Oxygen Vacancies in Oxide Nanoclusters: When Silica Is More Reducible Than Titania

Oxygen vacancies are related to specific optical, conductivity and magnetic properties in macroscopic SiO2 and TiO2 compounds. As such, the ease with which oxygen vacancies form often determines the application potential of these materials in many technological fields. However, little is known about the role of oxygen vacancies in nanosized materials. In this work we compute the energies to create oxygen vacancies in highly stable nanoclusters of (TiO2)N, (SiO2)N, and mixed (TixSi1−xO2)N for sizes between N = 2 and N = 24 units. Contrary to the results for bulk and surfaces, we predict that removing an oxygen atom from global minima silica clusters is energetically more favorable than from the respective titania species. This unexpected chemical behavior is clearly linked to the inherent presence of terminal unsaturated oxygens at these nanoscale systems. In order to fully characterize our findings, we provide an extensive set of descriptors (oxygen vacancy formation energy, electron localization, density of states, relaxation energy, and geometry) that can be used to compare our results with those for other compositions and sizes. Our results will help in the search of novel nanomaterials for technological and scientific applications such as heterogeneous catalysis, electronics, and cluster chemistry.


INTRODUCTION
Metal oxides are an important class of materials in many scientific and technological fields. Silica and titania are abundant compounds and play crucial roles in geology (Howie, 1964;Lakshtanov et al., 2007;Lyle et al., 2015), astrochemistry (Lambert et al., 2012;Lee et al., 2015;Komatsu et al., 2018), environmental and chemical sciences (Joo et al., 2014;Kapilashrami et al., 2014), biology and medicine (Mal et al., 2003;Nguyen et al., 2005;Das et al., 2009;Bawazer et al., 2012;Lucky et al., 2016;Saroj and Rajput, 2018). Their ability to exchange oxygen drastically determines their properties. In the case of TiO 2 , the loss of lattice oxygen results in a change of color from white to blue, the appearance of magnetism, and is connected with photocatalytic properties (Houlihan et al., 1975;Diebold, 2003;Di Valentin et al., 2006;Na-Phattalung et al., 2006;Vásquez et al., 2016;Li et al., 2018). On the other hand, oxygen vacancies present in amorphous silica have been reported to modify its electronic and optical properties (Rudra and Fowler, 1987;Skuja, 1998;Manveer et al., 2017). Oxygen substoichiometry in silica-based materials is linked to dielectric breakdown and electroforming in resistive random access memory devices (McPherson and Mogul, 1998;Yao et al., 2010;Wang et al., 2014;Mehonic et al., 2018). Whereas, the effect of creating an oxygen vacancy in bulk and surfaces of both titania and silica is well-reported, little is known about the role these defects may play in nanosized materials and clusters. By means of density functional theory (DFT) based calculations, we characterise the energetics of creating an oxygen vacancy in silica, titania and titanosilicate clusters recently derived from global optimization studies. Low energy clusters can be generated with cluster beam experiments and stabilized by soft landing techniques. Such studies are increasingly looking into the reactivity of the cluster species formed for technologically important reactions (Yin and Bernstein, 2014;Vajda and White, 2015;Sun et al., 2016). With our work we hope to elucidate the reactivity of such nanoclusters as estimated through their reduction by oxygen removal.
From a computational point of view, the energetic cost of removing a neutral oxygen atom from a stoichiometric metal oxide can be calculated with the following equation: (1) A reducible oxide like titania tends to have small (positive) E vac values, while the energy to form an oxygen vacancy in an irreducible oxide like silica is relatively higher. E vac values can thus be used to compare different systems and provide an initial ranking of reducibility (Ganduglia-Pirovano et al., 2007;Deml et al., 2015;Helali et al., 2017). Typical values for bulk and surface E vac values in rutile and anatase TiO 2 are 3.7-4.5 eV whereas for SiO 2 the values are much higher, 5-8 eV (see Sushko et al., 2005). In addition, the localization of the electrons remaining after the removal of the oxygen in the lattice provides crucial information related to the electronic structure of the defective material (Helali et al., 2017): It is commonly accepted that removing an oxygen atom from TiO 2 leads to the formation of paramagnetic Ti 3+ sites in both bulk and surfaces (Houlihan et al., 1975;Di Valentin et al., 2006;Li et al., 2018). The electronic state of reduced titania systems is typically open-shell. In amorphous SiO 2 and quartz the removal of a lattice oxygen results in the formation of a Si-Si covalent bond where the electron pair is stabilized by two Si sites (Sushko et al., 2005). In the quartz surface the removal of an oxygen atom leads to an electron pair localized on a surface silicon site (Silvi and D'Arco, 2006;Causà et al., 2015). This typically leads to electronic states that are closed-shell. We focus on the effects that the system size reduction to the nanoscale has on the type of oxygen defects exhibited and their resultant E vac values. As has been previously reported for ZrO 2 (Ruiz Puigdollers et al., 2016a,b), CeO 2 (Kozlov et al., 2015), TiO 2 (Morales- García et al., 2018), this may result in a significant change in the materials' properties. Specifically, in this work we investigate the energetic, structural and electronic properties of silica, titania and mixed titanosilicates as regards their tendency to lose neutral oxygen atoms. These properties are then compared between the different oxides and with respect to the system size, including up to the bulk. At the nanoscale level, we consider a set of globally optimized silica and titania clusters with sizes between 2 and 24 MO 2 units. Moreover, we compare our results for these pure oxides with a comparative set of titanosilicate clusters for the size of 10 MO 2 units. At the bulk level, we consider alpha quartz and rutile phases, respectively, for silica and titania, which are the two most stable phases under ambient conditions. Such systems are then reduced by a single and neutral oxygen vacancy and the results are analyzed to elucidate the role of cluster size, structure and oxide type with respect to the formation of oxygen vacancies.

METHODOLOGY
All nanocluster structures selected in this study correspond to the lowest energy global minima candidates currently reported in the literature as derived by us and/or other authors: SiO 2 systems are derived from Bromley (2003, 2004), Lu et al. (2003), Bromley and Flikkema (2005) Cuko et al. (2018). A two-step procedure is followed to compute E vac (Equation 1): (i) a selected oxygen atom is removed from a structurally frozen stoichiometric nanocluster and the pre-removal/post-removal energy difference is defined as E unrel , (ii) the post-removal non-stoichiometric nanocluster structure is then fully optimized, with the pre-optimized/post-optimized energy difference defined as E vac . The relaxation energy E rel is then derived as the difference between E unrel and E vac . For the smaller sizes, N = 2-10, every symmetrically distinct oxygen site was tested and only the most representative ones were reported. For larger sizes, an exhaustive approach was found to be too computationally demanding and a sampling of approximately 10 oxygen sites was performed, always including all symmetrically non-equivalent terminating oxygens. All DFT based calculations involving reduced nanoclusters were carried out using a spinpolarized formalism, employing the PBE0 functional (Adamo and Barone, 1999) and a tier-1/tight numerical basis set as implemented in the FHI-AIMS code (Blum et al., 2009). In most of the calculations, we did not force the spin multiplicity of the system. However, in a few cases, especially for TiO 2 systems, in order to overcome convergence problems, we forced the spin multiplicity to be either an open shell singlet or a triplet. Recently, room temperature ferromagnetism has been reported for zirconia nanoparticles (Rahman et al., 2016;Albanese et al., 2018). This effect might also take place in titania and could be studied by considering multiple vacancies in future works.

RESULTS AND DISCUSSION
Pure (SiO 2 ) N Nanoclusters Figure 1 shows the calculated values of E vac for the lowest energy SiO 2 nanoclusters together with some selected nanocluster structures. Figure S1 shows the structures of all stoichiometric silica nanoclusters used in this work and Table S1 includes the corresponding values of E vac , E unrel , and E rel for the most stable reduced systems. Generally, stoichiometric silica global minimum nanoclusters tend to possess quite open symmetric structures and typically have between 2 and 4 unsaturated (terminal) oxygen sites. The majority of these structures present silanone centers, which are triply-coordinated planar Si centers involving a terminal oxygen atom (i.e., formally >Si=O, but arguably more accurately >Si + -O − ) (Avakyan et al., 2006;Zwijnenburg et al., 2009). For nearly all the silica nanoclusters considered, the terminal oxygen atoms at these sites are found to cost the least energy to be removed, 2.6-2.8 eV, with E vac increasing slightly and monotonically with the size. The (SiO 2 ) 12 nanocluster is the only exception as it only displays non-bridging oxygen (NBO) terminal species (i.e., ≡Si-O species where Si is 4fold coordinated) rather than silanones. Removing the terminal oxygen atom of an NBO center results in a higher E vac value (3.60 eV) as compared with silanone defects (2.6-2.8 eV). We note that the values of E vac for the removal of oxygen atoms at both silanone and NBO defects are much lower than those for the removal of 2-fold coordinated oxygen atoms in the corresponding bulk systems. From our calculations, for example, we obtained E vac values between 5.06-5.39 eV for a-quartz with a range of vacancy concentrations between 1/24 and 1/3 vacancies per SiO 2 units. These values are also consistent with other work where an E vac value of 5.15 eV was obtained using plane-wave based DFT calculations at the PBE level for the alpha-quartz structure with a vacancy concentration of 1/48 (Helali et al., 2017). We note that, removing a 2-fold oxygen atom in our nanoclusters typically costs between 4.2 and 5.7 eV (see Figure S2 which shows selected values for Si 10 O 20 ), which is comparable to the E vac values obtained for bulk alpha quartz. This confirms that the terminal silanone oxygens are least energetically costly in silica nanoclusters. From a structural point of view, reducing a silanone defective site in a nanocluster leads to a 2-fold Si site displaying a Si-O distance of 1.71 Å. This is slightly longer than the Si-O bond length of 1.62 Å as calculated by Pacchioni and Ferrario (1998) for a 2-fold coordinated Si defect in alpha quartz using a cluster approach at both wave function theory level employing unrestricted Hartree Fock, and DFT level employing the hybrid B3LYP functional. Further comparing our results with these bulk cluster calculations, in our clusters the O-Si-O angle of a reduced silanone site is found to be between 87 and 111 • , depending on whether the defect is part of a two or three membered ring. This compares with a value of 102 • found from bulk cluster calculations. Also, the vicinal Si-O-Si II angle (where Si II corresponds to the 2-fold coordinated silicon atom) is found to be between 90 and 133 • in our nanoscale clusters against the corresponding values for the same defective site of 141-161 • from bulk cluster calculations.
We note that for silica nanoclusters, relaxation is found to have little impact on the energetics of oxygen removal. An analysis of Figure 1 (see Table S1 for the values) shows that E rel is generally between 0.06 and 0.12 eV, and is thus <5% of the corresponding E vac . The structures of the relaxed O-deficient nanoclusters are very similar to the original stoichiometric structures. The only exception is the nanocluster structure for N = 12 that possesses two NBO sites. Oxygen vacancies originating from 2-fold coordinated oxygen atoms, which at nanoscale are less energetically favored than those generated from mono-coordinated oxygen sites, are also well-studied for bulk silica in the literature (Skuja et al., 1984;Skuja, 1998;Sulimov et al., 2002). Specifically, the ≡Si-Si≡ equilibrium distance is reported to be 2.3-2.5 Å in α-quartz (Skuja et al., 1984;Skuja, 1998;Sulimov et al., 2002). At the nanoscale, after removal of two-coordinated oxygens we find the ≡Si-Si≡ equilibrium distance to be between 2.12-2.37 Å, slightly lower with respect to the range reported for the bulk. Moreover, bulk oxygen removal is known to induce a long range structural distortion and asymmetric relaxation of atoms surrounding the vacancy (Sulimov et al., 2002). Such long-range effects are more difficult to evaluate for clusters for which the sizes range between 5 and 20 Å. However, generally we observe a relatively strong local relaxation for the neighboring atoms, whereas no significant long-range relaxation is observed (usually <0.1 Å of total displacement for distances >3 Å from the vacancy).
The electronic structure of the oxygen-deficient nonstoichiometric silica clusters is consistently found to be a singlet, as expected. The electron density of the highest occupied state is mainly located on the O-deficient silicon site and has the shape of a sp orbital, see Figure S3.
Pure (TiO 2 ) N Nanoclusters Figure 2 shows the calculated values of E vac for the lowest energy (TiO 2 ) N nanoclusters together with selected nanocluster structures. Table S1 shows the corresponding values of E vac , E unrel , and E rel obtained and Figure S4 shows the (TiO 2 ) N structures used. It can be observed that the (TiO 2 ) N nanocluster structures are more compact and less symmetric than silica clusters for the range selected, with titanium atoms being in 4-, 5-, and 6-fold coordinated environments. Many of these nanocluster structures, especially for sizes smaller than N = 20, possess terminal oxygen sites bonded to a Ti atom in a tetrahedral environment (≡Ti-O species). If present, these terminal oxygens are generally the least energetically costly to remove. In some cases (e.g., N = 4, 9, 11, 12), although the removal of a terminal oxygen does not have the lowest associated E unrel value, removing a 2-fold oxygen atom nearby can lead to a reduced nanocluster with the same topology as the one that results from removing the terminal oxygen itself. E vac values for (TiO 2 ) N nanoclusters are found to oscillate between 2.48 and 5.01 eV and display no clear size-dependent trend, contrary to the case of silica nanoclusters. The energetic cost to remove an oxygen atom seems to depend critically on the structure of each cluster. In very few cases (i.e., N = 17, 22), the E vac values for TiO 2 nanoclusters was found to be comparable with that found for SiO 2 nanoclusters. In such cases, after the relaxation, the TiO 2 nanocluster structure was found to have neither terminal oxygen sites (usually the site of the oxygen atom removal) nor 3-fold coordinated Ti defective centers, known to be highly destabilizing when left after the removal of a terminal site. We were not able to obtain a E vac value for bulk systems with the computational setup used for the nanoclusters due to severe convergence problems associated with the presence of Ti 3+ centers. Other authors have calculated E vac for bulk and surfaces of anatase and rutile using DFT-based calculations employing hybrid functionals incorporating between 20 and 25% Hartree Fock exchange, obtaining values between 4.8 eV (Finazzi et al., 2008;Yamamoto and Ohno, 2012;Deák et al., 2014) and 5.4 eV (Islam et al., 2007;Janotti et al., 2010;Lee et al., 2012). We also note that the E vac value for a terminal oxygen in an anatase bulk cut (TiO 2 ) 35 nanoparticle was calculated to be 3.95 eV, using the same methodology as employed herein . This value is similar to the average value of 3.65 eV, calculated for the lowest E vac values over our set of nanoclusters. Interestingly, for the (TiO 2 ) 35 nanoparticle, the removal of an internal bulk-like three-coordinated oxygen resulted in a lower E vac (i.e., 3.65 eV) with respect to that for removing a terminal oxygen atom. This behavior probably derives from the strong geometrical relaxation induced from the vacancy to the already metastable anatase bulk cut structure.
The relaxation of the TiO 2 nanoclusters after oxygen removal is found to involve more energy than in the case of silica nanoclusters. Specifically, the average E rel value for the lowest energy clusters is found to be 1.50 eV, and in some cases it accounts for more than 2.5 eV (N = 21, 23). With a few exceptions, such as for N = 4, 17, 22, the removal of terminal oxygens induces a moderate degree of local relaxation. However, when 2-fold coordinated oxygen atoms are removed, significant structural rearrangements take place (i.e., N = 10, 20, 21, 23, 24). In Figure S3 we show the O-deficient structure for N = 11 where a 2-fold oxygen atom is removed in the presence of a terminal oxygen, which then subsequently moves during the relaxation to fill the vacancy.
The electronic structure of the O-deficient clusters is either a triplet with two unpaired electrons occupying two titanium sites or an open shell singlet with unpaired electrons equally delocalized around three Ti centers neighboring the vacancy. Figure S3 displays the electron density associated with the highest occupied state of the (TiO 2 ) 10 and (TiO 2 ) 11 nanocluster after the removal of an oxygen atom, which is localized on Ti 3+ sites that carry the electrons left in the vacancy.

Mixed (Si x Ti 1-x O 2 ) N Nanoclusters
In order to study the effect of mixing SiO 2 and TiO 2 on E vac values, we have selected (Ti x Si 1−x O 2 ) 10 nanoclusters and a Ti content x between 0 and 1. The nanocluster structures used are taken from the global optimized structures reported in Cuko et al. (2018) (see also Figure S5). The nanoclusters exhibit different isomers for pure and mixed structures. All the structures possess terminal ≡Ti-O oxygen sites, with the exception of the pure (TiO 2 ) 10 nanocluster. The pure silica (SiO 2 ) 10 nanocluster displays only silanone terminations, whereas mixed systems display typically two terminal oxygen centers bonded with FIGURE 3 | Top: E vac vs. x plot; global minima isomers for (Ti x Si 1−x O 2 ) 10 with 0 < x < 1, the red crosses indicate the O atom that, after removal, leads to the lowest E vac . Bottom, the corresponding oxygen vacancy formation energies, E vac (blue), and relaxation energies, E rel (red), with respect to nanocluster composition. titanium atoms. The presence of titanium thus seems to allow for relatively more energetically stable terminal oxygen sites than silicon (Cuko et al., 2018). Figure 3 shows that the E vac values obtained for the mixed nanocluster systems oscillate around 3.7 eV, with the lowest value being found for x = 0.1 (E vac = 3.29 eV) and the highest value for x = 0.3 (E vac = 4.54 eV). The mixed nanocluster structure with x = 0.1 possesses two terminal oxygen sites bound to a Si and Ti atom. The removal of the terminal oxygen is more energetically facile (i.e., E vac is relatively lower) when it is bound to a silicon atom rather than a titanium atom. As the content of TiO 2 increases, the E vac values are found to initially increase up to x = 0.30, and afterwards decrease and oscillate with no obvious trend.
Over the range of (Ti x Si 1−x O 2 ) 10 nanoclusters, relaxation effects are relatively less significant for clusters with titania contents of x = 0.0, 0.1, 0.3. In the first two cases, indeed, the less energetically costly oxygen to be removed is from a silanone or a Si-NBO site, and therefore, the local structural relaxation effects are similar to those of pure silica systems. The system with x = 0.2 is a special case since lowest E vac value we could find is related to the removal of a two coordinated oxygen as shown. The removal of this oxygen atom leads to a significant structural change during the geometry optimization with a consequent relatively large associated E rel value (see Figure 3). For higher Ti content, E rel energies are found to be in the range of 0.6-1.5 eV which is typical for pure TiO 2 nanoclusters. Overall, the mixed (Ti x Si 1−x O 2 ) 10 nanocluster systems tend to behave more like titania nanoclusters rather than silica nanoclusters in terms of reduction through O-vacancy formation.

DISCUSSION
The results obtained point to a (sub)nanosize dependency of the formation of oxygen vacancies in silica-and titania-based structures. Firstly, the removal of singly-coordinated terminal oxygen atoms is often associated with low E vac values. This is explained by the low energetic cost of breaking an M-O bond compared with the energy required to break two M-O bonds for oxygen atoms in 2-fold coordinated sites. This is observed in the three types of nanoclusters studied in this work and has been reported in the literature for other oxides, especially in systems exhibiting structural stable dangling bonds. For instance, V 2 O 5 in bulk, surface and clusters exhibit structurally stable terminal oxygen sites. The coordination of oxygen sites in vanadia is commonly associated with chemical reactivity (Calatayud and Minot, 2006;Ganduglia-Pirovano et al., 2007;Calatayud et al., 2008b). The lower E vac found for nanoclusters compared to bulk values indicates higher reducibility of the nanosized materials as has been reported for other oxide systems like CeO 2 and ZrO 2 (Bruix and Neyman, 2016;Ruiz Puigdollers et al., 2016b).
It is, however, worth noting that the lowest E vac values found for silica clusters, 2.3-3.6 eV, are generally lower than for titania clusters, 2.48-5.01 eV as also shown from Figures 1, 2 and Table S1. A direct comparison between bulk SiO 2 and bulk TiO 2 was not possible in this study due to the high computational cost and convergence problems with TiO 2 systems. However, there are several studies on O vacancy defects formation in metal oxides (Pacchioni, 2008;Deml et al., 2015;Helali et al., 2017) that agree on associating a higher reducibility to titania (either rutile and anatase phases) with respect to silica bulk (mainly α-quartz). Our results suggest that silica becomes more reducible than titania at the nanoscale, which is contrary to the properties observed for respective bulk materials. The reason for such inverted behavior seems to be connected to the presence of terminal silanone oxygen atoms in low energy silica nanoclusters. The electronic structure (projected density of states) of this site is displayed in Figure 4, showing that the energy levels are highly localized in two sharp peaks (one between −9 and −10 eV, and the other between −10.5 and −11.5 eV) associated to higher reactivity. In comparison, the oxygen levels of the 2-fold oxygen in (TiO 2 ) 10 are distributed over a 3 eV range of energies (between −9 and −12 eV). In the (TiO 2 ) 11 cluster, the electronic energy levels associated with the dangling oxygen lay closer to the Fermi level, between −9 and −11 eV, and those associated with the 2-fold coordinated site levels spread between −9 and −13 eV. The electronic structure of the dangling silanone oxygen in silica is consistent with an enhanced reactivity of this site and with the low E vac values shown. Interestingly, the oxygen vacancy in bulk silica has been reported to exhibit specific electronic transitions associated with the electron pair localized on the silicon atom after reduction (Cannizzo and Leone, 2004;Sushko et al., 2005). We also observe the highest occupied electronic level of O-deficient (SiO 2 ) 10 cluster localized on the resulting Si< site ( Figure S3 top right), which is consistent with the presence of an electron pair localized on the silicon site.
A second important point is the structure-dependency of the E vac values. In the case of silica nanoclusters, the E vac value is almost constant and related to the presence of Si sites with dangling silanone oxygen sites. However, titania nanoclusters display a greater range of E vac values, depending on the structure near to the removed oxygen atom. Relaxation effects can also be significantly stronger in titania nanoclusters than in silica nanoclusters, which is consistent with the greater variety of E vac sites and values found. The size dependency of E vac values is also different for each nanomaterial. For the system sizes considered here, the majority of silica nanoclusters exhibit a near constant value of E vac ∼ 2.6 eV associated with silanone sites, and exceptionally an E vac value of 3.6 eV associated with the NBO in the (SiO 2 ) 12 nanocluster. For larger sizes, silica nanoclusters are predicted to become fully-coordinated (Flikkema and Bromley, 2009), which will result in a jump of E vac to near bulk values ∼5 eV. As can be seen in Figure S2, 2-fold coordinated oxygens cost 4.4-5.5 eV. In the case of pure titania nanoclusters there seems to be no clear trend with size.
Finally, mixing nanosilica and nanotitania results in chemically and structurally rich nanocluster systems displaying a variety of oxygen sites. Interestingly the presence of titanium induces the disappearance of silanone sites in favor of pyramidal ≡Ti-O species. Whereas terminal oxygen sites are relatively unstable when bonded to silicon, they are stabilized when bonded to titanium. As for pure titania nanoclusters, the values of E vac are found to strongly depend on the structure, the coordination of the oxygen removed, and the degree of relaxation after oxygen removal.
In order to further study the role of the chemical nature of Si and Ti in the oxygen vacancy energy, we consider a set of (Ti x Si 1−x O 2 ) 10 structural isomers with the same topology ( Figure 5), with selected compositions between x = 0-1. Such isomer structures are global minima for titanosilicates with x = 0.1, 0.2, and 0.3, and are slightly less stable than the global minima for pure systems. They have been geometrically optimized in their stoichiometric composition. We then remove FIGURE 5 | Top: a set of (Ti x Si 1−x O 2 ) 10 cluster structures exhibiting the same structural isomer for pure silica (x = 0), pure titania (x = 1) and all intermediate compositions. Bottom: the corresponding oxygen formation energy without relaxation (E unrel ) in eV for all non-equivalent oxygen sites. Vacancies are generated after removing a 2-fold coordinated oxygen (gray), terminal NBO 1 (blue), and terminal NBO 2 (green). each non-equivalent oxygen atom keeping the initial geometry frozen. In Figure 5 we report the resulting unrelaxed oxygen vacancy formation energies (E unrel ). Figure 5 shows E unrel as a function of the mixing composition x TiO2 of the cluster. In the plot there are three families of oxygen vacancies according of the type of oxygen removed: the vacancies originating from the removal of two-coordinated oxygen atoms are denoted in gray, whereas those originating from removing the terminal oxygen sites labeled NBO 1 and NBO 2, respectively, are denoted in blue and green. In most of the cases, vacancies at terminal position are found to provide the lowest E unrel value. For the pure silica cluster isomer, the E unrel values for the NBO 1 and NBO 2 are 3.38 and 3.45 eV, respectively, which values are significantly lower than the corresponding values for pure titania systems, 4.69 and 5.38 eV. This result further confirms that the oxygen vacancy formation energy is driven by the presence of unsaturated O centers and, particularly when such centers are bonded to Si atoms, are more easily removed than when they are bonded to Ti atoms. This is clearly seen in the x = 0.1 isomer that possesses one terminal oxygen on Si and one on Ti: the E unrel for the Si-bonded oxygen NBO 1 is 3.50 eV whereas for the Tibonded oxygen NBO 2 it is 5.65 eV. Although relaxation effects have not been considered, based on the results discussed above, they are not expected to be significant. Therefore, the nature of the cationic site, Si or Ti, seems to critically determine the stabilization of the terminal oxygen deficient systems.

CONCLUSIONS
In this work we use DFT-based calculations employing the PBE0 hydrid functional to explore oxygen vacancy formation in globally optimized TiO 2 , SiO 2 , and mixed Ti x Si 1−x O 2 nanoclusters for sizes between 2 and 24 stoichiometric oxide units. The properties computed (oxygen vacancy formation energies, electronic structure, nanocluster structure, relaxation effects) are found to critically depend on the nature of the oxide. The behavior of silica nanoclusters is found to be rather constant and dominated by the presence of dangling oxygens in silanone >Si=O sites. In titania and titanosilicate nanoclusters; however, we find a strong dependence of the properties with respect to the local geometry. When unsaturated oxygen centers are present in the system, removing such centers is energetically less costly than removing two-coordinated oxygen atoms. Since at the nanoscale such unsaturated centers are naturally present in low energy systems, contrary to the bulk and extended surfaces, we can predict that the reduction of nanosized silica clusters is energetically more favorable than in the bulk. Furthermore, we found that the oxygen vacancy formation in silica nanoclusters is also more favorable than from similar-sized low energy titania nanoclusters. This demonstrates the emergence of an unexpected chemical behavior induced by the small size of the systems considered. We hope that our results will help in the search of novel materials for applications in scientific and technological fields such as heterogeneous catalysis, electronics, and cluster chemistry.

AUTHOR CONTRIBUTIONS
AC performed all the calculations, figures, tables, analyzed the data, discussed results, and participated in the elaboration of the manuscript. SB and MC directed the work, discussed the data, and wrote the manuscript.