PHYSICAL REVIEW B 70, 115101 (2004)
Cubic TiO2 as a potential light absorber in solar-energy conversion M. Mattesini,1,2,* J. S. de Almeida,1 L. Dubrovinsky,3 N. Dubrovinskaia,3 B. Johansson,1,4 and R. Ahuja1 1Condensed
Matter Theory Group, Department of Physics, Uppsala University, Box 530, SE-75121 Uppsala, Sweden de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049, Spain 3Bayerisches Geoinstitut, Universität Bayreuth, D-95440 Bayreuth, Germany 4Applied Materials Physics, Department of Materials and Engineering, Royal Institute of Technology, SE-10044 Stockholm, Sweden (Received 14 April 2004; revised manuscript received 9 June 2004; published 2 September 2004) 2Departamento
Materials are currently sought for use in the photo-induced decomposition of water on crystalline electrodes. Titanium dioxide is valuable in this respect. The electronic structural properties of cubic TiO2 polymorphs were investigated by means of first-principles methods. We demonstrate that both fluorite- and pyrite-type TiO2 have important optical absorptive transitions in the region of the visible light. A cubic TiO2 phase that can efficiently absorb the sunlight would be an important candidate material for the development of the solar cells. Also, we present results on the Ti L edges for the two different titania forms. We predict that a qualitative spectroscopic discrimination of the cubic polymorphs can be achieved by following the Ti 2p → 3d x-ray transitions. DOI: 10.1103/PhysRevB.70.115101
PACS number(s): 71.15.Mb, 71.20.⫺b, 78.20.Bh, 61.10.Ht
I. INTRODUCTION
The most abundant forms of titanium dioxide 共TiO2兲, namely rutile and anatase, are largely used as antireflection coatings for solar cells and more, in general, in the development of photoelectrodes for photochemical energyconversion processes.1 The ideal material for high-efficiency photoelectrodes must satisfy several specific requirements in terms of semiconducting and electrochemical properties.2–4 Titanium dioxide is chemically inert and is certainly one of the best materials that can be exposed to aqueous solutions owing to its outstanding corrosion resistance. Nonetheless, an important drawback for its application as a photoelectrode is related to the limited ability for light absorption due to a relative large band gap 共Eg兲 value 共3.0– 3.2 eV兲.1,5 Accordingly, TiO2 will absorb only in the ultraviolet part of the solar emission spectra, thus imposing low conversion efficiency. The band gap is therefore a highly relevant parameter for material candidates for photoelectrodes. The optimal Eg for high-performance electrodes has been fixed to ⬃2 eV (Ref. 2). Unfortunately, up to now, high corrosion-resistant materials with such a band gap have not yet been identified. CdTe and InP, for example, have band gaps that match reasonably well with the spectral distribution of the sunlight, but when used as photoelectrodes in aqueous solution they either corrode or become inert.6,7 Another very important requirement is imposed by the potential of the photoexcited electron in the semiconductor. Very often, when trying to reduce the value of Eg in metal oxides (such as ZnO and Fe2O3), this potential becomes more positive than the potential needed to split H2O into H2 and O2. The overall effect is, therefore, to make the reaction of water thermodynamically unfavorable at ambient conditions.8 A number of attempts to shift the spectral response of TiO2 into the visible region 共380 nm艋 艋 750 nm兲 have so far failed. In particular, many tentatives were focused on the doping of TiO2 with aliovalent ions, such as V4+ / V5+ to form the solid solution 共Ti1−xVx兲O2 (Refs. 8 and 9). How1098-0121/2004/70(11)/115101(9)/$22.50
ever, despite of the narrowing of Eg to values of about 2 eV, doped TiO2 systems have often shown a noticeable diminution of the photoactivity due to an enhancement of the recombination mechanism of the photoexcited electron-hole pairs.2 Nitrogen-doped Ti共2−x兲Nx films have also been recently proven to be important for band-gap narrowing.10 Nevertheless, preliminary results have shown that a substantial amount of recombination processes may occur to reduce the photocatalitic activity.11 The presence of trapping states in both cation- and anion-doped TiO2 systems strongly enhance the recombination of the electron-hole pairs, thus lowering the photoactivity of the electrode. In the case of Ti共2−x兲Nx, efforts are currently being directed to determine whether such kinds of localized states represent an intrinsic property of the doped material or instead are originated by surface states, interstitial N atoms or, more in general, by the poor crystallinity of the analyzed samples.12 There is no doubt, however, that a pure crystalline TiO2 phase with a smaller band gap is likely to be a good corrosion-resistance electrode that will also hamper the undesired recombination effects of the photoabsorption process. The recent discovery of a titania polymorph (cotunnite)13 has opened a great expectation towards the possibility to synthesize new high-pressure TiO2 forms with smaller band gaps and to quench them at room conditions for practicable applications. As a matter of fact, titanium dioxide is a naturally occurring mineral with an extraordinary rich phase diagram. For instance, rutile and anatase (the most stable forms of TiO2) can transform at high pressure to polymorphs isostructural with columbite 共␣-PbO2兲,14,15 baddeleyite 共ZrO2兲,15,16 and cotunnite 共PbCl2兲.13,17 Furthermore, based on the fact that various rutile-structured metal oxides (SnO2 , PbO2 , HfO2, and RuO2) could transform to the fluorite-type phase at high pressure, it has also been proposed that TiO2 might convert to a cubic fluorite 共CaF2兲 system.18,19 In this structure each Ti ion is eight coordinated with O ions 共dTi−O = 2.06 Å兲, while each oxygen is tetrahedrally surrounded by Ti atoms. The crystal structure belongs
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FIG. 1. (Color online) Unit cell of fluorite-structured TiO2 along the [001] plane [space group Fm3m (225)]. Larger spheres represent the titanium 共Ti兲 atoms, while small spheres indicate the oxygen 共O兲 ions. The local-density approximation (LDA) structural parameters computed at 0 GPa are: a = 4.748 Å, Ti (0.00,0.00,0.00), and O (0.25,0.25,0.25).
to the Fm3m (225) space group, with titanium occupying the (0,0,0) position and the two oxygen atoms at ±共 41 , 41 , 41 兲. Although there have been a number of high-pressure experiments that indicate the formation of the cubic structure at about 60 GPa,15,20 so far it is not completely certain whether the fluorite phase exists or not. More recent investigations with Rietveld refinement of the x-ray diffraction data from SnO2 , PbO2, and RuO2 have also revealed the possibility that the high-pressure phases adopt a distorted fluorite struc¯ ) isostructural to pyrite 共FeS 兲.21 ture (with space group Pa3 2 The main difference between fluorite (Fig. 1) and pyrite (Fig. 2) concerns the position of the oxygen atoms; in fluorite they are located at ±共0.25, 0.25, 0.25兲, while in pyrite they are positioned at ±共0.34, 0.34, 0.34兲. This gives rise to a geometrical change into the coordination sphere around the Ti atoms. In particular, each cation has now an inner shell of six oxygen atoms (with dTi−O = 1.96 Å) plus two O ions at a longer distance 共dTi−O = 2.83 Å兲. Unfortunately, a clear and detailed experimental determination of these structures has been generally prevented by the various technical difficulties that characterize highpressure experiments. Previous ab initio calculations were also performed in order to support the identification of the cubic phases by investigating both the CaF2 (Refs. 22 and 23) and the FeS2 (Ref. 23) model systems. It was theoretically demonstrated that the pyrite form is generally more stable than the fluorite structure, although neither of the two polymorphs can be stabilized over rutile at pressures below 60 GPa. Therefore, it is very likely that an efficient synthesis route for the cubic TiO2 form will demand high-temperature
FIG. 2. (Color online) Projection of the pyrite-type TiO2 phase ¯ (205)]. The computed LDA along the [001] plane [space group Pa3 zero-pressure structural parameters are: a = 4.813 Å, Ti (0.00,0.00,0.00), and O (0.34,0.34,0.34).
conditions to avoid the competition with the formation of the cotunnite phase.23 So far as that is concerned, experiments conducted on an anatase sample using an electrically and laser-heated diamond-anvil cell have shown that at a pressure of 48 GPa and temperatures between 1900– 2100 K, the x-ray diffraction pattern can be indexed in the framework of a cubic lattice with a = 4.516共1兲 Å. Reflections of the cubic phase can be followed on decompression at ambient temperatures.24 The obtained sample is translucent, and intensities and positions of the cubic reflections can be interpreted as due to the CaF2-structured TiO2. Furthermore, from the calculated sets of elastic constants we found that both cubic TiO2 polymorphs fulfill the requirements for lattice stability (results will be published elsewhere25). This fact greatly increases the possibilities to obtain the cubic form as metastable phase. The paper is organized as follows. The methods and computational details are explained in Sec. II. Theoretical analysis of the electronic properties is developed in Sec. III. The optical features are described in Sec. IV, while the x-ray absorption spectra are discussed in Sec. V. II. METHODS AND COMPUTATIONAL DETAILS
Theoretical calculations were performed with the fullpotential linearized augmented plane-wave method 共APW + lo兲 as implemented in the WIEN2K code.26 The scalar relativistic version without spin-orbit coupling was employed. Exchange and correlation effects were treated within the density-functional theory (DFT) by using the common localdensity approximation (LDA).27,28 The plane-wave cutoff 共Kmax兲 was adjusted so that approximately 120-plane waves
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FIG. 3. Total and partial density of states for the fluorite-structured TiO2 form given in states per eV. Insert (b) shows the crystal-field splitting of the Ti 3d electrons due to the Oh 共m3m兲 symmetry of the Ti site. The local coordinate system is 3储共111兲, where x , y, and z point along the original crystal axes.
per atom were used for each of the investigated TiO2 phase. For titanium, s and p local orbitals were added to the APW basis set to improve the convergence of the wave function, while for oxygen only s local orbitals were added to the basis set. The charge density and potentials were expanded up to ᐉ = 10 inside the atomic spheres, and the differences in total energies were converged to below 0.001 eV with respect to the Brillouin zone integration. All the full-potential calculations were carried out on the set of structural parameters (see Figs. 1 and 2) optimized through an ab initio plane-wave program (VASP),29 where the interaction between the ions and the electrons is described by LDA potentials generated with the Blöchl’s projector augmented wave (PAW) method.30 The optimized geometrical data have shown small residual forces (less than 0.01 eV/ Å) once plugged into the fullpotential APW+ lo code. III. ELECTRONIC STRUCTURAL PROPERTIES
In Fig. 3, we show the calculated density of states (DOS) at the equilibrium geometry for TiO2 in the fluorite structure. The valence band (VB) density of states at −17.2 eV is composed predominantly of oxygen 2s orbitals with a small amount of mixing of the Ti s and p states. At the top of the VB, in the region between −7.5 and 0 eV, the O 2p states hybridize mostly with the Ti 3d orbitals and to a less extent with an admixture of s and p states. The bottom of the conduction band (CB), just above the Fermi level 共EF兲, is primarily determined by the unoccupied Ti d states and the O orbitals with p character. Finally, the higher portion of the CB (from 10 to 20 eV) consists mostly of hybridized s and p states of both titanium and oxygen atoms.
The VB DOS for the pyrite phase (Fig. 4) is very similar to the one calculated for the fluorite-type system. However, two small changes have been found in the calculated energy window. The first one is related to a certain contraction of the higher valence bands, which slightly increases the localization of the Ti d and O p states. The full bandwidth has been computed to be 1.5 eV smaller than for the fluorite system. We attribute this electronic effect to the presence of two rather long Ti-O bond distances 共2.83 Å兲 in the inner shell of the pyrite structure. The second modification simply relates to the high-energy shift 共⬃0.6 eV兲 of the oxygen 2s states. The conduction band, on the other hand, varies significantly and shows features that originate from the change of the local symmetry around the Ti site. In both phases the Ti atoms are eightfold coordinated with the oxygen atoms. These anions are arranged around the central metal ion as to form either a cube (fluorite) or an octahedron trans bicapped polyhedra (pyrite). Hence, the fluorite structure shows a perfect octahedral symmetry 共Oh兲 around the Ti atoms, producing a crystal-field splitting of the Ti 3d orbitals into eg and t2g states (Fig. 5). The two groups of unoccupied orbitals recall the crystal-field splitting of the Ti 3d states of the 关TiO8兴−12 ion into a triply degenerate t2g and doubly degenerate eg states. Similarly, in the rutile TiO2 phase the Oh symmetry of the Ti site is lowered to D2h, which splits the d orbitals into the b3g , ag , b2g and the b1g , ag states, respectively.31 When considering the case of the pyritestructured TiO2 (Fig. 5) the degeneracy of the 3d orbitals is further removed as a consequence of the change of the metal site symmetry, which lowers from Oh to C3i 共S6兲. The lowsymmetry spatial arrangement of the oxygen ions all around the central Ti atoms determine the additional splitting of the
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FIG. 4. (Color online) Density of states for the pyrite-structured TiO2 phase. Insert (b) shows the splitting of the Ti-d states according to the S6 共−3兲 local symmetry. The coordinate axis of titanium is −3储z, where the z axis has been moved into the (111) direction by rotating by 45° around both the original x and y crystal axes.
Ti 3d orbitals. The group of electronic states found at the bottom of the CB is therefore a natural consequence of the crystal-field effects on the titanium d states. In Fig. 6, we show the computed LDA self-consistent band structure for the TiO2 fluorite polymorph. This phase has a direct-forbidden (i.e., dipole forbidden) band gap of 1.79 eV at the symmetry point X and an indirect band gap of 1.04 eV with the top of the valence band being at the X point and the bottom of the conduction band at ⌫. For the pyrite phase (Fig. 7) we found a minimum direct band gap of 1.81 eV at ⌫ and an indirect gap 共⌫ → L兲 of 1.44 eV. Both phases can be defined as indirect semiconductors, which means that the lowest-energy transition from the valence to conduction bands involves a change in the crystal momentum. Employing the same calculational scheme we have estimated for rutile a direct band gap at the ⌫ point of 1.88 eV. As one would have anticipated, the calculated LDA gap is much lower than the experimental value of 3.0 eV.32 Such an underestimation amounts generally to 30– 50% of the experimental band gaps (37.3% in the case of rutile) and can be attributed to the ground-state formalism of the densityfunctional theory.33,34
IV. OPTICAL PROPERTIES
The optical properties have been evaluated through the frequency-dependent complex dielectric tensor, 共兲 = 1共兲 + i2共兲, employing the self-consistent APW+ lo method35 and the dipole approximation.36 The imaginary part of the dielectric function is given by37
2共 兲 =
8 2e 2 2m 2V
兺ជ兩具c,kជ兩eˆkជ · pជ 兩v,kជ典兩2␦共Ec,kជ − Ev,kជ − ប兲,
c,v,k
共1兲 where pជ is the momentum operator, eˆkជ the external electric field vector, e the electron charge, m its mass, V the crystal volume, and En,kជ the computed LDA eigenvalues. The eigenkets 兩v , kជ 典 and 兩c , kជ 典 are the LDA Bloch functions for the valence and conduction bands, respectively. As for the k space integration we used the linear tetrahedron method38 with 560 and 924 k points in the irreducible wedge for fluorite and pyrite, respectively. The calculated imaginary part of the dielectric function is shown in Fig. 8 for fluorite, pyrite, and rutile TiO2 structures. The fundamental absorption edge for fluorite occurs at 1.82 eV, resulting from transitions between the topmost VB and the bottom of the CB along the ⌳ and ⌬ directions. The other absorptive transitions (cf. the labeling in Fig. 8) correspond essentially to the electronic transitions from the set of occupied oxygen p states to the empty bands with Ti d character. In the case of the pyrite phase we found a fundamental absorption at 1.81 eV, which corresponds to transitions between the valence band 48 and the conduction band 49 along the ⌫ point. The character of the other most important features are labeled in Fig. 8. The LDA band-gap underestimation was treated through a scissor operator,37 whereby the empty and occupied bands are displaced relative to each other by a rigid shift. We used a band-gap shift of 1.12 eV in order to match the experimental band gap of rutile. By doing this we have assumed that
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FIG. 5. (Color online) Partial unoccupied Ti density of states for different Ti local symmetries. The coordinate system for rutile is 2 ⬜ z , m ⬜ y, and 2 ⬜ x, where both x and y axes have been rotated by 45° around the original crystal axis z.
the amount of the band-gap underestimation in rutile is very similar to that of the cubic TiO2 polymorphs. As we mentioned earlier in this paper, the materials required for photoelectrodes in photoelectrochemical cells must satisfy specific requirements in terms of semiconducting properties, including the band gap. In particular, the reduction of Eg has an important consequence. It allows the use of the main part of the solar spectrum, improving the photocatalytic activity of the TiO2 electrode. However, in the cubic titanium dioxide forms the band gaps close only slightly with respect to the rutile phase. For the fluorite and pyrite the calculated direct band gap narrows only amounts to 0.09 and 0.07 eV, respectively. Nonetheless, the main advantage in employing cubic TiO2 phases as electrodes is related to an efficient use of those optical transitions that take place at energies close to the fundamental absorption. In Fig. 8 it is clearly shown that in the wavelength range between 380 and 450 nm both fluorite- and pyrite-structured TiO2 phases present absorptions that are significantly more intense than rutile. This behavior has been attributed to the presence of a considerable amount of localized Ti d states at the bottom of the CB, which are determined by the local cubic symmetry. For instance, in fluorite (Fig. 5) the Oh symmetry of the Ti site imposes the formation of degenerate Ti bands that are positioned exactly at the onset of the CB. This translates to an increased absorption probability for those optical transitions that are close in energy to the fundamental one. Therefore,
even though the direct band gap is of the same order of magnitude as for rutile, the absorption efficiency in fluorite is greater in the region of large wavelengths, i.e., in the visible region. This effect is less pronounced in the pyrite phase since the metal site symmetry has been lowered to C3i. Such an effect is however still more pronounced than rutile, where the Ti local site symmetry 共D2h兲 moves the localized Ti d -z2 states rather far away from the CB minimum. It is worth to note that both cubic TiO2 forms present active wavelengths within the main peak of the solar irradiation energy (which has its maximum at ⬃460 nm), thus providing the possibility to capture a considerable amount of energy from the sunlight available in the Earth’s atmosphere. Another important aspect is related to the fact that the two cubic polymorphs are pure crystalline materials. A large part of the problem arising from the photoexcited electron-hole recombination found in doped TiO2 systems will therefore be avoided. V. X-RAY ABSORPTION SPECTRA
The x-ray absorption spectroscopy (XAS) is a powerful tool for investigating the electronic structure of materials by probing the angular momentum content of the unoccupied electronic states. In order to produce reference spectroscopic data for the cubic TiO2 polymorphs, x-ray absorption near edge structures (XANES) were calculated within the single-
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FIG. 6. Band structure of fluorite-structured TiO2 along high-symmetry directions of the irreducible Brillouin zone (IBZ). The valence band maximum is taken as the energy zero.
particle transition model by using the APW+ lo bandstructure approach. As a first main approximation we have neglected many-body effects, such as the influence of the core hole on the band states and interactions between the excited electron and the core hole. The electric-dipole ap-
proximation was employed, meaning that only the transitions between the core state with orbital angular momentum ᐉ to the ᐉ ± 1 components of the conduction band were considered. The contribution c of the cth core level c = 共n , ᐉ , J兲 to the absorption coefficient can be written in cgs units as39
FIG. 7. Band structure of pyrite-structured TiO2 along the high-symmetry directions of the cubic IBZ.
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FIG. 8. Calculated imaginary part of the dielectric function 共2兲 for various TiO2 polymorphs. The present data were averaged over the three (x , y, and z) polarization vectors. We label the valence bands from 1 → 12 共48兲 and the conduction bands from 13 (49) to upwards for fluorite (pyrite).
c共E兲 =
2 2e 2ប Fc共E兲, mc V
E ⬎ EF ,
共2兲
where is the number of atoms in the primitive unit cell with volume V and Fc共E兲 the so-called spectral distribution given by39–41 Fc共E兲 =
2m 共ប兲 3ប2
J
兺 兩具cM兩⑀ˆ qជ · rជ兩kជ j典兩2␦共E − Ekជ j兲. 兺ជ M=−J kj
共3兲 In the above expression cM identifies the core wave function, while Ekជ j and kជ j are the energy and the wave function of the jth conduction band at vector kជ . The energy of the absorbed photon is represented by = E − Ec, where Ec is the core level energy. In this work we have simulated polycrystalline samples by averaging over the polarization ⑀ˆ qជ and the direction of the wave vector qជ of the incident photon. The calculations were converged with respect to the k-point integration as mentioned earlier in Sec. IV. A direct comparison of the calculated spectra with the experimental data was achieved by applying a convolution mechanism that accounts for both the initial- and final-state lifetime broadening as well as for instrumental resolution. These effects were treated in the same way as described by Schwarz and Neckel.42 In this section we intend to present a qualitative spectroscopic discrimination of the investigated high-pressure titania polymorphs by means of x-ray absorption spectra. We report the XANES spectra for both fluorite- and pyritestructured phases. The titanium 2p edge is obtained when a p core electron is promoted to an excited electronic state, which is coupled with the starting core level through the dipole selection rule 共⌬ᐉ = ± 1兲. The titanium LII,III edges correspond therefore to the p → d and p → s transitions. Nevertheless, from the cal-
culated matrix elements (not shown here), it is evident that the ᐉ − 1 transitions are much weaker than those of the ⌬ᐉ = + 1 channel. The contribution of the former is therefore negligible and the LII,III edges can be viewed as essentially reflecting the Ti 2p → 3d transitions. In Fig. 9 we present the calculated Ti LII,III edges for various TiO2 polymorphs. The positions of the different peaks are reported in Table I. One of the most evident features is the spin-orbit splitting found in between the LIII and LII white lines [see Fig. 9(a)]. The calculated value 共5.48 eV兲 is only slightly different from the one found experimentally for both rutile and anatase 共5.44 eV兲.43 Furthermore, each of the L lines splits into different peaks (A1 to A2) according to the crystal-orbital splitting of the Ti 3d bands. In the case of rutile, the separation between peak A1 and A2⬘ has been computed to be around 1.98 eV, which is in very good agreement with the experimental value of 1.97 eV (Ref. 43). In this section we focus the attention only on the shape of the LIII edge since the LII shows strong similarities to the former one. Experimentally, the LII edge resembles to the broadened version of the LIII edge. The LIII / LII white-line intensity ratio has been fixed to 1 for all the investigated phases in order to keep the calculated edges close to the experimental XAS spectra of rutile. As a matter of fact, band-structure methods tends to give white-line intensity ratios, which are always close to 2 : 1 due 4 2 and 2p1/2 to the number of electrons in the 2p3/2 43,44 subshells. However, substantial deviations from this ratio are often found experimentally and only an atomic approach investigation that includes excitations from 2p63dn to 2p53dn+1 multiplet states can provide a theoretical explanation to this phenomena.44 As one might expect, each of the calculated LIII edges clearly reflects the band structure of the Ti 3d states and provides characteristic fingerprints that can be used to distinguish one phase from the other. The calculated edges of rutile and fluorite have, however, a very similar shape that only differs on the energy position of the peaks. This similarity is here attributed to the local point group symmetry of rutile 共D2h兲, which is the result of a
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TABLE I. Assignments of peaks in band-structure calculations 共EBS兲 for the Ti LII,III edge. All positions are scaled with respect to the main peak A1. Values are given in units of eV.
Peaks
⌬EBS
Rutile ⌬Eexpa
Fluorite ⌬EBS
Pyrite ⌬EBS
A1 A⬘1 A⬘2 A2⬘
0.0 ¯ 1.98 3.02
0.0 ¯ 1.97 2.86
0.0 ¯ 1.66 2.81
0.0 1.11 2.99 4.14
aExperimental
data from Ref. 43.
were here neglected because of the enormous amount of computer time needed for such an investigation. VI. CONCLUDING REMARKS
FIG. 9. Theoretical XANES spectra at the Ti LII,III edges in various TiO2 phases. The onset energies for (b) and (c) have been adjusted with respect to rutile by accounting for the Ti 2p43/2 core energy level shifts. All the Ti L edges were computed by using an instrumental resolution of 0.5 eV.
slightly distorted Oh symmetry, i.e., that of fluorite. However, such a kind of resemblance does not prevent the possibility to differentiate one system from the other since consistent differences in the energy peak positions have been reported for the two structures (Table I). On the contrary, when comparing the pyrite form of TiO2 with fluorite, an extra peak (namely A1⬘) has been detected in the former phase thus providing a secure way of discriminating the two polymorphs. It should be mentioned that core-hole effects
*Electronic address:
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This paper reports on the ab initio investigation of the electronic band structure of fluorite- and pyrite-type TiO2 polymorphs. In summary, we have shown that high Ti local site symmetries, like for instance Oh, account for the existence of a large amount of localized Ti d states at the bottom of the conduction band. An analysis of the optical properties was also carried out through the computation of the imaginary part of the dielectric function. Structural features in the optical spectra were then assigned for the two model systems. Our first-principles calculations indicate that such a cubic phase (either fluorite- or pyritelike) has potential applications as a light absorber in solar-energy conversion. In particular, from the computation of the optical properties we have shown that both cubic polymorphs will have important optical absorptive transitions in the region of the visible light. Finally, x-ray absorption near edge spectra were provided as a precious tool for the characterization and identification of the cubic titania forms. ACKNOWLEDGMENTS
The authors acknowledge the Swedish Research Council (VR), EU network (EXCITING), ATOMICS (SSF), and CNPq, Brazil for financial support. One of the authors (M. Mattesini) also wishes to acknowledge the support of Dr. G. Romualdo-Torres for fruitful discussions.
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