Abstract
A highly fluorinated anatase lattice has been recently reported, providing a new class of materials whose general chemical formula is Ti_{1−x}□_{x}X_{4x}O_{2−4x} (X^{−} = F^{−} or OH^{−}). To characterise the complex structural features of the material and the different F environments, we here apply a computational screening procedure. After deriving a polarisable force—field from DFT simulations, we screen in a stepwise fashion a large number of possible configurations differing in the positioning of the titanium vacancies (□) and of the fluorine atoms. At each step only 10% of the configurations are retained. At the end of the screening procedure, a configuration is selected and simulated using DFTbased molecular dynamics. This allows us to analyse the atomic structure of the material, which is strongly disordered, leading to a strong decrease (by 0.8 eV) of the band gap compared to conventional anatase.
Introduction
Titanium dioxide, TiO_{2}, is a widely studied material. TiO_{2} has in fact several promising applications, for example in the fields of photocatalysis, green chemistry and energy storage^{1,2,3,4,5,6,7,8}. Naturally occurring polymorphs of TiO_{2} include rutile, anatase and brookite. Recently, interest in the polymorphs of TiO_{2} has been sparked in particular by their possible application as anodic materials in Li ion batteries^{9,10,11,12,13,14}. Fluorinated TiO_{2} has also been investigated^{15,16,17,18,19,20} since the presence of F in the compound might improve the sought characteristics of the material^{17} or stabilise the highly reactive {001} facets of the anatase crystal^{19,21}. The nature of the fluorinated compound depends strongly on the fluorination technique employed^{18,22}. So far, the stabilisation of fluorine within the anatase lattice of TiO_{2} has been poorly understood, probably because of the structural complexity of the fluorinated material.
Pure anatase is a tetragonal crystal, with c ≃ 2.5a and its lattice is characterised by TiO_{6} octahedral units. Recently, a novel synthesis technique conducted in our laboratory^{23} has led to the preparation of a highly fluorinated anatase material in which fluoride or hydroxide anions replace the oxides in their lattice sites and the resulting charge deficiency is compensated by the formation of a cationic vacancy (□) every four substitutions. The material obtained has thus the general formula Ti_{1−x}□_{x}X_{4x}O_{2−4x}, where X^{−} = F^{−} or OH^{−} (the amount of F^{−} may vary depending on the synthesis conditions). Elemental analysis and synchrotron diffraction have revealed the existence of more than 20% cation vacancies. In fact the stoichiometric formula Ti_{0.78}□_{0.22}X_{0.88}O_{1.12} has been assigned to the most fluorinated composition of the material. By using ^{19}F NMR spectroscopy, it has also been possible to discern three different coordination modes for the F atoms: F − Ti_{1}□_{2}, F − Ti_{2}□_{1} and F − Ti_{3}, highlighting the complex structural arrangement present in the material.
Here we report the results of a computational study of the fullyfluorinated, hydroxidefree material (i.e. Ti_{0.78}□_{0.22}F_{0.88}O_{1.12}) performed in order to better characterise its structural features and the effect of fluorination on the electronic structure. The enormous number of possible structural arrangements of the vacancies and of the F atoms in the anatase structure render the problem untreatable directly by ab initio simulations. Therefore we apply a screening procedure on the possible configurations of the material, in the spirit of the emerging high—throughput techniques^{24,25,26}, by using classical Molecular Dynamics (MD). Several force—fields have been previously proposed for pure TiO_{2}^{27,28,29,30,31,32,33}. In this work, we use a polarisable force—field valid for the pure phase^{34} as well as for the fluorinated material. We have extracted its parameters from Density Functional Theory (DFT) simulations, via a wellestablished force and dipole fitting procedure^{35,36}. We have chosen to derive a new force—field instead of using an already available one for TiO_{2}. This is motivated by the fact that we want the force—field to be compatible with O to F substitutions, as well as with other oxide species, e.g. SiO_{2}, for future studies^{34}. The details on the force—field employed are discussed in Supplementary Section S1, while an additional validation of the parameters involving fluorine atoms is presented in Supplementary Section S2.
In order to generate fluorinated samples starting from the pure TiO_{2} anatase, we apply a screening procedure, similar in spirit to what done by Wilmer et al. for metalorganic frameworks^{37} or by Coudert for zeolites^{38}. At the fixed target composition Ti_{0.78}□_{0.22}F_{0.88}O_{1.12}, we consider samples containing F in all possible environments F − Ti_{1}□_{2}, F − Ti_{2}□_{1} and F − Ti_{3}, as suggested by NMR^{23}. We leave the ratio of F in the different environments free to vary at random. The starting fluorinated structures are generated from the 4 × 4 × 2 pure anatase TiO_{2} structure^{39} (Ti_{128}O_{256}) leading to a system thus composed: Ti_{100}□_{28}F_{112}O_{144}. We generate these configurations by erasing 28 Ti ions at random with no constraints on the creation of adjacent vacancies and we randomly substitute 112 O with 112 F. We impose that all F and O must be attached to at least one Ti.
The screening procedure is then initiated. The protocol is as follows:

1
we perform singlepoint energy calculations on ≃1.5 ⋅ 10^{5} configurations; we then retain the ≃1.5 ⋅ 10^{4} configurations with the lowest energy for the following step.

2
we perform 0 K geometry optimisations of the atomic positions, keeping the length of the cell vectors fixed; we retain at maximum the 1.5 ⋅ 10^{3} configurations with the lowest energy for the following step.

3
we perform 0 K cell optimisations of both the atomic positions and the lengths of the cell vectors, while keeping the box angles fixed at α = β = γ = π/2; we retain at maximum the 1.5 ⋅ 10^{2} configurations with the lowest energy for the following step.

4
we temper the configurations performing 10 ps NVT runs at finite temperatures from T_{1} = 25 K to T_{12} = 300 K, every ΔT = 25 K. The 15 configurations with the lowest energy at T_{12} = 300 K are retained for the following step.

5
for the remaining samples, we perform a series of longer MD simulations at 300 K, first in the NVT and then in the NPT ensemble.

6
we then simulate the configuration with the lowest potential energy for 10 ps using using DFT—based molecular dynamics. We extract structural (bond length, fluorine environments) and electronic (density of states) characteristics of the material from this simulation.
Testing all the starting configurations in a generic, entirely ab initio based highthroughput procedure would be impossible. Generally, such studies involve static calculations only since performing ab initio MD simulations is computationally too expensive. Nevertheless, it is interesting to test whether our selected configurations, i.e., the 10 configurations remaining at the end of step 5) of the screening procedure would have also been selected if ab initio static calculations had been performed. To test this, we take their initial structures and perform a full DFT relaxation. Then we take the same number of random configurations from the starting pool of configurations. We find that the configurations given by the classical screening all have a lower final DFT energy than the ones taken at random. The results of this validation are shown in Supplementary Fig. S2.
Next, we analyse how the initial structural arrangements correlate with the energy of the configurations. The results are shown in Fig. 1. We see that the lowest energies (at 0 K) correlate with a higher fraction of F − Ti_{2}□_{1}. This is consistent with previous static DFT calculations performed on a system with only one vacancy and four O/F substitutions^{23}, which showed that having the F closest to the vacancy stabilises the structure. In Fig. 1 we also report the initial energies of the best configurations given at the end by the screening procedure. We observe that these final screening configurations are found closer to the average F speciation values rather than at the highest F − Ti_{2}□_{1} relative compositions. Some of them have strongly been stabilised during the procedure, showing the importance of taking into account relaxation and thermal effects (see also Supplementary Fig. S3).
In order to compare the structural properties of the material as found in the experiments with our simulations, we plot together the experimental xray structure factor S(k) and the one that we calculate from our trajectories using the Ashcroft—Langreth partial structure factors according to the formula:
where α,β = Ti, O, F. x_{α} are the relative atomic concentrations of atoms of type α, S_{αβ}(k) are the partial structure factors calculated from the simulation trajectories using
where the dynamic variable represents the Fourier component of the atomic density of type α atoms at wave vector k:
with r_{i} the position of atom i and N_{α} the number of atoms of type α in the system. The angular brackets denote a thermal average, which was in practice evaluated as the time average over the whole simulation. Finally, f_{α}(k) are the kdependent atomic x—ray scattering factors. They are calculated using the analytic approximation:
where the coefficients a_{α,i}, b_{α,i} and c_{α} are taken from Ref. 40 for O^{2−} and from Ref. 41 for Ti^{4+} and F^{−}. The structure factor calculated from the DFTbased molecular dynamics simulation performed on the final configuration is compared to the experimental signal in Fig. 2. The agreement between the two sets of data is good, taking into account that the experiments have been performed on nanoparticles, which leads to a strong broadening of the peaks and that part of the fluoride ions are replaced by hydroxide groups. This may also affect the comparison, notwithstanding that F and OH are isoelectronic and thus their contribution to xray diffraction should not differ much if they occupy similar sites.
We also calculate the speciation of fluoride during the DFTbased molecular dynamics simulation. Contrarily to the initial configurations analysed in Fig. 1, the local relaxation of the F atoms (especially around the vacancies) leads to a wide distribution of Ti—F distances. It is therefore necessary to introduce a cutoff distance for assigning an environment to the F atoms. In Fig. 3 we show the time evolutions of the concentrations of F − Ti_{1}□_{2}, F − Ti_{2}□_{1} and F − Ti_{3} for a cutoff of 2.7 Å which corresponds to the first minimum of the Ti—F radial distribution function. We observe that after 2 ps of simulation, the concentrations equilibrate around average values of 13/66/21% for F − Ti_{1}□_{2}, F − Ti_{2}□_{1} and F − Ti_{3} respectively. This compares very well with the percentages measured by NMR in the experimental sample, i.e., 13/70/17%^{23}. We can therefore conclude that the structure yielded by our screening procedure is realistic. This allows us to analyse it further in order to predict the material properties. We note that the F − Ti_{2}□_{1} average concentration is larger than the corresponding fraction in the initial pool of configurations as shown in Fig. 1, because the fluorine atoms positions relax around the titanium vacancies during the first 2 ps of the simulation. However, no strong lattice rearrangements are observed, as can be seen from Supplementary Fig. S4.
The electronic structure is of particular interest for many applications, since TiO_{2}based materials are widely used in photocatalysis. We have therefore calculated the electronic density of states of fluorinated anatase on a series of snapshots extracted from our DFTbased molecular dynamics simulation and compared it with the case of pure TiO_{2} anatase. We have used the hybrid functional HSE06^{42,43} for these calculations. In agreement with previous works^{44}, we see in Fig. 4 that the valence band edge of pure TiO_{2} anatase is dominated by O 2p and the conduction band edge is formed by Ti 3d. The band gap is much narrower in Ti_{0.78}□_{0.22}O_{1.12}F_{0.88}, by 0.8 eV. Unlike the case of conventional doping with heteroatoms^{45}, the additional 2p states associated with fluoride ions do not locate at the top of the valence band, but rather at its bottom. The strong narrowing of the band gap is therefore due to the different structure of the material. In a previous study on TiO_{2} nanocrystals, Chen et al. have shown that, due to the presence of structural disorder, their materials exhibit a band gap substantially smaller than the one of pure bulk materials^{46}. It is very likely that similar effects are at play here.
The structural disorder is apparently at the origin of these strong electronic structure changes. To test this idea, in Fig. 5 we show the partial radial distribution functions at ambient conditions g_{αβ}(r) for the simulated pure anatase TiO_{2} and for the fluorinated anatase configuration selected by the screening procedure. The effect of the disorder introduced by the vacancies is immediately evident looking at the g_{Ti−Ti}(r) and at the g_{O−O}(r). The g_{Ti−O}(r) structure seems to be conserved to a large extent at least for the first two shells, although the presence of vacancies induces a shortening of the first neighbour distance. The effect of disorder is also clear when looking for example at the region in between the first two peaks. We also observe that on the one hand, g_{Ti−O}(r) and g_{Ti−F}(r) are very similar and so are the g_{O−O}(r), g_{F−F}(r) and g_{O−F}(r). This confirms that the fluorine atoms substitute the oxygen ones inside the anatase structure.
In conclusion, in order to characterise fluorinated anatase Ti_{0.78}□_{0.22}F_{0.88}O_{1.12}, we have developed a screening procedure employing a polarisable force—field. It has allowed us (i) to select the best configurations starting from a very large pool (hundreds of thousands) of possible configurations; (ii) to reproduce the experimental structure, (iii) to study details of the partial atomic and electronic structure using DFTbased molecular dynamics. Our results show that fluorinated anatase has a highly disordered structure, which results in a lower band gap, by 0.8 eV, compared to conventional anatase. Therefore we conclude that fluorination appears as a very promising route for tuning material properties. This may be exploited for several applications, for example photocatalysis.
Methods
We have performed the classical simulations using the software CP2K (single point calculations/geometry/cell optimisations, i.e., steps 1) to 3) of the screening procedure) and the inhouse simulation software PIMAIM (molecular dynamics simulations, step 4) and 5) of the screening procedure). We have cut off the short—range interactions at half the norm of the shortest box vector (or less in NPT runs). The time step for the integration of the equations of motion has been set to 1 fs.
The DFTbased MD simulation has also been performed using the software CP2K^{47}, using the Quickstep algorithm. We have used the GGA PBE^{48} exchangecorrelation functional and we have employed the DZVPMOLOPTSRGTH basis set^{49}. Moreover, we have used the GoedeckerTeterHutter^{50} pseudopotentials; for Ti atoms, the electronic orbitals explicitly represented are 3s^{2}3p^{6}3d^{2}4s^{2}, for O atoms 2s^{2}2p^{4} and for F atoms 2s^{2}2p^{5}. We have set a plane wave cutoff of 400 Ry. We have added dispersive interactions through the use of the DFTD3 correction^{51}, with a cutoff radius of 30 Å. We have accumulated the trajectory for 10 ps, with the simulations time step being 0.5 fs. We have conducted the simulation in the NVT ensemble with a target temperature of 300 K. We have calculated the electronic density of states on a series of snapshot extracted from the trajectory, using the HSE06 functional^{42,43}.
Additional Information
How to cite this article: Corradini, D. et al. Tuning the Electronic Structure of Anatase Through Fluorination. Sci. Rep. 5, 11553; doi: 10.1038/srep11553 (2015).
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Acknowledgements
We thank FrançoisXavier Coudert for introducing us to the screening techniques. We thank Paul A. Madden, Benjamin J. Morgan and Benjamin Rotenberg for discussions. The research leading to these results has received funding from the the European Union through the FP7—framework (FLUOSYNES, Contract PCIGA2012321879). We also thank Karena W. Chapman for providing the experimental S(k) data. The work done at the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DEAC0206CH11357.
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D.C. and M.S. have designed research. D.C. has implemented the screening procedure and has performed most of the simulations. M.S. has conducted the band gap calculations. D.C. and M.S. have written the manuscript and prepared the figures. D.D. has provided the experimental input. All the authors have participated in the discussions and reviewed the manuscript.
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Corradini, D., Dambournet, D. & Salanne, M. Tuning the Electronic Structure of Anatase Through Fluorination. Sci Rep 5, 11553 (2015). https://doi.org/10.1038/srep11553
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DOI: https://doi.org/10.1038/srep11553
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