Sb co-doped TiO2 from first principles calculations

Chemical Physics Letters 469 (2009) 166–171

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Cr/Sb co-doped TiO2 from first principles calculations Cristiana Di Valentin a,*, Gianfranco Pacchioni a, Hiroshi Onishi b, Akihiko Kudo c a b c

Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, Via R. Cozzi, 53, 20125, Milano, Italy Department of Chemistry, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan Department of Applied Chemistry, Faculty of Science, Science University of Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

a r t i c l e

i n f o

Article history: Received 6 October 2008 In final form 22 December 2008 Available online 29 December 2008

a b s t r a c t Co-doping of TiO2 with Cr and Sb was recently found to have a beneficial effect on the photocatalytic activity under visible-light irradiation. With the present comparative standard and hybrid density functional study we get new insight into the electronic structure of the system and provide a theoretical support to the experimental findings. Hybrid DFT better describes (i) the Cr d states splitting and thus the semiconducting properties of the Cr-doped system, and (ii) the localized nature of the Ti3+ states produced by Sb doping. An electron transfer from the Sb-induced states to the Cr 3d levels is considered to be the reason for the enhanced photostability of the co-doped Cr/Sb system. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction Doping with metal atoms, although being a common way to induce visible-light absorption of TiO2 [1], is not an efficient way to improve its photocatalytic activity because the presence of metal impurities in the bulk of the semiconductor increases the rate of recombination of the charge carriers thus reducing the photostability of the catalyst [2,3]. Recently, however, it was reported as a remarkable and peculiar result that co-doping of Cr with Sb has a beneficial effect on both the vis-light absorption and on the photocatalytic activity of TiO2 with respect to that of the simply Crdoped TiO2 [4,5]. The ‘co-doping effect’ is actually receiving a noticeable attention [6–8], also in the case of non-metal doping [9–14]. This is emerging as a ‘hot’ subject in the field of titania photoactivation, even though concomitant insertion of different dopants does not always result in an enhancement of the photocatalytic activity [11]. The present work was performed with the aim of getting new insight in the co-doping effect, in particular for the case of Cr and Sb, by performing a thorough density functional theory (DFT) study, where the details of the electronic structure for increasing Cr content in the system, also in the eventual presence of oxygen vacancies and of Sb, are analyzed. This study could be relevant not only for the specific case analyzed but may introduce some more general useful concepts related to the co-doping of semiconductors for photocatalytic and photochemical purposes. Moreover, by performing a comparative analysis of standard (PBE) and hybrid (B3LYP) DFT calculations we provide an improved description of the strongly localized d states of the transition metal (Cr or Ti) and of their position in the band structure of the material. We

* Corresponding author. E-mail address: [email protected] (C. Di Valentin). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.12.086

found that Cr-doped TiO2 presents metallic properties when computed at PBE level because of the insufficient splitting of the t2g states, while is described as a semiconductor according to B3LYP calculations, in agreement previous calculations by Gao et al. performed within the LDA + U approach [15]. Also, by introducing some Hartree–Fock (HF) exact exchange as with B3LYP it is possible to obtain, for the Sb-doped TiO2, a localized Ti3+ state in the band gap, which otherwise is fully delocalized on several lattice Ti atoms when standard DFT functionals are used. 2. Computational details The computations have been done using two approaches: (1) The plane-wave-pseudopotential approach, together with the Perdew–Burke–Ernzerhof (PBE) [16] exchange-correlation functional, and ultrasoft pseudopotentials [17] (kinetic energy cut-offs of 25 ad 200 Ry for the smooth part of the electronic wavefunctions and augmented electron density, respectively). The Quantum-ESPRESSO code, PWSCF package [18], was used to perform the calculations. The k-space sampling was limited to the low-symmetry k-point (0.25 0.25 0.274945). (2) The hybrid density functional approach (B3LYP [19,20]) with the expansion of the Kohn–Sham orbitals in Gaussian type orbitals (GTO), as implemented in the CRYSTAL06 code [21]. In B3LYP 20% of the exact HF exchange is mixed in with the DFT exchange. The following all electron basis-sets have been used for Ti and O atoms: Ti 86411(d41) [22] and O 8411(d1) [23]. Cr atoms have been treated with the all electron Cr 8411(d41) [24] basis set. Sb atoms have been described with a Durand–Barthelat [25] effective core potential (ECP) together with a 21(d1) [26] valence shell

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electron basis set. The k-point sampling was limited to 8 points. The total and projected densities of states (DOS and PDOS) have been obtained with a 36 k-points mesh.

3. Results and discussion Cr-doped TiO2 has been object of theoretical studies because of the interest in its ferromagnetic properties as a new high Tc dilute magnetic semiconductor [15,29,30]. In the present context the interest is on the electronic properties which might influence the optical and photocatalytic activity of the material. Thus in the following the attention will be essentially focused on the electronic structure of Cr-doped, Sb-doped and Cr/Sb co-doped TiO2 systems.

All calculations are spin-polarized. We considered nearly cubic p p 2 2  2 2  1 supercells to model anatase. The optimized bulk lattice parameters, taken from previous calculations, are a = 3.786 Å, c = 9.737 Å (PBE) [27] and a = 3.776 Å, c = 9.866 Å (B3LYP) [28]. Cr-doping was modeled by replacing 1, 2, or 3 Ti atoms in the 96-atoms supercell. The resulting stoichiometry is Ti1xCrxO2 with 0.031 < x < 0.094. The procedure of including more Cr atoms in the same supercell is more accurate than using smaller supercells as it allows a direct comparison of the various levels of doping on the band structure of the material. The lowest Cr concentration is comparable to that used in the experiment (Cr 2– 2.3 mol%) [4]. The co-presence of Cr and oxygen vacancies (VO) was simulated by introducing two Cr atoms in substitutional position to Ti and removing one O atom. The co-presence of Cr and Sb was analyzed for an anatase model with one Cr and one Sb atom in substitutional position to Ti. Various relative positions of the two defects have been considered, as discussed below. The atomic coordinates were optimized with the Broyden–Fletcher–Goldfarb– Shanno (PWSCF) and a modified conjugate gradient algorithm (CRYSTAL06) technique until all components of the residual forces were less than 1  103 au and 5  104 au, respectively.

3.1. One–two–three Cr atoms in substitutional position of Ti in anatase TiO2 The electronic configuration of Cr is 3d5 4s1. In substitutional position to a Ti atom (3d2 4s2) Cr should assume a formal 4 + state (3d2 4s0 configuration). In Fig. 1 the density of states (DOS) curves obtained with PBE and B3LYP calculations for the lowest Cr concentration are reported. The spin-up and spin-down contributions are displayed separately (top and bottom, respectively) and only the valence and conduction bands are reported. The zero energy value is set at the top of the valence band in order to easily allow identification of the band gap and of the relative position of the impurity states introduced by the metal atom. The PBE band gap, obtained as the difference between highest occupied and lowest unoccupied Khon–Sham states at the low-symmetry k-point, is

1 Cr B3LYP

PBE

up

up EF

t2g

DOS (States/eV/Cell)

DOS (arb. units)

EF

eg

t 2g

down -4

t2g

eg

down -2

0

2

4

-4

-2

0

2

4

Energy (eV)

Energy (eV)

Fig. 1. PBE (left) and B3LYP (right) DOS and PDOS (on the Cr d states) for Cr–TiO2 with one Cr atom in the 96-atoms model. The zero energy value is set at the top of VB. The dotted line indicates the Fermi energy. Inset: B3LYP spin density plot. Cr–O bondlengths (PBE/B3LYP): eq.: 1.909/1.905 and ax.: 1.940/1.986 Å (eq.: 1.942/1.940 Å and ax.: 2.002/2.020 Å for undoped TiO2).

+ VB

Cr/TiO2

Sb/TiO2 Scheme 1.

Cr-Sb/TiO2

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state just above the valence band, indicating a semiconducting character of the system, in agreement with the LDA + U results by Gao [15]. These results confirm that the Cr species is in a formal 4+ oxidation state with a 3d2 4s0 valence shell configuration. The two electrons occupy two t2g d states in a triplet spin configuration (see left side of Scheme 1 and inset in Fig. 1). Electron excitations under vislight irradiation could take place from the top of the valence band to the Cr states in the gap or to the bottom of the conduction band states, as proven by the optical absorption spectra reported in the literature [4]. When two Ti atoms are substituted by Cr, two Cr4+ (3d2 4s0) species are formed (see the spin density plot in the inset of Fig. 2). In the reported PBE DOS curves in Fig. 2 (left), the states associated to the Cr species fall, as for the previous case, in the middle of the band gap (1.4 eV above the top of the valence band) and given the partial occupation of the t2g states (two 3d2 species overall quintet spin state), they are separated in two peaks, either

underestimated as 2.6 eV (to be compared to the experimental value of 3.2 eV). This is a well-know short-coming of standard DFT and the energy value here obtained confirms previously reported data for similar systems [31]. In B3LYP the band gap is overestimated (3.9 eV) but this allows an improved description of the impurity states, as we will se below. Within the PBE approach (Fig. 1, left) a distinct peak can be distinguished in the middle of the band gap which is due to the d states of the Cr dopant according to the projected density of states (PDOS). The Fermi energy falls in the middle of this peak (1.2 eV above the top of the valence band) indicating a partial occupation or half-metallic character, in agreement with what was found by Ye et al. [29]. With B3LYP (Fig. 1 right) the situation is quite different: the splitting between the occupied and unoccupied part of the Cr t2g states is large. The occupied t2g states are largely mixed with the O sp states and produce a small peak just above the top of the valence band. The remaining unoccupied t2g state falls in the middle of the band gap. The Fermi energy is set at the top of the defect

2 Cr B3LYP

PBE

up

up

t2g

DOS (States/eV/Cell)

DOS (arb. units)

EF

eg

EF

t2g

t2g

eg

down

down -4

-2

0

2

4

-4

-2

0

2

4

Energy (eV)

Energy (eV)

Fig. 2. PBE (left) and B3LYP (right) DOS and PDOS (on the Cr 3d states: different colors identify different Cr atoms) for Cr–TiO2 with two Cr atoms in the 96-atoms model. The zero energy value is set at the top of VB. The dotted line indicates the Fermi energy. Inset: B3LYP spin density plot. Cr–O bondlengths for both Cr ions (PBE/B3LYP): eq.: 1.95/ 1.97 Å and 1.89/1.91 Å and ax.: 1.79/1.79 Å and 2.09/2.09 Å (eq.: 1.942/1.940 Å and ax.: 2.002/2.020 Å for undoped TiO2).

3 Cr B3LYP

PBE

up

up

EF

t2g

DOS (States/eV/Cell)

DOS (arb. units)

EF

eg

t 2g

t 2g

down -4

eg

down -2

0

Energy (eV)

2

4

-4

-2

0

2

4

Energy (eV)

Fig. 3. PBE (left) and B3LYP (right) DOS and PDOS (on the Cr 3d states: different colors identify different Cr atoms) for Cr–TiO2 with three Cr atoms in the 96-atoms model. The zero energy value is set at the top of VB. The dotted line indicates the Fermi energy. Inset: B3LYP spin density plot. Cr–O bondlengths for the three Cr ions (PBE/B3LYP): (1) eq.: 1.95/1.91–1.99 Å and 1.88/1.84–1.89 Å and ax.: 1.79/1.95 Å and 2.09/2.01 Å; (2) eq.: 1.99/2.06 Å, 1.89/2.00 Å, 1.898/1.91 Å, and 1.88/1.78 Å and ax.:1.83/1.92 Å and 2.04/ 1.97 Å; (3) eq.:1.92/1.81 Å, 1.92/1.86 Å, 1.80/1.98 Å and 2.02/2.03 Å and ax.: 1.93/1.95 Å and 2.00/1.98 Å (eq.: 1.942/1.940 Å and ax.: 2.002/2.020 Å for undoped TiO2).

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above or below the Fermi energy (EF). The PDOS indicates the contribution of the d states of two Cr atoms to the impurity peak in the band gap. The B3LYP DOS curves are essentially similar to those reported for one Cr-dopant and differ from the PBE DOS because of the large splitting between the occupied and unoccupied t2g states. The Fermi energy is thus just above the top of the valence band. When three substitutional Cr atoms are introduced in the system, different electron distributions are conceivable, within the overall sextet spin state. It is possible to suppose two Cr species in a 3+ oxidation state at the expenses of the third one which would undergo full oxidation to Cr6+. This compensating electron transfer was proposed to be the reason for the two registered XPS peaks, assigned to Cr3+ and Cr6+, respectively, in rutile Crdoped TiO2 [4]. However, the present calculations seem to exclude this possibility, since the electron distribution is consistent with three Cr4+ species in 3d2 4s0 electron configuration (see the spin density plot in the inset of Fig. 3). Of course, is possible that other positions in the lattice, e.g. interstitial sites, might provide a more stable environment for the Cr(VI) species. The PBE DOS and PDOS

spectra in Fig. 3 (left) are very similar to those for one or two Crdopants, with the Fermi energy falling in the middle of the impurity peak, at about 1.4 eV above the top of the valence band, providing a half-metallic character to the material. As mentioned above, with B3LYP the DOS and PDOS in Fig. 3 (right), the t2g splitting for the Cr4+ species is much larger and the occupied t2g states fall essentially at the top of the valence band, with partial mixing with the O 2p states, while the unoccupied t2g component is in the middle of the band gap for all the three Cr atoms. 3.2. One O vacancy in the presence of two Cr atoms in substitutional position of Ti in anatase TiO2 The possibility of having oxygen vacancies together with Cr impurities has been often invoked [4,15,29]. The removal of one neutral O atom leaves two extra electrons which can more easily reduce two Cr4+ species to Cr3+ rather than two Ti4+ ions to Ti3+. Our calculations provide theoretical support to this mechanism and indicate the formation of two Cr3+ species in a 3d3 4s0 config-

2 Cr + Vo

PBE

B3LYP

up

up

EF

DOS (States/eV/Cell)

DOS (arb. units)

EF t2g eg

t2g

eg

Vo

down -4

down -2

0

2

4

-4

-2

0

2

4

Energy (eV)

Energy (eV)

Fig. 4. PBE (left) and B3LYP (right) DOS and PDOS (on the Cr 3d states: different colors identify different Cr atoms) for Cr–TiO2 with two Cr atoms and one O vacancy in the 96atoms model. The zero energy value is set at the top of VB. The dotted line indicates the Fermi energy. Inset: B3LYP spin density plot. Cr–O bondlengths for both Cr ions (PBE/ B3LYP): eq.: 1.95/1.99–2.02 Å and ax.: 1.99/2.03 Å (eq.: 1.942/1.940 Å and ax.: 2.002/2.020 Å for undoped TiO2). These values are on average longer than those computed for the Cr-doped species in Figs. 1–3. The reason is attributable to the different Cr oxidation state.

1 Sb

B3LYP

PBE

up

EF

Ti

Sb

DOS (States/eV/Cell)

DOS (arb. units)

up

3+

Ti

down -30

-28

EF

3+

down -4

-2

0

Energy (eV)

2

4

-4

-2

0

2

4

Energy (eV)

Fig. 5. PBE (left) and B3LYP (right) DOS and PDOS (on the Sb 4d states (PBE); on the Ti3+ 3d states (B3LYP)) for Sb–TiO2 with one Sb atom in the 96-atoms model. The zero energy value is set at the top of VB. The dotted line indicates the Fermi energy. Inset: B3LYP spin density plot. Sb–O bondlengths (PBE/B3LYP): eq.: 1.995/1.945 Å and ax.: 2.02/1.97 Å (eq.: 1.942/1.940 Å and ax.: 2.002/2.020 Å for undoped TiO2).

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side). On the contrary, with B3LYP the peak associated to the Ti3+ species is localized in the band gap, about 0.8 eV below the bottom of the conduction band (see Fig. 5, right side and the spin density plot in the inset), in agreement with experimental observations [40,41].

uration. The three species (two Cr dopants and one O vacancy) are located as far apart as possible in the 96-atoms supercell. The PBE band gap of the reduced system is 2.7 eV (see Fig. 4). The Fermi energy is set at 2.2 eV above the top of the valence band and the impurity peak in the middle of the band gap is, entirely below EF because the spin-up t2g states are all occupied for both Cr atoms. The electron transfer from the Ti3+ states (deriving from the removal of the O atom) to the Cr4+ species is proven also by the full localization of the spin density on the two Cr3+ species (inset of Fig. 4). The B3LYP DOS curves are qualitatively similar. However, the position of the fully occupied d t2g states is much closer to the top of the valence band. This should better account for the visible-light absorption of the Cr-doped samples at 400–500 nm due to a Cr3+ ? Ti4+ charge transfer transition [32]. Another interesting aspect of the concomitant presence of Cr dopants is related to the energetics of the O vacancy formation. As proven by the following equations:

3.4. One Cr and one Sb atoms in substitutional position of Ti in anatase TiO2 The most interesting system for the purpose of this work is TiO2 co-doped with Cr and Sb impurities. The Cr dopant requires an extra electron to achieve the stable 3+ oxidation state; the Sb dopant introduces an extra electron into the system. Thus the overall codoping effect is synergistic (see right side of Scheme 1): the extra electron of Sb is transferred to the Cr impurity so that the Sb species is in a 5+ oxidation state (4d10 5s0) and the Cr species is in a 3+ oxidation state (3d3 4s0). This result is consistent with a previous XPS study on Cr/Sb co-doped TiO2 [4]. In Fig. 6 the DOS, the PDOS and the spin density plot are reported. When comparing Fig. 5, Sbdoped TiO2, with Fig. 6, it is clear that the extra electron on the Ti3+ species is transferred to the Cr states in the band gap. This occurs for both PBE and B3LYP, Fig. 6. As observed in Section 3.2, the B3LYP DOS is qualitatively similar to the PBE one. However the position of the fully occupied 3d t2g states is much closer to the top of the valence band which should better account for the visible-light absorption of the Cr/Sb co-doped samples at 400–500 nm due to a Cr3+ ? Ti4+ charge transfer transition [4]. The presence of an electron donor such as the Sb dopant does not require formation of oxygen vacancies to provide the extra electron for Cr impurities. This means that Cr/Sb co-doped TiO2 should be characterized by a smaller degree of defectivity which is probably the reason for the reported enhanced photocatalytic activity [4] and reduced rate of recombination, as already proposed on the basis of a recombination dynamics study by transient IR absorption [5]. For the co-doped system we have considered three configurations with different Cr–Sb distances. In one case Cr and Sb are far apart in the supercell; in the second are close (in axial and equatorial position to the same O atom, respectively); in third are adjacent (bridging the same O atom). The difference in energy of the three configurations is relatively small, about 0.1 eV. Thus it is not possible to assess whether there will be any clustering of the dopants on the basis of this small energy gain. Another aspect related to the synergistic effect of co-doping has been evaluated by using the following thermodynamic processes:

Ti1x Crx O2 ! Ti1x Crx O2x=2 þ x=4O2

DE ¼ 2:2 eV ðPBEÞ; 0:9 eV ðB3LYPÞ TiO2 ! TiO2x=2 þ x=4O2

DE ¼ 4:2 eV ðPBEÞ; 4:8 eV ðB3LYPÞ for x = 0.0625, the presence of the Cr impurities largely reduces the cost to remove one lattice O atom. As often observed for doped TiO2, the presence of dopants or impurities is accompanied by formation of oxygen vacancies, with the consequence of a higher defectivity and a lower crystallinity of the sample [33–36]. 3.3. One Sb atom in substitutional position of Ti in anatase TiO2 The introduction of one Sb atom (4d10 5s2 5p3) in substitutional position to a lattice Ti atom (3d2 4s2) should leave Sb in a formal 4+ oxidation state (4d10 5s1 electronic configuration). However, calculations show that the 5s state is very high in energy and therefore the extra electron is preferentially transferred to a Ti4+ cation which is reduced to Ti3+, while the Sb is in a 5+ oxidation state (see central part of Scheme 1). This is confirmed by the analysis of the character of the highest occupied state. Unfortunately, however, the solution obtained with standard DFT (PBE functional) suffers not only of the well known problem of underestimated band gap for TiO2, as mentioned above, but also of the excessive delocalization of Ti3+ defect states (as previously reported for reduced [37,38] or F-doped TiO2 [39]). The Fermi energy is set a few tenth of an eV above the bottom of the conduction band (see Fig. 5, left

Cr + Sb

PBE

up

up

EF

Sb

EF

DOS (States/eV/Cell)

DOS (arb. units)

B3LYP

Cr

Cr

down -30

-28

down -4

-2

Energy (eV)

0

2

4

-6

-4

-2

0

2

4

6

Energy (eV)

Fig. 6. PBE (left) and B3LYP (right) DOS and PDOS (on the Cr and Sb d states (PBE); on the Cr d states (B3LYP)) for the co-doped Cr/Sb–TiO2 with one Cr and one Sb atoms in the 96-atoms model. The zero energy value is set at the top of VB. The dotted line indicates the Fermi energy. Inset: B3LYP spin density plot. Cr–O bondlengths (PBE/B3LYP): eq.: 1.95/2.01 Å and ax.: 1.99/2.04 Å. Sb–O bondlengths: eq.: 1.995/1.945 Å and ax.: 2.02/1.97 Å. (eq.: 1.942/1.940 Å and ax.: 2.002/2.020 Å for undoped TiO2).

C. Di Valentin et al. / Chemical Physics Letters 469 (2009) 166–171

TiO2 þ xCr ðbulk bccÞ ! Ti1x Crx O2 þ xTi ðbulk hcpÞ

DE ¼ 4:1 eV ðPBEÞ Ti1x Sbx O2 þ xCr ðbulk bccÞ ! Ti12x Crx Sbx O2 þ xTi ðbulk hcpÞ

DE ¼ 3:0 eV ðPBEÞ TiO2 þ xCrO2 Cl2 ! Ti1x Crx O2 þ xTiO2 þ xCl2 DE ¼ 0:2 eV ðB3LYPÞ Ti1x Sbx O2 þ xCrO2 Cl2 ! Ti12x Crx Sbx O2 þ xTiO2 þ xCl2

DE ¼ 2:2 eV ðB3LYPÞ which differ for the reference system, metallic Cr (bcc) for PBE calculations or CrO2Cl2 complex for B3LYP calculations (x = 0.031). The precise values obtained for the energy changes associated with these processes are not an essential information. What is important is that, independently of the reference used, the energy cost of doping with Cr is reduced in the presence of the Sb dopant. The Cr/Sb co-doping effect can thus be summarized in three main points which are all intimately interconnected: (i) charge compensation between Cr and Sb dopants through an internal charge transfer; (ii) reduction of the number of oxygen vacancies associated with Cr-doping in the presence of Sb, resulting in less defective Cr/Sb co-doped TiO2; (iii) reduction of the energy cost to dope the material. 4. Conclusions In this work the electronic structure of Cr- and Sb-doped TiO2 has been studied in detail by means of standard and hybrid DFT calculations. Hybrid functionals are found to better describe the d states splitting at the Cr center and the localized nature of the Ti3+ states produced by Sb doping. The detailed theoretical analysis is relevant for understanding the role of the metal dopants in the modification of the electronic structure (especially as related to the band gap) for applications in vis-light photocatalysis. The concomitant presence of the Cr dopant and one oxygen vacancy (lattice defect) is found to induce an electron transfer producing stable Cr3+ impurities. A similar electron transfer is present in the Cr/Sb co-doped TiO2. Sb donates one electron to the Cr impurity without the need to create oxygen vacancies. We suggest that this is the reason why this system is characterized by an improved photostability and consequently by a larger photocatalytic activity. Acknowledgments C.D.V. is very grateful to Japan Science and Technology Agency (JST) for financing her visit to Kobe University and to Tokyo Univer-

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sity of Science. The authors thank Prof. A. Selloni for helpful discussions. Computational resources were provided by CINECA computing center through the INFM Parallel Computing Initiative and CILEA computing center (Italy). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

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