16232 DOI: 10.1021/la101359m Langmuir 2010, 26(21), 16232–16238Published on Web 06/24/2010

pubs.acs.org/Langmuir

© 2010 American Chemical Society

Modeling Localized Photoinduced Electrons in Rutile-TiO2 Using Periodic

DFTþU Methodology†

Abdesslem Jedidi,‡,§ Alexis Markovits,‡ C. Minot,*,‡ Sarra Bouzriba,‡,§ and Manef Abderraba§

‡Universit�e Pierre et Marie Curie-Paris6, UMR CNRS 7616 LCT (Laboratoire de Chimie Th�eorique), Paris,F-75005, France, and §Unit�e de Recherche de Physico-Chimie Mol�eculaire, Institut Pr�eparatoire des Etudes

Scientifiques et Techniques de Tunis, Boite postale BP51, 2070 La Marsa, Tunisia

Received April 6, 2010. Revised Manuscript Received June 7, 2010

We propose a theoretical model for photocatalytic processes on titanium dioxide, described by its most stable phaseand surface, rutile-TiO2(110). The excitation induced by light promotes electrons from the valence band to theconduction band. In this context, one important requirement is having a correct value of the magnitude of the electronicgap. The use of GGAþU or LDAþU functional with an appropriate U value allows this. The U correction has littleconsequence on the adsorption strength itself on the TiO2(110) surface. For the ground state, it only yields a slightincrease of the interaction strength of some test molecules; the surface basicity is somewhat enhanced. This is interpretedby the shift of TiO2 vacant levels. Photoexcitation is taken into account by imposing two unpaired electrons per cell ofthe same spin. The size of the cell therefore determines the number of excitations per surface area; the larger the cell, thesmaller the electron-hole surface concentration and the smaller the energy for electronic excitation. For the excitedstate, careful attentionmust be focused on the localization of the excited electron and of the hole which are crucial for thedetermination of the lowest electronic states and for the surface reactivity.We found that the excited electron is localizedon a pentacoordinated surface titanium atom while the hole is shared by two surface oxygen atoms not too far from it.The electronic levels associated to the reduced titanium atoms are low in energy; the projected density of states issuperposed onto the valence band.

1. Introduction

Among the properties of TiO2, the best known and the leaststudied by theoretician concerns its use as photocatalyst. It wasfirst recognized in 1972 for the photoelectrolysis of water on TiO2

anodes.1 Under radiation, TiO2 is capable of oxidizing organicimpurities in aqueous solution and decomposing water moleculesinto hydrogen and oxygen.2 Many studies were then carried outon TiO2 or SrTiO3(111) surfaces, for understanding how H2Ocould be an interesting source for H2 production.3-6 Somorjaiand co-workers have contributed to this effort, demonstrating,for instance, that water dissociation over TiO2 surfaces wasfavored with reduced surface Ti3þ.7 Since then, many other appli-cations have been presented,8-10 including photoelectrolysis,11

photocatalysis,12-15 and color photography.12 TiO2 is applied tothe treatment of pollutants and the chemical conversion of solar

energy;13 a wide variety of new designs are being investigated,including dye-sensitized semiconductor solar cells orGr€atzel cells.Intensive research activity recently has been prompted by the keyrole of TiO2 in the injection process in a photochemical solar cellwith high conversion efficiency.14 TiO2 is a wide band gapsemiconductor (3.05 eV for rutile and 3.18 eV for anatase) andcan only absorb about 5% of the sunlight in the ultraviolet lightregion, which substantially limits its practical application. TiO2

crystallizes in three different phases: rutile (the most stable one),anatase, and brookite. However, opinion is divided about theimportance of the specific nature of the phases; differences inchemical behavior for different phases may be large. Somorjaisuggested that the lower efficiency in the rutile phase originates inthe very fast recombination of the electron-hole pair and therelatively low amount of reactants and hydroxides attached to thesurface.16 According to Wachs et al., it could also originate fromthe preparation and impurities.15 H adsorption is structureinsensitive, being similar when relaxations of the surfaces areincluded,17 whereas H2O adsorption, molecular or dissociative,depends on the surface structure.18 Anatase was first thought tobe a better photocatalyst.19,20 The standard TiO2 powder21

contains anatase and rutile phases in a ratio of about 3:1. It hashowever been reported22 that the surface of anatase particles is

† Part of the Molecular Surface Chemistry and Its Applications specialissue.*Towhomcorrespondence should be addressed. Telephone:þ33(0)144272505.

Fax: þ33(0)144274117. E-mail: minot@lct.jussieu.fr.(1) Fujishima, A.; Honda, K. Nature 1972, 238, 37.(2) Linsebigler, A.; Lu, G.; Yates, J. T., Jr. Chem. Rev. 1995, 95, 735–758.(3) Ferrer, S.; Somorjai, G. A. Surf. Sci. 1980, 97(1), L304–L308.(4) Ferrer, S.; Somorjai, G. A. Surf. Sci. 1980, 94(1), 41–56.(5) Wagner, F. T.; Ferrer, S.; Somorjai, G. A. Surf. Sci. 1980, 101(1-3), 462–

474.(6) Somorjai, G. A. J. Met. 1979, 31(12), 146–146.(7) Lo, J. W.; Chung, Y. W.; Somorjai, G. A. Surf. Sci. 1978, 71, 199–219.(8) Diebold, U. Surf. Sci. Rep. 2003, 48, 53–229.(9) Duncan, W. R.; Prezhdo, O. V. Annu. Rev. Phys. Chem. 2007, 58, 143–184.(10) Duncan, W. R.; Craig, C. F.; Prezhdo, O. V. J. Am. Chem. Soc. 2007, 129,

8528–8543.(11) Lewis, N. S. J. Electroanal. Chem. 2001, 508, 1–10.(12) Liu, D.; Hug, G.; Kamat, P. J. Phys. Chem. 1995, 99, 16768–16775.(13) Ohno, T.; Sarakawa, K.; Matsumara, M. New J. Chem. 2002, 26, 1167–

1170.(14) O’Regan, B.; Gr€atzel, M. Nature 1991, 353, 737–740.(15) Wachs, I. E.; Saleh, R. Y.; Chan, S.; Chersich, C.CHEMTECH 1985, 756–

761.

(16) Somorjai, G. A. Chemistry in two dimensions: Surface; Cornell UniversityPress: Ithaca, NY, 1981.

(17) Bouzoubaa, A.; Markovits, A.; Calatayud, M.; Minot, C. Surf. Sci. 2005,583, 107–117.

(18) Di Valentin, C.; Tilocca, A.; Selloni, A.; Beck, T. J.; Klust, A.; Batzill, M.;Losovyj, Y.; Diebold, U. J. Am. Chem. Soc. 2005, 127, 9895–9903.

(19) Gr€atzel, M. Comments Inorg. Chem. 1991, 12, 93–111.(20) Tang, H.; L�evy, F.; Berger, H.; Schmid, P. E. Phys. Rev. B 1995, 52, 7771–

7774.(21) Ohno, T.; Sarukawa, K.; Tokieda, K.; Matsumura, M. J. Catal. 2001, 203,

82–86.(22) Bickley, R. I.; Gonzalezcarreno, T.; Lees, J. S.; Palmisano, L.; Tilley, R. D.

J. Solid State Chem. 1991, 92, 178–190.

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transformed to the rutile structure. Rutile particles with a smallsurface area are efficient for splitting water,22 which is animportant reaction to convert light energy into chemical energy.Ohtani et al.23 reported the markedly high photocatalytic activityof brookite nanocrystallites as compared to that of rutile andanatase. Koelsch et al.24 deposited brookite as a thin film from astable dispersion and proposed brookite as a good candidate forphotovoltaic devices. The rutile TiO2(110) surface is one of themost important surfacemodels formetal oxides. The perfect rutileTiO2(110) surface has been extensively studied (see, for instance,refs 2 and 25-30). The structure ismade of alternating horizontaland vertical polymers31 which makes the surface at the same timereactive and stable.2,32,33 The reconstruction is weak, contrastingwith other surfaces that form (110) facets uponheating,26,29,34 andis restricted to a small relaxation and rumpling of the bridgingoxygen atoms.27,30 The TiO2 valence band (VB) is formed byoxygen orbitals while the conduction band (CB) originates fromthe d-orbitals of the titanium atoms. The gap between the valenceand CBs of bulk TiO2 is 3.05 eV,

25,28 while the first exciton energyis 3.57 eV.A gap is also found by calculations35,36 for regular slabswith a [110] orientation preserving the stoichiometry (2.06 and1.49 eV for LDAþUandGGAþU, respectively). The adsorptionon the (110) surface is then controlled by the electron counts thatmaintain this gap.35

In this paper, we investigate the nature of the excited state of arutile TiO2(110) surface using a periodic density functional theory(DFT) approach, testing LDAþU and GGAþUmethodologies,using plane waves as implemented in the VASP code. We showthat the U correction allows a reasonable description of theexcited state provided that attention is paid to localization. Such

a model should be useful to understand the early stage ofphotocatalytic processes. To our knowledge, the only similarapproaches37,38 were done using ab initio embedded clustermethodology. The paper is organized as follows. We first presentmodels and strategy (section 2) andmethodology used (section 3).Then, in section 4, we present tests for the validity of theU correction for adsorption in the ground state, showing thatthe main results are preserved. Finally, in section 5, we discuss theresults for the excited state, focusing on the electron-holelocalization.

2. Models and Strategy

In this paper,we investigate consequences of absorbing light onthe (110) surface of rutile, clean or covered.We choose to describethe solid using periodicity, since this is more appropriate for adescription of a solid, even though an accurate methodology forexcited states such as TD-DFT is then lacking. For the rutilesurface, the ground state is a low spin state (singlet). An excitedstate is obtained by imposing a high spin state that must promotean electron from the VB to the CB. Per unit cell, this correspondsto impose two electrons with the same spin. It also creates aFrenkel exciton (hole in theVB, electron in theCB).Hereafter, wecall “excitation energy”, EE, the energy difference between thetriplet electronic state and the fundamental singlet state. In orderto describe reactivity after light absorption, we are more con-cerned by an appropriate description of the excited state afterelectronic and geometric relaxation than by excitation itself. Notethat the photon energy required for the absorption of light shouldcorrespond to a vertical transition (which does not include therelaxation of the excited state); then it should be more directlyrelated to the magnitude of the band gap. The transition shouldalso lead to a singlet state (antiferromagnetic state) that is difficultto model. Nevertheless, the triplet state (ferromagnetic) shouldnot be very different for energy and localization than the singlet.The amount of EE varies with the size of the unit cell considered.The convergence with the unit cell is therefore essential to checkand will be discussed in section 4.

The model consists of slabs of nine atomic layers (three Ti2O4

layers) of rutile oriented in the (110) direction (Figure 1).We haveused the experimental cell parameters which yield 1.9485 and1.9800 A Ti-O bond lengths.39 Theoretical results obtainedfromDFT are close to them as discussed in ref 40 (1.932/1.962 Afor LDA; 1.961/2.002 A for GGA-PW91). The U correction

Figure 1. The 110 surface of rutile with labeling of the fivefold coordinatedTi atoms and of the bridging atoms. Localization on the Ti atomsis always made on Ti0.

(23) Ohtani, B.; Handa, J.; Nishimoto., S.; Kagiya, T. Chem. Phys. Lett. 1985,120, 292–294.(24) Koelsch, M.; Cassaignon, S.; Guillemoles, F. J.; Jolivet, J. R. Thin Solid

Films 2002, 403, 312–319.(25) http://www.oxmat.co.uk/Crysdata/tio2.htm.(26) Barteau, M. A. Chem. Rev. 1996, 96, 1413–1430.(27) Charlton, G.; Howes, P. B.; Nicklin, C. L.; Steadman, P.; Taylor, J. S. G.;

Muryn, C. A.; Harte, S. P.; Mercer, J.; McGrath, R.; Norman, D.; Turner, T. S.;Thornton, G. Phys. Rev. Lett. 1997, 78, 495–498.(28) Cronemeyer, D. C. Phys. Rev. 1952, 87, 876–886.(29) Henrich, V. E. Rep. Prog. Phys. 1985, 48, 1481–1541.(30) Ramamoorthy, M.; Vanderbilt, D.; King-Smith, R. D. Phys. Rev. B 1994,

49, 16721–16727.(31) Fahmi, A.; Minot, C. Surf. Sci. 1994, 304, 343–359.(32) Minot, C. Theoretical approaches of the reactivity at MgO(100) and

TiO2(110) surfaces. In Progress in Theoretical Chemistry and Physics; ChaerNascimento, M. A., Ed.; Kluwer: Dordrecht, 2001; Vol. 7, pp 241-249.(33) Ahdjoudj, J.; Markovits, A.; Minot, C. Catal. Today 1999, 50, 541–551.(34) Firment, L. E. Surf. Sci. 1982, 116, 205–216.(35) Calatayud, M.; Markovits, A.; Minot, C. THEOCHEM 2004, 709, 87–96.(36) Vogtenhuber, D.; Podloucky, R.; Neckel, A.; Steinemann, S. G.; Freeman,

A. J. Phys. Rev. B 1994, 49(3), 2099–2103.(37) Shapovalov, V.; Stefanovich, E. V.; Truong, T. N. Surf. Sci. Lett. 2002, 498,

L103–L108.

(38) Belelli, P. G.; Ferullo, R. M.; Branda, M. M.; Castellani, N. J. Appl. Surf.Sci. 2007, 254(1), 32–35.

(39) Hyde, B. G.; Anderson, S. Inorganic Crystal Structures; JohnWilley & Sons:New York, 1989.

(40) Labat, F.; Baranek, P.; Domain, C.; Minot, C.; Adamo, C. J. Chem. Phys.2007, 126, 154703.

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contributes to a slight increase (1.995/2.001 for LDAþU; 2.01/2.03 for GGA-PW91þU). To avoid spin delocalization on thetwo opposite surfaces of the slab, we have fixed the atoms of theback face at the bulk position and saturated them by adsorptionof water molecules (OH on Ti5 and H on bridging O2, with theindices 5 or 2 indicating the atom coordination). The geometryof the three top layers was optimized. This model allows us toconsider large unit cells (small amount of excitations) and shouldbe sufficient to draw conclusions on trends. It allows spinlocalization on the unsaturated surface and improves the con-vergence of properties with the slab thickness. Note that thesaturationof the danglingbonds from the back face contributes toenlarge the energy gap for the slab (from 1.77 to 2.06 eV usingLDAþU).

3. Computational Details

We performed spin polarized calculations based on densityfunctional theory DFTþU in the local density approxima-tion, LDA, or in the generalized gradient approximation, GGA(using the PW91 exchange-correlation functional), LDAþU orGGAþU, as implemented in the VASP code,41-44 which uses aplane wave basis set (with a kinetic energy cutoff at 400 eV). Theelectron-ion interactions were described by projector augmentedwave (PAW) pseudopotentials.45 Relativistic effects were par-tially taken into account through the use of relativistic scalarpseudopotentials. The calculations were performed by samplingthe Brillouin zone in a 6 � 12� 1 Monkhorst-Pack set forthe unit cell and adapted to the cell multiplicity (6� 2� 1 for thep(1� 6) cell). The densities of stateswere computedwith the sameor denser grids. Some test calculations have been carried out forchecking the energy convergence of supercells with respect tok-points. The energies were computed within the tetrahedronmethod with Bl€ochl correction.

For the LDAþU, we first made calculations for the bulk rutilestructure with different U. The gap increases nearly linearly withU and reaches 3 eV for U = 10 eV. Similarly, this value isobtained with U= 8 eV using GGAþU. The gap is indirect; thehighest occupied molecular orbital (HOMO) is at the Γ pointwhile the lowest unoccupied molecular orbital (LUMO) is at the(0.5, 0.5, 0.) k-point. Slab calculations were done imposing thesevalues. As alreadymentioned, this leads to the presence of smallergaps: 2.06 eV (LDAþU) and 1.49 eV (GGAþU),with the surfacestates reducing the HOMO-LUMO energy difference.

The geometry optimizations were carried out until the forcesremaining on the atoms were less than 0.01 eV/A, and a dipolecorrection has been considered to minimize dipole-dipole inter-actionbetween successive slabs. The calculations being periodic inthree dimensions, a vacuumwidth of at least 10 A ensures that theinteraction between successive slabs is negligible.

We report results obtained after imposing an initial localizationof the spin. This has been performed using the MAGMOMoption in VASP. Without this option, spin is much deloca-lized; corresponding energies are much higher and results areunphysical.

The use LDAþU and GGAþU has the advantage of simpli-city. The B3LYP46,47 methodology is superior but more difficultto run with codes using plane wave basis sets; it requires the use ofatomic basis sets (or projection on such basis sets). We conductedtests using the CRYSTAL code48 that is also periodic, using thesame slabs and atomic basis set.49

4. Tests for Adsorption on the Ground State

Before studying adsorption for an excited state, we must verifythat adsorption on the ground state is well described usingLDAþU. In the comparison between reactivity before or afterexcitation, we want to be sure that the U parameter does notchange the known results without light absorption. Besides, localelectron excitation should not modify the binding of adsorbatespresent at sites that are not sites of excitation.

We have chosen to adsorb molecules on a p(1 � 2) unit cellallowing pairs of surface sites, with one being available for alocalized excitation and a possible specific photochemical process.Besides, considering a p(1� 1) unit cell would correspond later toa too large excitation concentration.

The results are shown inTable 3, and representative adsorptionmodes are shown in Figure 2. Adsorption energies are calculatedwith the formula:Eads=Esupersystem- (EsurfþEadsorbate). Accord-ing to the convention, an exothermic process has positive adsorp-tion energy.

Themain results expected for adsorption on the ground state ofthe (110) rutile surface are as follows: (i) The dominant acidiccharacter of the clean surface; molecules adsorb with the forma-tion of a dative bond to the Ti5 surface cations. The most basicmolecules are more firmly bound to Ti from the (110) surface,NH3 more than H2O (without dissociation) and much morethan CO2. (ii) GGA for the p(1� 2) unit cell gives the water

Figure 2. Adsorption on rutile TiO2: (a) dissociated water, (b) ammonia, and (c) CO2 in parallel mode (top-view).

(41) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558–561.(42) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251–14269.(43) Kresse, G.; Hafner, J. Mater. Sci. 1996, 6, 15–50.(44) Kresse, G.; Furthm€uller, J. Phys. Rev. B 1996, 54, 11169–11186.(45) Kresse, G.; Joubert, J. Phys. Rev. B 1999, 59, 1758–1775.

(46) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652.(47) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37(2), 785–789.(48) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; Zicovich-Wilson,

C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; D’Arco, P.;Llunell, M. CRYSTAL06 User’s Manual; University of Torino: Torino, 2006.

(49) Markovits, A.; Fahmi, A.; Minot, C. THEOCHEM. 1996, 371, 219–235.

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dissociation. Dissociation is controversial andmay depend on thecoverage and the presence of defects. Experimentalmeasurementshave detected surface hydroxyl groups.50,51 Theoretical studiesyield different results:water can bedissociated52-58 or not59-62 onTiO2 surfaces.

The LDA and GGA equally reproduce these features, LDAwith larger adsorption energies than GGA. A difference appearsfor the CO2 adsorption. LDA favors the mode parallel to thesurface where two O atoms are bound to the surface Ti atoms.GGA with smaller values privileges the binding of a single Oatom, leading to the perpendicular mode; in both cases, CO2

behaves as a weak base while the adsorption site for TiO2 is theacidic center.

Introducing aUcorrection shifts theTiO2 vacant levels upwardin energy; therefore, the balance between the role of Frontierorbitals is modified, making the influence of the HOMO moreimportant. It follows that the basicity of the surface O atomsincreases and that dissociation is easier. In agreement with thisanalysis, water dissociation is facilitated for the U correction (seeTable 3).

A second remark emerges from Table 3 that displays the heatsof adsorption for test molecules. All the adsorptions are largerthan those for U = 0. At first sight, this is unexpected for amolecular adsorption; indeed, if the LUMO levels (CB) areshifted toward upper energies, we should observe a decrease ofthe heats of adsorption following an increase in the energydifference of the frontier orbitals. The reason is to be found inthe ionicity of the adsorption site. On the naked surface, un-saturated Ti atoms reinforce their binding to their neighbors bydeveloping a partial covalent character for the Ti-Obondswhichimplies a certain amount of population on Ti. The U correction,effective only on the Ti orbitals, is then destabilizing. Underadsorption, the Ti cation has a larger coordination and is more

ionic. It is then less populated and the destabilization with U islower. This explains an overall increase of the heats of adsorptionwith U that was unexpected to us.

5. Results and Discussion

5.1. Excitation Energies Using Periodic DFT and Con-

vergence with the Size of the Unit Cell. We force an electronexcitation by imposing a spin state. In a rigid band model,one electron must then occupy the lowest energy level of theCB. One electron promotion per primitive cell leads to a highconcentration, since there are as many promoted electrons asthere are equivalent sites. This leads to a ferromagnetic arrange-ment. The excitation should then correspond to the promotion ofelectrons occupying the complete highest bandof theVB toa statewhere the entire lowest band of the CB is occupied. The averageenergy difference between excited and ground states is larger thanthe band gap. The lowest-energy promotion corresponds tothe band gap and a convergence to this value is expected whenthe excitation concentration decreases. Since the lifetime of theexcited state should be small, we should not expect a largeexcitation concentration. In a periodic model, we must thereforeuse a large enough cell. When the size of the unit cell increases bya factor n, the promotion affects a fraction 1/n of these bands (theupper part of the VB and the lower part of the CB). The energydifference is then smaller, and the excitation energy shoulddecrease.

In Figure 3, we display the excitation energies calculated forsingle excitation, increasing the cell size (n= 1, 6) along the [001]direction. Tests have also been performed for the p(2 � 2) andp(3� 2) cells using a GGAþU functional. The excitation energiesare the sameas those for thep(1� 4) andp(1� 6) cells of equivalentmultiplicity. The very first observation is that the results are muchmore sensitive to the U parameter than to the choice of the DFTfunctional. Indeed, EEs calculated with LDA andGGA are nearlythe same while the introduction of U induces a decrease of ∼1 eV.

Let us first note that, using LDAþU or GGAþU, the excita-tion values decrease with increasing n, that is, decrease when theconcentration of excited electrons decreases. They converge on alimit, with the convergence being reached in practice already forn=3.Note that the initial electron localization is very importantfor a correct description of the excited state. Otherwise, spin isdistributed among several surface Ti ions and the results are notphysical. The excitation energy considering localized states is∼0.87 eV, a value clearly smaller than the band gap of the slabcalculated for the ground state. This will be discussed in moredetail in section 5.2 hereafter.

In Figure 3, the dependence on n (size of the unit cell) shouldbe correlated to the interaction of the spin on neighboring sites.

Figure 3. Excitation energy (EE in eV) as a function of the cellmultiplicity, n, for the p(1� n) TiO2 slab (three layerswith saturation). Circlescorrespond to p(2 � 2) and p(2 � 3) cells; EEs are the same than for the p(1 � n) cells of the same size within 8% or less.

(50) Henrich, V. E.; Dresselhaus, G.; Zeiger, H. J.Solid State Commun. 1977, 24,623–626.(51) Pan, J.-M.;Maschoff, B. L.; Diebold, U.;Madey, T. E. J. Vac. Sci. Technol.

1992, A 10, 2470–2476.(52) Fahmi, A.; Minot, C. J. Organomet. Chem. 1994, 478, 67–73.(53) Ferris, K. F.; Wang, L.-Q. J. Vac. Sci. Technol. 1998, A 16, 956–960.(54) Goniakowski, J.; Bouette-Russo, S.; Noguera, C. Surf. Sci. 1993, 284, 315–

327.(55) Goniakowski, J.; Gillan, M. J. Surf. Sci. 1996, 350, 145–158.(56) Goniakowski, J.; Noguera, C. Surf. Sci. 1995, 330, 337–349.(57) Lindan, P. J. D.; Harrison, N. M.; Gillan, M. J. Phys. Rev. Lett. 1998, 80,

762–765.(58) Lindan, P. J. D.; Harrison, N. M.; Holender, J. M.; Gillan, M. J. Chem.

Phys. Lett. 1996, 261, 246–252.(59) Brinkley, D.; Dietrich, M.; Engel, T.; Farrall, P.; Gantner, G.; Schafer, A.;

Szuchmacher, A. Surf. Sci. 1998, 395, 292–306.(60) Casarin, M.; Maccato, C.; Vittadini, A. J. Phys. Chem. B 1998, 102, 10745–

10752.(61) Langel, W. Surf. Sci. 2002, 496, 141–150.(62) Stefanovich, E. V.; Truong, T. N. Chem. Phys. Lett. 1999, 299, 623–629.

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For the primitive cell, promotion occurs on all the Ti5 surfaceatoms and leads to a ferromagnetic spin arrangement. Comparedwith the p(1 � 6) unit cell, the single promotion for the primitive(1 � 1) cell corresponds to six successive excitations. The trendshows that successive excitations involve larger and larger EEs(the EEs are larger for small n values in Figure 3), reflecting thatan increase in the number of excitations is not energeticallyfavorable. The consideration of successive p(1� n) unit cells theninvolves the most uniform description for a given excitationconcentration without two excitations occurring at neighboringplaces: the use of the p(1 � 2) cell, corresponding to threeexcitations per p(1 � 6) cell, represents the most favorable casewhere excitations do not take place at vicinal places.5.2. Localization of Electron and Hole. Saturation of the

back face of the slab helps to localize the electron and hole on thebare surface. The holes and excited electrons within triplet struc-tures tend to be localized on the least coordinated atoms andtherefore on the bare surface. These sites are less charged anddonotrequire as much as the regular sites to be stabilized by neighboringcounterions. This is a general rule,63 with some exceptions possiblyoccurring due to the electron-hole interaction.64,65 Upon photo-excitation, the fivefold coordinated Ti4þ ions are reduced to Ti3þ

and the bridging oxygen O2- ions are oxidized to O-. Figure 4shows the spin distribution on these atoms.

Our result resembles those ofBelelli et al.38who found, accordingto M€ulliken population analysis, spin density on fivefold coordi-nated Ti and twofold bridging oxygen in the case of photoactivatedTiO2(001) anatase. They are in contrast with the conclusion ofShapalov et al.37 These authors have used an embedded cluster tomodel the rutile TiO2(110) surface, and they have found for thetriplet state that the unpaired electron is localized in two-sublayertitanium and the hole is on one-sublayer oxygen. They concludedfrom this localization that both the hole and the unpaired electronare unlikely to participate in the surface reactions.

Doubling or more the unit cell allows distinguishing bet-ween several fivefold coordinated Ti or bridging oxygen atoms.

As mentioned in the previous section, we have forced the initiallocalization of the spin on individual atoms; this spin distributionwas not always strictly maintained where it was initially imposed,and we have found some electrons switching place; however, inthe final result, we always obtained a localized spin on very fewnumber of atoms and this localization always led to a stabilizationof the excited state.

Localization for the multiple cells is always important on asingle Ti atom (see Table 1), and we call hereafter Ti0 the reducedTi atom. Then, localization onO atoms is always referred relativeto Ti0 (see Figure 1), with the index indicating the distance toTi0 (0 for the first neighbors, 1 for the second neighbors ...). Thelocalization on O is less pronounced than that on Ti0; however,there is 1 order of magnitude between the O atoms bearing thelargest spin density and the others (Table 1).

For the double unit cell, localization on the bridging O atomstakes place on O1. Localization on O0 would result in sharingthe distribution of these atoms in stripes, while localization onO1 makes two-dimensional nets. The localization splits the set ofatoms (Ti5 and bridging O) into a set of atoms with spin and a setof atoms not affected by the excitation (neither reduced noroxidized). The latter remain strongly charged and are betterconnected by nets.

For larger multiple unit cells, the localization remains similar,always occurring on O1 (and O-1 equivalent to O1). We did notsucceed to localize on a single oxygen, breaking the symmetrybetween O1 and O-1. Localization did not take place on a moredistant O for the quadruple, quintuple, or sextuple unit cells.

We present in Figures 4 and 5 the LDAþU spin distributionand the projected density of states (PDOS) curves for the triplecell in the triplet state, respectively. It is worth noticing thatspin integration shows that, with pure LDA and GGA, we donot obtain spin localization. For instance then, every surface Ti6bears some nonnegligible spin. We conclude that the use of U isnecessary.

Figure 5 shows the PDOS LDAþU curves on Ti0 and O1 forthe p(3 � 1) cell in triplet electronic state with an energy rangefrom ∼-15 to ∼-1 eV, with the Fermi level (at 8 eV) erasingthe upper part of the VB (extending from∼-13 to-8 eV). Theintegrated curve of the total DOS (not shown) shows two steps;the first one, lower in energy, is due to a large Ti contribution ofalpha spin; it corresponds to the electron that reduces thepentacoordinated Ti surface site. The unpaired electron onTi corresponds to a broad PDOS peak overlapping the valenceband mostly made of the 2p(O) orbitals. The other step, closeto the Fermi energy, corresponds to the PDOS on O1 forthe main part and corresponds to the unmatched electron ofthe hole. The hole itself is visible on the beta peak just above theFermi level.

The DOS analysis makes understandable why the EEs forLDAþU (GGAþU) are not larger than those for LDA (GGA),although the introduction of U enlarges the magnitude of theelectronic band gap: the electron of reduction on Ti0 is not a statein the gap that poorly detaches from the VB; it is significantlystabilized below the top of the VB. On the contrary, the Fermilevel separates the two spin components of the hole.

Figure 4. LDAþU spin density isosurface distribution for thephotoactivated TiO2 surface (one excitation per primitive cell).(a) Top view of p(1� 3). Spin is shown in yellow. (b) Side view ofp(1 � 1). Saturation of the face below (red labels) allows localiza-tion on the face above. Electrons are on the fivefold coordinated Tiatoms, and holes are on the bridging oxygen atoms.

Table 1. Main Contributions to the Spin Density for the Different

p(1 � n) Cells Calculated by Integration of the Spin Density

cell double triple quadruple quintuple sextuple

Ti0 0.992 0.984 0.982 0.932 0.983O1 þ O-1 0.463 0.470 0.396 0.356 0.357O0 0.096 0.036 0.037 0.004 0.002

(63) Nakamura, R.; Okamura, T.; Ohashi, N.; Imanishi, A.; Nakato, Y. J. Am.Chem. Soc. 2005, 127, 12975–12983.(64) Qu, Z.-w.; Kroes, G.-J. J. Phys. Chem. B 2006, 110(18), 8998–9007.(65) Qu, Z.-w.; Kroes, G.-J. J. Phys. Chem. C 2007, 111, 16808–16817.

DOI: 10.1021/la101359m 16237Langmuir 2010, 26(21), 16232–16238

Jedidi et al. Article

We have also performed two periodic calculations with loca-lized basis sites described in ref 66 using the CRYSTAL code andHartree-Fock and B3LYP46,47 methodology. The geometry ofthe atoms of the slab is frozen at their bulk position. The DOSobtained are similar to those of the LDAþU or GGAþU results.The EEs calculated using Hartree-Fock and B3LYP metho-dologies are 1.62 and 0.75 eV, respectively. These values arenoticeably smaller than the gap calculated for the slab: 8.3 eV,overestimated by Hartree-Fock, and 1.9 eV using B3LYP thatprovides a value close toLDAþU.A rigid bandmodel is thereforean oversimplified view of the excited slab, and the LDAþU andGGAþU methods correctly describe the surface after excitation.

Let us add that we also investigated the DOS for the DFTcalculationswithoutU.A spin polarization occurs at theFermi levelgiven what is indicated on the output. However, a careful attentionto theDOSdoes not give confidence to this result: the electron countwhere the spin polarizationoccurs is less than it should be. The exactelectron count corresponding to a small increase shifts the Fermilevel into the gap where no polarization occurs. Calculations there-fore failed to give a correct description of an excited state.

The excitation induces a modification of the geometry atthe excitation sites. Vertical relaxations are displayed in Table 2.

The atoms bearing the spin (electron or hole) always moveoutward toward the surface. Several explanations are consistentwith these relaxations. These atoms, that are always surface ions,have the smallest charges and thus can be less bound than theothers, since large charges have to be balanced by interactionwithneighboring ions of opposite charge. In terms of orbitals, Ti3þ

should be hybridized to accommodate an electron, with the4s contribution being stabilizing. As a result, the odd electronoccupies a dangling bond emerging from the surface available toreact with an appropriate radical species.

6. Conclusion

We have proposed a model in order to study photocatalysisinvolving the use of a periodic slab representing the TiO2(110)surface of the rutile phase and the DFTþU methodology.

We first carried out some tests on adsorption showing thatU functionals do not affect the adsorption modes when adsorp-tion is thermal. Only small differences appear; the dominantsurface character is still acidic but it is reduced. Indeed, thevacant levels, mainly associated with surface Ti, are shifted andthe role of frontier orbitals is changed: the influence of theHOMO is increased. From a quantitative point of view, all theinteraction strengths are increased. The introduction of theU parameter, when calculating adsorption energies, destabilizesmore the clean surface, that is, the reference, than the surfacewith an adsorbate.

In order to model the excited state after excitation inducedby light absorption, we imposed two electrons of the same spinper unit cell. At variance with DFT without U, the use of theLDAþU or GGAþU functional provides a reasonable des-cription. It permits reproduction of the experimental electronicgap magnitude which is required in this approach. In a rigidband model, an electron is supposed to be promoted from thevalence band (mainly located on surface oxygen), where a holeis created, to the conduction band (mainly with titaniumcharacter). However, the rigid band model then appears asoversimplified. The stabilization of the reduced Ti atom isstrong, reducing the excitation energy to a value that is smallerthan the band gap.

Localization of the electron has to be carefully considered. Theunpaired excited electron is on a single surface pentacoordinatedtitanium atom, and holes are on the two surface O atoms whichare second neighbors to the titanium.

Figure 5. LDAþUDOS for the triple cell. Projected density of states onTi0 (full line) andO(1 (dotted line). Both of theunpaired electrons liebelow the Fermi level. Our results are in contrast with a rigid bandmodel where an unpaired electron is transferred from the valence band tothe conduction band.

Table 2. Relaxation Occurring at the Surface under Electron

Excitationa

cell double triple quadruple quintuple sextuple

z(Ti1)-z(Ti0) 0.07 0.07 0.07 0.08 0.09z(O1)-z(O0) 0.060 0.025 0.025 0.016 0.016

aThe vertical displacements (outward) are in angstroms (A).

Table 3. Adsorption Energy (eV) on the p(1 � 2) Unit Cell for the

Ground State (eV)a

CO2 H2O NH3

parallel perpendicular molecular dissociated molecular

LDA 0.51 0.31 1.16 1.33 1.47

LDAþU

(U = 10 eV)

0.64 0.59 1.49 1.99 1.83

GGA 0.13 0.23 0.71 0.84 0.97

GGAþU

(U = 8 eV)

0.16 0.15 0.97 1.39 1.26

aA positive value corresponds to an exothermic process.

(66) Markovits, A.; Ahdjoudj, J.; Minot, C. Surf. Sci. 1996, 365, 649–661.

16238 DOI: 10.1021/la101359m Langmuir 2010, 26(21), 16232–16238

Article Jedidi et al.

The concentration of hole-electron pairs on the surfacedepends on the size of the unit cell. A small cell yields a highconcentration, while a very large cell decreases it. The excitationenergy decreases with increasing size of the cell and quicklyreaches a limit.

Acknowledgment. The authors thank Dr. Ilaria Ciofini,Prof. Carlo Adamo, and Prof. Michel Van Hove for fruitfuldiscussions. Bilateral agreements between France and Tunisiaare acknowledged for their support (PHC-Utique, CMCUn�09G1212).