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2009, 113, 21–25 Published on Web 12/05/2008
A New Family of Heterofullerenes: Stoichiometric TiO2 Nanoclusters Dongju Zhang,*,† Hui Sun,† Jianqiang Liu,‡ and Chengbu Liu† Key Laboratory of Colloid and Interface Chemistry of Ministry of Education, Institute of Theoretical Chemistry, and School of Physics, Shandong UniVersity, Jinan, 250100, People’s Republic of China ReceiVed: October 06, 2008; ReVised Manuscript ReceiVed: NoVember 01, 2008
On the basis of the stoichiometry of TiO2 and the general bonding principles of Ti and O atoms, we show new defect-free and fullerene-like forms of TiO2 nanostructures. The proposed heterofullerenes of TiO2 possess the frameworks of carbon fullerenes and can be considered as arising from Ti2O4 units, the basic building blocks for TiO2 nanostructures, which are of structural stability and appropriate growth activity. By performing density functional theory calculations, we have presented theoretical evidence for the structural and thermal stabilities of the heterofullerenes. These stoichiometric and structurally defect-free nanocages display unique frequency modes at ∼827-854 cm-1 and a larger HOMO-LUMO energy gap than bulk TiO2 materials. The present study provides a practical guide for the experimentalists who are devoting their attention to novel TiO2 polymorphs. TiO2 heterofullerenes, if synthesized, may find novel applications in nanotechnology. Titanium dioxide (TiO2), an important transition-metal oxide, is a wide band gap semiconductor which has been extensively utilized in a number of technological areas, such as heterogeneous catalysis, microelectronics, and solar energy harvesting.1,2 Of particular recent interest is its photoactivation since the pioneer discovery of water splitting on TiO2 electrodes by Fujishima and Honda in 1972.3 Over the past two decades, extensive efforts have been focused on developing various experimental techniques4-7 to fabricate different TiO2 nanostructures,includingnanoclusters,8-10 nanoparticles,11 nanowires,12,13 nanosheets,14 nanotubes,15,16 and nanospheres.17-19 On the other hand, to promote various technological applications of TiO2 nanomaterials, a lot of theoretical studies have also been performed on nanosized titanium-oxygen systems.20-29 Previous experimental and theoretical studies have provided useful information for understanding the structures and properties of TiO2 nanomaterials. However, our basic knowledge is still far from complete. It is well known that nanosized materials generally possess unusual structures and properties which cannot be derived from the bulk.30 TiO2 in bulk may exist as rutile, anatase, and brookite crystalline phases, where the covalent three-dimensional networks consist of six-coordinated Ti and three-coordinated O atoms. In contrast, recent theoretical studies24-28 showed that the structures of TiO2 nanoclusters and nanoparticles are very complex, exhibiting a diverse spectrum of geometries. In particular, Qu et al.27,28 found that the Ti and O atoms in TiO2 nanoparticles are mainly four- and two-fold coordinated, respectively, to form defect-free structures and to support the formal oxidation states of Ti and O in TiO2, that is, Ti4+ and O2-. The structural diversity provides possibilities for materials with designed structures and properties. Compared to the * To whom correspondence should be addressed. E-mail: zhangdj@ sdu.edu.cn. † Key Laboratory and Institute of Theoretical Chemistry. ‡ School of Physics.
10.1021/jp808819x CCC: $40.75
extensively studied TiO2 properties in bulk phases and on surfaces, our understanding for its various new forms of nanostructures is in the primitive stage. The importance of theoretical studies in guiding relevant experiments has been proved on many occasions. For example, before the synthesis of single-wall carbon nanotubes,31 theoretical calculations had foretold that they might be either semiconducting or metallic depending on their geometries.32 Another example is that the smallest carbon nanotube with a diameter of 4 Å was also first predicted by theory33 and was subsequently synthesized by Iijima et al.34 These facts demonstrate that extensive theoretical studies for novel nanostructured materials can provide valuable guides for relevant experiments. In this letter, on the basis of the stoichiometry of TiO2 and the general bonding principles of Ti and O atoms, we propose a new polymorph of TiO2 nanostructures, that is, fullerene-like forms of TiO2. By performing density functional theory (DFT) calculations, we present theoretical evidence for the structural and thermal stabilities of the new heterofullerene polymorph of TiO2 and study their growth characteristics and electronic properties. Previous investigations showed that the dimer of TiO2 adopts a three-dimensional structure with C2h symmetry, where a rhombic Ti2O2 ring is terminated by two O atoms which are bent out of the Ti-Ti axis.35 As shown by Figure 1a, this C2h isomer possesses a kite-shaped geometry and is the ground state of Ti2O4. On the other hand, this isomer is expected to be relatively reactive due to its defect on the terminal Ti-O bonds. We find that its highest occupied molecular orbital (HOMO) dominantly consists of the p orbital of the terminal O atoms, while the lowest unoccupied molecular orbital (LUMO) mainly comes from the dz2 orbital of Ti atoms. The efficient overlay between the HOMO of one Ti2O4 unit and the LUMO of another such unit can bring them together to grow into the larger fragments (Figure 1b-h). On the basis of its structural stability and appropriate growth activity, the C2h isomer of Ti2O4 is 2009 American Chemical Society
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Figure 1. Molecular motifs for forming the (TiO2)60 heterofullerenes. Titanium atoms are gray, and oxygen atoms are red. The same color scheme is also used in Figures 2 and 3.
Figure 2. DFT-optimized TiO2 heterofullerenes. Symbols in brackets denote the symmetries.
expected to be qualified for serving as a basic building block for TiO2 nanostructures. Using the basic building block, we have constructed a family of TiO2 heterofullerenes by replacing each C2 unit of carbon fullerenes. The so-constructed TiO2 heterofullerenes satisfy the formal oxidation state of TiO2, where each Ti atom coordinates to four O atoms and each O atom coordinates to two Ti atoms to form structurally defect-free clusters. Figure 2 shows several representative structures of the family with high point group symmetry, that is, the D5d, C6V, D2d, D6h, D5h, and Ih isomers for the heterofullerenes with n ) 20, 24, 28, 36, 50, and 60, respectively (n is the number of TiO2 units). All of these heterofullerenes have the corresponding frameworks of the most stable carbon fullerenes. To understand the heterofullerene growth characteristics, as an example, Figure 1 gives several molecular fragments for forming the (TiO2)60 heterofullerenes. We have performed DFT calculations using the DMol3 program36 based on a quantum chemistry software package in Cerius2.37 The optimization and numerical second derivative calculations were carried out at the all-electron level within the generalized gradient approximation (GGA)38 to describe the exchange-correlation effects. The exchange-correlation energy in the GGA was parametrized by Perdew and Wang’s scheme,39 and all-electron Kohn-Sham wave functions were expended in a double numerical basis set including p-polarization function (DND). For the numerical integration, the MEDIUM quality mesh size of the program was adopted. The tolerances of energy, the change of the maximum force on the atom, and the maximal
Letters displacement were set to 2 × 10-5 Hartree, 4 × 10-3 Hartree/ Å, and 5 × 10-3 Å, respectively. The accuracy of our computational method was tested by computing the geometries of the isolated TiO2 molecule and its dimer, for which experimental findings and/or previous theoretical results are available. 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 values40 of 1.62 ( 0.08 Å and 110 ( 15° and also with the previous theoretical values by Grein41 from the BPW91/6-311+G(3df) calculations. For the dimer Ti2O4, 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-LDA24 and B3LYP23,27 results. In Figure 2, the energy-minimized structures are shown. A common structural characteristic is noted in these heterofullerenes: Ti-O bonds naturally divide into a Ti-Oring-in set, a Ti-Oring-out set, and a Ti-Obridge set, where Oring-in and Oring-out mean the inner and outer O atoms in the Ti2O2 ring, and Obridge denotes those O atoms bridging the Ti2O2 rings. Calculated results show that the geometries of Ti2O4 units in all structures are not remarkably different. As an example, in Figure 3, we show the optimized geometrical parameters for two representative Ti2O4 units in the smallest (TiO2)20 heterofullerene (panel a) and in the largest (TiO2)60 heterofullerene (panel b) considered in the present work. The Ti2O2 rings in these Ti2O4 units are also geometrically very similar to that of the isolated dimer (panel c), indicating that the Ti-O bonds in Ti2O2 rings are less affected during the cluster’s assembling, that is, the formation of the heterofullerenes mainly involves the terminal Ti-O bond interaction between the building blocks. The conventional geometry optimizations have provided the initial evidence for the existence of TiO2 heterofullerences. However, questions may arise about whether the heterofullerences are real minima on the conformational landscapes and, if so, how about their thermal stability. To confirm that the heterofullerences are indeed a stable allotropic form of TiO2 nanostructures, harmonic vibrational analysis at the same level was performed, and the calculated spectra are given in Figure 4. No imaginary frequencies were found for all six heterofullerences, suggesting that these structures are minima on the conformational landscapes. As shown in Figure 4, the strongest normal modes correspond to the asymmetrical stretching vibrations of the Ti-Obridge bonds, and the corresponding frequencies are at 827-854 cm-1, having a red shift with the heterofullerene size. These spectroscopic fingerprints should provide guidance for their experimental detection. The fact of the structural stability of the heterofullerenes prompts us to examine further their thermal stability. We have carried out ab initio molecular dynamics (MD) simulations at several temperatures (300, 500, and 1000 K) for the two smallest heterofullerences, (TiO2)20 and (TiO2)24. The MD simulations were performed in the NVT ensemble using the massive generalized Gaussian moments (Massive GGM) thermostat with a Nose´ Q ratio of 2.0 and Yoshida parameter of 3 as implemented in Dmol3. The simulations were run for 2 ps with a time step of 1 fs in the updates of atomic positions. Throughout the whole runs at each temperature, it was found that the two heterofullerenes are particularly resistant to collapse or rupture and that none of the Ti and O atoms are ejected from the cages. In other words, the heterofullerenes maintain the cage structure skeleton without any old bond breaking and new bond formation during runs, although all constituent atoms have increased
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J. Phys. Chem. C, Vol. 113, No. 1, 2009 23
Figure 3. Optimized geometrical parameters for (a) the (TiO2)2 unit in the (TiO2)20 heterofullerene, (b) the (TiO2)2 unit in the (TiO2)60 heterofullerene, and (c) the isolated (TiO2)2 unit.
Figure 4. Calculated IR spectra for the TiO2 heterofullerenes.
∆E(n) ) E[(TiO2)] - 1 ⁄ nE[(TiO2)n]
Figure 5. Geometries of the (TiO2)20 heterofullerenes before and after MD simulations for 2 ps. Bond lengths in Å.
kinetic energy due to the temperature. This fact indicates that the atomic orderings in the heterofullerenes are stable against heating. As an example, Figure 5 shows the geometries of the (TiO2)20 heterofullerenes before and after the MD simulation at 1000 K for 2 ps. The relative stability of the heterofullerenes (TiO2)n is evaluated by calculating the monomer binding energy (∆En), as defined in eq 1
(1)
in which E[(TiO2)] is the ground-state energy of the TiO2 monomer and E[(TiO2)n] is the energy of the heterofullerenes (TiO2)n. In Figure 6a, we plot the calculated ∆E(n) as a function of the inverse number of the heterofullerene size, 1/n, a scale factor of the curvature of the heterofullerene. There is a dependence of ∆E(n) on the cluster size, which was well fitted by a linear slope with a limiting value for 1/n f 0. This 1/n linear behavior has also been found for carbon,42 boron nitride,43 and silica44 fullerenes and attributed to strain due to the deviation of the cage surface from planarity. In the case of the present heterofullerenes, the 1/n dependence of ∆E(n) is due to the combined strain effects of the curvature of heterofullerenes and the Ti2O2 rings contained in cages. The binding energies of these heterofullerenes ranging from 4.87 to 4.97 eV are not far from the limiting value of rutile, the most stable phase of bulk TiO2, 5.57 eV. To further show their relative stability, we also calculated the energies per TiO2 in the heterofullerenes relative to rutile, as shown in Figure 6b. It is noted that all relative energy values are smaller than 0.70 eV, confirming the thermodynamic accessibility of these heterofullerenes.
24 J. Phys. Chem. C, Vol. 113, No. 1, 2009
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Figure 7. Calculated HOMO-LUMO gap as a function of the heterofullerene size n. The curve is the first-order exponential decay fit of the data.
Figure 6. (a) Binding energy [∆E(n), in eV] of the heterofullerenes as a function of the inverse number of TiO2 units (1/n). (b) Energy per TiO2 in the heterofullerenes relative to rutile. The line and curve are the fitting results of the data.
Apart form geometrical and energetic aspects, the stabilities of these heterofullerenes can be alternatively tested by computing the energy gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO), which has important effects on the photophysics and photocatalysis of TiO2 nanostructures. To establish a comparable criterion, we calculated the energy gap of rutile, the thermodynamically most stable phase of bulk TiO2 under ambient condinations.45 The calculation was performed with periodical boundary conditions along three directions, which predicted a band gap of 1.85 eV. This value is smaller than the experimental value of 3.0 eV.46 This is ascribed to the well-known deficiency of DFT methods, which in general significantly underestimate the energy gap.47,48 Although DFT methods cannot describe accurately the energy gap, they provide a trend of the gap evolvement with reducing material size. In Figure 7, we show the changes in the HOMO-LUMO gap as a function of the heterofullerene size (n). Clearly, we see that the HOMO-LUMO gaps of the heterofullerenes, ranging from 3.587 eV for (TiO2)20 to 3.307 eV for (TiO2)60, are remarkably larger than the calculated value for the bulk phase (rutile), 1.85 eV. This is in agreement with what we expect from quantum confinement effects. It is known that the HOMO-LUMO gap is a signature of the chemical stability of a system. The large energy gap of the heterofullerenes provides supports for their high structural and thermal stability. We must stress that the present work aims at providing a theoretical evidence for a new possible heterofullerene polymorph of TiO2 nanostructures. There is no guarantee, however,
that the TiO2 heterofullerenes present the global minima. In fact, ground-state structures are not necessary for nanomaterials, but rather, metastable structures are sometimes preferred, as confirmed by the recent experiment by Chelikowsky et al.49 The actual structures of nanoparticles depend on a complex interplay of energetic, thermodynamic, and kinetic effects,50 which may cause either equilibrium or metastable structures to be produced. With the fast development in nanoscience and nanotechnology, nanomaterials with tailored structures can now be produced via various experimental techniques. On the basis of the present calculated results, we believe that there is a potential possibility for synthesizing TiO2 heterofullerenes, although this idea is highly speculative at present. In this sense, the present theoretical study is expected to provide appropriate guidance for exploring the novel forms of TiO2 nanostructures. Acknowledgment. This work described in this paper was supported by the National Natural Science Foundation of China (Grant Nos. 20773078 and 20873076), the Natural Basic Research Program of China (973 Program) (No. 2007CB936602), the Natural Science Foundation of Shandong Province (Grant No. Y2007F02), and the Postdoctoral Innovation Item Special Foundation of Shandong Province (No. 200703079). References and Notes (1) Hagfelt, A.; Gra¨tzel, M. Chem. ReV. 1995, 95, 49. (2) Hadjivanov, K. I.; Klissurski, D. G. Chem. Soc. ReV. 1996, 25, 61. (3) Fujishima, A.; Honda, K. Nature 1972, 238, 37. (4) Lin, J.; Lin, Y.; Liu, P.; Meziani, M. J.; Allard, L. F.; Sun, Y. P. J. Am. Chem. Soc. 2002, 124, 11514. (5) Macak, J. M.; Tsuchiya, H.; Schmuki, P. Angew. Chem., Int. Ed. 2005, 44, 2100. (6) Feng, X. J.; Macak, J. M.; Schmuki, P. Chem. Mater. 2007, 19, 1534. (7) Chen, X.; Mao, S. Chem. ReV. 2007, 107, 2891. (8) Yu, W.; Freas, R. B. J. Am. Chem. Soc. 1990, 112, 7126. (9) Guo, B. C.; Kerns, K. P.; Castleman, A. W. Int. J. Mass Spetrom. Ion Processes 1992, 117, 129. (10) Wu, H.; Wang, L. S. J. Chem. Phys. 1997, 107, 8221. (11) Kotsokechagia, T.; Cellesi, F.; Thomas, A.; Niederberger, M.; Tirelli, N. Langmuir 2008, 24, 6988. (12) Francioso, L.; Taurino, A. M.; Forleo, A.; Siciliano, P. Sens. Actuators., B 2008, 130, 70. (13) Jitputti, J.; Suzuki, Y.; Yoshikawa, S. Catal. Commun. 2008, 9, 1265. (14) Wei, M. D.; Konishi, Y.; Arakawa, H. J. Mater. Sci. 2007, 42, 529. (15) Chung, C. C.; Chung, T. W.; Yang, T. C. K. Ind. Eng. Chem. Res. 2008, 47, 2301.
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