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2008, 112, 16729–16732 Published on Web 10/04/2008
Thinnest Titanium Dioxide Nanowires Assembled by Ti2O4 Building Blocks Dongju Zhang,* Peng Liu, and Chengbu Liu* Institute of Theoretical Chemistry, Key Laboratory of Colloid and Interface Chemistry, Ministry of Education, Shandong UniVersity, Jinan, 250100, P. R. China ReceiVed: August 14, 2008; ReVised Manuscript ReceiVed: September 15, 2008
We show by performing density functional theory calculations that the dimer of titanium dioxide (TiO2) molecule, Ti2O4, is qualified for serving as a basic building block of TiO2 nanostructures owing to its structural stability and appropriate growth activity. In particular, the two thinnest titanium dioxide nanowires, as the prototypes of TiO2 nanostructures, have been assembled and proved to be geometrically graceful and dynamically stable. Calculated results show that the size and shape of TiO2 nanowires have important effects on their structural stabilities and energy gaps, proposing that tailoring the size and shape of TiO2 nanowires may be an effective way to modulate the band gap and finally improve their optical properties. It is well-known that the atomic structure of one-dimensional (1D) nanomaterials is fundamentally important for their sizeand dimensionality-dependent physical and chemical properties. Currently, there is a great deal of interest in building up wellcontrolled nanostructures using small atomic clusters. Titanium dioxide (TiO2) is an indirect bandgap material with many industrial applications.1,2 In recent years, TiO2 nanostructures have attracted increasing attention in both fundamental studies and applications. Impressive progress has been achieved in fabricating various 1D structures of TiO2, including nanoclusters,3-6 nanowires,7,8 and nanotubes.9,10 On the other hand, to promote various technological applications of TiO2 nanomaterials, a lot of theoretical studies have also been performed on small titanium oxide clusters.11-19 Most existing theoretical investigations have placed emphasis on structural stabilities of small and medium-sized titanium-oxygen systems. However, the microscopic structures and properties of nanometer-sized TiO2 are still not well understood at atomic-scale levels. Some fundamental issues also remain unclear. For example, up to now, not much is known about the basic building principle for TiO2 nanostructures and their nucleation and growth mechanisms,14,20 which could give an important clue for improving the quality and morphologies of the nanostrcutures. In contrast, considerable progress has been achieved in the studies of other 1D materials of technological importance such as silicon and silica where the atomic structures and growth modes of the 1D nanostructures have been well understood.21-24 In this paper, we explore the basic building principle of 1D TiO2 nanowires to provide insight into their growth mechanism. By performing density functional theory (DFT) calculations, we propose the dimer of the TiO2 molecule, Ti2O4, a rhombic Ti2O2ring with two dangling O atoms (Figure 1a,b), may be an appropriate basic building block (superatoms) for fabricating TiO2 nanostructures due to its structural stability and appropriate growth activity as demonstrated below, from which we have assembled the two thinnest TiO2 nanowires (Figure 1c,d). Our * To whom correspondence should be addressed. E-mail: (D.Z.)
[email protected]; (C.L.)
[email protected].
10.1021/jp807264n CCC: $40.75
DFT calculations show these two wires are structurally and dynamically stable. Our calculations were performed at the all-electron level within the generalized gradient approximation (GGA)25 to describe the exchange-correlation effects. The calculations have been carried out using DMol3 code.26 The exchange-correlation energy in the GGA was parametrized by Perdew and Wang’s scheme,27 and all-electron Kohn-Sham wave functions were expanded in a double numerical basis set including the ppolarization function (DND). To obtain the local-minimum structures unbiasly, optimization calculations were undertaken without imposing symmetry constraints throughout the clusters (TiO2)n for n ) 1-30. In the present work, all calculations used finite-size cluster models. The accuracy of our computational method was tested by comparing the calculated geometries of the isolated TiO2 molecule and its dimer with available experimental findings or previous theoretical results. Our calculations predict a singlet ground state (1A1 electronic state) with C2V symmetry of the monomer, and the theoretical bond length and angle are 1.659 Å and 110.3°, respectively, which are in good agreement with the experimental values28 of 1.62 ( 0.08 Å and 110 ( 15° and also with the previous theoretical values given by Grein29 from the BPW91/6-311+G(3df) calculations. For the dimer Ti2O4, the optimized global minimum is found to adopt a threedimensional structure with C2h symmetry, where a rhombic Ti2O2 ring is terminated by two O atoms bending out of the Ti-Ti axis, which is in agreement with previous studies. The Ti-O bond lengths in the Ti2O2 ring and ends are 1.86 and 1.65 Å, and the Ti-Ti distance is 2.73 Å. The results agree well with previous DFT-LDA15 and B3LYP14,18 calculations. Note that the ground-state Ti2O4 structure is very similar to that of Si2O4, apart from a topological difference of two terminal O atoms in Ti2O4 from those in Si2O4, which has a D2h symmetry with the two terminal O atoms in alignment with the Si-Si axis.30 Such rhombic geometry has also been found for the dimer of SiOS.31 2008 American Chemical Society
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Figure 1. Two views of the basic building block Ti2O4 (panels a and b) and two thinnest nanowires of TiO2 (panels c and d). The red balls represent oxygen atoms, and blue balls represent titanium atoms.
Figure 2. Four schematic paths for forming the C2h dimer of Ti2O4. The red balls represent oxygen atoms, and blue balls represent titanium atoms.
We first discuss the formation of the dimer with our primary concern how the dimerization of TiO2 proceeds and whether there is a significant barrier or not during the dimerization. For these purposes, we have considered many different approach modes of two isolated TiO2 molecules, in particular, those that are not geometrically favored for forming the rhombic Ti2O2 ring of the C2h dimer. Four representative paths are shown in Figure 2. The initial separation between two TiO2 molecules in all considered configurations is set to 4.0 Å. After full optimizations, all considered initial configurations go directly into the most stable C2h isomer of Ti2O4 with two exceptions (Figure 2a,b, two geometrically most unfavorable modes for forming the C2h dimer), which converged to a noncyclic Cs dimer and a C3V dimer, respectively. The force constant matrix reveals that the Cs structure has three negative eigenvalues corresponding to a distortion leading to the C2h structure. Although the C3V dimer is indeed a minimum with all positive frequencies, this structure is less stable by 0.68 eV than the C2h structure, indicating the perpendicular approach of two TiO2 molecules (Figure 2b) is very unfavorable in energy. For the dimerization process, the paths shown in Figure 2c,d may be geometrically most favorable modes, where two TiO2 molecules
Figure 3. Variation of ∆E(n) (solid circles for wire I and solid triangles for wire II) and HOMO-LUMO gap (empty circles for wire I and empty riangles for wire II) with n for the two thinnest TiO2 nanowires.
are approaching each other with their polarized Ti+-O- bonds antiparallel in favor of forming two new Ti-O bonds. We have minimized their energies at the different separation distance between two TiO2 units and found that the system energies decrease monotonously upon going from two isolated molecules to the dimer product, indicating that there is no appreciable barrier during the dimerization. The C2h isomer not only is structurally very stable but also has appropriate growth activity. We find that its highest occupied molecular orbital (HOMO) dominantly consists of the P orbital of the terminal O atoms, and the lowest unoccupied molecular orbital (LUMO) mainly come from the dz2 orbital of Ti atoms. These two orbitals are symmetrically matched, which can make efficient overlay between the HOMO of one such basic unit and the LUMO of another one to bring them together to grow into larger clusters. On the basis of its structural stability and appropriate growth activity, we propose that the C2h isomer the may be a basic building block for TiO2 nanostructures.
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Using the most stable dimer as a basic building block, we have assembled the two thinnest TiO2 nanowires according to the growth modes shown in Figure 1 (c, wire I; d, wire II). In these two nanowires, apart from the ends, all oxygen atoms coordinate to two titanium atoms and all titanium atoms coordinate to four oxygen atoms to form defect-free structures and to support the formal oxidation sate of oxygen and titanium in TiO2, i.e., O2+ and Ti4+. These two wires possess respective unique characteristics. All of the Ti atoms in wire I (Figure 1c) form a line with the rhombic Ti2O2 rings perpendicular to each other, and the Ti atoms in wire II (Figure 1d) divide into two parallel arrays linked by the bridging oxygen atoms. Note that wire I contains either even-n TiO2 units of C2h symmetry or odd-n TiO2 units of C2 symmetry, unlike wire II, which consists of only even-n TiO2 units of C2h symmetry. To evaluate the relative stabilities of so-assembled TiO2 nanowires, we define the adding energy as
∆E(n) ) E(n) + E(2) - E(n+2)
n ) 2, 4, 6, ... (1)
where E(2) is the energy of the basic building block, Ti2O4, E(n) and E(n+2) are the energies of the clusters (TiO2)n and (TiO2)n+2, and ∆E(n) is the energy gain in adding a Ti2O4 unit to (TiO2)n cluster. In Figure 3, we plot the variation of ∆E(n) as a function of the cluster size for the two thinnest TiO2 nanowires (solid circles and triangles in Figure 3). We can see that there are remarkable energy gains from n ) 2 to n ) 4 for both two kinds of wires, but then ∆E(n) saturates at n ) 4 with the value of 4.04 eV for wire I (solid circles in Figure 3) and at n ) 8 with the value of 4.95 eV for wire II (solid triangles in Figure 3). At all cluster size considered from n ) 2 to n ) 30, wire II is found to be more stable than wire I, indicating the growth mode shown in Figure 2d may be energetically more favorable than that given in Figure 2c. Figure 3 also shows the variation of the HOMO-LUMO gaps of TiO2 clusters as a function of size. We find that the two kinds of wires have different the gap characters: the gap of wire I monotonously decrease with size (empty circles in Figure 3), in line with that expected according to the normal quantum size effects),32 in contrast to that of wire II which initially decreases but rapidly level off to a constant, 2.56 eV, as n > 8 (empty triangles in Figure 3). As seen from Figure 3, the HOMOLUMO gap of wire I is larger than that of wire II, which may imply that TiO2 nanowies with smaller diameters possesses larger gaps. This fact demonstrates that the size and shape of TiO2 nanostructures have important effects on their electronic properties, as found in a previous study by Zapol et al.33 Thus, tailoring the size and shape of TiO2 nanostrucutres can modulate the band gap and finally improve the optical properties of TiO2 semiconductors. On the other hand, it is well-known that the band gap of bulk TiO2 is 3.2 eV for anatase and 3.0 eV for rutile. The calculated HOMO-LUMO energy gap for the TiO2 nanowires is clearly smaller than the bulk value. This is possibly due to lower coordinate number of Ti and O atoms in the nanowires compared to that of bulk TiO2.4 To test the dynamic stabilities of wires I and II, we have performed calculations of the vibrational spectra. It is found that there is no imaginary frequency for all clusters considered, confirming that these two kinds of wires are dynamically stable. We find that the strongest spectroscopic signatures blue shift with cluster size for both wires I and II, and that for the clusters with the same size, the sharp peak for wire I appears at smaller frequency area with larger intensity with respect to wire II. Figure 4 shows the calculated vibration spectra for the (TiO2)12 cluster with the structures of wires I and II, respectively. These respective spectroscopic fingerprints should provide good
Figure 4. Calculated IR spectra of (TiO2)12 wires with the structure of wire I (panel a) and the structure of wire II (panel b).
signatures for the experimental detection of TiO2 clusters with specific structures. It should be noted that the specific attention in the present work focuses on the structural building principle of TiO2 nanostructures. We do not guarantee these thinnest nanowires of TiO2 represent the global minima. In fact, ground-state structures are not necessarily formed, but rather, metastable structures are usually formed in real 1D nanomaterials,34 as demonstrated by recent experiments.35 Finally, we must stress that the nanowires proposed in this work are highly speculative, although TiO2 nanostructures have been controllably fabricated in various topological forms. With the progress of nanotechniques, however, we feel that there is real possibility for synthesizing these novel 1D TiO2 polymorphs. In this sense, the present study may provide a practical guidance for the experimentalists who are devoting their attention to novel TiO2 polymorphs. The present work is the first example of our systemic studies on the basic building principle of 1D TiO2 nanostructures. Acknowledgment. This work is supported by the National Natural Science Foundation of China (Grants No. 20773078, 20873076, and 20633060) and the Major State Basic Research Development Programs (Grant No. 2004CB719902). References and Notes (1) Bavykin, D. V.; Friedrich, J. M.; Walsh, F. C. AdV. Mater. 2006, 18, 2807. (2) Peng, X.; Chen, A. AdV. Funct. Mater. 2006, 16, 1355. (3) Yu, W.; Freas, R. B. J. Am. Chem. Soc. 1990, 112, 7126. (4) Wu, H.; Wang, L. S. J. Chem. Phys. 1997, 107, 8221. (5) Matsuda, Y.; Bernstein, E. R. J. Phys. Chem. A 2005, 109, 314. (6) Zhai, H. J.; Wang, L. S. J. Am. Chem. Soc. 2007, 129, 3022. (7) Francioso, L.; Taurino, A. M.; Forleo, A.; Siciliano, P. Sens. Actuators, B 2008, 130, 70. (8) Jitputti, J.; Suzuki, Y.; Yoshikawa, S. Catal. Commun 2008, 9, 1265. (9) Chung, C. C.; Chung, T. W.; Yang, T. C. K. Ind. Eng. Chem. Res. 2008, 47, 2301. (10) Pradhan, S. K.; Mao, Y.; Wong, S. S.; Chupas, P.; Petkov, V. Chem. Mater. 2007, 19, 6180. (11) Hagfeldt, A.; Bergstrom, R.; Siegbahn, H. O. G.; Lunell, S. J. Phys. Chem. 1993, 97, 12725. (12) Bergstrom, R.; Lunell, S.; Eriksson, L. A. Int. J. Quantum Chem. 1996, 59, 427. (13) Walsh, M. B.; King, R. A.; Schaefer, H. F. J. Chem. Phys. 1999, 110, 5224. (14) Jeong, K. S.; Chang, C.; Sedimayr, E.; Sulzle, D. J. Phys. B: At. Mol. Opt. Phys. 2000, 33, 3417. (15) Albert, T.; Finocchi, F.; Noguera, C. J. Chem. Phys. 2000, 113, 2238.
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