optimized unreconstructed (001) surface displays a marked tensile stress along [100] direction and a much smaller compressive one along [010]. We see that the hydrated configuration partially releases these stresses reducing the [100] tensile stress by one third and practically halving the compressive stress along [010] with respect to ones of the ground state surface. The stress release here measured was already evidenced in the ADM model of the reconstructed (1x4) (001) surface, 22 the theoretical model that is currently accepted as the one that best describes the (1x4) reconstruction. Comparing the ADM model with our water induced reconstruction, we notice marked similarities in terms of structural and the energetic features. First of all, the computed surface energy of the reconstructed surface is γADM = 0.48J/m2 , 55 larger than the one of the water induced (2x4) reconstruction reported in the present work γ ≈ 0.376J/m2 . In addition, from the structural point of view, we can appreciate from Fig. 9 that the bond lengths in the terrace is between 1.82-.1.85 ˚ A for both of the structures with a clear tendency to recover the symmetry along

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Figure 8: Stress evolution all over the chosen 5 calculations and the related final configurations. Each color specifies the different relaxation process relative to the number of H2 O (red: O, grey: Ti, sky blue: H, dotted blue line: H-bond). the [100] direction typical of the bulk structure. In order to better evidence the role of the ridge formation in terms of the stress release, we have also reported in Table 4 its contribution as gridge = g4H2 O - gdry that is compared to the one from Shi and co-workers 26 for the ADM reconstructed surface.

Figure 9: Structural comparison between the hydrated ridge configuration (a) and the ADM model (b) 22

We observe that the optimized unreconstructed (001) surface displays a marked tensile stress along [100] and a much lower compressive stress along [010]. The stress along [010] 21



found here is markedly different from the unreconstructed surface reported in a recent paper on the ADM model: 26 in this case, indeed, large tensile stresses along both of the surface directions were found. We think that this difference might be related to the number of bottom layers that are kept fixed during the optimization: just one in our case and two for Shi and coworkers. 26 Indeed we have observed a not negligible relaxation of the third layer that, in the case of the unreconstructed surface, results in an increase of the tensile stress along [100] up to 36 GPa instead of 30 GPa (se Table 4 below). In any case we see that, in analogy with the results obtained for the ADM reconstructed surface, the hydrated configuration partially releases the stress along [100]. The water induced reconstructed surface, indeed, shows that the tensile stress reduces by one third along [100]. The moderate compressive stress along the [010] direction is halved due to the waterridge formation; in the ADM case, on the contrary, the ridge formation increases the tensile stress along [010] up to gyˆyˆ ≈ −52 kbar. Hence, while an overall contribution to the stress relief is observed in our model, the ADM ridge formation releases nearly all the stress along [100] but greatly increases it along [010]. In other words the ADM model is more efficient for the stress release along [100] but at the expense of increasing it along the ridge direction. In the hydrated model, instead, the stress is released along both the surface directions, but at a lesser extent than the ADM model along [100]. Table 4: Diagonal elements of the stress tensor for bulk-truncated surface, hydrated surface and ADM model. Tensile stress is represented by negative components. All values are in kbar. *Values taken from Shi et al. 26 gbulk [100] 0.0 [010] 0.0 [001] 0.0

gdry -30.0 5.2 0.0

g4H2 O -20.5 2.7 0.0

gridge g∗ADM −ridge 9.7 (-32.3 %) 28.5 (-95.6 %) -2.5 (-48 %) -16.6 (+46.6 %) 0.0 -

It is worth noting how, under a stress point of view, the ridge shaped by hydroxyl groups makes a valid alternative to the ADM model. Once the H2 O ridge is formed with the consequent surface stress release, the reactivity of 22


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Figure 10: The most favored molecular adsorption configurations on the reconstructed surface with a (2x4) reconstruction geometry. the surface is highly reduced because reactivity is closely related to the surface stress that, in the present case, is reduced along both the surface directions. As a consequence the water reactivity is reduced everywhere on the reconstructed surface, also along the ridge with a marked difference with respect to the results on the ADM reconstructed surface. Indeed in the present case, only molecular water adsorption occurs on the surface as shown in Fig. 10 where the adsorption configurations on the ridge and the terrace are reported. The measured adsorption energy values on the ridge are comparable with the ones also found on the (101) surface 57 (Ea,5 = −0.7 eV ) while on the terrace we have even lower values (−0.51 eV ≤ Ea,5 ≤ −0.45 eV ). Therefore the terrace sites show a weaker interaction with the surface than the molecular adsorption on the ridge because on the ridge adsorption is led by the formation of a couple of strong hydrogen bonds between the surface hydroxyl groups and the water molecule. A mixed state (dissociative and molecular) of the adsorbed water molecules occurs for coverage values larger than θ = (5/16 M L). Then, in agreement with previous studies, 13,55 water spontaneously dissociates on the (001) surface at low coverages up to a 1/4 ML in the present (4x4) supercell geometry. The so formed ridge geometry is further stabilized by a network of hydrogen bonds between the adjacent hydroxyl groups along the ridge ([010] direction). It is important to emphasize that the apparent (2x4) surface reconstruction induced by the ridge formation in the present case should be tested in terms of its stability in

23



comparison with other periodicity values along the [100] direction to clarify whether a (2x3) reconstruction is favored with respect to the (2x4) at different water coverage conditions, as predicted on the basis of (1x4) periodical systems. Then, similarly to the ADM model, stress release occurs on the reconstructed geometry. In the present case, however, further dissociative adsorption is totally inhibited so that the water reconstructed (001) T iO2 surface results inert to dissociative adsorption, even in a more pronounced way than the (101) anatase surface. On the contrary, according to recent results, 26,58 the ADM model still predicts dissociative adsorption on the ridge, up to 1.65 eV ( 58 ) or even larger, 26 that is in contrast with the experimental evidences. Due to the similarities discussed, we can title the reported surface reconstruction model as a Water Induced Reconstruction (WIR) model. As a further step, we have considered the ADM model and the interaction of this surface with water molecules both in the ridge and in the terrace sites (see Supplementary Information). It is worth to evidence that our calculation gives for the ADM model a surface energy of γADM ≈ 0.75 J/m2 that is significantly larger that the results reported in the literature of γADM ≈ 0.48 J/m2 . 55 The previous result, however, was obtained without the dispersion correction in the calculation scheme. Then we have re-calculated the same surface energy without the dispersion correction and we got γADM ≈ 0.51 J/m2 , thus basically recovering the results from the previous literature. In agreement with the past literature, the water adsorption on the ridge is strongly dissociative for the first water with an adsorption energy of Ea,1 = −3.03 eV , nearly 1 eV smaller than the one previously reported in the literature (calculated without the dispersion correction). It is important to emphasize that the adsorption energy values here considered has been calculated in vacuum. The dissociative adsorption is accompanied by a marked reduction of the surface energy with γADM +H2 O ≈ 0.54 J/m2 that, however, still remains much larger than the one obtained for the 2x4 water reconstructed surface. The adsorption at the terrace sites is molecular with −0.48 eV ≤ Ea,1 ≤ −0.23 (see Supplementary Information); after the dissociative water adsorption on the ridge, a second water is always adsorbed molecularly both at the ridge and the terrace sites sites in the

24


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adopted supercell with an adsorption energy of −0.52 eV ≤ Ea,2 ≤ −0.29 eV that is fully consistent with the adsorption energy values calculated at the terrace sites on the water reconstructed surface. Lastly we have examined the possible effect on the surface energy played by the bulk water that should be present on the surface. As we have emphasized, the calculated values are in vacuum but some role is expected to be played by the bulk water, especially concerning the dispersion energy that should be the major contribution to the total energy for the interactions involving water molecules in the reservoir and the slab. To this aim we have performed Born-Oppenheimer Molecular Dynamics run for both the bulk water and the (001) anatase- water system. A detailed description of these simulations are reported in the Supplementary Information. A key step was the measurement of the dispersion energy change in the system when a dissociative adsorption event occurs. Taking into account all the possible terms contributing to the total energy, we have estimated the correction that is needed to the above calculated adsorption energy and surface energy values due to all those terms related to the dispersion energy that arise from the interaction between the slab and the bulk water above it. The final values of the corrected average adsorption energy and surface energy values are reported in the following table Table 5: Dispersion corrected average adsorption energy and surface energy values. coverage

configuration

1 θ = 16 ML Fig. 4 1 θ = 8 ML Fig. 6(a) I, II 3 θ = 16 ML Fig. 6(d) 1 θ = 4 ML Fig. 6(g)

E’a eV/nH2 O -2.02 -2.15 -2.17 -2.24

γ0 J/m2 0.965 0.805 0.648 0.477

We see that, taking into account the dispersion energy change of the water molecules when they are adsorbed dissociatively on the unreconstructed TiO2 surface, the adsorption energy is reduced by around 300 meV and, consequently, the surface energy of the 2x4 reconstructed surface is increased to γs = 0.477 J/m2 . However the WIR model still has a 25



much lower surface energy than the ADM reconstructed surface (γADM = 0.75 J/m2 ). This circumstance still holds when one water molecule is dissociatively adsorbed on the ridge of the ADM reconstructed surface where we have γADM +H2 O = 0.54 J/m2 . A similar dispersion correction, as the one employed for the water reconstructed surface, could be employed in the ADM case with a dissociated water on the ridge. This would require a BOMD run to measure the dispersion energy change occurring in correspondence of dissociative adsorption event. In any case one can be sure that, using the same arguments are the ones detailed in the Supporting Information, such dispersion correction would further increase the surface energy of the ADM model above the value measured in vacuum, thus making the WIR model here adopted even more favored from the energetic point of view with respect to the ADM with a dissociated water.

4

Conclusions

Using an enlarged (4x4) supercell, we have revised the hydration pattern onto the unreconstructed (001) anatase surface that has been claimed to be a possible surface state in water environment. We have shown that dissociative water adsorption occurs up to 1/4 ML coverage and that the most probable hydration pathway implies the formation of a ridge-terrace reconstruction geometry similar to the reconstructed ADM model, and its modifications. A (2x4) reconstruction arises on the water patterned surface as a result of dissociative water adsorption with large adsorption energy values; after dissociation, a ridge, composed by the hydroxyl groups, is formed similarly to the well known ADM model. The stabilization of the so reconstructed surface is also enforced by the formation of an hydrogen bonds network along the ridge itself and is accompanied by a large surface stress relief in both the surface directions that induces a marked loss of reactivity on the reconstructed surface. Indeed only molecular water adsorption occurs on the reconstructed surface with adsorption energies as low as the ones on anatase (101) on the ridge and even values on the terrace. Hence, water

26


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reconstructed (001) anatase surface show an inert behavior for further water dissociation reaction and from the surface energy and stress relief point of view is a valid alternative to the ADM reconstructed surface in water environment. Further studies are required to compare, on the basis of the new (2xN) periodical surface reconstruction, the surface stability with varying N as a function of the coverage.

5

Acknowledgments

Most of the simulations were performed with resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC. Part of the computational resources were provided also by CRESCO/ENEAGRID High Performance Computing infrastructure and its staff. 59 CRESCO/ENEAGRID High Performance Computing infrastructure is funded by ENEA, the Italian National Agency for New Technologies, Energy and Sustainable Economic Development and by Italian and European research programmes, see http://www.cresco.enea.it/english for information

6

Supporting Information

Water adsorption configurations and energy values on the ADM reconstructed (001) surface; correction to the surface energy of the water reconstructed surface due to the bulk water dispersion energy.

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Figure 11: Table of Content

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Stress Relief and Reactivity Loss of Hydrated Anatase (001) Surface

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