ARTICLE pubs.acs.org/JPCC
CO Adsorption on Anatase Nanocrystals: A Combined Experimental and Periodic DFT Study Lorenzo Mino, Anna Maria Ferrari,* Valentina Lacivita, Giuseppe Spoto, Silvia Bordiga, and Adriano Zecchina Department of Inorganic, Physical and Materials Chemistry and NIS Centre of Excellence, University of Turin, via P. Giuria 7, 10125 Torino, Italy ABSTRACT: Periodic DFT calculations of the structure of (101), (100), (001), and (112) anatase faces and of the vibrational properties of CO adsorbed on them at two coverages allow assigning the main features of FTIR spectra of CO adsorbed at 60 K on highly dehydroxylated anatase nanocrystals. It is shown that the combination of spectroscopic and computational approaches is of extreme utility for the elucidation of the Lewis acid properties of the 5-fold coordinated Ti4þ centers present on the different surfaces and on their influence on the stretching frequencies of adsorbed CO, for the explanation of the coverage-dependent effect of dipoledipole interactions and for the determination of the average nanoparticle morphology. This study highlights that the close comparison of experimental and computational results forms the safest basis for the cross-validation of the two approaches.
’ INTRODUCTION Titanium dioxide is one of the most important metal oxides because of its applications as a white pigment, as an important component in solar cells, and as a photocatalyst.1 In the last two applications, the relevant phenomena are occurring at the surface of anatase nanoparticles, which are generally considered to be more active than rutile ones.2 Therefore, it is relevant for both technological and fundamental motivations to study the structure of the different surfaces terminating the anatase nanocrystals. This study can be performed both experimentally and theoretically. Concerning the experimental approach, the use of Fourier transform infrared (FTIR) spectroscopy of adsorbed probe molecules has emerged as the leading method.3 In particular, carbon monoxide, a weak Lewis base, is usually chosen to probe the Lewis acid sites of TiO2.48 The stretching frequency of the adsorbed CO is related to the electrophilicity and polarizing power of the surface Lewis acid sites: the greater the electrophilicity of the metal cation, the higher the blue shift with respect to the value in the gas phase (2143 cm1).4 The variation of the stretching frequency originates from the combination of different mechanisms: (1) the interaction between the CO dipole moment and the surface electric field (Stark effect), (2) the repulsive potential due to the vibration of the CO molecule against a rigid surface (wall effect), and 9 (3) the dipoledipole interactions between the adsorbed molecules.10 r 2011 American Chemical Society
However, when highly dispersed phases are concerned, the particles expose a variety of faces, and consequently, the IR spectra of adsorbed CO can be constituted by the superposition of several components whose unambiguous assignment is troublesome. For oxides characterized by a rock salt structure, such as MgO, a satisfactory interpretation of the spectra of adsorbed CO has been obtained by comparing the IR spectra with high-resolution transmission electron microscopy (HRTEM) results.11 This has been made possible by the simple cubic morphology of the MgO particles, which definitely exposes a predominant family of faces, a fact which makes the interpretation of the HRTEM images straightforward. In the case of highsurface-area TiO2, the determination of the nanoparticles' morphology by HRTEM is much more difficult, and consequently, the combined use of electron microscopy and IR spectroscopy of adsorbed CO is not so fruitful. This is the case where the help of a computational study on the structure of the most probably exposed surfaces and on the vibrational properties of CO adlayers adsorbed on them can be of invaluable utility. This approach has dual importance: in fact, while on one side, it helps the interpretation of IR results, on the other side, it allows one to
Received: February 21, 2011 Revised: March 18, 2011 Published: March 30, 2011 7694
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Table 1. Basis Set Combinations Used for the Description of the AnataseCO Interaction B0 CO two outermost O surface Ti
B1
TZ-Pa
B2
TZ-PPc d
8-411G(d) f
TZ-PP
b
8-6411-31
TZV-P d
inner O
8-411G(d)
inner Ti
f
8-6411-31
a
a
TZ-PP
b
TZV-P
B3
TZ-Pa
B4
TZ-Pa d
8-411G(d)
HW/411-31 d
TZV-Pb
TZV-P
d
8-411G(d)
HW/411-31
a
b
d
e
TZ-PPc
TZ-P
TZV-P
8-411G(d) e
TZ-PPc
a
b
TZV-P
B6
TZ-Pa
8-411G(d)
b d
8-411G(d)
HW/411-31
TZ-PPc
8-411G(d) d
B5
HW/411-31
8-411G(d)d
8-411G(d) e
HW/411-31 31 b
e
HW/411-31e 32
Ahlrichs TZ basis set augmented with one d polarization function taken from the polarization set of Ahlrichs. Ahlrichs TZV basis set modified by removing the most diffuse s function. c Ahlrichs TZ basis set31 augmented by two d polarization functions. d All-electron [8-411-1]/(1s/3sp/1d) basis set.33 e The HayWadt small-core pseudopotential34 and a [411/31]/(3sp/2d) basis set. f All-electron [8-6411-31]/(1s/4sp/2d) basis set.33
validate the adopted computational approaches that must be able to simulate the accurate spectroscopic results. Recent calculations reported the shift of the CO stretching frequency, Δν(CO), due to the interaction of CO with the different cationic centers showed by the rutile (110) surface1214 and anatase (101)13 and (001)15 surfaces. However, in these investigations, a close comparison of experimental and computational results, allowing the cross-validation of the two approaches, was lacking also owing to the small basis sets employed for the calculations. In this work, we report the results of a joint experimental and computational study where accurate density functional theory (DFT) calculations of the vibrational stretching frequencies of CO molecules adsorbed at both low and high coverages on highly dehydroxylated anatase nanocrystals have been compared for the first time with FTIR spectra acquired at 60 K. The extremely low temperature allowed us to obtain spectra of improved quality (experimental data already present in the literature are all recorded at 100 K),4,5,7,8 especially for the features related to CO interacting with very weak Lewis acid sites.
Hessian matrix only for the CO fragment, once checked that its stretching vibration is not coupled with other crystal phonons. FTIR Spectroscopy. Anatase TiO2 (BET surface area = 140 m2/g) was purchased from Sigma-Aldrich. The rutile content of the sample, evaluated considering the intensity of the (110) rutile diffraction peak and the intensity of the (101) anatase diffraction peak,22 was found to be below 2%. Before CO adsorption, the TiO2 sample, in the form of a thin self-supporting pellet suitable for transmission FTIR measurements, was outgassed under high vacuum (residual pressure < 104 mbar) at 773 K in the same cryogenic cell (a properly modified closed-circuit liquid helium Oxford CCC 1204 cryostat), allowing the infrared investigation of species adsorbed in controlled temperature (between 300 and 14 K) and pressure conditions. After the thermal treatment, the samples were oxidized with 15 mbar of O2 to obtain stoichiometric TiO2. After outgassing O2 at room temperature, 40 mbar of CO gas were dosed on the samples. The infrared spectra were recorded at 60 K on a Bruker Equinox 55 FTIR spectrometer, equipped with an MCT cryogenic detector, with the sample compartment modified to accommodate the cryogenic head; 128 interferograms (recorded at 2 cm1 resolution) were typically averaged for each spectrum.
’ COMPUTATIONAL AND EXPERIMENTAL DETAILS Computational Parameters. Anatase surfaces and CO ad-
sorption properties have been modeled employing the periodic CRYSTAL09 code,16 using the hybrid B3LYP17 and PBE018 DFT functionals. The PBE0 functional has been reported to give accurate structural and electronic properties for TiO2 crystals,19 whereas the B3LYP functional provides accurate estimates of vibrational frequencies in solid-state systems.20 The level of accuracy in evaluating the Coulomb and the exchange series is controlled by five parameters16 for which 107, 107, 107, 107, and 1018 values have been used for all calculations. The convergence threshold for the SCF energy was set to 1010 Ha. The reciprocal space was sampled according to a regular sublattice determined by the shrinking factor,16 which was set to 6 (1320 independent k-points in the irreducible part of the Brillouin zone, depending on the dimension of the adopted cell). The surfaces of crystals were modeled with bidimensional slabs characterized by two infinite dimensions (x, y) and a finite thickness. Low-coverage CO adsorptions have been modeled by employing a supercell of an appropriate size: 2 2 for (101) and (001) surfaces and 2 1 for the (100) surface. The basis set superposition error (BSSE) was corrected using the counterpoise approach.21 Several basis set combinations of increasing size (B0B6 in Table 1) have been tested to achieve a suitable compromise between accuracy and computational cost. CO frequencies have been computed at the Γ point, within the harmonic approximation, by diagonalizing the mass-weighted
’ RESULTS AND DISCUSSION Setup of Anatase Surface Models. The surfaces relevant in anatase nanocrystals have been identified by computing the surface energy of several low-index surfaces and with the help of HRTEM measurements7 and previous calculations.19,23 The performances of the different basis set combinations have been tested on the properties of CO adsorption (θ = 1) at the (101) surface (see Table 2) in order to find an appropriate compromise between accuracy and the high computational cost of the low CO coverage simulations. Basis sets denominated B0 and B5 seemed to perform as well as the larger tested basis sets and, therefore, were selected for the present calculations. It is also worth noticing that the selected basis sets are characterized by a basis set superposition error (BSSE) that does not exceed 5 kJ/mol (see Table 1), a value considerably lower than those reported in previous papers (e.g., 15 kJ/mol)13 in which considerably smaller basis sets have been employed.1315 The thickness of the slab is usually a critical parameter, and therefore, in order to select feasible models, the effect of the slab thickness on the adsorption properties has been checked considering as a benchmark the case of CO adsorbed at the (101) surface (PBE0/B0 approach). As reported in Table 2, a thickness of about 810 Å (six Ti layers) provides negligible differences in the adsorbed CO properties (i.e., binding energy, variation in the CO bond length, CO stretching frequencies) with respect to thicker slabs. 7695
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Table 2. Dependence of CO Adsorption Properties on Several Basis Set Combinations (See Table 1 for Basis Set Nomenclature)a d (CTi) (Å)
Δd (CO) (Å)
BEC (kJ/mol)
BE (kJ/mol)
Δν (cm1)
B0
2.5706
0.0038
21.8
26.5
43
B0
2.5843
0.0036
20.6
25.3
41
101-6L
B1
2.5913
0.0038
20.3
23.8
41
101-6L
B2
2.5582
0.0037
19.7
27.3
42
101-6L
B3
2.5924
0.0035
20.1
24.8
41
101-6L
B4
2.5908
0.0037
20.4
24.9
41
101-6L
B5
2.5623
0.0039
22.9
27.0
44
101-6L
B6
2.5768
0.0039
21.4
25.3
43
surface model
basis set
101-10L 101-6L
All calculations have been performed for CO adsorbed at the (101) surface with θ = 1 and employing the PBE0 functional. Two sizes of slabs have been considered: a large one (101-10L) exhibiting 10 Ti layers and 16 Å of thickness and a medium one (101-6L) characterized by 6 Ti layers and 9 Å of thickness. BE and BEC are the binding energy and the BSSE-corrected binding energy, d are the bond distances, ν is the CO stretching frequency, and Δ are differences with respect to the free molecule. For free CO, d (CO) = 1.1240 Å and ν = 2249 cm1 (TZ-P/PBE0) and d (CO) = 1.1240 Å and ν = 2235 cm1 (TZ-PP/PBE0). a
Figure 1. (a) Comparison of the surfaces energies (E0 S) of the most relevant anatase surfaces as a function of the slab thickness obtained optimizing only the internal coordinates. The calculations were performed at the PBE0/B0 level. (b) As in (a), relaxing also the cell parameters (E00 S).
Surface Analysis. To identify the most stable anatase surfaces, the surface energy ES of a series of low-index surfaces has been computed at the PBE0/B0 level and reported in Figure 1 as a function of the slab thickness (T). Slabs consisting of 6, 8, and 10 TiO2 layers, corresponding approximately to T = 920 Å have been considered. ES has been computed exploiting the usual expression
ES ¼
1 ðEn nEb Þ 2A
where A is the area of the unit cell in the slab, En is the total energy of the slab containing n Ti layers, and Eb is the energy per unit cell of the bulk anatase. Surface energies have been computed either keeping fixed the lattice parameters at the bulk values (E0 S in Figure 1a) or relaxing them (E00 S in Figure 1b) and thus modeling, in the latter case, the particle size effects. The (101) and (100) surfaces are the most stable and exhibit smooth changes of ES with the slab thickness that almost vanishes when the sheets contain at least six Ti layers (T = 810 Å, as already observed for the computed CO properties). The third surface in order of stability is the (112), followed by the (001). In the case of the (101), (100), and (112) surfaces, both E0 S and E00 S and their relative difference do not exhibit significant variation with T (Figure 1a,b), indicating a negligible size effect; on the contrary, E00 S of the (001) shows a huge drop by reducing T,
providing clear evidence of a more relevant exposition of this surface in extremely small crystals. It is also worth noticing that the surface energy of the (001) face increases quasi-linearly as a function of the slab thickness: in general, such a behavior is quite unusual, and it has been found in oxide ultrathin films of polar orientations, which show an uncompensated polar character.24 In these systems, the increase of ES with the size is also accompanied by a decrease of the energy gap, which, at a critical size, vanishes, and by strong variations in the surface charges. This is not the case since we computed an almost constant value of the surface charges (from 19.64 to 19.63 au for surface Ti and from 9.14 to 9.17 au for surface O) and a limited decrease of the Eg (from 4.8 to 3.7 eV), which, nevertheless, does not vanish, probably owing to the semicovalent character of TiO2. The order of stability of the different surfaces can be rationalized considering the surface geometry: as visible in Figure 2a, the (101), (100), and (112) surfaces, which show the lower surface energies, exposes both 2-fold oxygen atoms O(2f) bonded to 5-fold titanium atoms Ti(5f) and atomic species in bulklike coordination (i.e., 6-fold titanium atoms and 3-fold oxygen atoms). In contrast, on the (001) surface, only Ti(5f) cations and O(2f) anions are present. Finally, the (103) and (110) surfaces exhibit very undercoordinated Ti(4f) atoms and are, therefore, more unstable. Anyway, all selected surfaces expose 5-fold titanium atoms Ti(5f) and 2-fold oxygen atoms O(2f), which represent the 7696
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Figure 3. (a) Side view of the bulk-terminated (001) surface. (b) Side view of the (001) surface optimized without symmetry constraints showing that the bridging oxygen moves closer to the Ti(5f) atom, resulting in two remarkably different bond lengths.
distances, present in the bulk-terminated structure, is not preserved: the bridging oxygen moves closer to one of the Ti(5f) atoms, resulting in two remarkably different bonds: d (TiO) = 1.713 and 2.245 Å (Figure 3). CO Adsorption. According to the above analysis, CO has been adsorbed on the (101), (100), (001), and (112) surfaces: full CO coverage (θ = 1, Figure 2a) and low-coverage conditions (θ = 0.25 or θ = 0.5 for the (112) surface, which guarantees negligible lateral interactions because the distance between adsorbed molecules is always larger than 5.3 Å, Figure 2b) have been considered. CO binding energies were calculated according to the usual expression Figure 2. (a) Optimized geometry of CO adsorbed on anatase (101), (100), (001), and (112) surfaces with (1 1) periodicity (full coverage: θ = 1). (b) Optimized geometry of CO adsorbed at low coverage (θ = 0.25) on anatase (101), (100), and (001) supercells and at θ = 0.5 on the anatase (112) surface.
Table 3. Displacements along the z Axis of the Exposed 2-Fold Oxygen Atoms O(2f) and of the Ti Atoms Belonging to the First Three Ti Layers (Ti1, Ti2, Ti3) with Respect to the Bulk-Terminated Positionsa (101)
(100)
(001)
(112)
Δz Ti1(5f) (Å)
0.21
0.16
0.06
0.07
Δz Ti2(6f) (Å)
0.18
0.16
0.01
0.02
Δz Ti3(6f) (Å)
0.15
0.12
0.01
0.00
Δz O(2f) (Å)
0.04
0.02
0.04
0.06
a
The slabs used to model the (101), (100), (001), and (112) surfaces contain six Ti layers. The calculations have been performed at the PBE0/ B0 level.
surface Lewis acid and basic sites, respectively: in fact, because of the lower coordination with respect to bulk anatase, they can interact in a more effective way with the adsorbed molecules. The displacements of the exposed O(2f) atoms and of the Ti atoms belonging to the first three Ti layers with respect to the bulkterminated positions are reported in Table 3: the values are comparable to already published data.15,19 In particular, Ti(5f) ions show a considerable downshift owing to the reduced coordination,25 whereas the displacements of the anions are almost negligible. A peculiar behavior is displayed by the (001) surface, where the symmetry of the two surface Ti(5f)O(2f)
BE ¼
Esys ðEslab þ nECO Þ n
where Eslab is the energy of the slab, ECO is the energy of the isolated CO molecule in its equilibrium configuration, n is the number of CO molecules in the adsorbate/slab system, and Esys is its total energy. Considering the low-coverage situation, the inspection of Table 4 shows that, for all surfaces, the adsorption gives rise to a decrease of the CO bond length that is in linear correlation with the corresponding blue shift of ν(CO). This correlation can be explained according to the Stark effect and can be described by perturbation theory.26 The differences in the blue shift for the considered surfaces can be rationalized considering the electrostatic potential maps of the bare TiO2 slabs (Figure 4): the computed electrostatic potential at the position corresponding to the center of mass of CO in the adsorbate/slab system progressively increases from 0.16 V for the (001), to 0.33 V for the (100), to 0.43 V for the (101), and to 0.48 V for the (112) surface, in agreement with the progressive increase of Δν(CO) for the different surfaces (see Figure 5 and Table 4). The good linear correlation between these two parameters (see Figure 5) confirms that the blue shift originates mainly from the surface electric fieldCO dipole interaction9 as observed for cations without d electrons.27,28 Moving to high coverage, the binding energies and the vibrational frequencies decrease (Table 4) owing to the dipoledipole interaction between the CO molecules. This effect is particularly evident for the (001) surface where the COCO distance is the shortest in both x and y directions, that is, 3.773.77 Å for the (001), 3.775.49 Å for the (101), 3.803.84 Å for the (100), and 5.344.56 Å for the (112). 7697
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Table 4. Main Computed CO Adsorption Properties for the (101), (100), (001), and (112) Slab Models Containing Six Ti Layersa d (CTi) (Å)
Δd (CO) (Å)
BEC (kJ/mol)
BE (kJ/mol)
ν (cm1)
Δν (cm1)
1
2.5623
0.0039
22.9
27.0
2185
44
0.25
2.5329
0.0053
25.3
29.6
2193
52
1
2.5637
0.0027
17.7
21.1
2174
33
0.25
2.5031
0.0044
23.9
27.7
2185
44
1
2.5383
0.0003
13.9
17.8
2156
14
0.25
2.3961
0.0035
27.7
32.3
2177
36
(112)
1
2.5212
0.0037
17.3
21.7
2184
43
(101)
0.5 1
2.5198 2.6482
0.0054 0.0035
29.5 13.4
34.2 17.3
2193 2181
52 39
0.25
2.6026
0.0049
17.5
21.7
2187
46
1
2.6716
0.0023
8.9
11.9
2169
27
0.25
2.4423
0.0033
16.5
21.2
2175
33
1
2.6914
0.0004
3.1
6.6
2147
4
0.25
2.4429
0.0033
16.5
21.2
2174
32
1
2.5893
0.0034
5.7
10.0
2180
38
0.5
2.5770
0.0048
18.5
23.1
2186
45
θ
surface PBE0
(101) (100) (001)
B3LYP
(100) (001) (112) a
B3LYP and PBE0 functionals with the B5 basis set have been adopted for all calculations. BE and BEC are the binding energy and the BSSE-corrected binding energy; d are the bond distances, ν is the CO stretching frequency scaled to match the experimental and computed frequencies in gas phase, and Δ are the absolute differences with respect to the free molecule. For free CO, d (CO) = 1.1240 Å and ν = 2249 cm1 (TZ-P/PBE0) and d (CO) = 1.1270 Å and ν = 2219 cm1 (TZ-P/B3LYP).
Figure 5. Linear fit of the blue shift of the CO vibrational frequency (PBE0 values for low-coverage conditions; see Table 4) as a function of the electrostatic potential for the bare surfaces computed in the position corresponding to the center of mass of the CO molecule in the adsorbate/slab system.
Figure 4. Electrostatic potential (EP) maps for the bare (101), (100), (001), and (112) anatase surfaces. The crosses highlight the position of the carbon and oxygen atoms of the CO molecules in the optimized adsorbate/slab system. Solid and dashed lines indicate positive and negative values of the EP, respectively.
The B3LYP functional produces bond distances always longer and BEs and Δν(CO) always lower than the PBE0 values, in
agreement with the less satisfactory capabilities of B3LYP to deal with weak interactions.29 Nevertheless, the trends in the computed properties with respect to the different surfaces are the same for both B3LYP and PBE0, confirming that the physical interpretation of the data is not biased by the considered functional. On the basis of the computed results reported in Table 4, it is possible to proceed to a trustful assignment of the main bands of FTIR spectra, recorded at 60 K, of CO adsorbed at different coverages on highly dehydroxylated anatase nanocrystals (Figure 6): (i) The intense, broad, and easily reversible band at 2138 cm1 is readily ascribed to physically adsorbed CO forming a surface multilayer.27 (ii) The broad band in the 21542157 cm1 range is due to CO interacting with residual OH groups. This assignment 7698
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Figure 6. FTIR spectra, recorded at 60 K, of CO adsorbed at increasing coverages on anatase nanocrystals. The sample has been previously outgassed for 4 h at 773 K in order to highly dehydroxylate the nanoparticles. The colored bars highlight the position of the vibrational frequencies for the different surfaces calculated with the PBE0 functional (see Table 4): solid and dashed lines indicate full-coverage and lowcoverage frequencies, respectively.
is demonstrated by the fact that its intensity decreases in samples containing fewer OH groups and its presence is associated with a perturbation of the OH signals in the 36503750 cm1 region (results not shown for the sake of brevity). (iii) The weak band at 2165 cm1 can be assigned to CO adsorbed on Ti Lewis centers located on flat (001) surfaces. In this case, ab initio modeling confirms previous assignments5,30 based on the consideration that the (001) cations are qualitatively different with respect to those exposed by the other investigated surfaces because they form TiO rows where each Ti center is strongly bound to two O(2f) anions: the result is a more screened electrostatic potential at these sites and, therefore, a reduced acidity. (iv) The main component of the group of overlapped signals centered at 2179 cm1, showing a blue shift of about 12 cm1 at low coverage with respect to full coverage, can be ascribed to CO interacting with Ti centers located on flat (100) surfaces. (v) The shoulder centered at 2184 cm1, overlapped with the main peak at 2179 cm1, can be assigned to CO adsorbed on Ti Lewis sites located on flat (101) and (112) surfaces, which exhibit very similar calculated Δν(CO) (see Table 4). (vi) The weak band at 2209 cm1 is related to CO adsorbed on highly acid Ti Lewis sites exhibiting very low coordination and, therefore, located on edges, steps, and corners. It is worth noting that, when the CO pressure is decreased, after removing the physically adsorbed CO and the CO interacting with OH groups, the band centered at 2165 cm1 is progressively reduced while the signals at 2179 and 2184 cm1 are still unchanged. Upon further decrease of the CO pressure, the signals centered at 2184 cm1 gradually shift until 2193 cm1 and are the last to disappear. These observations are in agreement with the proposed assignments because the (001) surface shows the lower binding energy for full-coverage conditions (13.9 kJ/mol for the PBE0 functional; see Table 4) and the (112) surface exhibits the higher binding energy for low-coverage conditions (29.5 kJ/mol for the PBE0 functional; see Table 4).
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’ CONCLUSIONS In summary, this study has shown the unrivalled power and the synergy between DFT calculations and low-temperature FTIR spectra in the assignment of the vibrational spectra of adsorbed species. The joint approach has provided a crossvalidation of the two techniques, leading to the full assignment of the main features of the FTIR spectra of adsorbed CO and to a trustful identification of the exposed surfaces in anatase nanocrystals. The extreme complexity and richness of the FTIR spectra, which are characterized by the presence of many overlapped signals, prevented us from doing a reliable deconvolution of the different bands in order to provide a quantitative determination of the average presence of each surface in the investigated nanocrystals. Nevertheless, the final result is an outstanding description of the surface properties of this material. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors kindly acknowledge BASF for the financial support and CINECA for the availability of high-performance computing resources ’ REFERENCES (1) Fujishima, A.; Zhang, X. T.; Tryk, D. A. Surf. Sci. Rep. 2008, 63, 515–582. (2) Diebold, U. Surf. Sci. Rep. 2003, 48, 53–229. (3) Busca, G. Catal. Today 1998, 41, 191–206. (4) Hadjiivanov, K. I.; Klissurski, D. G. Chem. Soc. Rev. 1996, 25, 61–69. (5) Hadjiivanov, K.; Lamotte, J.; Lavalley, J. C. Langmuir 1997, 13, 3374–3381. (6) Hadjiivanov, K. Appl. Surf. Sci. 1998, 135, 331–338. (7) Martra, G. Appl. Catal., A 2000, 200, 275–285. (8) Minella, M.; Faga, M. G.; Maurino, V.; Minero, C.; Pelizzetti, E.; Coluccia, S.; Martra, G. Langmuir 2010, 26, 2521–2527. (9) Pacchioni, G.; Ferrari, A. M.; Bagus, P. S. Surf. Sci. 1996, 350, 159–175. (10) Scarano, D.; Spoto, G.; Bordiga, S.; Zecchina, A.; Lamberti, C. Surf. Sci. 1992, 276, 281–298. (11) Spoto, G.; Gribov, E. N.; Ricchiardi, G.; Damin, A.; Scarano, D.; Bordiga, S.; Lamberti, C.; Zecchina, A. Prog. Surf. Sci. 2004, 76, 71–146. (12) Scaranto, J.; Giorgianni, S. Mol. Phys. 2008, 106, 2425–2430. (13) Scaranto, J.; Giorgianni, S. THEOCHEM: J. Mol. Struct. 2008, 858, 72–76. (14) Scaranto, J.; Giorgianni, S. Chem. Phys. Lett. 2009, 473, 179–183. (15) Scaranto, J.; Giorgianni, S. Mol. Phys. 2009, 107, 1997–2003. (16) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; D’Arco, P.; Llunel, M. CRYSTAL09 User’s Manual; University of Torino: Torino, Italy, 2009. (17) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. Rev. B 1992, 46, 6671–6687. (18) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158–6170. (19) Labat, F.; Baranek, P.; Adamo, C. J. Chem. Theory Comput. 2008, 4, 341–352. (20) Ferrari, A. M.; Valenzano, L.; Meyer, A.; Orlando, R.; Dovesi, R. J. Phys. Chem. A 2009, 113, 11289–11294. (21) Turi, L.; Dannenberg, J. J. J. Phys. Chem. 1993, 97, 2488–2490. 7699
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