Electronic and Optical Properties of Doped and Undoped (TiO2)n

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J. Phys. Chem. C 2010, 114, 17333–17343

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Electronic and Optical Properties of Doped and Undoped (TiO2)n Nanoparticles S. A. Shevlin and S. M. Woodley Department of Chemistry, UniVersity College London, Gower St, London, WC1E 6BT, United Kingdom ReceiVed: May 13, 2010; ReVised Manuscript ReceiVed: September 2, 2010

The geometry and electronic structure of bare and anion-doped nanoscale (TiO2)n clusters, where n ) 1, 2, 3, 4, 5, 6, 7, 10, and 13, were calculated using density functional theory (DFT) and time dependent density functional theory (TDDFT). Initial (TiO2)n structures were chosen from the global minima obtained using an evolutionary algorithm. With increasing nanoparticle size we find the HOMO-LUMO transition energy saturates toward bulk values for surprisingly small values of n. For the C-, N-, and S-substitutional doped nanoparticles, all dopant formation energies are lower than those calculated for bulk rutile. Both C- and N-dopants prefer to reside on the 4-fold oxygen site, maximizing their coordination, while the S-dopants reside on 2-fold sites on the exterior of the cluster. The anion dopant with the lowest formation energy is sulfur, then nitrogen, with carbon having the largest formation energy. All of the dopants reduce the transition energy, with nitrogen-doping giving a transition energy that is too low (at approximately 1.0 eV) for watersplitting applications. Carbon and sulfur dopants give transition energies that are close to the peak in the solar spectrum (∼2.5 eV), and thus are more efficient at photoconversion than undoped nanoparticles. Through analysis of the frontier molecular orbitals and determination of the optical spectra (within TDDFT) we conclude that carbon is the optimum dopant for maximizing the photoactivity of subnanometer (TiO2)n nanoparticles. 1. Introduction The generation and utilization of clean energy fuels is an urgent problem that needs to be addressed by societies in the 21st century. Current fossil fuel-derived sources emit large amounts of CO2, with associated anthropogenic contributions to global warming. There is thus a need for a clean replacement, of which hydrogen (H2) is the favorite, as it possesses a large energy density.1,2 Typical methods of generating H2 rely on high temperature cracking of methane and other petroleum-based fossil fuels,3 with corresponding energy efficiency and CO2 release penalties. Carbon emissions would be greatly decreased if an alternative method of H2 generation could be developed and scaled up for industrial usage, i.e., from the photoelectric decomposition of water as catalyzed by incident solar photons, such as photocatalysis.4 Photocatalytic materials have emerged as potentially very important solutions to the problem of clean H2 production via the heterolytic dissociation of water to form hydrogen,

1 H2O f H2 + O2 2 where H2 is generated via a two electron reduction and O2 via a two hole oxidation. Indeed, the first report of photocatalytic water-splitting was reported on a TiO2 electrode by Honda and Fujishima in 1972,5 and since then over 130 materials have been identified as photocatalytic water-splitters. Photocatalysis occurs when a photon promotes an electron from the valence band to the conduction band, generating a photoelectron (or photohole) that reduces (oxidizes) the reactant (in this case H2O). The efficiency of a semiconductor photocatalyst in converting incident light into mobile charge carriers depends on several factors. First, photocarrier production is maximized when the bandgap is approximately the same as the energy of the peak number of incident photons, i.e., visible light at energy 2.50

eV. Second, it is important to separate the electron-hole pair so as to prevent charge recombination and thus allow attack of the reactant. As no material currently investigated both catalyzes watersplitting at visible light wavelengths and has a quantum efficiency of 10% (this been the limit for commercial applications),4 there is thus much research that focuses on either developing new materials,6-12 or doping current materials so as to possess improved electronic structure. In particular, TiO2, due to its ubiquity, stability, and nontoxicity, is still of interest, with considerable research in the literature devoted to its use as a photocatalyst.4,13-17 However, the main drawback for both photocatalytic phases of TiO2 is that for the bandgap is rather large (3.03 eV for rutile,18 3.18 eV for anatase19) and thus only a small part of the solar spectrum can be harvested. Anion doping, in particular with C-,20-23 N-,24-27 or S-dopants,21,28,29 has been investigated as a way to reduce the bandgap and thus increase photoactivity. Often the dopant acts as a pinning center, with the defect state possessing a very small dispersion and thus unfortunately limiting photocarrier mobility.27,30 Compared to bulk phases, nanoparticles and clusters are, by definition, composed of fewer atoms, and consequently have discrete electronic states rather than bands. Thus, an alternative method of modifying the electronic structure and, in particular, the bandgap (HOMO-LUMO gap), is to reduce the particle size. Our previous work on In2O3,30 BN,31 and SiC32 provide good examples of this size effect. Furthermore, changes in nanoparticle size can also modify the structure and bonding connectivity of the nanoparticle, with implications for the thermodynamics of doping. Smaller particle sizes will also have a greater effective surface area when compared to the bulk. Finally, dopants will be closer to the surface and thus any photocarriers that are generated on these sites will be more readily available to attack H2O, rather than pinned to the dopant as occurs for the bulk. For the particular case of TiO2, there is evidence to suggest that reducing

10.1021/jp104372j  2010 American Chemical Society Published on Web 09/29/2010

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nanoparticle size both modifies the structure33,34 and reduces the HOMO-LUMO gap.35,36 It is thus of interest to determine the structure, thermodynamics, and electronic structure of these nanoparticles. In this work, we present the results of state-of-the-art simulations on the properties of (TiO2)n nanoparticles, where n ) 1 to 7, 10, and 13. We will initially outline the methods we used to generate the stable and metastable atomic structures of the nanoparticles. We then use ab initio Density Functional Theory (DFT) calculations to determine the ground-state electronic structure and thermodynamics of both bare and C-, N-, and S- doped (at O sites) nanoparticles. We demonstrate that with increasing size the HOMO-LUMO transition energy saturates toward bulk values for surprisingly small values of n. Furthermore, the DFT transition energy is reduced with respect to the undoped nanoparticles. Finally, as it is known that DFT inaccurately treats excited states,37 we use Time Dependent Density Functional Theory (TDDFT) to accurately determine the optical gaps of all nanoparticles considered and the absorption spectra of a selected subset. Both CO× and SO× substitutionals, where × indicates a neutral defect and O indicates the oxygen site, possess good optical gaps. More significantly though, the CO× substitutionals have greater oscillator adsorption strength near the energy of the peak in the solar spectrum, and a more delocalized Frontier Molecular Orbital (fMO), and thus are the superior dopant. 2. Computational Details 2.1. Derivation of Nanoparticle Structures. To obtain the lowest energy atomic structures formed from stoichiometric (TiO2)n units, plausible stable and metastable atomic configurations, as defined by analytical interatomic potentials, are first sought. Searches on this computationally cheaper (than DFT) energy landscape were performed using an evolutionary algorithm (EA) technique,38 as implemented in the GULP package,39 which has also been successfully applied to other materials, e.g., ZnO.40 In our EA, a population of candidates, configurations of n titanium and 2n oxygen atoms, compete both to procreate (new children candidates created by mixing configurations from two current configurations) and to survive into the next EA cycle (population). All candidates in each population are either local minimum or saddle points on the energy surface, i.e. all clusters are immediately subjected to local optimization. Survival into the next EA cycle is based purely on the energies of the relaxed clusters; typically only the best twenty or thirty unique structures survive. During the EA search, clusters are constrained to be within a sphere with a 16.0 Å diameter, the first population are made of randomized configurations, typically ten randomized clusters are added to the population on each cycle and procreation is a process of a applying a phenotype crossover and mutation move-class (self-crossover or atom exchange).41-43 For each cluster size, the EA is used several times, each initiated with a different random seed. The lowest energy candidate structures (in the final EA populations for each n) were then subject to geometric minimization using DFT. More details on our approach to generating plausible atomic configurations can be found elsewhere.30,33,40 2.2. Density Functional Theory. The VASP code44 was used to determine the geometry, ground-state electronic structure, and thermodynamics of nanoscale (TiO2)n nanoparticles, where n ) 1, 2, 3, 4, 5, 6, 7, 10, and 13, within DFT. A plane-wave cutoff of 450 eV was used, with the exchange and correlation terms treated with the Perdew, Burke, and Ernzerhof functional,45 and with the Projector Augmented Wave method used

Shevlin and Woodley to treat the core electrons.46 For the smaller nanoparticles (n ) 1, 2, 3, 4, 5, and 6) a unit cell of dimensions 15 × 15 × 15 Å3 was used, while for the larger nanoparticles (n ) 7, 10, and 13) a unit cell of dimensions 20 × 20 × 20 Å3 was used. Spinpolarization was used for all calculations, although typically it was only for NO× -doped nanoparticles that this had an effect as these are the only systems which have an open electronic shell. All atoms were fully relaxed until the change in force upon ionic displacement was less than 0.01 eV/Å. In order to correctly determine the geometry, especially for the smaller nanoparticles, we found it necessary to use the GGA+U method,47 as initial calculations of the excitation energy using structures obtained with just the PBE exchange correlation functional found negative excitation energies, regardless of whether the PBE or PBE0 exchange correlation functionals were used. This is an indication that the PBE structures are metastable, however upon using the GGA+U treatment to obtain nanoparticle structures we find positive excitation energies, thus indicating we do find stable structures. An on-site Coulomb interaction (U) of 3.0 eV and exchange interaction (J) of 0.8 eV is placed on the d-orbitals of titanium.48 This is very similar to the on-site value of 3.3 to 3.4 eV determined for the rutile and anatase phases from linear response calculations.49 Defect formation energies are only changed by ∼0.1 eV upon inclusion of Hubbard localization. On occasion, we also compare our results (specifically defect formation energies and HOMO-LUMO gaps within DFT) to those of bulk rutile TiO2. Our theoretical lattice parameters are a ) 4.628 Å, c ) 2.967 Å, in good agreement with the experimental lattice parameters (at 15 K) of a ) 4.586 Å, c ) 2.954 Å.50 We model a (3 × 2 × 2) supercell composed of 72 atoms, using a (2 × 2 × 2) Monkhorst-Pack net to sample the reduced Brillouin zone. For anion substitution, we replace one oxygen atom in these supercells with a carbon, nitrogen, or sulfur atom, this results in a dopant concentration of 1.4%. As the GGA + U approach is essentially an empirical approach (fitted to experimental data such as the observed lattice parameters of the primitive unit cell, or the bandgap of the bulk system), it is not transferable to systems where there is a paucity of such data. In particular, there are few unifying bulk-like (such as a uniform Ti-O connectivity) structural motifs for the set of TiO2 nanoparticles considered here. Furthermore, the GGA + U approach relies on using the Hubbard localization to raise the unoccupied states with respect to the occupied states and thus correcting for the HOMO-LUMO gap underestimate in normal DFT. The DFT description of unoccupied states is not appropriate for accurately determining the transition energies and optical spectra of the nanoparticles. We therefore perform Time Dependent Density Functional Theory (TDDFT) simulations on the VASP-derived nanoparticle structures using the Gaussian-based NWChem code,51,52 for which we have employed a split valence triple-ζ basis.53 For these simulations, we use the PBE0 exchange correlation functional, a parameter free modification of the PBE exchange correlation functional that contains 25% exact exchange.54 It is well-known that exchange-correlation functionals that contain a portion of exact exchange more accurately calculate excited state properties within TDDFT than functionals without exact exchange. We also make use of the asymptotically corrected functional of Casida and Salahub (CS′00).55 Our TDDFT calculations of optical spectra employ the linear response theory using the Tamm-Dancoff approximation as implemented in NWChem.56 Only five roots are determined for the calculation of transition

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Figure 1. Relaxed geometries of (TiO2)n clusters (a) (TiO2), (b) (TiO2)2, (c) (TiO2)3, (d) (TiO2)4, (e) (TiO2)5, (f) (TiO2)6, (g) (TiO2)7, (h) (TiO2)10, and (i) (TiO2)13. The purple spheres represent the Ti atoms while the red spheres represent the O atoms.

energies, compared to 100 roots when we compute the optical spectra of undoped and doped (TiO2)6. 3. Results and Discussion 3.1. Bare Nanoparticles. We find that the structures generated from the evolutionary algorithm are stable upon DFT relaxation, see Figure 1. All electronic ground state structures are singlets. We especially note that in comparison with all phases of bulk TiO2, where each oxygen atom binds to three titanium atoms and each titanium atom binds to six oxygen atoms, the clusters contain a range of coordination numbers for each atom type. Unsurprisingly, coordination number increases with n, however there is not a smooth and uniform transition to bulk coordination. For example, even though the coordination number of all titanium atoms in the (TiO2)3 clusters is three, the coordination number of oxygen atoms vary: two have onefold coordination, three have 2-fold coordination, and one has 3-fold coordination. Oxygen atoms in the larger clusters (n ) 10 and 13) are coordinated to at least two titanium atoms. Furthermore, oxygen coordinations greater than that for bulk rutile, e.g., 4-fold coordination for n ) 4, 5, 6, 7, 10, and 13, and 5-fold oxygen coordination for n ) 13 are also observed. Titanium atom coordination also varies with nanoparticle size. Beginning with (TiO2)3 the titanium atoms are 4-fold coordinated, with (TiO2)6 titanium atoms with 5-fold coordination appears, and for (TiO2)13 a titanium ion in the center of the cluster has a coordination of seven. The electronic and optical properties of these nanoparticles are, therefore, expected to differ from the bulk. One-, two-, three-, four- and five-fold oxygen atoms have Ti-O bond lengths between 1.65 to 1.66 Å, 1.77 to 1.96 Å, 1.83 to 2.13 Å, 1.96 to 2.00 Å, and 2.07 to 2.17 Å, respectively. Typical bond lengths are larger than those found from MD simulations of larger TiO2 nanoparticles,57 which we attribute to particle size effects and in particular the fact that their structures still resemble the bulk phase. We also considered alternative structures based on the global minima predicted for (SiO2)n clusters,58 but these were found to be higher in energy than our chosen clusters in Figure 1 (ranging from a minimum of 0.36 eV for n ) 3 to a maximum of 7.93 eV for n ) 7).

For the smaller clusters, the energy difference between the global minimum (GM) and the next lowest metastable configuration is sufficiently large that the GM configuration is not dependent on the choice of energy function. Thus we can expect the same GM configurations to be reported in the literature for smaller clusters. However, as the size of the cluster increases the energy difference decreases, thus for larger clusters the GM configuration can be dependent on the choice of energy function. It is still possible to select representative configurations for these larger sizes. For completeness, we still compare our structures with that already in the literature. Since we have access to previously refined, as calculated within DFT, structures of (TiO2)n nanoclusters33,59 we were able to initialize our calculations from configurations obtained directly from the evolutionary algorithm (where interatomic potentials were used) or from our previous DFT study. Note that the previous calculations were performed with Gaussian-based basis sets, and hybrid exchangecorrelation functionals. Unfortunately, for small Ti-O compounds it has been found that hybrid exchange-correlation functionals perform worse than “pure” exchange-correlation functionals, especially for the calculation of binding energies.60 Thus, we use a computer code that uses a plane-wave basis-set and a GGA exchange-correlation functional with no hybridization. Most of the (TiO2)n structures we find are the same as in previous work, however (TiO2)5 and (TiO2)6 are different. For n ) 5, we obtained a structure very similar to the (ZrO2)5 structure reported by Hamad et al.,33 with a single onefold oxygen atom, whereas n ) 6 is essentially our (TiO2)5 structure with an additional TiO2 unit adsorbed onto it. Our result that clusters that have at least one oxygen atom with a coordination number of one, as opposed to more compact clusters composed of atoms with higher coordination numbers, are energetically preferred is not surprising as it has been reported that the most favorable cluster structures are sometimes quite open.35,61 Moreover, both anatase and rutile are not as compact as other MO2 phases, e.g., fluorite. Note that refinement of the cluster structures is important as interatomic potentials favored denser clusters.33 Our global minimum (GM) n ) 1, 2, and 3 structures are the same as the lowest energy structures obtained with DFT-

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Shevlin and Woodley none of our structures corresponds to theirs and thus we do not compare any further. Our n ) 7 structure is not reported by Qu et al., but is the third lowest structure found by Calatalyud et al. Our n ) 10 structure is the second lowest energy structure found by both Qu et al.62 and Calatalyud et al. Interestingly, neither paper agrees on what the lowest energy structure is, with the former reporting a structure with no onefold oxygen atoms and consisting of purely 4-fold and 2-fold oxygen atoms, while the latter reports a structure which is composed of a cut of zincblende that possesses four one-fold oxygen atoms. Our n ) 13 structure is a slightly distorted version of the lowest energy structure reported by Qu et al.62 In order to assess the stability of the nanoparticles we determine the cohesive energy per TiO2 trimer, as determined using the following:

Figure 2. The cohesive energy per TiO2 trimer (for bulk rutile and the series of (TiO2)n nanoparticles), as plotted for inverse n. Note that the (TiO2)15 nanoparticle, otherwise not discussed, is less stable than the (TiO2)13 nanoparticle. This suggests that the (TiO2)15 nanoparticle, based on the work of Hamad et al.33 is not a global minimum on our energy landscape.

B3LYP calculations, specifically those of Qu et al. who considered n ) 1 to 16,35,62 Calatalyud et al. who considered n ) 1 to 10,61 and Weng et al. who considered n ) 1 to 6.34 Furthermore, these structures are the same as those reported from the high-level CCSD(T) calculations of Li et al..63 As the difference in energy between GM and lowest metastable structures decreases with increasing cluster size, it is not a surprise that for the lowest cluster sizes our GM structures and those in the literature agree. For n ) 4, only Qu et al.35 reported a different GM; the GM reported by us and the other three groups is their second lowest energy configuration. Our n ) 5 structure does not correspond to any of the lowest energy structures reported by Qu et al., Calatalyud et al., or Weng et al., whereas our n ) 6 structure is a distorted version of the second lowest energy structure found by Qu et al.35 For the n ) 5 to 9 series of nanoparticles an additional set of structures has been found by Mowbray et al.,64 who used RPBE (a “pure” exchange correlation functional) in their calculations. However

ECoh ) E(TiO2)n /n - E(TiO2) where E(TiO2)n is the total energy of a nanoparticle, and E(TiO2) is the total energy of the isolated TiO2 trimer, see Figure 2. There is a general trend that cohesive energy increases with increasing cluster size. Of special note is that the n ) 5, 7, and 13 clusters are not as stable as would be expected from a simple line-fitting. This can mean either that the structures we consider are not the most stable structures for those sizes or, alternatively, that the possible configurational space for these particular sizes does not permit the particularly stable arrangements that are possible for neighboring sized clusters. The former reason is more likely for larger n, as the number of possible atomic configurations, which our evolutionary searches through, increases. For rock salt compounds or (MgO)n, particular sizes which are significantly more stable than neighboring sized clusters have been matched to larger “magic number” peaks in mass spectra of particles ablated from a surface.42,65-67 In Figure 3, we show the Frontier Molecular Orbitals (fMOs) for the n ) 6, 7, 10, and 13 clusters, namely the HOMO-1, HOMO, LUMO, and LUMO+1 states. For the smaller clusters there is a mixture of O(2p) orbitals and Ti(3d) orbitals for all fMOs. However for the larger clusters there is a clear separation, whereby the HOMO and HOMO-1 states are composed of O(2p)

Figure 3. Calculated frontier molecular orbitals (with the contour chosen to be 0.1eÅ3) for the n ) 6 (a) and (b), n ) 7 (c) and (d), n ) 10 (e) and (f), and n ) 13 (g) and (h) clusters. Purple and red spheres represent the titanium and oxygen atoms. Superimposed and semitransparent, HOMO-1 and HOMO states are colored blue and orange respectively, whereas, in the other panels, green and yellow are chosen for the LUMO state and the LUMO+1 state, respectively. In comparison, the HOMO and LUMO states for bulk rutile (not shown) are uniformly dispersed over the material, with the HOMO residing solely on the O(2p) states and the LUMO on the Ti(3d) states.

Electronic and Optical Properties of (TiO2)n NPs

J. Phys. Chem. C, Vol. 114, No. 41, 2010 17337 TABLE 1: Experimental Transition Energy, Calculated HOMO-LUMO Energy (EHL), Singlet-Triplet Energy Difference (EST), Singlet Transition Energy (ETD), and Triplet Transition Energy (ETD3), As Well As the Reported HOMO-LUMO Energy As Found by Qu and Coworkers35,62 (EHL(Qu))a

Figure 4. Plot of experimental gap (Eexp), DFT transition energy (HOMO-LUMO energy difference) (EHL), and TDDFT singlet transition energy (ETD), for inverse n. All units are in eV.

states and the LUMO and LUMO+1 states are composed of Ti(3d) states. All fMOs are not localized on one type of atom, and in addition they are spatially separated. The spatial separation would tend to indicate that the value of the overlap integral for the direct HOMO-LUMO transition is small, and thus this transition is not likely to happen. Finally, for the n ) 6 and 7 clusters there is a small difference in energy between HOMO-1 and HOMO states (of maximum magnitude 0.04 eV) and a larger difference in energy between LUMO and LUMO+1 states (of maximum magnitude 0.26 eV), reflecting the spatial degeneracy of the former and the lack of the degeneracy of the latter. Interestingly, the reverse is found for the HOMO-1 and HOMO states of the larger n ) 10 and 13 clusters (the difference in energy is 0.28 eV), whereas we found a slightly smaller energy difference between LUMO and LUMO+1 states (0.22 eV). Note that (within an energy of 0.2 eV of the HOMO and LUMO states) there are more unoccupied fMOs for our larger clusters than for our smaller clusters, and vice versa for the occupied fMOs. In Figure 4 we plot the experimental (Eexp), DFT transition energy (EHL), and TDDFT singlet transition energy (ETD) as a function of cluster size and compare to the bulk. Furthermore, these values together with the energy difference between singlet and triplet ground states (EST) (which represents the DFT triplet transition energy), and the triplet TDDFT transition energy (ETD3) are reported in Table 1. From photoelectron spectroscopy measurements of the adiabatic detachment energy, Zhai et al. have determined the transition energy for (TiO2)n,36 where n ) 1-10. The nanoparticles have smaller optical gaps than the bulk but reach the bulk value at n ) 7. As expected, the EHL does not reproduce this trend. Additionally it is not systematic in reproducing trends. For the smaller clusters it is larger than the experimental values,36 while for the larger clusters it is smaller. In comparison with the work of Qu et al.35,62 our calculated DFT HOMO-LUMO gaps are smaller; this is a reflection of the different exchange correlation functionals and basis sets used. The TDDFT singlet transition energies, although not matching experiment for the smaller clusters, do saturate toward the bulk gap value with increasing cluster size. Furthermore, they are in much better agreement with experiment, with the TDDFT gaps, for n ) 5 and higher, oscillating around a value of about 3.0 eV, which is approximately the bandgap for rutile TiO2. The triplet transition energies we calculate within DFT are also smaller than the equivalent singlet transition energy, a qualitative trend in agreement with Qu.62 As already mentioned

rutile TiO2 (TiO2)1 (TiO2)2 (TiO2)3 (TiO2)4 (TiO2)5 (TiO2)6 (TiO2)7 (TiO2)10 (TiO2)13 a

Eexp

EHL

EST

3.06

2.04

3.05

2.22 2.59 2.26 2.60 2.85 3.00 3.10 3.10

2.00 3.18 1.84 3.00 2.85 2.57 2.47 2.76 2.35

1.86 2.72 1.81 2.39 2.22 1.38 2.02 2.51 1.91

ETD

ETD3

EHL (Qu)

2.13 3.04 2.83 3.30 3.06 3.23 2.88 3.14 2.93

1.98 2.96 2.78 3.23 2.97 3.16 2.82 3.11 2.87

4.89 3.69 3.15 4.54 4.53 3.96 4.49 3.76

All units are in eV.

above, DFT is known to give inaccurate transition energy gaps, so it is no surprise that they do not match the experimental results. Furthermore, we also note that experimental measurements of transition energies may involve an ensemble averaging over several different cluster configurations. The TDDFT triplet transition energies are only five hundredths of an eV lower in energy than the singlet transition energies, as also found by Li et al.63 Excitation of a triplet state would involve spin-polarized photons and would cost almost as much energy as the singlet state. The CCSD(T) calculations of Li et al. only report adiabatic energy gaps, e.g. gaps after relaxation, whereas we report only optical gaps. They thus cannot be compared directly. 3.2. Doped Nanoparticles. Considering only the GM (TiO2)n configurations for n ) 1-7, 10 and 13, we find a total of 33 unique oxygen sites, and thus 99 C-, N- or S- doped (TiO2)n configurations to model. As shown in Figure 5, the preferred dopant site depends upon the choice of dopant. To understand the preferred site for each type of dopant we choose to consider both the ionic and covalent pictures of bonding. As sulfur is in the same group as oxygen, i.e., Group VI, we would expect it to easily accommodate itself in a covalent Ti-O network, where oxygen atoms are bound to two titanium atoms. Alternatively, using an ionic description, the preferred dopant site will be influenced by the larger ionic radius of sulfur, which will typically increase the bond strain on the surrounding Ti-O bond network. For n ) 6 (the example chosen in Figure 5), this would suggest sulfur preferring one of the two one-fold sites. However, the larger anion can also accommodate a higher coordination, so ideally a higher coordination site is favored; four is the highest coordination number for an oxygen site. In fact, a compromise is found, as the favored doping sites are the 2-fold oxygen sites on the exterior of the nanoparticle. Nitrogen, as a Group V dopant, prefers to covalently bond with three titanium atoms. Therefore, nitrogen should typically favor 3-fold oxygen sites, as found by Mowbray et al.64 However, using an ionic description, nitrogen should prefer a higher coordination than oxygen. Thus, although the nitrogen would prefer a 3-fold site, it is more beneficial for the nitrogen to substitute for the highest coordinated oxygen. For example, see configurations shown in Figure 5 where the nitrogen replaced the oxygen on the 4-fold site and, after relaxation, maintained only three bonds to the neighboring titanium. Note that the titania clusters doped by Mowbray et al.,64 which from our previous work resemble the zirconia clusters n5a (distorted so as to create a second one-

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Figure 5. Representative lowest energy anion substitution structures, in this case for the (TiO2)6 (top) and (TiO2)10 (bottom) nanoparticles, where (a) and (d) is the CO× dopant, (b) and (e) is the NO× dopant, and (c) and (f) is the SO× dopant. Gray represents the carbon atom, light blue nitrogen, and yellow sulfur.

TABLE 2: Calculated Dopant Formation Energies (in eV) of the CO×, NO×, and SO× Dopants bulk rutile (TiO2)1 (TiO2)2 (TiO2)3 (TiO2)4 (TiO2)5 (TiO2)6 (TiO2)7 (TiO2)10 (TiO2)13

Figure 6. Calculated CO×, NO×, and SO× dopant formation energies (EF) (in eV).

fold site59), n6b, n7k, n8l, and n9c (distorted), and only have one-, two- and 3-fold oxygen sites. Finally, as carbon is a Group IV dopant, we would expect it to bond to four titanium atoms, and should also prefer a higher ionic coordination than oxygen (and indeed nitrogen). In fact, preferential doping for the 4-fold oxygen does occur. However, as well as binding to four titanium atoms, the CO× dopant also has a strong affinity for oxygen, distorting the nanoparticle structure and forming a CO complex with an approximate C-O bond length of 1.40 Å. The creation of a CO complex and the resulting distortion will have a strong effect on the defect formation energy. The defect formation energy for these systems was calculated using the following:

1 EF(TinO2n-1X) ) ETot(TinO2n-1X) + ETot(O2) 2 ETot(TinO2n) - ETot(X) where ETot(TinO2n-1X) is the total energy of the doped system, ETot(O2) is the total energy of an O2 molecule, ETot(TinO2n) is the total energy of the undoped (TiO2)n nanoparticle, and ETot(X) is the total energy of a reference material for the particular dopant (e.g., energy per carbon atom in graphite, or half the energy of either the N2 or S2 molecule). Our results are shown in Figure 6 and tabulated in Table 2. The SO× dopant is the easiest to insert into the nanoparticles, then the NO× dopant, while CO× dopants have the largest defect formation energies. We also

EF(CO×)

EF(NO×)

EF(SO×)

8.52 9.22 8.04 6.83 6.36 5.79 5.00 5.67 5.27 5.17

4.93 5.44 5.00 4.58 4.43 5.22 2.94 4.33 4.48 4.23

4.26 3.34 1.54 1.48 1.58 1.39 1.61 1.06 1.79 0.83

calculate the formation energies of these dopants in the bulk rutile phase and compare to the nanoparticle formation energies. Our formation energies for the bulk (8.52 eV for CO×, 4.93 eV for NO×, and 4.26 eV for SO×) are in good agreement with that published elsewhere: 8.20 eV for CO×,22 5.53 eV for NO×,27 and 4.10 eV for SO×.68 The only theoretical research that calculates defect formation energy for dopants in clusters is that of Mowbray et al.,64 who found EF ) 4.25, 4.20, and 6.65 eV for NO× doping of n ) 5, 6, and 7 respectively. However, not only are their structures different to that used in this study, but they also used a different exchange correlation functional. Both CO× and SO× dopants have much lower formation energies for the nanoparticles than for the bulk, while formation energies for NO× dopants in nanoparticles (and the CO× dopant for n ) 1) are quite similar to those in bulk. Nitrogen can be accommodated on the 3-fold oxygen sites, which are present in both the bulk and the nanoparticles, however, carbon and sulfur are much harder to accommodate in the bulk due to coordination character (CO×) and larger ionic radius (SO×). The nanoparticles, which have a range of structural motifs and greater effective surface area, can more easily accommodate these dopants. Note that the formation of CO× and NO× dopants will cause the generation of excess holes, which typically require the formation of oxygen vacancies to compensate. We do not model oxygen vacancies in our bulk calculations. Indeed, for the nanoparticles we find that charging to induce charge compensation increases the formation energy, which we attribute to the small size of the nanoparticles precluding easy charging, i.e., the reduction in defect formation energy due to charge compensation is more than compensated by the energy needed to charge the nanoparticle. With increasing nanoparticle size CO× dopants have lower formation energies, while there is no strong equivalent trend for the other two dopants. We argue that this can be

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Figure 7. Calculated Frontier Molecular Orbitals (where green represents the HOMO state and orange represents the LUMO state) for the (a) CO×, (b) NO×, and (c) SO× doped (TiO2)6 nanoparticle, and for the (d) CO×, (e) NO×, and (f) SO× doped (TiO2)10 nanoparticle. Contours are chosen to be 0.1 eÅ3.

attributed to the strain induced by CO formation upon carbon doping which can be more easily distributed over the Ti-O bond network for the case of larger nanoparticles. Finally, we note that (TiO2)6 in particular is much easier to dope than the other nanoparticles, which is due to the (TiO2)6 cluster having a shape very similar to a (TiO2)5 cluster with an additional TiO2 unit added on. The resulting structure allows a great deal of relaxation upon doping, lowering the formation energy. The fMOs of two representative nanoparticles are shown in Figure 7. As seen earlier for the bare nanoparticles, the fMOs are located on the surface of the doped nanoparticles. The SO× doped nanoparticle has a HOMO of S(3p) character that is strongly localized on the sulfur, and for the smaller nanoparticles the one-fold oxygen, atoms, therefore the photohole that would be produced upon photoexcitation would be unable to diffuse to other sites. The NO× doped nanoparticle has a localized HOMO (N(2p)) on the nitrogen atom, but which overlaps with the surrounding O(2p) orbitals, therefore photoholes will be able to diffuse throughout the nanoparticle. However, the optical transition moment for the HOMO-LUMO transition is likely to be small as there is no overlap between HOMO and LUMO states. Interestingly, for the smaller nanoparticles, the dopant does not have an overlap with the fMOs. Structural distortions are likely to be easier for smaller nanoparticles and coincide with a transfer of electron density to the oxygen atoms as oxygen is more electronegative than nitrogen. Such distortions do not occur for the larger nanoparticles. Finally, the CO × doped nanoparticle has a delocalized HOMO extending over several oxygens, facilitating photohole diffusion through the nanoparticle. Additionally, there is an overlap between the LUMO (Ti(3d)) and HOMO states, implying that this transition is likely to be optically active. The fMO for a doped nanoparticle is on the surface and thus is able to oxidize or reduce adsorbed species. In comparison with the bare nanoparticles, one of the fMOs are well separated from the other states, CO× and SO× dopants raise the HOMO with respect to the isolated nanoparticle, while the NO× dopant lowers the LUMO with respect to

the isolated nanoparticle. This is further reflected in the DFT transition energies. Experimentally, sol-gel synthesized TiO2 nanoparticles of diameter 5 to 10 nm with a 5% N-doping concentration,69 and codoped N/Au anatase phase nanoparticles with a diameter between 10-12 nm were found to shift light adsorption from the UV to the visible region, suggesting that the bandgap is reduced.70 The sol-gel synthesis of carbon and sulfur doped anatase nanoparticles of 7-9 nm diameter was found to also shift light adsorption from the UV to the visible.71 Interestingly, sulfur and carbon have very similar shifts. As opposed to the isolated bare nanoparticles there is little experimental information on the electronic and optical properties of sub nanometer doped-TiO2 nanoparticles. We show, in Figure 8 and in Table 3, the calculated DFT (spin-permitted excitations only) and TDDFT transition energies of our nanoparticles. For all of the nanoparticles, doping reduces the gap with respect to the undoped system. Our results are thus qualitatively in agreement with the simulations of N-doped titania nanoparticles (n ) 5 to 9) by Mowbray et al.64 For DFT transition energies (which we emphasize are qualitative) the order is NO× < CO× < SO×. For the TDDFT singlet gaps, the trend is more complicated; typically, the order is the same as for the DFT gaps but often the CO× and SO× transition energies will overlap. For the smaller nanoparticles (up to n ) 10) the transition energy is much smaller for NO× doped structures (at approximately 1.0 eV) than for CO× and SO× doped nanoparticles (at approximately 2.0 eV). For the latter dopants, photoexcitation of an electron from the HOMO to the LUMO will generate excitons with enough energy to dissociate H2O (1.22 eV) while the NO× doped nanoparticles will not generate excitons of sufficient energy. Clearly N-doping of subnanometer nanoparticles is not ideal for H2 generation. For the specific case of NO× doped (TiO2)13, however, the TDDFT singlet transition energy is approximately the same as that for CO× and SO× doped (TiO2)13. We cannot state, due to the current limitations of our methodology, whether this is an outlier from the general trend for (TiO2)n nanoparticles or represents a

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Figure 8. (a) Calculated DFT transition energies (EHL), and (b) and TDDFT singlet transition energies (ETD) for CO×, NO×, and SO× doped (TiO2)n nanoparticles. For spin-polarized system only the spin-permitted excitation energies are shown. All units are in eV.

transition to a point where NO× doped nanoparticles can produce excitons of sufficient energy to dissociate H2O. Finally, doped nanoparticles have TDDFT triplet transition energies that are significantly lower than singlet transition energies, in particular CO× doped n ) 2, 3, and 7 nanoparticles and SO× doped (TiO2)6. For the larger clusters, triplet excitation energies will be lower than the singlet energies, by approximately 0.25 eV (for CO× doping) and 0.20 eV (for SO× doping). Thus both types of

photoexcitation are likely to occur, singlet excitation with no spin flip, and a lower energy triplet excitation with an associated change in spin. 3.3. Optical Spectra. In this section, we report the full optical spectra of the bare and doped (TiO2)6 nanoparticle, as calculated within TDDFT. This allows us to characterize the optical response of the nanoparticles over a range of excitation energies rather than just the HOMO-LUMO transition energy. Furthermore, the calculation of singlet-singlet oscillator strengths enables a direct evaluation of the efficiency of any particular excitation and thus the likelihood of that excitation occurring. We do not calculate the optical DOS of the singlet-triplet excitations as in principle they are spin-forbidden. The (TiO2)6 nanoparticle in particular was chosen because we found it is the easiest nanoparticle to dope, and thus a structure of interest. The optical spectra are shown in Figure 9. For the bare, or undoped, nanoparticle we find a broad optical DOS for energies over 3.25 eV. We note that the shape of the optical DOS is similar to the optical DOS for (TiO2)15, as calculated by Qu et al.62 However, for the bare (TiO2)6 nanoparticle there is very little absorption spectra. The implication is that the bare nanoparticle is not particularly photoactive. This is not the case for the doped nanoparticles. For CO× doped (TiO2)6 the optical DOS has a similar shape to the bare nanoparticle over 3.25 eV, however, there are also additional peaks below that energy reflecting the lower transition energy. Furthermore, there are several strong absorption peaks, indicating a higher photoactivity. Of special note is the lowest energy absorption peak at ∼2.50 eV, which corresponds to the peak energy of the solar spectrum. For NO× doped (TiO2)6 the optical DOS is redshifted to lower energies (with onset of broad adsorption over 2.50 eV). Furthermore, there are isolated optical DOS peaks below this energy. There are two very strong absorption peaks for this system, but at 1.00 and 1.30 eV, they are too low for efficient solar harvesting. Additionally, the absorption peak at 1.00 eV would not generate an exciton with sufficient energy to dissociate H2O. Finally, for the SO× doped (TiO2)6 there is a broad optical DOS from 1.55 eV, however, the few strong absorption peaks present occur at energies greater than 2.75 eV. Comparing the absorption spectra of CO× doped (TiO2)6 and SO× doped (TiO2)6 we conclude that carbon is the better dopant for promoting photoactivity under visible light as it has a strong adsorption peak at a lower energy than the sulfur-doped system. This is in qualitative agreement with Hamal et al.,71 who found that C and S codoped anatase nanoparticles had a better

TABLE 3: Calculated DFT Transition Energy (EHL), Singlet-Triplet Energy Difference (EST), TDDFT Singlet Transition Energy (ETD), and Triplet Transition Energy (ETD3) for the CO×, NO×, and SO× Doped (TiO2)n Series of Nanoparticles and Bulk Rutilea CO× EHL Rutile (TiO2)1 (TiO2)2 (TiO2)3 (TiO2)4 (TiO2)5 (TiO2)6 (TiO2)7 (TiO2)10 (TiO2)13 a

CO×

0.76 1.12 1.97 1.53 1.88 2.08 2.23 1.85 2.20 1.58

NO×

EST

ETD

0.04 0.69 1.16 1.14 1.39 0.85 1.62 1.15

0.08 2.22 1.51 1.95 2.18 2.15 1.70 2.15 1.81

SO×

ETD3

EHL

ETD

EHL

EST

ETD

ETD3

1.34 0.89 1.61 1.99 1.88 0.85 1.89 1.58

0.81 1.30 1.08 0.26 0.39 1.36 0.52 1.38 0.54 1.18

0.38 0.74 0.24 0.18 0.74 0.58 1.43 1.06 2.02

1.53 0.77 2.61 1.73 2.35 2.08 2.17 2.59 2.35 2.06

1.42 1.64 1.80 1.66 1.18 1.90 1.85 1.85

0.80 2.25 2.74 1.96 1.69 1.59 2.48 2.02 1.95

2.05 2.40 1.75 1.54 0.67 2.15 1.90 1.81

All units are in eV. As all NO× systems are doublets, we cannot report triplet states. Furthermore, the TiOC, TiON, and TiOS trimers and doped rutile are all triplets.

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Figure 9. Calculated optical DOS and absorption spectra of TDDFT singlet-singlet excitations, of (from top to bottom): bare (TiO2)6, CO× doped (TiO2)6, NO× doped (TiO2)6, and SO× doped (TiO2)6. For all plots the absorption spectra has been rescaled by a factor of 50 so as to be visible when compared with optical DOS.

photocatalytic production rate for CO2 from CH3CHO than nanoparticles that are purely S-doped. 4. Conclusions Detailed ab initio simulations were performed to determine the structural, thermodynamic, and electronic properties of subnanometer (TiO2)n nanoparticles (n ) 1, 2, 3, 4, 5, 6, 7, 10, and 13), a paradigm system of interest for photocatalytic watersplitting. The thermodynamics and effects on the electronic structure of nonmetal anion (C-, N-, and S-) doping of the nanoparticles were also calculated in order to determine their effects on photoactivity. The structural motifs of the (TiO2)n nanoparticles are found to substantially differ from those of the bulk. Our predicted global minima structures for the (TiO2)n nanoparticles are broadly similar to stable or low energy metastable structures found by other authors, where different ranking is typically due to using a different energy landscape, for example, the use of hybrid exchange correlation functionals rather than a pure GGA used here. There is a clear spatial separation between frontier molecular orbitals, thus direct excitation from the HOMO to the LUMO would have small oscillation strength. However, the fMOs are on the surface of the nanoparticle and thus are available to interact with adsorbed species. In agreement with experiment, subnanometer nanoparticles (n ) 1 to 7) have smaller singlet transition energies (as calculated by TDDFT) than the bulk, with triplet excitation energies of almost exactly the same magnitude. The larger nanoparticles we consider do not possess onefold oxygen atoms and have transition energies of the same magnitude as the bulk. Therefore, we conclude that the physical mechanism responsible for gap narrowing in TiO2 nanoparticles is the formation of onefold oxygen atoms, and that nanostructuring TiO2 can reduce the gap. Nonmetal anion doping and the corresponding atomic structures were determined. In general, sulfur prefers two-fold oxygen

sites, whereas nitrogen and carbon typically bonded to three and four neighboring titanium atoms, respectively. Importantly, as both dopants prefer a greater number of bonds than oxygen, both typically favored the highest coordinated oxygen sites. Sulfur doping has the lowest formation energy, then nitrogen, and then carbon. All three dopants are easier to emplace in nanoparticles than in the bulk. Additionally, with increasing nanoparticle size the defect formation energy for carbon substitutionals decreases. This paradoxically implies that it is easier to carbon dope larger nanoparticles than smaller ones, although we expect that at the point where the global minima structure resembles that of a bulk phase this trend will reverse. The (TiO2)6 nanoparticle in particular is easy to dope, suggesting that this is the ideal size for nonmetal doping. All dopants modify the fMOs. Sulfur doped nanoparticles have a HOMO of S(3p) character (and for the smaller nanoparticles strong O(2p) character arising from the onefold oxygens) strongly localized on the dopant, affecting the photoactivity of the nanoparticle by trapping photoholes at the dopant site. The nitrogen-doped nanoparticles have HOMO states that overlap with the oxygen atoms thus permitting easier diffusion of the photohole. The carbon-doped nanoparticles have HOMO states with C(2p) character that is delocalized over both oxygen and titanium atoms. Photohole diffusion through the nanoparticle will be quite easy, and the overlap of the HOMO with the LUMO will allow HOMO-LUMO transitions with significant oscillator strength, i.e., is likely to be optically active. Furthermore, the presence of both fMOs on the same site would allow the nanoparticle to simultaneously oxidize and reduce H2O, allowing whole cycle electrochemistry. From a fMO perspective, carbon is the best dopant for TiO2 nanoparticles. All of the dopants reduce the transition energy within TDDFT, nitrogen reducing the transition energy to ∼1.0 eV, too low for water-splitting applications, and both carbon and sulfur dopants reducing the transition energy to ∼2.0 eV. Triplet excitation

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energies for the carbon- and sulfur-doped nanoparticles are ∼0.25 and 0.20 eV lower in energy; thus spin-forbidden excitations are competitive with spin-permitted excitations. Calculations of the excitation spectra within TDDFT show that bare nanoparticles have a broad optical DOS but little absorption strength up to 5.0 eV, whereas nonmetal anion doping redshifts the onset of the optical DOS to lower energies. Additionally, the doping increases the absorption spectra strength, improving the photoactivity. Carbon doping has the onset of absorption spectra at 2.50 eV, while for sulfur doping this is at 2.75 eV. The lower energy for absorption onset for the carbon doped system suggests that carbon is better for improving nanoparticle photoactivity, in qualitative agreement with experiment. Our detailed calculations thus show, from both chemical and optical requirements, carbon anion dopants are the best for improving the photoactivity of TiO2 nanoparticles. It remains a challenge to reliably synthesize anion-doped TiO2 nanosystems. We therefore urge that further experimental and theoretical investigations be performed in order to fully understand the properties of these new materials which are of considerable interest for clean energy production, photocatalysis, and other applications. Acknowledgment. S.A.S. acknowledges that this work was supported by the EPSRC under a Platform Grant (GR/S52636/ 01, EP/E046193/1). National HPC resources, namely HPCx, were provided by S.A.S. membership of the UK-SHEC consortia. S.M.W. acknowledges financial support from EPSRC (EP/F067496). We also thank Prof. C. R. A. Catlow, Prof. Z. X. Guo, Dr A. A. Sokol, and Dr A. Walsh. References and Notes (1) Vishnyakov, V. M. Vaccum 2006, 80, 1053–1065. (2) Shevlin, S. A.; Guo, Z. X. Chem. Soc. ReV. 2009, 38, 211–225. (3) Esswein, A. J.; Nocera, D. G. Chem. ReV. 2007, 107, 4022–4047. (4) Osterloh, F. E. Chem. ReV. 2008, 20, 35–54. (5) Fujishima, A.; Honda, K. Nature 1972, 238, 37–38. (6) Kiwi, J.; Gra¨tzel, M. J. Phys. Chem. 1987, 91, 6673–6677. (7) Maeda, K.; Teramura, K. Nature 2006, 440, 295. (8) Li, Z.; Dong, T.; Zhang, Y.; Wu, L.; Li, J.; Wang, X.; Fu, X. J. Phys. Chem. C 2007, 111, 4727–2733. (9) Wang, X.; Maeda, K.; Thomas, A.; Takanabe, K.; Xin, G.; Carlsson, J. M.; Domen, K.; Antonietti, M. Nat. Mater. 2009, 8, 76–80. (10) Inoue, Y. Energy EnViron. Sci 2009, 2, 364–386. (11) Rangan, K.; Arachigage, S. M.; Brown, J. R.; Brewer, K. J. Energy EnViron. Sci 2009, 2, 410–419. (12) Walsh, A.; Ahn, K.-S.; Shet, S.; Huda, M. N.; Deutsch, T. G.; Wang, H.; Turner, J. A.; Wei, S. H.; Yan, W.; Al-Jassim, M. M. Energy EnViron. Sci 2009, 2, 774–782. (13) Linsebegler, A. L.; Lu, G.; JYates, J. T., Jr. Chem. ReV. 1995, 95, 735–758. (14) Thompson, T. L.; Yates, J. T., Jr. Chem. ReV. 2006, 106, 4428– 4453. (15) Tachikawa, T.; Fujitsuka, M.; Majima, T. J. Phys. Chem. C. 2007, 111, 5259–5275. (16) Ni, M.; Leung, M. K. H.; Leung, D. Y. C.; Sumathy, K. Renew. Sust. Energy ReV. 2007, 11, 401–425. ´ .; Qu, Z.-W.; Kroes, G.-J.; Rossmeisl, J.; Nørskov, J. K. (17) Valde`s, A J. Phys. Chem. C 2008, 112, 9872–9879. (18) Tang, H.; Le´vy, F.; Berger, H.; Schmid, P. E. Phys. ReV. B 1995, 52, 7771–7774. (19) Tang, H.; Berger, H.; Schmid, P. E.; Le´vy, F.; Buri, G. Solid State Commun. 1993, 87, 847–850. (20) Khan, S. U. M.; Al-Shahry, M.; Ingler, W. B., Jr. Science 2002, 297, 2243–2245. (21) Wang, H.; Lewis, J. P. J. Phys.: Condens. Matter 2005, 17, L209– L213. (22) Di Valentin, C.; Pacchioni, G.; Selloni, A. Chem. Mater. 2005, 17, 6656–6665. (23) Yang, K.; Dai, Y.; Huang, B.; Whangbo, M.-H. J. Phys. Chem. C 2009, 113, 2624–2629. (24) Diwald, O.; Thompson, T. L.; Goralski, E. G.; Walck, S. D.; Yates, J. T., Jr. J. Phys. Chem. B 2004, 108, 52–57.

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