Water reactions on reconstructed rutile TiO_2: a DFT / DFTB approach
Filippo Balzaretti, Verena Gupta, Lucio Colombi Ciacchi, Bálint Aradi, Thomas Frauenheim, Susan Köppen
aa r X i v : . [ c ond - m a t . m t r l - s c i ] F e b Water reactions on reconstructed rutile TiO : aDFT / DFTB approach Filippo Balzaretti, ∗ , † , ‡ Verena Gupta, ¶ , ‡ Lucio Colombi Ciacchi, † , ‡ , § B´alintAradi, ¶ , ‡ Thomas Frauenheim, ¶ , ‡ , § and Susan K¨oppen ∗ , † , ‡ , § † Hybrid Materials Interfaces Group, Faculty of Production Engineering, University ofBremen, Bremen, Germany ‡ Bremen Center for Computational Materials Science, University of Bremen, Bremen,Germany ¶ Computational Materials Science Group, Faculty of Physics and Electrical Engineering,University of Bremen, Bremen, Germany § MAPEX Center for Materials and Processes, University of Bremen, Bremen, Germany
E-mail: fi[email protected]; [email protected]
Abstract
Far from being conclusively understood, the reactive interaction of water with rutiledoes still present a challenge to atomistic modelling techniques rooted on quantum me-chanics. We show that static geometries of stoichiometric TiO /water interfaces canbe described well by Density Functional Tight Binding (DFTB). However, this methodneeds further improvements to reproduce the low dissociation propensity of H O af-ter adsorption predicted by Density Functional Theory (DFT). A reliable descriptionof the surface reactivity of water is fundamental to investigate the non-stoichiometricreconstruction of the (001) facet rich in Ti interstitials. Calculations based on (DFT)predict the transition temperature for the onset of reconstruction in remarkable agree- ent with experiments and suggest that this surface, in contact with liquid water, canpromote spontaneous H O splitting and formation of H molecules. Introduction
The impact of titanium dioxide as a fundamental material for new technologies is world-wide recognized. TiO with negligible amount of impurities can be synthesized in the formof powder at very affordable prices, which has enabled its use in mass markets such ascosmetics or construction dyes. Moreover, its two main phases, anatase and rutile, are ca-pable of major photocatalytic activity under UV light irradiation, and are thus employedin process-engineering applications such as water splitting or environmental cleaning. Anatase presents a larger electronic band gap than rutile (3.20 eV vs. 3.02 eV respectively ),which is advantageous for photo-catalysis because of the lower likelihood of electron-holesrecombination. However, rutile is more stable thermodynamically, and thus offers betterresistance to high temperatures and pressures.
For this reason, the broad surface-sciencecommunity has devoted much attention to the molecular features of both anatase and rutilesurfaces, with the aim of elucidating the key structure-function relationships at the basisof their (photo)chemical properties.
Experimental information about both pristine anddefective surface features of anatase and rutile has been acquired mainly via atomic forcemicroscopy (AFM) and scanning tunneling microscopy (STM). Theoretical studies of thesurface termination in vacuum, in oxygen-rich atmospheres or in the presence of water arebased especially on Density Functional Theory (DFT).
Despite the huge progress made in the past few decades, accurate atomistic models ofTiO /water interfaces are still rare, with several contributions coming from our own work oncrystalline oxides and amorphous Ti oxidation layers. Especially the issue of surfacereconstructions, which occur for several TiO facets, still needs to be investigated in greaterdetail. However, since such reconstructions result in much larger surface primitive cells,2FT-based predictions of the dynamical behaviour of interfacial water molecules quicklybecome extremely expensive from a computational point of view.In the present work, we investigate the atomistic structure and relative thermodynamicstability of reconstructed rutile (100) and (001) surfaces, in comparison with the unrecon-structed (110), (100) and (001) surfaces. In particular, the reactivity of water on the recon-structed surfaces will be studied in both static and dynamic simulations. While most elec-tronic structure calculations and First-Principles Molecular Dynamics (FPMD) simulationswill be performed at the full DFT level, we will also test the accuracy of a slightly modi-fied set of parameters for self-consistent-charge Density Functional Tight Binding (DFTB).Especially for larger-scale TiO /water interface models, we believe that a combination ofDFT and DFTB might represent a viable path to tackle the (photo)chemical behaviour ofrealistic (nanosized) titanium oxide surfaces. This is far from being a trivial task, as the twolevels of theory shall reproduce in a satisfactory way both the structural geometries and theelectronic energies in different situations.Rutile (110) is the most stable and therefore most studied surface. It has been a longdisputed issue, up to the present day, to which extent water molecules adsorb dissociativelyor molecularly on this surface. Although some researchers assume that fully dissociativeadsorption leading to terminal hydroxyl groups is the most favourable scenario, the morewidely hold opinion is that mixed molecular/dissociative or entirely molecular adsorptiontakes place. In fact, theoretical investigations considering disordered oxide layers orkink surface sites have suggested water dissociation to be promoted only by strongly un-dercoordinated Ti sites, bound to four or less oxygen atoms, and not by five-fold coordinatedTi atoms such as those present on rutile-(110). Different studies attributed this discrepancyto the fact that the adsorption mechanism depends on two main factors: the thickness of thesimulated surface slab model and the coverage of water at the surface, with higher coveragesor bulk liquid water stabilizing molecular adsorption (fully or at least partly). In the common natural rutile powder, the (100) facet is present with a proportion of at3east 20%. At first glance, this surface looks quite different from rutile (110), although thecoordination numbers of both O and Ti surface atoms are exactly the same in the two cases.Upon annealing at more than 800 K under UHV conditions, rutile (100) tends to reconstructalong (110) microfacets presenting a 1 ×
3, 1 × × Therefore, both the smooth and reconstructed surfaces have been studiedregarding their atomic arrangement and their interaction with adsorbate molecules.
Also in this case, there has been some diatribe about water molecules adsorbing molecularlyor dissociatively, but according to the latest literature molecular adsorption should bepreferred.Due to its lower stability, only little information is available for rutile (001). However,this surface is interesting because it supports the highest electrical conductivity among otherrutile facets. First investigations on the annealing of this surface were performed alreadyabout forty years ago and then retaken into account twenty years later, in 1999, byN¨ornberg et al. In this work, the authors were able to clearly observe a (7 √ × √ R ◦ reconstruction of the surface, which was later rationalised by Fukui, Tero and Iwasawa in terms of a stairs-like model which spontaneously forms after annealing the sample at atemperature of about 1050 K. This model suggests a surface enriched with Ti interstitialatoms, presenting a Ti O stoichiometry in the primitive surface cell. Such a reconstructionwas also found to form after high-temperature epitaxial growth as well as after pulsed-laserirradiation. Recently, LEED experiments proposed a similar model for (011)-faceted rutile(001) annealed at 683 K, leading to a theoretical stoichiometric reconstructed surface which has been lately considered of main interest for the adsorption of CH OH and H Omolecules. To the best of our knowledge, no study has ever addressed the relative thermodynamicalstability and reactivity of these reconstruction models when interfaced with bulk water atthe full DFT level. These issues will be investigated in the present article, in which we alsoassess the performance of DFTB in reproducing the obtained results at a fraction of the4omputational cost.
Simulation Details
Software and Methods
In this work we employed the Vienna Ab initio Simulation Package (VASP) and the DensityFunctional based Tight Binding (and more) software (DFTB+) both for static electronicstructure calculations and geometry optimizations, and for Molecular Dynamics (MD) sim-ulations. The system geometries and trajectories were visualized with the Visual MolecularDynamics (VMD) program. The DFT calculations were performed both with the Local Density Approximation (LDA) and the Generalized Gradient Approximation with the Perdew-Burke-Ernzerhof functional(GGA-PBE), in the the framework of the Projector Augmented Wave (PAW) method. The exchange-correlation functional was extended with the zero-damping DFT-D3 methodof Grimme for all calculations including water molecules. The plane-wave cutoff energy wasset at 700 eV and the Self Consistent Field (SCF) absolute errors at 10 − eV. The k-pointsmeshes corresponded to a 3 × × All MD simulations were performed sampling the cell only atthe Γ-point, which was accurate enough for the purpose of the simulated reactions.The DFTB calculations used the Tiorg Slater-Koster file set, where the electronicpart was created using GGA-PBE, whereas the repulsive part was fitted on B3LYP energies.Because the repulsive potential in the Tiorg set has some numerical noise, we decided tosmooth it by polynomial fits. These modifications are very close to the original set, butvanish much smoother at their cutoffs. The electronic part was unchanged. The set with5he smoothed repulsion will be referred to as Tiorg-smooth. For all calculations the self-consistent charge (SCC) error was set to 10 − electrons and the forces were allowed to relaxto values below 10 − a.u. The k-points meshes were chosen as in the DFT calculations. Inorder to include Van der Waals interactions, the DFT-D3 method with zero damping wasused, setting the parameters s r, = 1 .
217 and s = 0 .
722 as provided for GGA-PBE by theMulliken Center for Theoretical Chemistry. The MD simulations were performed using a timestep of 0.5 fs, assigning the mass ofDeuterium to the H atoms. Thermalization of the systems was carried out by increasing thesystem temperature to 320 K over 1 ps by means of a Nos´e-Hoover thermostat. Afterwards,longer runs were continued in the NVE (microcanonical) ensemble.
System cells
All surface slabs were constructed starting from a 3 × × − au led tothe equilibrium lattice parameters shown in Table 1 in comparison with experimental andtheoretical references. The pristine rutile (110), (100) and (001) surfaces were obtained bysplitting the bulk crystal along the respective directions leading to slab thicknesses of at leastsix atomic planes separated by a vacuum region of at least 15 ˚A between the periodicallyrepeated slabs. During geometry relaxations only, this distance was increased up to 60 ˚A inTable 1: Lattice parameters of rutile estimated with DFT and DFTBMethod a = b cLDA 4.570 ˚A 2.931 ˚AGGA-PBE 4.663 ˚A 2.968 ˚ATiorg 4.671 ˚A 2.993 ˚ATiorg-smooth 4.677 ˚A 2.971 ˚AExp. √ × { x, y } surface plane. Thenon-reconstructed (100) and the reconstructed (100)-rec surfaces were represented by a 3 × × √ × √ { x, y } surface plane. All surfaceslabs were terminated symmetrically along the z direction to avoid formation of spuriousmacroscopic dipoles in the cell. The used models are shown in Figure 1. The fully solvatedFigure 1: Side view of the simulated rutile slab systems, in the top line (110), (100) and(001) and in the bottom line the two reconstructed models (100)-rec and (001)-rec. Redspheres refer to oxygen atoms, rose ones to titanium atoms. For the (100)-rec and (001)-recslab models, the periodic images are highlighted with brighter colors.systems were obtained by the iterative addition of H O molecules through the GROMACSbox solvation tool. The empty space in the unit cells was first filled at a standard waterdensity of 1000 g/l. MD simulations at a constant temperature of 320 K were then performedfor about 1 . Results and discussion
In the first part of this section, we will present static calculations with geometry relaxation ofall pristine and reconstructed surfaces, both regarding their energy and their electronic struc-tures. In the second part, the different reactivities of the surfaces towards water molecules,with particular attention paid to the reconstructed surfaces in contact with bulk liquid water,will be presented.
Surface structures and energies
For stoichiometric systems, the surface energy of a slab model can be calculated as γ Surf = E Slab − N Ti E Bulk
2A , (1)where E Slab is the total energy of the slab model containing N Ti atoms and E Bulk is theenergy of a bulk TiO unit. The exposed surface area is twice the area A of the { x, y } planein the surface primitive cell.As expected, γ Surf converges only slowly and with a typical oscillatory behaviour withrespect to the number of atomic layers in the slab, as shown in Figure 2. Due to the differenttruncation geometries along the z axis (see Figure 1), this behaviour is most pronouncedfor the strongly asymmetric (001) surface and barely appreciable for the perfectly symmet-ric (100) surface. The values for 12 atomic layers, reported in Table 2, are in very goodagreement with previous theoretical works both for DFT and DFTB. The correct8rder of stability, (110) < (100) < (001), is adequately described in all the different meth-ods. However, the surface energy values differ significantly depending on the used method.Figure 2: The surface energy γ surf with respect to the number of layers for the respectiverutile slab models is plotted for the (a) DFT and (b) DFTB approaches. The surfaces areindicated by different colors, namely (110) in red, (100) in blue and (001) in green withlighter nuances for the DFTB approach.Table 2: Converged values of the surface energy γ Surf in Jm for rutile-(001), (100) and (110)for the different approachesLDA GGA-PBE Tiorg Tiorg-smooth HF B3LYP (001) 1.75 1.26 1.94 1.87 2.08 1.45(100) 1.15 0.69 1.18 1.16 1.13 0.70(110) 0.89 0.53 1.14 1.05 0.92 0.46Whereas the GGA-PBE values agree well with the most precise B3LYP literature values, the LDA values are overestimated, similarly to the values predicted by pure HF. Notably,both DFTB parameter sets also overestimate γ surf in all cases, giving results that are verysimilar to LDA, despite the fact that the parametrization was performed with GGA-PBEas a reference for the attractive interactions. Among the two choices of parameter sets,the Tiorg-smooth performs slightly better, especially regarding the difference between thesurface energy of the (110) and the (100) facets.The reconstructed (100)-rec surface presents a repeated roof-like structure consistingof sharp edges and grooves faceted along the (110) and the chemically equivalent (110)directions. While the Ti atoms at the bottom of the groove are six-fold coordinated by O9toms, as in the bulk, the edges consist of rows of five-fold coordinated Ti atoms boundto bridging O atoms. During geometry relaxation, these O atoms move from their bulkposition to a symmetric position at the edge top and the edge-angle increases from 45 ◦ toabout 65 ◦ as a consequence. Overall, however, the facets maintain almost perfectly thechemical features of the (110) surface. Since the resulting exposed facet area is √ γ surf is referred to), we can expect thesurface energy of (100)-rec to be approximately √ γ surf is higher for (100)-rec than the pristine (100) facet (0.73 vs 0.69 J/m ). Experimentally, theroof-like reconstruction occurs at high temperature probably due to favourable vibrationalentropy. Regarding the different approximation levels used to compute γ surf , GGA-PBEpresents an energy ratio of 1.38, and thus a lower reactivity than LDA, for which the energyratio is exactly √
2. The Tiorg DFTB set strongly underestimates the energy ratio, whilethe Tiorg-smooth is in good agreement with the GGA-PBE value.Table 3: Surface energy values γ Surf in Jm of the (100)-rec slab model for the DFT and DFTBapproaches, listed as absolute values and in relation to the pristine (110) surface γ Surf
Ratio w.r.t. (110)LDA 1.26 1.41 ∼ . √ ∼ . √ ∼ . √ ∼ . √ The final DFT structure resembles the model proposed byIkuma et al. for rutile-(001) after annealing at 683 K, in particular regarding the flatteningof the sharp groove bottom and the presence of kinks along the (011) directions.The relaxed surface structure is evidently different for DFTB, where the interstitial Tirows moves from a sub-surface position to an ad-atom position on top of both islands,and remains coordinated by only two O atoms. Unfortunately, the available experimentalinformation does not allow us to judge whether the DFT or the DFTB predicted structureis correct. Both configurations are compatible with the LEED symmetry and with theperiodicity of the features observed in top-view with STM and AFM experiments. Hence,we carried out an analysis of the surface energies, in particular attempting a prediction of theexpected transition temperature between the pristine (001) termination and the (001)-recreconstruction.The evaluation of the surface energy for this reconstructed case shall be treated differentlythan before, since the presence of Ti interstitials leads to a surface stoichiometry equivalentto Ti O . The Ti excess can be taken into account by an ab initio thermodynamic ansatz,in which the surface is thought to be in equilibrium with an oxygen atmosphere at a certainpressure p and temperature T , in which the chemical potential of the O atoms is µ O ( T, p ) = ˜ µ O ( T, p ) + 12 k B T ln pp . (2)Here, ˜ µ O ( T, p ) is a reference O chemical potential at the standard pressure p = 1 atm,11igure 3: Optimized geometries of the (001)-rec model are plotted for the DFT and DFTBapproaches as side and top view. Only GGA-PBE (DFT) and Tiorg-smooth (DFTB) con-figurations are illustrated, as they are representative for LDA (DFT) and Tiorg (DFTB) aswell. Oxygen atoms are shown as red spheres and titanium atoms as pink ones.as tabulated in the JANAF thermochemical tables, and k B is the Boltzmann constant.Neglecting the entropy differences between the bulk and the surface system, which introducesan error of the order of only a few meV per cell for oxide systems of similar size, the surfaceenergy of the non-stoichiometric surface system including N T i
Ti atoms and N O O atomscan be expressed as: γ Surf ( T, p ) = E Slab − N Ti E Bulk + (2 N Ti − N O ) µ O ( T, p )2A . (3)The resulting γ Surf ( T ) values at a pressure p = 5 · − atm, as set in the experiments byTero et al., are reported in Fig. 4(a) for the DFT and DFTB structures shown in Fig. 3.12he constant lines correspond to the surface energies obtained with the various formalisms(GGA, LDA, Tiorg and Tiorg-smooth) for the stoichiometric, pristine (001) surface. Theintersections with the γ Surf ( T ) curves relative to the (001)-rec surface represent the predictedtransition temperatures at which spontaneous surface reconstruction occurs. Experimentally,Figure 4: (a) The surface energy γ Surf of the reconstructed (001)-rec slab model, as indicatedin Figure 3 and the pristine (001) slab model against the temperature is plotted for the DFTapproach with GGA-PBE (brown, solid line) and LDA (brown, dashed line) functionals.Results for the DFTB approach are illustrated for the Tiorg-smooth set (beige, solid line)and the Tiorg set (beige, dashed line). (b) The dependence of the surface energy γ Surf on thetemperature was calculated here using the optimized (001)-rec structure of the respectiveother methodological approach: GGA-PBE/ DFT calculation with the Tiorg-smooth/ DFTBoptimized structure (brown/solid line), LDA/ DFT with Tiorg/ DFTB (brown/ dashed line),Tiorg-smooth/ DFTB with the GGA-PBE/ DFT (beige/ solid line) and Tiorg/ DFTB withthe LDA/ DFT optimized structure (beige/ dashed line). All formation temperatures areshifted to higher values in comparision to the approaches in (a).the reconstruction was observed to take place right above 1050 K in the work of Tero etal., and at 1027 K in the work of N¨orenberg et al. These values agree remarkably wellwith the GGA-PBE prediction of 1048 K (Table 4), while the LDA prediction of 1098 K isslightly larger. Severely overestimated, instead, are the values predicted by DFTB, whichlie above 1400 K independently of the used set of parameters. In order to check whetherthe obtained structures at the two approximation levels may be trapped in local minima oftheir respective potential energy surface, the structure obtained with GGA-PBE was furtherrelaxed using DFTB, and the structure obtained by DFTB was relaxed using DFT. In bothcases, relaxation did not lead to major structural rearrangements, but the obtained total13nergies were higher than with the original models. This leads to a shift of the transitiontemperatures for the reconstruction towards larger values, as reported in Figure 4(b) and inTable 4.It has thus to be concluded that DFT, being able to predict very well the experimentallyobserved transition temperature (especially at the GGA-PBE level), most probably alsodelivers a correct atomic configuration of the reconstructed surface structure. On the otherhand, both DFTB parametrizations are not able to reproduce the correct structural andenergy features of this surface. Since the attractive part of the DFTB interaction wasparametrized on GGA-PBE calculations, most probably the source of discrepancy lies in thetwo-body repulsive interaction, which appears not to be transferable to non-stoichiometricsituations. In particular, DFTB tends to underestimate the penalty associated with thepresence of strongly undercoordinated Ti atoms (the apex Ti row in the reconstructed islandsvisible in Fig. 3), and to overestimate the penalty associated with the formation of stronglydistorted coordination shells around partially reduced Ti atoms, which is a structural featureclearly observed in DFT.Table 4: Calculated formation temperatures for the reconstruction on rutile-(001) evaluatedfrom Figure 4. Standard relaxation Reversed relaxationGGA-PBE 1048 K 1131 KLDA 1098 K 1257 KTiorg 1445 K 1601 KTiorg-smooth 1433 K 1549 K
Density of states
Before starting the investigation of the reaction of water with the surface models presentedin the previous section, it is important to gain information about their electronic structure.To this aim, we perform an analysis of the partial density of states (PDOS), limiting thestudy to the GGA-PBE functional in DFT and the Tiorg-smooth parameter set in DFTB.14he PDOS of all atoms belonging to the topmost surface layers of the three pristine surfacesare shown in Figure 5(a). The most notable difference between the two formalisms is thatDFTB predicts band gaps about 1.1 eV larger than DFT (Table 5). While underestimationof the band gap is a classic problem of DFT in the local approximation due to the self-interaction error,
DFTB corrects for this effect by adjusting the compression radii inthe repulsive part of the Slater-Koster files. Another important difference is the very steepincrease of the DOS at the valence-band edge obtained with DFTB, whereas DFT predictsa much smoother band edge. 15igure 5: Top view: (a) Density of States (DOS) provided by the surface atoms of rutile-(110), (100) and (001). Bottom view: Projected Density of States (PDOS) provided by thesurface atoms of (100)-rec (b) and (001)-rec (c). all shifted at the valence band edge (VBE).Table 5: Band gap values in eV of both the pristine and reconstructed surfaces.DFT DFTBSurface (GGA-PBE) (Tiorg-smooth) Difference(110) 1.75 2.87 1.12(100) 1.94 3.14 1.20(001) 2.18 3.26 1.08(100)-rec. 1.59 2.78 1.19(001)-rec 0.00 0.00 0.0016his difference is attributable to the larger electron density on the O atoms, whichcontribute for the largest part to the valence-band edge, whereas the Ti atoms contributemostly to the conduction-band edge above the band gap. This is exemplified for the case ofthe (100)-rec surface model in Figure 5(b). This surface does present a slightly smaller bandgap than the pristine (110) facets which terminate the surface (cf. Figure 1). Otherwise, thesame differences between the DFT and DFTB features as for the pristine facets are observed,in particular regarding the steeper onset of the valence-band edge.The electronic structure of the (001)-rec model is quite different, because the excess Tiinterstitials confer to the surface a metallic character, as shown in Figure 5(c). Here, theconduction-band edge shifts below the Fermi level, to a larger and more evident extent inDFT than DFTB. In fact, while SCC-DFTB is in principle able to describe correctly metallicsystems, both the Tiorg and Tiorg-smooth sets predicted the wrong structure and energeticsfor this particular reconstruction. However, it is not easy to determine the reason of thismismatch, as it could rather be the combination of three main factors. First, the differencein the geometry already results in different electronic structures. Secondly, the gap sizesin the two methods are not the same either and, lastly, the Slater-Koster parametrizationshould be specific for the metallic or the isolator case.
Interaction with water
We turn now to the investigation of water interacting with the surfaces both as singlemolecule and as part of a bulk liquid. Particular emphasis will be given to the abilityof the Tiorg-smooth DFTB parameter set in reproducing the GGA-PBE DFT results. Inboth cases, the calculations are corrected with the DFT-D3 dispersion term of Grimme. Static calculations at low water coverage
As a first step, single H O molecules were adsorbed on the pristine (110), (100) and (001),and the reconstructed (100)-rec surfaces. Two scenarios were taken into account: molecular17dsorption and dissociative adsorption, in line with much of the known literature.
Thefinal, optimized geometries are shown in Figure 6 and the correspondent adsorption energiesper molecule ∆ E molads = N H2O (cid:0) E slab+H O − E slab − N H O · E H O (cid:1) are reported in Table 6.Figure 6: Final geometries of the adsorption of a single water molecule on the pristine (110),(100), (001) and reconstructed (100) surface slab models are illustrated as ball and stickmodel with metallic red and pink colors for the surface oxygen and titanium atoms. Wateris colored in pure red and white balls for oxygen and hydrogen atoms. The DFT resultsrefer to GGA-PBE exchange-correlation functional calculations and the DFTB results areperformed with the Tiorg-smooth set of parameters. For each pristine surface, the molecularand dissociative adsorption mode has been analysed. Relevant distances are labeled withtheir equilibrium values.In the case of molecular adsorption, stable geometries were found in DFT on all ofthe three pristine surfaces with Ti(surf)-O(water) distances slightly larger than the usual18i(bulk)-O(bulk) value of 1.95 ˚A. The configurations were further stabilized by hydrogenbonds with adjacent O surface atoms. Comparable geometries were found in the DFTBsystems with systematically slightly shorter hydrogen bond distances, but in overall goodagreement with the DFT references. In the case of dissociative adsorption, the Ti(surf)-O(surf) of the covalently bonded OH group was even shorter than the Ti(bulk)-O(bulk)value. The corresponding proton transferred to an adjacent oxygen surface atom formeda hydrogen bond with the adsorbed hydroxyl group. This configuration was found on allof the three pristine surface models. Also in this case, DFTB reproduced the geometriesin very good agreement with DFT. The additional adsorption configuration on the (100)-rec structure, which included exclusively hydrogen bonds at the tip of the edges, is againstabilized with the same geometry in both DFT and DFTB. In this case, though, we foundthe H(water)-O(surf) distances in DFTB to be 0 . DFTB, instead, favours dissociativeadsorption in all cases apart from the pristine (100) surface. Interstingly, the ∆ E molads valuescomputed with DFTB for molecularly adsorbed water agree well with the corresponding DFTreferences, whereas the values for dissociatively adsorbed water are strongly overestimated.We believe that this inconsistency originates from two factors. First, the strength ofH-bonds is overestimated by DFTB. Therefore, configurations with larger amount of in-surface H-bonds, such as the ones rich in terminal OH groups, become over-stabilized. Infact, in the only case where molecular adsorption is favored by DFTB (the pristine (100)surface), the molecule is involved in two hydrogen bonds at once with neighbor O atoms(see Figure 6). Second, the O atoms of the surface, including those of water adsorbates that19able 6: Adsorption energies ∆ E molads (eV) of water with respect to different adsorption modesas illustrated in Figure 6 on rutile-(110), (100) and (001) as well as (100)-rec are listed. Thereported values rely either on single molecule water adsorption modes or water embedded in amonolayer configuration. The most stable configuration for each surface model is highlightedin bold. Coverage Surface Ads. mode DFT DFTB(GGA-PBE) (Tiorg-smooth)1 H O (110) Mol. -0.99 -1.00Diss. -0.82 -1.29 (100) Mol. -1.21 -1.28
Diss. -0.97 -0.94(001) Mol. -1.23 -1.46Diss. -1.09 -1.61 (100)-rec Hydr. -0.21 -0.381 ML (110) Mol. -1.11 -1.52Diss. -0.84 -1.86
Mix. -1.25 -1.56saturate Ti dangling bonds, have larger electronegativity in comparison with DFT. This wasevident by the steeper valence-band edges and larger electron density in the PDOS stemmingfrom O atoms (see Figure 5). As a result of the stronger electron donation from Ti into theO atom of the adsorbing water molecule, the O-H bonds becomes more polarized than inthe DFT case, and thus more prone to proton transfer to a neighboring O acceptor.
Molecular Dynamics in the presence of liquid water
In addition to the static calculations at low water coverage presented above, MD simulationsof bulk water in contact with the different surface models were performed. In this way,we studied which surface terminations are the most favourable in the presence of a fullydeveloped water hydrogen-bond network. The final equilibrium configurations after ther-20alization of the system and production MD runs lasting between 6 and 12 ps are shown inFigure 7.At the DFT level, only on the pristine (001) surface four out of nine chemisorbing watermolecules dissociated within 6 ps of MD. In all other systems, water adsorbed molecularlyand did not dissociate for the entire duration of the simulations up to more than 10 ps.This was true even for the pristine (110) surface, where a mixed adsorption mode is stableat the coverage of 1 ML. However, starting from this configuration in contact with liquidwater led to complete recombination of the originally dissociated water molecules within 3 ps.Typically, the adsorbed water molecules arranged in a more upright position with respectto the minimum configurations obtained with single water molecules, in order to engage inhydrogen bonds with the upper liquid water layers. In-surface hydrogen bonds were alsopresent in some cases, notably in the deep grooves of the (100)-rec surface model, wherewater molecules adsorbed on five-fold coordinated Ti atoms on one slope, forming one oreven two hydrogen bonds at once with bridging O atoms of the opposite slope (Figure 7).At the DFTB level, again a much stronger tendency to adsorb dissociatively was observed.Mixed layers including both dissociated and non-dissociated water molecules were obtainedon all systems, with the exception of the pristine (100) surface, as in the static calculations.In agreement with the behaviour observed in DFT, the adsorbed OH and OH groups readilyengaged in hydrogen bonds with the layers of liquid water above the surface, although in-surface hydrogen bonds were also observed. 21igure 7: Representative snapshots of bulk water-titania surface systems after MolecularDynamics simulations at 300 K. The surface slab model is colored in metallic red and pinkballs for the oxygen and titanium surface atoms. The first layer of water is highlighted asball and stick model with the following coloring code: molecular adsorption (purple), hy-droxylation (blue) and protonation (yellow) upon dissociation of water and hydrogen bondedwater (green). Bulk water and bulk slab models are illustrated as transparent lines. Water reactions with the reconstructed (001) surface
Particular attention was given to the reaction of the non-stoichiometric (001)-rec surfacewith water, because of two reasons. First, this system may be considered representative ofsevere reconstructions that take place either after treatment of low-Miller-index single-crystalfactes at high temperature or as the result of relaxation of high-Miller-index facets, presentfor instance in TiO powder materials. Second, the presence of excess Ti interstitials inthe system is intriguing, given the overall reduced character of the surface, which couldthus behave qualitatively similar to surfaces with Ti defects that are known to form afterinteraction of titania with UV light. Our calculations were performed only at the GGA-PBE DFT level, since DFTB was22ot able to predict the correct structure and energetics of this system (see above). Due tothe large system size, we decreased the cutoff energy to 400 eV and increased the simulationtemperature to 350 K to speed up the water diffusion in the MD production run, which lasted6 ps after thermalization. Taking into account both the top and bottom surfaces of the slabmodels, a total of 36 water molecules formed direct bonds with Ti atoms of the surface.Out of these, 24 remained adsorbed molecularly and 12 dissociated to form terminal OHgroups, saturating all dangling bonds of the fivefold and four-fold coordinated Ti atoms ofthe dry surface. Furthermore, other 21 molecules became incorporated into the first surfacehydration layers, physisorbed via hydrogen bonds to surface O atoms. All these adsorptionmodes were already observed in the static calculations (see Fig. 6).23igure 8: (a) The (001)-rec surface model is illustrated in transparent side view. Threereactive oxygen surface atoms from either the island (b) or valley positions (c, d) and thecorresponding adsorbed water molecules are highlighted as opaque ball and stick models. Theadsorption configuration mode of the water molecule is represented with the color schemeused in Figure 7. The displacements of these highlighted oxygen atoms are plotted in (b), (c)and (d), the z coordinate of which is illustrated at each time step as brown solid line. Themean height is plotted as black dashed line. All panels show a clear dragging of the respectiveoxygen atom towards the water network and the involvement of neighbored adsorbed watermolecules. The inserts indicate the starting and representative final configuration of eachdepicted oxygen surface atom. (b) The surface oxygen atom is lifted up by 2 ˚A and takesover the position of an adsorbed water molecule. (c) The surface oxygen atom is lifted upby 1 ˚A and loses a coordination number. (d) A proton flip within a chain reaction along twowater molecules leads to the formation of one hydroxyl with the surface oxygen atom and asecond surface hydroxyl upon dissociation of an initial molecular adsorbed water molecule.24he formation of a dense water layer at the surface promotes quite substantial (albeitlocal) rearrangement of the surface features, the most evident effect being the protrudingof O atoms from their original positions towards the liquid solvent. The height of these Oatoms with respect to the surface plane changes by as much as 1.5 ˚A, as shown in threerepresentative examples in Figure 8. As a result, the O atoms break one of their originalbonds with Ti atoms underneath, decreasing their coordination number from 3 to 2, andinstead become involved in direct hydrogen bonds with either chemisorbed or physisorbedwater molecules of the first hydration cell. Moreover, the transfer of a proton from oneto another acceptor site on the surface was frequently observed, in some cases proceedingvia a Grotthuss mechanism involving the adsorbed water molecules. Effectively, the protontransfers led to a redistribution of the terminal OH and OH groups over the surface, consol-idating the hydrogen-bond network in immediate surface proximity. Over the course of ourshort simulation, reactions of this kind took place especially at the bottom of the valleys, asalready observed for the (100)-rec surface, due to the high density of surface terminal groups(O, OH, OH ) and physisorbed H O molecules in those regions.Whereas only reactions involving transfers of protons between terminal sites were ob-served to occur spontaneously on the (001)-rec surface during our short MD simulation, thepresence of excess Ti interstitials may promote thermally activated redox reactions with de-velopment of H , as a consequence of direct surface oxidation by adsorbing water molecules, according to 2H O (aq) + Ti O −→ − (ads) + H + Ti O (4)To test whether such a reaction may in principle take place, we compared the total energyof the (001)-rec model with only its first hydration shell (as obtained after geometry opti-mization at the end of the MD run described above) and of three other systems in whichtwo protons were removed from adsorbed H O molecules while a H molecule was placed inthe vacuum space between the periodically repeated surface slabs (Figure 9). In the threesystems the two protons were chosen pseudo-randomly: from water adsorbed in the valleys,25n top of the islands and from the islands’ slopes.Figure 9: Three different scenarios are investigated for the process of water splitting andthe formation of molecular H upon reaction of adsorbed H O molecules on the reactivereconstructed (001) surface. The surface is shown as ball and stick model with metallicred oxygen and pink titanium atoms. The first adsorbed water layer is illustrated as smalltransparent ball and stick model, whereas the according water molecules chosen for theformation of molecular hydrogen are highlighted with the color code analogous to Figure7. From the top to the bottom water molecules are chosen in random, islands or valleypositions: (before) the chosen molecular waters before the suggested reaction turn to (after)surface hydroxyls and molecular hydrogen in its geometry optimzed configuration.Only in one case (proton removal from valley sites) the total energy after formation ofthe H molecule increased by about 0.1 eV. In the other two cases, the total energy decreased by -2.8 eV (slope sites) and -3.0 eV (islands’ top sites). After correcting those values for theGibb’s free energy of solvation of H from a reference gas state at 1 atm to bulk liquid water26t 300 K, which amounts to +6.6 kcal/mol (about +0.3 eV), a driving force of at least-2.5 eV can be estimated for the H development reaction. This suggests that water splittingwith development of hydrogen gas can be promoted by TiO surfaces in the presence ofpartially reduced Ti ions. Whether similar mechanisms play a role during photocatalyticwater splitting after UV irradiation of titanium oxide remains of course to be investigated. Conclusions
Our comparative analysis of structural and energetic features of dry and wet rutile TiO surfaces by means of DFT and DFTB shows that the latter formalism can be trusted to pre-dict structural features (cell parameters, bond length and angles) of stoichiometric systemsand static TiO /water interfaces. However, it tends to overestimate the values of surfaceenergies and the electron affinity of surface O species, even with the Tiorg-smooth parame-ter set. This, combined with the general tendency of overstabilizing hydrogen bonds, leadsto prediction of predominantly dissociated surface hydration layers, especially in unbiaseddynamical simulations, as already observed for other oxide systems such as ZnO. This is incontrast with GGA-PBE DFT, which predicts molecular adsorption to be favoured both atvery low coverages and in the presence of bulk liquid water on most of the studied interfaces.Exceptions occur in the presence of peculiar in-surface hydrogen-bonded patterns such as onthe (110) facet at the water coverage of 1 monolayer, and whenever Ti atoms are stronglyundercoordinated (fourfold or less), such as on the pristine (001) facet. A certain amountof dissociative adsorption does also occur on the most complex and so far least studiedreconstruction, namely the non-stoichiometric (001)-rec model.The investigation of chemical reactions on surfaces of such conformational and chemicalcomplexity, which can be modelled under periodic boundary conditions only with very largeunit cells and include Ti atoms with oxidation states lower than 4, would benefit very stronglyfrom the availability of accurate semiempirical formalisms such as DFTB. Unfortunately,27owever, the current parameter sets fail in predicting the correct range of thermodynamicstability of this surface and also to reproduce the structural atomic arrangement obtainedby DFT. In order to overcome the problems experienced with the Tiorg and Tiorg-smoothSK-sets, a new DFTB parametrization is being currently developed. It offers a betterdescription of the electronic part of the Ti-O interaction as it uses the more recent 3oborganic set for the description of the oxygen atoms. Additionally, it introduces three-bodyterms in the repulsive energy, resulting in an improved representation of undercoordinated Tiatoms on various TiO surfaces. Until this new parametrization is completed and validated,in the present study we are limited to the rather short simulation time (5 to 10 ps) accessibleto DFT to understand the chemical behaviour of this surface in an aqueous environment.Standard DFT does present the well-known inconvenience of strongly underestimatingthe band gap of all surface models, but is able to predict the predominantly molecular ad-sorption at very low coverage in line with all experimental findings. It also predictsthe transition temperature towards the non-stoichiometric (001) reconstruction in remark-able agreement with the available experimental literature.
We thus trust the formalismregarding its ability to predict the correct chemical behaviour of this system, which is inter-esting because of the presence of excess Ti interstitials and thus an overall reduced characterwith respect to bulk TiO .Spontaneous reactions in a liquid environment are limited to dissociative adsorption andproton-exchange among different surface sites. However, with the help of static calculationswith geometry optimization we suggest that this surface can promote the thermally-activatedsplitting of water and release of H molecules. This finding opens up the possibility thatsimilar reactions may occur during photocatalytic water splitting on TiO materials uponexposure to UV light and formation of under-oxidised Ti defects at the surface or in sub-surface sites. 28 cknowledgement This work has been supported by the Deutsche Forschungsgemeinschaft through the ResearchTraining Group 2247, Quantum Mechanical Material Modeling - QM . Computational timehas been provided by the North-German Supercomputing Alliance (HLRN). The authorsare thankful to Eric Macke for fruitful discussions. References (1) Husain, A. A.; Hasan, W. Z. W.; Shafie, S.; Hamidon, M. N.; Pandey, S. S. A review oftransparent solar photovoltaic technologies.
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Journal of Chemical Theory and Computation , , 338–35437 raphical TOC Entry Figure 10: reactive titania reconstructionslead to the formation of charged surface groupsand molecular H2