J. Phys. Chem. C 2008, 112, 16087–16095
16087
Reactivity of (TiO2)N Clusters (N ) 1-10): Probing Gas-Phase Acidity and Basicity Properties Mo`nica Calatayud, Lluis Maldonado, and Christian Minot* Laboratoire de Chimie The´orique, CNRS UMR 7616 UniVersity Paris 06, 4 Place Jussieu case 137, 75252 Paris Cedex 05, France ReceiVed: April 2, 2008; ReVised Manuscript ReceiVed: July 26, 2008
We present B3LYP calculations on a selection of small-size clusters with (TiO2)N stoichiometry (N ) 1-10) built on previous works on TiO2 and SiO2 or derived by kinship with stable clusters of different sizes. Their reactivity is analyzed as a function of size and electronic structure. Gas-phase acidity is probed by H+ interaction with the oxygen sites, while basicity is tested by interaction of molecular NH3 with titanium sites. Correlation with size, topology, or electronic properties is observed for some systems. In general, the correlation with electronic levels (highest occupied and lowest unoccupied molecular orbitals, HOMO and LUMO) is good criteria of reactivity, although this is not always observed. The calculated values generally decrease with the size. The HOMO-LUMO gaps show oscillations and a general decrease with the size. Coordination of the active site influences both the levels of the frontier orbitals and their effect upon reactivity. The protonation testing the cluster basicity is found to be higher for clusters with N ) 3 and N ) 9 in accordance with the high HOMO values. A remarkable exception is found for N ) 4 for which the most stable protonated structure is different from the most stable naked cluster. We have not tested here the flexibility of the naked cluster; however, this case means that structure reorganization should be considered for reactivity. Regarding ammonia adsorption testing cluster acidity, clusters with N ) 3 and N ) 8 present the highest adsorption energy toward NH3 in accordance with a low LUMO value for the former but because of the local topology of the adsorption site for the latter. Acidic and basic character decreases for N ) 8-10 probably because of the increase in cohesive energy. A structure with N ) 9 emerges as the strongest base with the largest protonation energy. A tetrahedral structure with N ) 10 is remarkably stable and presents the lowest adsorption energy values. 1. Introduction It is a broad and general assumption that the size of a material is an important factor for reactivity. In general, we associate reactivity with materials of small size; powders and dispersed catalysts are indeed more reactive than terraces of crystalline materials. On the contrary, the interest in nanotechnologies contains the idea that there is an optimal size between the atomic scale and very large systems. The ultimate goal of this paper is to bring some contribution to the understanding of the influence of size supported by calculations of clusters using density functional theory (DFT). Metal oxide materials are major catalysts for environmental, energy, and petrochemical industries. Their catalytic activity is related to the size of the particles. TiO2 is an important material,1 and the thermodynamic stable phase is rutile. Concerning TiO2 nanoparticles, there are several papers on isolated TixOy systems (x ) 1-8, y ) 1-16).2-5 There has been a recent interest in identifying the stable structures of gas-phase cluster structures6-8 and determining their electronic structure.9-11 The following step is to study their reactivity. This paper investigates the reactivity of neutral TiO2 structures in interaction with H+ and NH3. First, the structures of various clusters of different sizes (TiO2)N N ) 1-10 have been characterized in terms of thermodynamic stability and electronic structure. Next, the reactivity of these systems as a function of size is studied. We consider two types of reactivity: basicity and acidity. The * To whom correspondence should be addressed.
basicity of the oxygen sites is measured as the reaction energy for the adsorption of a proton H+. This reaction involves the formation of a strong OH bond without any electron transfer. Similarly, we probe the surface acidity by adsorbing NH3 without dissociation on the Ti cations. We analyze the interaction energies as a function of size and frontier orbitals, namely, the relative levels of the highest occupied molecular orbital (HOMO) and of the lowest unoccupied molecular orbital (LUMO). We do not consider processes involving electron transfers such as atomic hydrogen attachment. 2. Computational Details We have carried out ab initio calculations with the Gaussian03 code.12 The hybrid B3LYP functional13-16 is employed. The titanium atom is represented by the LANL2DZ pseudopotential12 with 12 valence electrons explicitly treated. An all-electron double-ζ basis set is used for O, N (6-31+G(d)) scheme17 and H (6-31G(d))18 including polarization and diffuse functions19 for oxygen and nitrogen. This scheme is a good compromise between accuracy and computational effort. Structures were fully optimized without any symmetry constraint. Table 1 shows some calculated values for geometry and electronic structure of the reference TiO2 molecule (also called monomer hereafter) in good agreement with experimental10,11,20 and previous calculated data.2,7,9,11,21,22 The adsorption energy for an adsorbate, X, on a cluster with N TiO2 units, (TiO2)N, is defined according to the expression
10.1021/jp802851q CCC: $40.75 2008 American Chemical Society Published on Web 09/19/2008
16088 J. Phys. Chem. C, Vol. 112, No. 41, 2008
Eads(X) ) E(X) + E(TiO2)N - E(X ⁄ (TiO2)N) and is positive for an exothermic adsorption. The interaction energy is calculated with respect to the most stable starting neutral structure (otherwise, it is specified). Basis set superposition error (BSSE) correction is below 6% in all cases. The cohesive energy Ecoh is calculated as
Ecoh )
E(TiO2)N - N × E(TiO2) N
where E(TiO2)N is the energy of the cluster with N TiO2 units and E(TiO2) is that of the monomer.
Calatayud et al. TABLE 1: Calculated Data for TiO2d TiO2 dTidO Å R (deg) νTi-O cm-1 IPa eV EAa eV H-L eV S-T eV a
exptl
this work
1.62a 110 965a 9.54b 1.59c
1.642 110.95 1037 9.86 1.58 3.88 2.01
1.96c b
Qu and Kroes7 1.658 110.8 1026 9.75 1.69 1.94
c
3. The Structures of (TiO2)N Clusters
Quoted in ref 22. Reference 20. Quoted in ref 21. d d, distance; R, O-Ti-O angle; ν, frequency; IPa, adiabatic ionization potential; EAa, adiabatic electron affinity; H-L, HOMO-LUMO gap; S-T, singlet-triplet energy difference.
In this section, we describe the structures of stoichiometric clusters that we have selected. We have made an effort to find those of lowest energy. It is, however, important to keep in mind that the stability of the cluster might not ease its formation. According to experimental conditions, metastable species may be formed instead of ground-state clusters.23 It is not obvious that conversion from one structure to another is as easy as the thermodynamics suggests. However, the complete investigation of all the structures of the clusters is already an impossible challenge as soon as N increases because of the rapidly increasing number of possible isomers, and we tried to sample a reasonable set of different clusters. Main guide lines are the presence of an electronic gap and the compactness and the coordination of the atoms. Pair-potential investigations6 favoring compactness are a useful tool to select stable candidates. In general, the formation of the largest number of bonds contributes to increasing the cohesive energy of a cluster. Qu and Kroes7 have, however, verified that this does not always lead to the most stable isomers. Moreover, the TiO2 crystal phases, rutile or anatase, are not the most compact MO2 crystal structures. The ratio of the ionic radii, rTi4+/rO2- ∼ 0.444, forbids having the most compact structures (the titanium coordination in TiO2 existing crystals is 6 and does not reach 8 as it would in fluorite AB2 structure; this structure would require rTi4+/rO2- > 0.732 in a hard sphere model). The cluster structures should avoid dangling bonds that are sign of instability. Large coordination also imposes proximity of ions with the same charge which is a repulsive contribution to the energy. To search for the most stable structures, it is also tempting to consider symmetry or kinships from one structure to another even though this often is not very successful. Analogy with (SiO2)n clusters for which more investigations have been made24-28 should help find some structures for (TiO2)N clusters. For stoichiometric silica clusters, factors favoring stability are a tetrahedral environment, the presence of rings (four-member Si2O2 rings for small clusters or six-member Si3O3 rings for larger systems28 and bulk), and the presence of functional groups (as dSi)O double bond termination or ≡Si-O). The Ti2O2 ring pattern exists in rutile structure. Small clusters do not appear as fragments of MO2 crystal structures since the number of dangling bonds would be too large. Reference to understoichiometric MO or M2O3 crystal might even be more productive because by completing with O atoms a substoichiometric MO fragment saturates the dangling bonds and leads to clusters with MO2 stoichiometry. Small clusters can also be simply viewed as fragments of polymers. In the following, such structures are qualified of oligomers. They refer either to the simple chain of tetrahedral Ti (spirolike structures see 3b and 4d in Figure 1) or to more complex chains made of rings, four-member Ti2O2 rings or six-member Ti3O3
rings, and the Ti atoms are then connected by bridging O atoms in the propagation direction. In Figure 1, we have displayed the selection of neutral structures that we have calculated. The topology of the most stable dimer is a noncoplanar fourmembered ring with two bridging O and two terminal O in agreement with previous works.2,3,7,29 Moving the terminal oxygen from the trans to the cis position is destabilizing by 0.27 eV (0.28 in ref 7). A C3V structure is less stable by 0.77 eV. In agreement with Qu and Kroes,7 the (TiO2)3 trimer of lowest energy is 3a (Figure 1). 3a represents an increase in coordination (11 bonds, an average of 3.67 per Ti). The trimer found by Hamad et al.6 evolved to this structure. The structure 3b (10 bonds) made of tetrahedral cations postulated by Albaret et al.2 is 0.37 eV higher in energy (0.37 eV in ref 7). The structure 3c with 9 bonds is 0.92 eV less stable. For the tetramers, the most stable structure (C2V symmetry, 4a) has 16 bonds (an average of 4 per Ti) associated to a large electronic gap (4.92 eV); the corresponding trans structure with C2h symmetry (not shown) is 0.29 eV less stable with a gap of 4.58 eV. Other structures (Cs 4b and C2h 4c) with 14 bonds are low in energy. The former is a tetrahedron with two terminal O. A distortion of 4b connecting the two Ti of coordination 3 to the O atom bridging the two Ti of coordination 4 leads to 4a. The distortion is easy and 4b is number two in the scale of stability. This distortion reduces the symmetry and widens the electronic gap. The difference in energy between 4a and 4b is relatively small (0.23 eV in the present work, -0.29 eV in ref 7; the labels 4a and 4b are inversed). The C2h structure (4d) made of tetrahedral cations, an oligomer of the simple chain, was 0.83 eV higher in energy than structure 4a. Finally, structure 4e is 1.22 eV less favorable than 4a. We present five (TiO2)5 pentamers in Figure 1. A growth preserving the average coordination of 4 consists to bridge two O atoms from 4a by a Ti of a TiO2 unit; the optimization led to the most stable cluster, 5a, that has 20 bonds; all the Ti atoms have four ligands and concerning the O atoms, seven are bridging, two are terminal, and the last one is 4-fold coordinated. This structure presents a gap of 4.69 eV. Structure 5b with 18 bonds is 1.52 eV less stable; structures 5c (Cs 18 bonds) and 5d (C3V 20 bonds) are more than 2 eV less stable than 5a. The number of bonds does not guarantee stability. The smallest gap is found for 5c, 3.50 eV, whose relative energy is high. The structure (TiO2)6 proposed by Qu and Kroes7 is that of lowest energy; in this structure, all the Ti atoms are 4-fold coordinated; one O is 4-fold coordinated and two are terminal. It can be built from 6d by connecting one terminal O to the three 3-fold coordinated Ti atoms; it can also be generated by
Reactivity of (TiO2)N Clusters
J. Phys. Chem. C, Vol. 112, No. 41, 2008 16089
Figure 1. Structures for (TiO2)N N ) 1-10. In parentheses are the relative energy and the HOMO-LUMO gap in eV.
optimizing a fragment of corundum. The most stable hexamer that we have found after that of Qu and Kroes is the structure 6b where all the Ti atoms are also 4-fold coordinated (four bonds per Ti atom). Two O atoms are 3-fold coordinated and two are terminal. The oligomer 6c of a developing chain of four-member rings connected by bridging O has only 22 bonds which only represents 3.67 bonds per Ti. The cage 6d, oligomer of a developing chain of six-member rings connected by bridging O, is 2.21 eV higher in energy with a small gap of 2.74 eV. We find the hexamer reported by Hamad et al.6 less stable by 2.43 eV. A compact cage structure not shown with 24 bonds (4 per Ti) with a high symmetry (D6d, two staggered Ti3O3 rings connected by six bonds and completed by six terminal bonds) is less stable. The gap of 6a, the structure of lowest energy, is 4.57 eV. The structures of lowest energy for the (TiO2)N structures (N ) 7-10) are derived from optimization of fragments of solids, zinc blende TiO or corundum Ti2O3. The fragmentation of zinc
blende leads to structure 10a proposed by Flikkema and Bromley27 and Zhao et al.28 for Si10O20; it is remarkably stable with a gap of 4.52 eV. In this structure, all the Ti atoms are tetrahedral. This structure indeed possesses 10 tetrahedral Ti atoms; for the O atoms 12 are bridging, 4 are 3-fold coordinated, and 4 are terminal. From structure 10a, we have removed TiO2 units and have optimized, and sometimes have promoted, the formation of bridging ligands. We have also started by fragments of corundum, even though these procedures led sometimes to large reorganizations. This introduces similarities in the sequence of the clusters (N ) 7-10) which helps the homogeneity of their properties. For the heptamer, the resulting structure 7a has 7 tetrahedral Ti atoms, and 10 O atoms are bridging, 2 are 3-fold coordinated, and 2 are terminal as in ref 7. Structure 7b (with a relative stability of 0.70 eV) is derived from the corundum structure. It has one 5-fold coordinated Ti atom and one tetrahedral O atom. It has a poorer average coordination than 7a (27 bonds instead
16090 J. Phys. Chem. C, Vol. 112, No. 41, 2008 of 28). In the structure 7c proposed by Hamad et al.,6 all the Ti atoms are tetrahedral as for 7a. It is even more coordinated counting Ti-O distances of 2.18 Å as bonds; then, one Ti atom becomes 6-fold coordinated. The geometry 7d proposed by Flikkema and Bromley for Si7O1427 is very close in energy to 7c. The structure 7e is 1.09 eV less stable than 7a: it possesses one 3-fold coordinated titanium and three terminal and one central 4-fold oxygen site. For Ti8O16, the most stable structure 8a has been found by optimizing a fragment of corundum. Counting a Ti-O bond for a distance of 2.22 Å, it has 32 bonds; one Ti is 5-fold coordinated and one is 3-fold coordinated. One O atom is 4-fold coordinated. The next cluster, following the order of relative energies, is again parent to 10a and to the zinc blende structure; it has three 3-fold coordinated and three terminal O atoms. The structure 8c deprived of terminal TidO bonds found by Hamad et al.6 is nearly as stable. In this structure, two Ti atoms have six ligands. Structure 8d, an oligomer parent to 6c, is 0.89 eV less stable. The C3V structure 8e (8a in ref 7) is less favorable and presents the smallest gap, 3.64 eV. It is an oligomer containing two six-member Si3O3 rings capped by a Si on one side (as in 4b) and a TiO on the other side. For Ti9O18, the most stable structure is that found in ref 7: a cagelike skeleton with one terminal and two 4-fold oxygen atoms. It may be seen as an oligomer made of Ti3O3 rings with reconstruction. The next isomer, 9b, is 0.73 eV higher in energy; it is derived from 10a and has nine tetrahedral Ti atoms; the O atoms are bridging except two 3-fold coordinated and two terminal O atoms. We have found two structures by optimizing corundum fragments: 9c and 9e. That of lowest energy, 9c, is only 0.07 eV above 9b. It does not seem to be a highly coordinated structure counting as bonds only the Ti-O associated with distances less than 2.11 Å. With this count, one Ti atom is 3-fold coordinated. However, four other Ti-O interactions corresponding to distances between 2.2 and 2.4 Å are stabilizing. Counting them makes two Ti atoms 6-fold coordinated. For 9e, including three bonds whose distances are less than 2.12 Å, all the Ti atoms are 4-fold coordinated except two that are 5-fold coordinated. Cluster 9d has two terminal O atoms as the second most stable cluster in ref 7; compared with 9a, it is an oligomer whose reconstruction is incomplete. The structure proposed by Hamad et al.,6 rather compact and containing only one terminal TidO group, is 1.49 eV higher in energy. It has 34 bonds plus three in the range 2.09-2.17 Å. For Ti10O20, the structure 10a is remarkably stable and has already been used to generate small clusters of high stability.27 Every Ti atom is 4-fold coordinated with a nearly perfect tetrahedral environment. This structure is then exceptional for the stability. Qu and Kroes have proposed two isomers without terminal oxygens, 10b and 10c, close in energy. We found them less stable than 10a by ∼1 eV. The oligomer 10d and the structure 10e are even less stable. The structure that we have calculated starting from the corundum structure underwent a strong reorganization ending with a very large relative energy (+5.6 eV, not shown). A complete investigation of all the structures is not a possibility. However, the increase of the cohesive energy with N (see Figure 2) gives an idea of the quality of the results. Many global minimum structures are those already found in ref 7; few of them are lower in energy. Figure 2a displays only the most stable isomers. Figure 2b focuses on the comparison of the cohesive energy of a TiNO2N cluster with the average of the values for N - 1 and N + 1; relative values are displayed. Other compact structures may be generated by simulated annealing
Calatayud et al.
Figure 2. (a) Cohesive energies Ecoh in eV for the clusters of highest stability as a function of the size N. (b) Deviation of the cohesive energy defined as ((Ecoh(N) - 1/2Ecoh(N - 1) - 1/2Ecoh(N + 1)). The value for N ) 10 is defined by interpolation.
techniques, although the use of pair potentials could also fail finding the global minimum as pointed out above. Structures 3, 4, 6, 9, and 10 emerge from Figure 2. This may suggest that isomers of larger stability may exist for N ) 5, 7-8 and that we have missed them. Alternately, it may also mean that 3, 6, and 10 are magic numbers allowing ideal topology for the neutral clusters. There is no evidence for a regular increase in stability with size; Figure 2b emphasizes the irregularity of the progression. 3.1. Structure Analysis. Despite the overall trend, no general rule really emerges to explain the stability of a particular cluster. Coordination of the oxygen atoms in general increases with the size, up to three, the value found for rutile and anatase structures or more. It reaches 4 in some stable structures derived from corundum. The average coordination of 2 for O is associated with that of 4 for the titanium coordination; it is found for the bridging atoms; however, this average value sometimes accounts for the simultaneous presence of terminal and 3-fold coordinated O sites as in 6b or 7a or terminal and 4-fold coordinated as in 6a or 10b. Titanium atoms increase their average coordination from 2 to 4 with the coordination in rutile and anatase being 6. This value is found in some clusters derived from the corundum but does not exist in the most stable clusters (N ) 3, 6, and 10). The highest coordination is not a guarantee of stability (see, for instance, 5d and 6e). For the series N ) 4-10, the titanium coordination is 4 which is probably a plateau until the cluster size allows Ti atoms from the core of the cluster to become 6-fold coordinated. Stable surfaces such as rutile (110)1 or anatase (101)30 show titanium atoms 5-fold and 6-fold coordinated. A conclusion for compactness does not emerge from these results. When the Ti coordination exceeds 4, the Ti-O bonds are elongated and optimization often makes an expansion of the volume. There is no systematic relation with extended structures except zinc blende and corundum. Symmetry did not help finding stable structures. Kinship (resemblance with (TiO2)N′ clusters with N′ d N ( 1) was useful to find 5a from 4a even if the structures were different. It has also been useful to find the clusters related to 10a; however, the topology of the clusters in Figure 1 shows a large variety of shapes; there is no simple relation between 5a, 6a, and 7a.
Reactivity of (TiO2)N Clusters A terminal TidO group (titanyl) is found to be present in all the most stable structures. The short Ti-O bond for the titanyl around 1.60 Å is often represented as a double bond although it is not purely covalent. With the exception of the TiO2 molecule, a titanium site is found to possess a maximum of one titanyl group combined with other oxygen ligands (two or three of them). The presence of terminal groups, however, may not be a sign of stability since it does not contribute to increasing the average coordination. It may be due to the small size of the cluster which otherwise would necessarily have dangling bonds in the direction normal to their core. The presence of a terminal ligand is the way to avoid them and to make the titanium environment more isotropic. In extended titania systems, singly coordinated oxygen centers would be reactive in oxidation reactions.31,32 The four-member ring Ti2O2 is present in most stable structures; the Ti2O2 molecule has been recently characterized by matrix isolation infrared spectroscopy.29 Such rings can combine basically in two ways to form larger structures: either sharing one titanium atom, leading to polymeric spirolike structures where the shared titanium site is tetrahedral (as in 3b or 4d), or sharing a Ti-O bond, which seems to be preferred as the size increases. Stable complex ring structures involving four-member rings are found, for instance, in structures 4a or 6b. A polymeric pattern of four-member cycles sharing one titanium atom is present in the rutile bulk structure even if cycles are in-plane. A polymeric pattern of Ti-O shared four-member cycles is found in the anatase bulk structure. Larger cycles like Ti3O3 (3c, 9a, 9d) or Ti4O6 (4c, 6c) are less common. Polycycles with Ti4Ox rings are present in the framework of 10a and related compounds. These cycles seem to be building blocks of small titanium dioxide nanoparticles. The coordination of the titanium sites is completed by the addition of titanyl sites giving rise to stable moieties. 4. Electronic Structure The electronic structure of the titanium dioxide clusters is that of an insulating material: the highest occupied molecular orbital HOMO is composed of 2p oxygen levels, while the lowest unoccupied molecular orbital LUMO is mainly of titanium 3d character. The HOMO and LUMO levels are important both in shape and magnitude as they are responsible for the chemical reactivity. In systems containing undercoordinated atoms, as we have verified, the HOMO and LUMO are centered on the undercoordinated atoms. Considering O (or Ti), the reason is that an increased coordination contributes to increasing the bonding (antibonding) character of occupied (vacant) orbital localized on this atom and shifts its energy level down (up). Frontier orbitals are then localized on the uncoordinated atoms. Thus, if a titanyl TidO group is present, the HOMO will be mainly composed of such levels and can express the reactivity of a lone pair of a singly coordinated O. In acid/base terms, the oxygen sites are basic and the titanium sites are acidic. Let us investigate their reactivity toward probe acidic and basic molecules like H+ and NH3. We will try to correlate the interaction energy with the HOMO-LUMO values. 4.1. The HOMO Values. The reactivity of anions is to be associated with the high energy of the HOMOs localized on the poorly coordinated O atoms. The overall trend, see Figure 3, exhibits smooth oscillations with a general slight decrease suggesting a decreasing basicity of the clusters with size. The monomer shows the highest values for both HOMO and LUMO. Clusters for N ) 3, 5, 7, and 9 correspond to peaks in the general
J. Phys. Chem. C, Vol. 112, No. 41, 2008 16091
Figure 3. HOMO and LUMO values in eV for the clusters of highest stability.
decrease trend and are therefore expected to correspond to more basic compounds. With the exception of N ) 3 and 9, stable clusters have HOMOs of low-lying energy compared with those of some clusters of the same size and lower stability. For a given N, the latter may be expected to be more reactive. In Figure 3, we have displayed the HOMO and LUMO levels of 4b whose relative energy is weak; the levels of its frontier orbitals suggest that it may lead to stable products even though it does not originate from the most stable cluster; in ref 7, the relative order of stability for these two compounds is not the same as in this work. More generally, the values for the most stable isomers do not represent extreme cases. On the contrary, the levels of the HOMOs that strongly deviate from the average value correspond to isomers of poor stability. Most often, clusters whose HOMO-LUMO gap is weak are not particularly stable. Among the (TiO2)6 compounds presented in Figure 1, compound 6e presents the smallest gap (2.74 eV) and the highest HOMO (-7.30 eV). Its relative energy is high. Another isomer not shown has an even smaller gap (0.82 eV) and a higher HOMO (-6.41 eV); its energy relative to 6a is 4.54 eV. In these cases, the original energy difference in the cluster stability dominates and the stability of the adducts is similar. Here, we did not systematically consider the clusters of poor stability and focused on the most stable compounds. The evolution of the HOMOs for this case is displayed in Figure 3 (lower curve). The general trend is a small decrease with smooth oscillations: the values for N ) 3 and N ) 9 emerge over the others. The experimental adiabatic detachment energies are found to increase with the size11 indicating a stabilization of the O 2p levels in agreement with our calculated HOMO decrease with N. 4.2. The LUMO Values. Interaction of small molecules with metal oxide surfaces takes place on the undercoordinated cations as an acid-base reaction.33-36 This suggests that the energy of the LUMO could monitor their adsorption. We also expect LUMOs of high energy for stable clusters, and 3a is an exception. On the contrary, less stable compounds should have lower LUMOs and be potentially more reactive. The calculated LUMO values (see Figure 3) lead to a situation similar to that for the HOMOs; the general trend with the size is again a small decrease. Zhai and Wang11 found that the electron affinity measured as adiabatic detachment energy increased with N for the Ti 3d levels. This suggests that the acidic properties relatively dominate for the clusters of large size. The oscillation is smooth and the clusters of size N ) 3 and 8 seem potentially more reactive. 4.3. The HOMO-LUMO Gap. In metal oxides, the band gap is often related to the stability, a large value indicating a stable compound; on the other hand, it is reasonable to think that structures showing lower gap values and being relatively close in energy should be more interesting for reactivity.
16092 J. Phys. Chem. C, Vol. 112, No. 41, 2008
Figure 4. Calculated HOMO-LUMO gaps in eV for the most stable (TiO2)N clusters. The values oscillate.
The HOMO-LUMO gap values calculated for all the structures are much dispersed. For the most stable structures, the values displayed in Figure 4 seem to oscillate in the range 3.5-5.0 eV. The main trend is a decrease with N ) 1, 3, and 10 being exceptions. The smallest gaps found for N ) 1, 3, and 9 remain large compared with the experimental values for the bulk rutile and anatase at ∼3.0-3.2 eV; these values have been noticed as well in previous sections for the HOMO and LUMO values. Comparison to experimental results is difficult. In a recent paper by Zhai and Wang,11 the gap is observed to converge to the rutile or anatase values for (TiO2)N- anions for N > 7. The adiabatic detachment energies for both the O 2p and Ti 3d bands increase with the size with the former at a major extent leading to gap values from 2.2 to 3.1 eV which is consistent with the singlet-triplet excitation; the gap values calculated as the HOMO-LUMO difference for the neutral TiO2 cluster, 3.88 eV, is significantly higher than that obtained from the singlet-triplet excitation, 2.01 eV. This is consistent with the conclusion from refs 7 and 37: singlet-triplet and HOMOLUMO gaps should represent lower and upper limits to the TiO2 bulk band gaps, respectively. Despite this overestimation, the trend of the gap calculated as HOMO-LUMO should, however, be comparable to experiment. The general trend is a decrease of the HOMO-LUMO gap. Oscillation is less marked in the experiment; only the values for N ) 1 and 3 differ from others. The origin of the misfit can be multiple. First, the experimental values are measured for anions, whose structure does not necessarily correspond to the neutral systems. Zhai and Wang11 indicate that the addition of an extra electron into the LUMO might induce a large geometry change. Also, what is measured is not necessarily the most stable structure but is a mixture of some structures. In general, the most stable structures have large gaps. Finally, the determination of the global minimum by computational techniques becomes a difficult task for larger structures. This explains the disagreement in the calculated gap values for N ) 4 between ref 7 and this work; their most stable structure with a gap of 3.14 eV (our 4b) is only 0.23 eV less stable than our structure 4a at 4.92 eV with the latter fitting better the experimental trend. The gap value seems thus to be extremely sensitive to the structure and much more than the size as unique parameter. 5. The H+/(TiO2)N structures The interaction with H+ is a measure of the gas-phase basicity. On (TiO2)N, H+ is adsorbed on the O atom to generate a strong OH bond. Such a reaction, not involving any electron transfer, is favored when basic oxygen sites are present. Terminal and bridging oxygen sites have been tested; on the many examples checked (not detailed here), the terminal ones always led to the most stable protonated structures, and we only present here the results for such cases. Figure 5 displays the
Calatayud et al. most stable clusters found. After H+ adsorption, the terminal TidO bond is elongated from 1.62 to 1.81 Å, and the final H-O-Ti angle is 170 degrees. The symmetry is reduced, but the skeleton remains the same as for the neutral clusters. Table 2 and Figure 6 show the adsorption energy of H+ on the selected clusters corrected with the zero-point energy. The values for the most stable naked structures oscillate around a mean value, 9.4 ( 0.3 eV. In any case, the value is superior to the protonation of the O atom from H2O, 7.31 eV. The O from titanium dioxide is indeed more basic than that of the water molecule, and the Ti-O-H bond strength seems a transferable value that is constant and independent from the size in a first approximation. The general trend is an increase in the adsorption energy that corresponds to an increase in the basicity. The results from Figure 6 are to be compared to the distribution of the HOMOs. The structures originate from the most stable naked structures for which the HOMOs are given in Figure 3. Clusters 3a and 9a, which presented high HOMOs, also present higher adsorption energies while cluster 10a with low HOMO also shows low adsorption energy. However, nothing from the high HOMO levels indicates a low reactivity for the monomer. In general, the protonation of the most stable naked structures leads to the most stable hydrogenated ones. The most remarkable exception is structure 4b which becomes the most stable protonated structure, 0.59 eV more stable than 4a. We have displayed the corresponding value in Figure 6 (the protonated 4b is referred to the most stable naked cluster 4a; if referred to naked 4b, the value is 10.25 eV). Probably, such cases also appear for more structures, but the number of isomers makes the investigation difficult. The extremes N ) 1 and N ) 10 show the smallest values: the former is less ionic and the latter is exceptionally stable. Let us say that opposite arguments could be evoked. On the one hand, large clusters are more stable per TiO2 unit and thus could appear as less reactive. On the other hand, an increase of basicity with the size could be expected because of an increase of ionicity. However, charge is not a good index of reactivity for metal oxides; large negative charges correspond to electron stabilization by developing Madelung field. These stabilized electrons are not reactive. Similar reasoning has been proposed to compare the reactivity of metal oxides of different ionicity.36 The small oscillation around a mean value could be an indication of the robustness of the hydroxyl OH group. 6. The NH3/(TiO2)N Structures The interaction with a base, NH3, should probe the acidic property of the cluster cations and should reflect the variations of the LUMOs. Table 2 summarizes the calculated adsorption energies for the most stable isomers corrected with the zeropoint energy. In Figure 5 are displayed the most stable clusters found. Figure 7 shows the results for the binding energies that match the LUMO shifts toward low energies (Figure 3). For the most stable structures, several adsorption sites are possible; we have selected the 3-fold coordinated Ti sites, and if the structure does not present such sites, we have selected the 4-fold sites not showing titanyl TidO groups. Ammonia is weakly bonded at a distance around 2.2 Å. The values for the most stable naked structures oscillate around a mean value, close to 1.6 eV, and there is no clear trend with the cluster size except a general decrease with size. Two clusters are more acidic, 3a and 8a. The high reactivity of 8a is not due to a low-lying LUMO. The reason is the topology of the adsorption site. The Ti at the adsorption site is very asymmetric at the bottom center of a face of a pyramid of its four ligands with the N completing
Reactivity of (TiO2)N Clusters
J. Phys. Chem. C, Vol. 112, No. 41, 2008 16093
Figure 5. The most stable clusters for H+ and NH3 adsorption.
a trigonal pyramid arrangement under adsorption. For 3a, NH3 may also be viewed as binding to a 3-fold coordinated Ti atom with a pyramidal shape. This pattern is very reactive. 10a is poorly acidic; this can be attributed to the large stability of this cluster and to the local tetrahedral environment of the Ti center; contrary to that present in 8a, the site of adsorption in the naked cluster is very isotropic. For 10a, the NH3 orientates perpendicular to a face of the cluster. The acidity of the clusters seems
then to be sensitive to the local structure of the reactive site and not only to the LUMO level. 7. Conclusion Clusters of TiO2 stoichiometry have been calculated for N ) 1-10 and have been compared to available experimental and theoretical results. Stable structures are characterized in terms
16094 J. Phys. Chem. C, Vol. 112, No. 41, 2008 TABLE 2: Calculated Adsorption Energies for H+ and NH3 on the Most Stable Clustersa
a
N
Eads (H+)
Eads (NH3)
1 2 3 4 5 6 7 8 9 10
9.05 9.13 9.38 9.18 9.45 9.45 9.46 9.59 10.25 9.08
1.52 1.61 1.78 1.54 1.68 1.57 1.46 1.91 1.49 1.09
Corrected with the zero-point energy (see Figure 5) in eV.
Calatayud et al. to be higher for clusters 3a and 9a in accordance with the high HOMO values even though correlation on the series is not satisfied. A remarkable exception is found for N ) 4 for which the most stable protonated structure, 4b, is different from the most stable naked cluster, 4a. We have not tested here the flexibility of the naked cluster; however, this case means that structure reorganization should be considered for reactivity. Regarding ammonia adsorption testing cluster acicity, clusters 3a and 8a present the highest adsorption energy toward NH3 in accordance with a low LUMO value for 3a but it is because of the local topology of the adsorption site for 8a. Acidic and basic character decreases for N ) 8-10 probably because of the increase in cohesive energy. Structure 10a is remarkably stable and presents the lowest adsorption energy values. Acknowledgment. We thank I. E. Wachs for stimulating discussions and J. A. Mejias and S. Hamad for kindly providing us with their most stable structures for N ) 1-10 in ref 6. The IDRIS and CCRE computational facilities are acknowledged. L. M. is grateful to the Erasmus Exchange European program. References and Notes
Figure 6. Energy of adsorption of H+, corrected with the zero-point energy, in eV on the most stable clusters referred to the naked cluster of lowest energy. For N ) 4, the most stable protonated cluster 4b does not correspond to the most stable naked one 4a; this is indicated with arrows.
Figure 7. Energy of adsorption of NH3 on the most stable clusters, in eV, corrected with the zero-point energy.
of cohesive energy, electronic structure (gap, HOMO, LUMO), and reactivity toward H+ and NH3 adsorption. Relation between size and reactivity has been analyzed. The main conclusion is that there are not general rules for predicting cluster stability. Structures presenting high compactness are not always the most stable ones. Titanyl groups and four-member ring Ti2O2 are present in almost all the stable structures. For N ) 4-10, the Ti atoms are 4-fold coordinated achieving for 10a a tetrahedral environment. This seems the main requirement for clusters of this size. Regarding the electronic structure, the HOMO and LUMO energetic values do not show a marked trend with the size. There is a general shift with size, however, as individual topology prevails over general trends. Their energy levels are associated to undercoordinated oxygen and titanium sites, respectively. The gap oscillates around a value of 4.5 eV. There is no clear trend for acidic and basic reactivity with the size. In general, the correlation with LUMO and HOMO levels, respectively, is good criteria of reactivity although this is not always observed. Coordination of the active site influences both the levels of the frontier orbitals and their effect upon reactivity. The protonation testing the cluster basicity is found
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