Single oxygen vacancies of ( TiO 2 ) 35 as a prototype of reduced nanoparticle : Implication to photocatalytic activity

Please do not adjust margins a. Department of Chemistry, Sungkyunkwan University, Suwon 16419, Korea. E-mail: jinylee@skku.edu; Phone: +82-31-299-4560; Fax: +82-31-290-7075 b. Departament de Química Física & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, 08028 Barcelona, Spain. Email: francesc.illas@ub.edu; Phone: +34-93-402-1229; Fax: +34-93-402-1231 † Electronic Supplementary Information (ESI) available: See DOI: 10.1039/x0xx00000x Received 00th January 20xx, Accepted 00th January 20xx


Introduction
4][5] To use solar energy as a sustainable energy source, semiconductors for water splitting photocatalyst have to satisfy demands such as optimal band gap, low cost, nontoxicity, stability, and so on.In spite of excellent properties of TiO 2 as a photocatalytic material, its wide band gap (~ 3.2 eV) leads to low efficiency for visible light absorption.Hence many strategies have been developed to reduce the band gap by means of native defects, 6 chemical doping, [7][8][9][10] and point defects. 11-14 Among three kinds of TiO 2 polymorph (anatase, rutile and brookite), rutile is the most stable bulk phase, while most nanomaterials prefer anatase structure due to the lower surface energy of anatase phase than others.15-17   Nanoparticles (NPs) show remarkably high catalytic performance compared with bulk phase due to large surface area and quantum confinement effect.Though many results have been reported on the properties of TiO 2 systems, theoretical studies are commonly concerning about periodic bulk or surface models.Compared to TiO 2 bulk, NPs are composed of strained lattices, mixed phases or interfaces with several defects. 18On the other hand, the isolated TiO 2 clusters, Ti n O 2n (n < 17), 10, 19-21 have been investigated to compare their structures and properties with those of the bulk phases.However, the structure of clusters composed of few atoms is substantially different from that of the TiO 2 bulk and the cluster size is too small to explain the experimental observation.Thus, a systematic investigation on geometric and electronic properties of TiO 2 NPs, with enough size to maintain lattice structure and facet, different from bulk or slab surface is challenging and attractive.Our recent study revealed that the calculated cluster (TiO 2 ) 35 retained the facets found in nanoparticles studied in experiment, 22 thus clusters smaller in size than (TiO 2 ) 35 may not give electronic and optical properties of nanoparticles.Point defects such as oxygen vacancy (O v ) and titanium interstitial play an important role in photocatalytic reaction.O v , one neutral oxygen vacancy, provides two excess electrons to TiO 2 system and these electrons are responsible for the reduction of Ti 4+ to Ti 3+ .The formation of Ti 3+ species upon reduced TiO 2 were confirmed by several kinds of experimental observations, such as photoelectron spectroscopy, 23 electron paramagnetic resonance (EPR), 11 and shift in the core level binding energies. 24The defect states originating from trapped electrons appear around 1.0 eV below the conduction band minimum (CBM), which induces band gap narrowing as optimal value for photocatalyst.and polaronic nature induced by O v 37-39 using various calculation methods.However, to the best of our knowledge, the property of O v in isolated system considering the effect of This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins various oxygen sites, even in small cluster model, is not reported yet.Therefore, understanding O v in TiO 2 NPs would be interesting for applications as an efficient photocatalytic material.
The analysis of excess electron or Ti 3+ centers is important to understand O v in TiO 2 NP.From theoretical aspect, the computational methods based on density functional theory (DFT) have been chosen to describe diverse properties of many materials, but there are several serious problems that could be addressed depending on methodology.2][43][44] Owing to such kind of dispersive effect on unpaired electrons, abnormally strong delocalized solutions were obtained for reduced TiO 2 systems.Moreover, PBE functional gives underestimated band gap for TiO 2 systems.To solve these problems, usage of hybrid DFT functionals containing certain amount of Hartree-Fock exchange was suggested.Among many hybrid DFT functionals, B3LYP (20 %Fock) 45 and PBE0 (25 %Fock) 46 have been most widely used in theoretical studies.Even though hybrid functional properly described the presence of localized defect state on reduced TiO 2 , 47 these popular hybrid functionals containing high amount of HF generally give the overestimated band gap of oxide semiconductors.

48
Herein, we systemically investigate the properties of stoichiometric (TiO 2 ) 35 anatase NP and neutral single oxygen removed one.The bipyramidal (TiO 2 ) 35 NP, maintaining anatase structure after geometrical relaxation, seems to be a proper model to study the physical and electronic properties of oxygen vacancy in TiO 2 NP by comparing those of bulk and slab surface.Furthermore, the size (~ 2 nm) is also appropriate to rationalize the experimental result about TiO 2 NPs.Various oxygen vacant sites, representing the whole one, are examined according to position, coordination number (CN) and bond length with adjoined Ti.A modified PBE0 hybrid, 34 which is considered to be suitable to describe O v properties of TiO 2 bulk, is used to compare with more popular functionals (PBE and PBE0).Unlike in the bulk material, the well-ordered TiO 2 anatase structure is partially changed for relatively high surface to volume ratio and also because of the appearance of some under-coordinated atoms (Ti 4c , Ti 5c and O 1c ) in the nanoparticle.Moreover, oxygen vacancy formation energy ( ) of the particular three-coordinated facet site is surprisingly small than those on other TiO 2 systems.

Computational detail
All calculations were carried out using the first-principles electronic structure theory based on DFT using all electron numerical atom-centered orbitals that is supplied by Fritz Haber Institute ab initio molecular simulations (FHI-aims) program package. 49DFT calculations have been conducted by different hybrid functionals (the exact HF exchange is partly mixed-in with the DFT exchange) with tight grid and tier-1 basis set.We have used PBE (0 %Fock), modified PBE0 (12.5 %Fock, hereafter referred to as PBEx) 34 and PBE0 (25 %Fock)   functionals in this study.PBEx functional was a newly devised one that contains the optimal %Fock confirmed by the calculated electronic structures and physical properties for O v in TiO 2 bulk polymorphs. 34

Results and discussion
Fig. 2 shows the structures of pristine (TiO 2 ) 35 .The TiO 2 NP was basically designed as the bipyramidal anatase structure (A) that was suggested by Barnard et al. 50The initial structure was constructed by cutting {101} surface planes known to have the lowest surface energy for anatase TiO 2 polymorph.Thus, the strategy of designing NP follows the Wulff-construction method. 51There are two different optimized geometries (denoted as B1 and B2) for B of (TiO 2 ) 35 NP.B1 coincides with the optimized geometry of TiO 2 NP in previous studies, 50, 52   where titanium atoms are relaxed inwards, oxygen atoms moves outward directions, and the O 1 -Ti-O 2 is almost linear (with angle of 179.9°).However, Ti-O at both tips of B2 are bent to opposite sides (with angle O 1 -Ti-O 2 of 113.2°) and titanium and oxygen atoms are more relaxed to each direction.As a result, the height of TiO 2 NP is more shortened and the width becomes wider than B1.To the best of our knowledge, B2 was not reported yet, but it is more stable than B1 by around 1.06 eV for all the DFT functionals used.Unlike TiO 2 bulk structure, the geometry of NP would easily change to decrease the higher surface to bulk ratio.In this study, the more stable B2 is adopted as TiO 2 NP structure (B in Fig. 1).In TiO 2 anatase bulk structure, axial Ti-O bond (Ti-O ax , 2.01 Å) is longer than equatorial ones (Ti-O eq , 1.94 Å) from DFT calculation (Fig. S1), 7, 28 which is slightly longer than experimental values (1.976 Å and 1.946 Å at 15 K). 53Despite the lengths of Ti-O ax and Ti-O eq were set as 2.003 Å and 1.946 Å, respectively, in the initial geometry (A), brought from our previous study of TiO 2 anatase bulk structure, 34  Table 1 lists the calculated geometrical parameters and energy values of (TiO 2 ) 35 NP depending on the structure types (B1 and B2) and DFT functional.The structural differences between B1 and B2 are similar in all DFT functionals used, as described above.In spite of the structural similarity, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) (∆ H-L ) depends highly on the functionals, as expected.For comparison, the calculated energy values of bulk anatase TiO 2 are given in Table S1.
28, 34, 39, 66 Actually, ∆ H-L is only an approximation to the band gap and the quality of approximation is determined by the calculation methods. 546][57] Among the values of ∆ H-L , the PBEx results are analogous with the experimental band gap of bulk anatase (3.20 eV 58-60 ) and the TiO 2 NP (mixture of rutile and anatase phase; ca.3.10 eV [61][62][63] ).
Moreover, previous studies reported that optical band gap of TiO 2 nanocrystal becomes large as crystal size decrease.

27, 64, 65
Therefore PBEx functional seems to be appropriate for the DFT calculation of TiO 2 NP on the basis of the calculated ∆ H-L value.Hence, the structures and data calculated using PBEx are mainly presented for the sake of simplicity.Nevertheless, the results of PBE and PBE0 are included in the electronic supplementary information.The properties of O v in (TiO 2 ) 35 NP were investigated by one neutral oxygen atom removal from B2.Among total 70 oxygen atoms in the (TiO 2 ) 35 NP, there are 25 nonsuperimposible oxygen atoms by symmetry operation.Thus, 25 oxygen sites (marked in gray color in Fig. 2) were selected and removed one by one to examine the properties of single oxygen vacancy, which covers entire single oxygen vancancies.These vacancies were classified as tip (T), edge (E), facet (F),    2).We name each single oxygen vacant state as Xm-n where X/m designates domain type/CN, and n is sequencially numbered accoring to the distance of the removed oxygen from the center of mass.For example, F2-2 represents the oxygen vacant state where the oxygen second nearest from the center of mass and coordinated with two Ti atoms (CN=2) in facet domain was removed.The structures and energy values calculated using PBE and PBE0 functionals were presented in supporting information (Fig. S2 and S3).The spin densities are mainly distributed on d-orbital (mostly d , and partially d -y ) and the degree of localization on the neighboring Ti atoms which are reduced to Ti 3+ and the corresponding distribution of spin density varies with the functional, which is similar to previous studies.28, 38 One should warn that when fully localized solutions are involved, possible low lying electronic isomers may exist which differ in the position of the Ti 3+ cation in the NP.However, these have not been further considered here.As %Fock increases in the DFT functional (PBE < PBEx < PBE0), O v from NP results in a solution that the spin density of two excess electrons are localized in some particular parts of NP.The excess electrons would initially move to the first-neighboring titanium atoms.In most cases, the spin density distribution is shown at these adjacent titanium atoms.Excess electrons stay at the only one nearest titanium atom in T1-1.For most of the reduced NPs with O v at edge and facet domains, excess electrons remain at least one nearest Ti atom and one disperse to other Ti atoms or transferred to another firtst-neighboring Ti.The excess electrons are mainly localized at the closer Ti atoms from the vacant site among two or three adjoined Ti atoms.In all O v states generated in Inside domain and several O v states in Facet domain that result in the reduced NPs having relatively more deformed structure, electrons transfer to Ti sites at longer distance from the oxygen vacant site.The geometrical distortion concomitant with localized spin stabilization contributes to relatively high E rel and thus decrease .I3-2 has the lowest value from the PBE result, while F3-8 from the PBEx and PBE0 results.This implies that the the effect of %Fock on the properties of O v may be site dependent and highlights the importance of using a DFT method properly describing as many properties of these materials as possible.

Top view
Reorganization of the structure around the vacant space (distance to neighboring titanium atoms) and the presence of two excess electrons induced by O v would be major factors in the relaxation of the reduced TiO 2 NP.The optimized structures and the lowest sites are different depending on

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Please do not adjust margins the exchange functionals because the distribution of two excess electrons is strongly affected by the amount of nonlocal HF exchange.Table 2 lists the values of E v [eq.( 3)], E rel [eq.( 4)], [eq. ( 2)], and energy level of oxygen vacancy defect state below LUMO (S v -1 and S v -2) as calculated using PBEx functional.The data from PBE and PBE0 functionals is listed in Table S2.E v generally increases with CN regardless of functional; the sites having the highest and lowest E v are tip (T1-1) and 3-coordinated facet (PBE: F3-8, PBEx and PBE0: F3-5), respectively.However, the tendency of E rel is quite different according to the functional due to the two factors, geometrical relaxation and distribution of excess electrons, which influence relaxation of reduced NP.
The range of is 2.81 ~ 5.61 eV in PBE, 2.27 ~ 5.46 eV in PBEx and 2.05 ~ 5.12 eV in PBE0; all functionals provide a similar qualitative picture but with some remarkable differences as well.The average value (PBE: 4.19, PBEx: 4.28, PBE0: 4.16 eV) is quite close to in TiO 2 Bulk (Table S1), 28, 34, 39, 66 but it is much lower when the O atom is removed from some specific sites.This is because of the relaxation of the reduced TiO 2 system upon vacancy formation which varies depending on the features of O v site that is determined by the influence of vacant space and excess electron on surrounding titanium atoms.In the reduced anatase TiO where removal of a low (2)-coordinated oxygen requires the lowest energy.Interestingly, however, high (3)-coordinated oxygen sites have the lowest in TiO 2 NP because relaxation effect is quite large.According to the definition of in eq. ( 2), the value of decreases as the E v decreases and E rel increases.Although T1-1 is the outermost site, is quite high as 4.28 eV because of the lowest E rel (0.26 eV).The F3-8 as the most stable O v site is coincident with previous result that the subsurface O v (CN=3) is more stable than the surface O v (CN=2) in TiO 2 anatase slabs from the calculation of for different surface and subsurface sites in various TiO 2 slab models using the hybrid DFT functionals; 36 a feature which is also in agreement with experiment.17 In order to understand the reason of F3-8 site having the lowest in PBEx and PBE0 calculations, we carefully analyzed the geometrical differences between each of oxygen sites in optimized pristine TiO 2 NP.Normally, the O 3c has two short Ti-O eq (ca.1.94 Å) and one long Ti-O ax (ca.2.01 Å) in bulk anatase lattice, 7, 28 as shown in Fig. S1.However, among 14 O 3c sites, we found that, in the pristine NP, only three O 3c sites showed that Ti-O ax is shorter than two Ti-O eq .The reduced NPs with oxygen removed at these O 3c sites were shown in Fig. 4 (PBE and PBE0 results are in Fig. S5).The lengths of Ti-O ax and Ti-O eq at three sites (I3-2, F3-7 and F3-8) are listed in Table S3.At I3-2, Ti-O ax is shorter than two analogous-lengths Ti-O eq .In other words, though Ti-O ax shortens, O 3c is still symmetrically located from both side titanium atoms.In reduced TiO 2 NP, the vacant space remains after relaxation and excess electrons tend to spread to surface along nearest-neighboring titanium atoms.It was found that the spin density is localized at low-coordinated surface titanium atoms as the %Fock increases.However, more complicated structural features appear for the reduced NP with O v at F3-7 (b) and F3-8 (c).Even though these two facet sites are opposite in approximately symmetrical TiO 2 NP structure, the properties of O v are quite different.At F3-7, vacant space is maintained and excess electrons are localized at two closer titanium atoms among three nearby titanium atoms, which is similar to the results at other O 3c sites.On the other hand, at F3-8, the location of atoms surrounding O v site changes obviously and two of three adjacent titanium atoms (black spheres) form additional coordination with nearby oxygen atom.In other words, after O v formation, Ti 1 and Ti 2 are additionally coordinated with nearby oxygen atom and only Ti 3 loses 1 CN through large geometrical change.Thus, CNs of Ti 1 , Ti 2 , and Ti 3 are 5, 5, and 6 in pristine NP and 5, 5, and 5 in reduced NP, respectively.At the PBEx level of theory, one excess electron is localized at next-neighboring titanium atom and the other is delocalized at One distinct difference between F3-7 and F3-8 sites is the dangling oxygen atom bending toward F3-8; for this reason, O 3c geometry seems to be much deformed at F3-8.Thus, we argue that the relaxation of oxygen vacant structure would be affected by the geometrical singularity of pristine TiO 2 anatase NP, in which the normal O 3c structure is broken and Ti-O of both tips are asymmetrically bent to opposite sides.At F3-8 site, E rel is predominantly large, and is the lowest.In other words, F3-8 would be the most preferred O v site from thermodynamic point of view.The geometrical change and localization of spin density are consistent with polaronic effect accompanying excess electron in reduced TiO 2 surface; excess electrons by O v are localized near the surface vacant site and lattice distortion is induced in polaronic (delocalized) solution.

17, 69
The presence of Ti 3+ ions in reduced TiO 2 system was confirmed by band gap narrowing that results from the electronic structure change induced by the O v .In the aspect of redox potential, 17-like sites would be suitable for photocatalyst, but the defect states of O v sites having low (F3-8 and I3-2) are higher than OER potential.However, the correlation between O v sites and photocatalytic activity was not shown.Actually, these results are not enough to be convinced that oxygen removed TiO 2 NPs can be applied to visible light adsorbing photocatalyst for water spliting.Future work should therefore include a more systematic study of reduced TiO 2 NPs in solution, the dynamics of photoexcited state of reduced TiO 2 NPs, O v site migration behavior, and multi-oxygen vacancy effect.

Conclusions
We investigated the properties of neutral single oxygen vacancy in (TiO 2 ) 35 anatase nanoparticle focusing on the effect of the different possible vacant sites by DFT calculations using various DFT methods including hybrid functionals.Oxygen sites in (TiO 2 ) 35 are classified by position with respect to the center Please do not adjust margins Please do not adjust margins of mass, coordination number and bond length with firstneighboring Ti.We examined 25 oxygen sites that could represent whole oxygen sites under symmetry operations.Atomic and electronic structures of pristine and reduced TiO 2 nanoparticles were obtained using PBE based hybrid functionals; PBE (0 %Fock), PBE0 (25 %Fock), and newly defined PBEx (12.5 %Fock). 34Slightly differently from bulk structure, upon oxygen vacancy formation, the symmetry is broken and the two dangling oxygen atoms at both tips are bent to opposite sides due to high surface to bulk ratio and some under-coordinated atoms (Ti 4c , Ti 5c and O 1c ) in nanoparticle.The properties of oxygen vacancy in the (TiO 2 ) 35 nanoparticle depend on vacant site and %Fock of the functional used.
Oxygen vacancy formation energy and the band edge energy levels of the defect state are quite dependent on vacant sites.Energetically most favourable oxygen atom for vacancy formation from nanoparticle is high (three)coordinated one in facet domain which is in contrast with results reported for ceria nanoparticles.
67, 68 This is because the relaxation energy is largest at the particular facet site of which 3-coordinated structure with surrounding titanium atoms is broken from normal one in TiO 2 anatase system.The result predicted by the PBEx functional corresponds to HOMO-LUMO gap of pristine nanoparticle of 3.81 eV and defect state of reduced nanoparticle in the 0.47 ~ 2.06 eV range below LUMO energy level.Finally, our study shows that introducing one O vacancy in the (TiO 2 ) 35 anatase nanoparticle gives rise to significant differences in the pristine and reduced structure in comparison with bulk system.Moreover, oxygen vacancy formation energy (2.27 eV) is surprisingly small compared with that of bulk or slab surface, and the energies of defect states induced by O vacancy are close to oxygen evolution potential.These could provide an evidence of the importance of the oxygen vacancy of TiO 2 nanoparticles for efficient photocatalyst.

Fig. 1
Fig. 1 The energy diagram according to Ov calculation sequence.A is initial bipyramidal TiO2 NP (Ti35O70) modeled from TiO2 anatase bulk structure and B is the optimized geometry of A. C (Ti35O69) has the same geometry as B with one oxygen removal.D is the optimized structure of C.
the distance of terminal Ti-O 1 changed to 1.592 ~ 1.619 Å (depending on DFT functionals) and Ti-O ax becomes shorter than Ti-O eq around some 3-coordinated oxygen atoms (O 3c ) in B2 structure.The symmetry of well-ordered TiO 2 anatase structure, consisting of Ti 6c and O 2c , is broken due to some under-coordinated titanium (Ti 4c , Ti 5c ) and oxygen atoms (O 1c ) and bent Ti-O 1 at tips.

Fig. 2
Fig. 2 Pristine TiO2 NP structures are presented.Blue and red spheres denote titanium and oxygen atoms, respectively.Oxygen atoms marked in gray color represent the single oxygen vacancy site domain.
and inside (I) type depending on the position of oxygen removed.Fig. 3 displays the calculated structure of B2 and five representative sructures for single oxygen vacant Ti 35 O 69 NP that were fully optimized after single oxygen atom removal from B2.These structures have the lowest in each domain type (T, E, F, and I) of vacant oxygen atom sites depending on position and CN (Table

Fig. 3
Fig. 3 Calculated structure of B2 and five representative structures for single oxygen vacant Ti35O69 NP (D) at various Ov sites.Yellow color shows the spin density in isosurface of 0.05 e•au -3 .Blue, red, and black spheres denote titanium, oxygen and first neighbored titanium atoms to the Ov site, respectively.values in eV are also included.
2 bulk, there is only single type (3-coordinated one) of O v site and the relaxation effects were smaller than in the TiO 2 NP; 32, 34 atoms surrounding vacant site maintained pristine TiO 2 structure, and excess electrons were distributed over the three Ti atoms directly adjacent to the O V site.For comparison, dissociation energy of O 2 molecule was calculated using three functionals.The value (PBE: 6.77 eV, PBEx: 7.69 eV, PBE0: 8.62eV) increases as %Fock increases.Fig. S4 presents the changes of against vacant oxygen atom distance from center of mass.The range of , except for particulary low (F3-8) in PBEx and PBE0 results, is narrowed as %Fock increases.As % Fock decreases, the localized and delocalized characters of the excess electrons are mixed, and the range of becomes broader.Even the same (3)-coordinated oxygen atoms have led to different features when the O v is formed in the TiO 2 NP.The oxygen sites having the lowest are I3-2 in PBE, and F3-8 in PBEx and PBE0.It is worth pointing out that the situation here is different from the O v tendency in ceria (CeO 2 ) NPs 67, 68

Fig. 4
Fig. 4 PBEx calculated structures of Ti35O69 NP with oxygen removed at three O3c sites that where Ti-Oax is shorter than the two Ti-Oeq distances.The isovalue of spin density is 0.05 e•au -3 .For clarity, atoms above the dotted line were removed in top view structures.

Fig. 5
Fig. 5 Kohn-Sham orbitals energy level diagram of Ti35O69 NPs and Ti35O70.The triplet state energy levels are for spin-up eigenvalues.The dotted lines indicate the standard redox potentials for water splitting at pH = 0.The singly occupied and doubly occupied defect states are denoted in blue and green for triplet and singlet states, respectively.Other occupied and unoccupied molecular orbitals are shown in black.

Table 1
Geometrical parameters (height and width, in Å) and the energy values (in eV) of HOMO, LUMO, and HOMO-LUMO gap (∆EH-L) of B1 and B2.
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Table 2 Calculated
(PBEx)values (in eV) of vertical energy (Ev), relaxation energy (Erel), oxygen vacancy formation energy ( ), and energy level of oxygen vacancy defect state below LUMO (Sv-1 and Sv-2).All values are lined up in order of vacant oxygen atom distance from center of mass within each classification.In each classification, the lowest value words in bold type.aCN is number of first neighboring titanium atoms to removed oxygen atom.b site is designated as combination of position, CN, and the order of vacant oxygen atom distant from center of mass.
most of the reduced TiO 2 NPs.It clearly showed that the defect states exist between HOMO and LUMO level and the values of ∆ H-L and S v vary with O v site and functional.Not only ∆ H-L but also S v increased with the increasing amount of %Fock in reduced TiO 2 NPs.The range S Because molecular orbital energy levels of up-and down-spin in triplet states were very similar except for defect states, only up-spin eigenvalues are presented.The spin-unrestricted triplet state was dominantly more stable than the closed-shell singlet one in v is 0.01 ~ 0.83 eV in PBE, 0.47 ~ 2.06 eV in PBEx and 1.42 ~ 3.32 eV in PBE0 and the results of PBEx are best matched to the experimental values.The position of the HOMO and LUMO energy levels was also changed upon O v formation.These changes allow for new electronic transitions from both HOMO and defect states to LUMO, and from HOMO to defect states.For this reason, oxygen vacancy leads to bandgap narrowing of TiO 2 NPs, which would be responsible for visible light absorption.Furthermore, in comparison with the standard redox potentials for water splitting (at pH = 0), 2, 70-72 the HOMO level must be located