Signatures in Vibrational Spectra of Ice Nanotubes Revealed by a

Signatures in Vibrational Spectra of Ice Nanotubes Revealed by a Density Functional Tight Binding Method ... Publication Date (Web): September 5, 2007...
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J. Phys. Chem. C 2007, 111, 14131-14138

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Signatures in Vibrational Spectra of Ice Nanotubes Revealed by a Density Functional Tight Binding Method C. Feng,† R. Q. Zhang,*,†,‡ S. L. Dong,§ Th. A. Niehaus,|,⊥ and Th. Frauenheim| Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, P. R. China, Centre of Super-Diamond and AdVanced Films (COSDAF) and Department of Physics and Materials Science, City UniVersity of Hong Kong, Hong Kong SAR, P. R. China, Department of Physics, Ocean UniVersity of China, Qingdao, P. R. China, Bremen Center for Computational Material Science, UniVersity of Bremen, 28334 Bremen, Germany, and German Cancer Research Center, Department of Molecular Biophysics, D-69120 Heidelberg, Germany ReceiVed: June 3, 2007; In Final Form: July 20, 2007

The geometry structures and vibrational infrared and resonant Raman spectra of ordered n-gonal water nanotubes, n ) 5-7, were systematically studied using a self-consistent charge density-functional tightbinding method complemented with an empirical van der Waals force correction. It is shown that water molecules can form cylindrical crystalline structures, referred to as ice nanotubes, by hydrogen bonding under confinement within single-walled carbon nanotubes. The hydrogen bond plays an important role not only in formation of the unique structures of ice nanotubes but also in the signatures in their vibrational spectra. The calculated infrared spectra in the low-frequency domain show a series of weak bands involving hydrogen bonds along with two librational bands which arise from the constraints induced by hydrogen bonding. In the middle-to-high-frequency region, the intramolecular bending bands of ice nanotubes are shifted to lower frequencies with regard to those of conventional hexagonal ice phase, whereas the intramolecular symmetric and asymmetric stretching bands are shifted to higher frequencies as the hydrogen-bond networks of ice nanotubes are weaker than those of conventional hexagonal ice. The predicted resonant Raman spectra also present distinctive features between those ice nanotubes.

1. Introduction Single-walled carbon nanotubes (SWNTs) have recently attracted great research interest due to their novel structural, mechanical, and electronic properties. In particular, SWNTs provide a well-defined nanoscale cylindrical pore that can serve as a nanometer-sized capillary in the fabrication of quasi-onedimensional (Q1D) materials by filling SWNTs with chosen materials.1,2 On the other hand, water is the universal solvent and plays an important role in the mechanisms of the majority of chemical and biochemical processes. Even though water has been extensively studied, some of its properties remain partially unknown. A significant number of them are related to the behavior of water under confinement within nanoscale Q1D channels such as SWNTs, and the confined water is expected to exhibit different physical properties from its bulk counterparts. Since many similar scientifically relevant systems can be found in nature, this issue is of great interest to biology, geology, and materials science.3-5 Recent theoretical works have reported several novel features of water encapsulated inside SWNTs, such as proton conduction, hydrogen-bond network, phase transitions, etc.6-13 In particular, based on classical molecular dynamics (MD) simulations Koga and co-workers14 revealed that at low temperatures the water confined in the zigzag (l,0) SWNTs (l ) 13-17) can freeze *

Corresponding author. E-mail: [email protected]. Chinese Academy of Sciences. City University of Hong Kong. § Ocean University of China. | University of Bremen. ⊥ German Cancer Research Center. † ‡

spontaneously from liquid-like disordered phase into crystalline structures, referred to as ice nanotubes (INTs), which differ from the 13 polymorphic phases of bulk ice identified experimentally thus far. The structures of those solid-like water are the Q1D arrays of orderly stacked n-membered rings of water molecules that interact with each other by hydrogen bonding.15 Subsequently, formation of ordered INTs with confinement in SWNTs at low temperature was confirmed by experimental studies with X-ray diffraction and neutron scattering.16,17 Moreover, the phase transformation behaviors of INTs confined within SWNTs were substantially studied via classical MD simulations.14,16,18 Recently, Byl and co-workers19 presented the first experimental vibrational spectroscopy study of confined water inside SWNTs. However, to our knowledge, theoretical calculations of vibrational spectra of INTs have been little studied, although there were extensive reports of theoretical studies of the vibrational spectra of liquid water adsorbed in the hole spaces of carbon nanotubes (CNTs).8,20,21 The vibrational calculations of INTs will motivate more experimentalists to investigate the interesting spectral characteristics of INTs and can be extended to other relevant systems, for example, recently predicted multiwalled ice nanotubes.22 The INT encapsulated in CNT is a typical weakly bound van der Waals (vdW)-type complex that involves intermolecular interaction between water molecules of INT and between INT and the confining CNT. To obtain qualitative information about these interactions the effect of vdW interactions should be taken into account in the adopted methods. The most widely used method for this purpose is the expensive second-order MøllerPlesset (MP2) perturbation theory, but its application is limited

10.1021/jp0742822 CCC: $37.00 © 2007 American Chemical Society Published on Web 09/05/2007

14132 J. Phys. Chem. C, Vol. 111, No. 38, 2007 to small systems due to the huge computational demands. Dealing with larger clusters or periodic structures, densityfunctional theory (DFT) often gives accurate solutions; however, the generally used DFT methods fail to describe the dispersion interaction that contributes significantly to the binding energy. To overcome this drawback, a common improvement is to introduce an empirical correction to calculate the additional attraction energy.23-25 The recently developed self-consistent charge density-functional tight-binding (acronym SCC-DFTB) method complemented by the empirical London dispersion correction (SCC-DFTB-D) and implemented in the same-name code is following this correction.26 In this study, we employed the SCC-DFTB-D method to investigate the energies, geometry structures, and vibrational frequencies and intensities of bands in the infrared (IR) and resonant Raman spectra of INTs confined in SWNTs. Particular attention was paid to the signatures in these vibrational spectra and the important role of hydrogen bonds in determining the structural and spectral properties of INTs. 2. Computational Method and Modeling Details The SCC-DFTB approach is an approximate DFT scheme, which is derived from a second-order expansion of the KohnSham total energy in DFT with respect to charge density fluctuations, and the Hamiltonian matrix elements are calculated with a two-center approximation, which are tabulated together with the overlap matrix elements with respect to the interatomic distance. A comprehensive description of the method can be found in the literature.26-30 SCC-DFTB has been proven computationally efficient and extremely reliable in the simulations of large systems with hundreds of atoms or highly periodical materials using either cluster models or supercells. In order to describe the vdW interaction between two separated fragments an empirical dispersion energy, consisting of a R-6 term, is added to the SCC-DFTB total energy.25 For hydrogen-bonded systems SCC-DFTB-D has been successfully applied to investigation of energies and geometry structures of biomolecules31,32 and the interaction between water clusters and the graphite surface which involves OH/π interactions.33 It is found that although the binding energies of hydrogen-bonded complexes were consistently underestimated by about 1-2 kcal/ mol, the SCC-DFTB-D energetic ordering of different conformers as well as the geometry structures are in good agreement with MP2 and DFT/B3LYP calculations.34 The SCC-DFTB method has been enhanced to calculate vibrational frequencies using an analytical expression for Hessian and calculate intensities of the bands in IR spectra using a numerical differentiation of analytical SCC-DFTB forces with respect to an external electric field.35 Resonant Raman spectra can be obtained by an additional determination of the excitedstate gradient using the time-dependent extension of the SCCDFTB method36 following the approach of Orlandi and coworkers.37 The quality of SCC-DFTB harmonic vibrational frequencies for estimating fundamental vibrational frequencies has been examined by calculation of a set of 66 molecules that comprises 1304 distinct vibrational modes.38 Compared to the experimental results, the mean absolute deviation is 6.4%, which is comparable to the accuracy of the DFT method with an error of 3-5%. The vibrational frequencies and intensities of the bands in the IR and Raman spectra have also been investigated for small peptide models39 and a set of typical organic molecules.40,41 Again the SCC-DFTB method provided a good fit to the experimental vibrational spectra. A Q1D crystal can be built by periodically stacking the unit cell along one direction. In this study, an INT can be produced

Feng et al. by periodically stacking a single n-gonal ring of hydrogenbonded water molecules along the axial direction (defined as the z-axial direction), and two neighboring n-gonal water rings comprise the unit cell of INT. For example, 5-gonal, 6-gonal, and 7-gonal rings of water molecules can be stacked to produce pentagonal, hexagonal, and heptagonal INTs, respectively. For the n-gonal, n ) 5, 6, or 7, INT that is confined in the hollow spaces of a zigzag (l,0) SWNT with index l ) 15, 16, or 17, respectively, we carried out geometry optimization by a conjugated gradient method using the SCC-DFTB-D code. The initial guesses of INTs for optimizations were generated under the constraints of two compulsory rules derived from the original ice rules and two elective rules special for INTs, which were discussed in detail in ref 15. The supercells of pentagonal, hexagonal, and heptagonal INT, stacked by four unit cells, comprised 40, 48, and 56 water molecules, respectively. A periodic boundary condition (PBC) was applied in the z-axial direction of the CNT supercell of length l. The lengths of supercells were about 7 Å shorter than those of the confining SWNT supercells, sufficiently large such that the INTs in adjacent cells can be well separated. After geometry optimizations of INT-CNT complexes the optimized INTs were drawn out of the confining CNTs and optimized again without SWNTs confined so as to calculate the binding energies of INTs. On the basis of these optimized models the vibrational frequencies and intensities of the bands in the IR and resonant Raman spectra of each n-gonal INT were then calculated by using SCCDFTB-D code. For comparison, the optimization and spectral calculations were also performed for bulk ice, conventional hexagonal ice phase (ice-Ih), using the same method. The periodic boundary conditions were applied in all three Cartesian directions of the supercell which consisted of 32 water molecules. 3. Results and Discussion Optimized Geometries. Shown in Figure 1a-dis the optimized pentagonal, hexagonal, and heptagonal INTs with confinement in the cylindrical hollow spaces of zigzag (15, 0), (16, 0), and (17, 0) SWNT. It is obvious that all the optimized INTs present ordered cylindrical structures with perfect hydrogen-bond networks. In these models, each oxygen atom has two donors and two acceptors of hydrogen atoms in a tetracoordinate configuration, which is different from the conventional tetrahedral arrangement of water molecules in ice-Ih phase. Therefore, each water molecule of INTs serves as a double donor and a double acceptor of a hydrogen bond and is hydrogen bonded to its four nearest-neighbor molecules. The geometric parameters (see Figure 1e) of the lowest energy structures of INT models are summarized as follows. (1) The mean distances R1between two oxygen atoms from the hydrogenbonded water molecules are about 2.81 Å, which are larger than the nearest-neighbor O-O distance of 2.74 Å in ice-Ih. (2) The mean distances between the oxygen of the acceptor molecule and the hydrogen of the donor molecule, R2 ≈ 1.88 Å, are also larger than the ice-Ih counterpart of 1.76 Å. (3) The mean intramolecular covalent O-H bond lengths R3 are about 0.975 Å, which are slightly smaller than the corresponding value in ice-Ih of 0.985 Å. (4) All the bond angles R between the hydrogen-bonded O-O directions and the covalent O-H directions of the donor molecules, where H is the hydrogen that forms the hydrogen bond, are lower than 20°. (5) The diameters D of n-gonal INTs, which can be defined as diameters of the circumcircles connecting the oxygen nuclei in the n-gonal rings

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Figure 1. Optimized (a) pentagonal, (b) hexagonal, and (c) heptagonal INT confined in zigzag (l,0) SWNT, l ) 15, 16, and 17, respectively, and (d) side view of hexagonal INT model; (e) structural parameters used for quantifying hydrogen bond as discussed in the text. Red, white, and gray spheres represent oxygen, hydrogen, and carbon atoms, respectively.

of water molecules, are in good agreement with the X-ray diffraction results.16,17 Therefore, it can be confirmed that each water molecule is hydrogen bonded to its four neighbor water molecules according to the geometrical criteria of the hydrogen bond.43 Furthermore, it can be concluded that the hydrogen bonds in the INTs are not as strong as those in ice-Ih, which is consistent with the previous MD simulation44 that revealed the distortion of hydrogen-bond network of confined liquid water in CNTs and the decrease in the average number of hydrogen bonds with regard to that of liquid bulk water, both due purely to the confinement effect. The binding energies per hydrogen bond (Eb/H-bond) of three n-gonal INTs as well as the Eb of water dimer and Eb/H-bond of ice-Ih are shown in Table 1. It is notable that although the vibrational entropy and counterpoise (CP) correction are not included, the binding energy of water dimer predicted by SCCDFTB-D is 3.40 kcal/mol, which agrees well with a previous experimental result (3.35 kcal/mol).42 It can be seen that the Eb/H-bond of INTs increases slightly with decreasing size of

TABLE 1: Binding Energies of Water Dimer, Conventional Hexagonal Ice Phase, and n-Gonal INTs (n ) 5, 6, and 7, respectively)

Eb/H-bond (kcal/mol) a

ice-Ih

pentagonal INT

hexagonal INT

heptagonal INT

water dimer

6.21

5.60

5.54

5.49

3.40, exp. 3.35a

Reference 42.

the n-gonal ring of water molecules. Moreover, Eb/H-bond of each INT is smaller than that of ice-Ih, which confirms that the hydrogen-bond network among water molecules in INTs is weaker than that in ice-Ih. It may be due to the distortion of hydrogen-bond structures in INTs induced by their unique cylindrical geometries. Our calculations show that for the confining CNTs, e.g., (16,0) SWNT, the highest occupied molecular orbital (HOMO)/ lowest unoccupied molecular orbital (LUMO) gap was slightly reduced from 0.567 to 0.554 eV while the Fermi level increased

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Figure 2. Isosurfaces of the wave functions of the HOMO (left) and LUMO (right) derived from bands at the Γ point for the 6-gonal INT confined in the zigzag (16,0) SWNT.

from -4.619 to -4.607 eV after it was filled with 6-gonal INT. Figure 2 also shows that both the HOMO and LUMO of INTCNT complex involve significant composition originating from the confining CNT and that there is no overlap between molecular orbitals from CNT and INT. Consequently, it can be derived that water molecules of INTs can hardly interact with confining CNTs via the ordinary OH/π interactions, which are the main intermolecular forces between the water molecule and aromatic rings, for instance, in water-benzene/graphite complexes.33 The reason is that each water molecule of INTs is hydrogen bonded to two water molecules with its two O-H bonds as hydrogen donors, and there is no other O-H bond available for a water molecule to interact with the hexagonal carbon rings of confining CNTs via OH/π interaction. IR Spectra. Each water molecule is of three vibrational degrees of freedom and undergoes three independent types of vibration, corresponding to two stretching vibrational modes and one bending vibrational mode. All three vibrations produce changes in the dipole moments and are thus IR active. In the vapor phase, the vibrations involve combinations of symmetric stretching (v1, 3657 cm-1), asymmetric stretching (v3, 3756 cm-1), and bending (v2, 1595 cm-1) of a covalent O-H bond.45 For ice-Ih and INTs, however, the IR spectra are far more complex due to vibrational overtones and combinations with librations (restricted rotations) induced by the hydrogen-bond network. In general, the IR spectra of INTs should be dominated by the low-frequency intermolecular motions (e.g., translational vibrations of hydrogen-bonded water molecules) and the middleto-high-frequency intramolecular motions (e.g., covalent H-O-H bending vibration and O-H stretching vibrations). It is noted that the focus of this study is on signatures in the vibrational spectra of INTs rather than INT-CNT complex. Furthermore, the unique structures of INTs are basically determined by the effect of steric confinement due to the presence of confining CNTs rather than OH/π interaction between INTs and CNTs, which was discussed in the last section and also revealed in ref 44. Consequently, during the vibrational spectra calculation only oxygen and hydrogen atoms of water molecules were allowed to be displaced and the Hessians were calculated from the interatomic forces of those displacements, while the positions of carbon atoms of confining CNTs were fixed during the calculations. The IR spectra of pentagonal, hexagonal, and heptagonal INTs as well as conventional hexagonal ice phase are shown in Figures 3-6 for the vibrational frequency between 100 and 500, 500 and 800, 1450 and 1650, and 3200 and 3800 cm-1, respectively. The absorption intensities of bands in the IR spectra are in an arbitrary unit, but the relative band heights are comparable. The following assignments of these bands were based on a detailed normal vibrational mode analysis.

Feng et al. In the low-frequency region between 100 and 500 cm-1 several weak vibrational bands can be observed, as shown in Figure 3, which arise from the intermolecular vibrations between water molecules, such as torsion, twist, stretch, bend, and wag modes. For instance, the weak band, located at 225 cm-1 for pentagonal and heptagonal INT and at 235 cm-1 for hexagonal INT, can be attributed to restricted translation of two hydrogenbonded water molecules against each other along the O-H‚‚‚ O direction (where O-H denotes the intramolecular covalent bond and H‚‚‚O the intermolecular hydrogen bond), i.e., the intermolecular stretching of hydrogen bonds, suggested by Walrafen46 to elucidate the low-frequency spectrum of liquid water (centered at about 200 cm-1 in liquid water). Note that the predicted spectrum of ice-Ih shows some inconsistency with the experimental one,47 for example, several measured peaks are absent in Figure 3d, which may be due to the incapability of the SCC-DFTB-D method to handle all the weak intermolecular vibrations in the low-frequency region. However, this discrepancy would not affect the identification of the signatures revealed in this and higher frequency regions. Figure 4 shows the vibrational bands, located in the frequency domain between 500 and 800 cm-1, which correspond to the restricted rotational motions of hydrogen-bonded water molecules. Besides a strong librational band centered at about 700 cm-1, an additional weak librational band is also shown whose vibrational frequency decreases from 570 to 550 cm-1 with increasing size of INTs from pentagonal to heptagonal. The major librational band consists of two peaks for pentagonal and heptagonal INTs, whereas it presents a sharp peak for hexagonal INT with much stronger absorption intensity. Both the weak minor librational band and the strong major librational band are due to restricted rotations of two hydrogen-bonded water molecules with the constraints imposed by hydrogen-bond networks.48 The major band appears around 686 cm-1 for bulk liquid water49 and around 650 cm-1 for confined liquid water.21 In the middle-frequency range a strong vibrational band is observed at about 1535 cm-1 with a weak higher frequency shoulder at about 1545 cm-1 (see Figure 5), although the shoulder band is rather weak for pentagonal INT. The former band can be accounted for as the bending vibrations of intramolecular covalent H-O-H bond. It is remarkable that the bending band of INTs is moved to lower frequencies with a 40 cm-1 shift, referred to that of ice-Ih, which is centered at 1575 cm-1 predicted by the SCC-DFTB-D method. In principle, the existence of a H-O‚‚‚H bridge will partially stiffen the bending mode since hydrogen bonding favors near-linearity in the H-O‚‚‚H arrangement of atoms; hence, the lower bending frequency should originate from the H-O-H unit with weaker hydrogen bonds. Consequently, it is natural that INTs vibrate at a lower bending frequency compared to that of ice-Ih for the reason that the hydrogen bonds between water molecules of INTs are weaker than those of ice-Ih, as discussed in the previous section. As shown in Figure 6 in the high-frequency region between 3200 and 3800 cm-1 there exist two bands involving symmetric stretching vibration at 3320-3340 cm-1 and asymmetric stretching vibration at 3420 cm-1 with an absorption intensity ratio of about 1:9. It is notable that due to the ordered hydrogenbond network of INTs that does not exist in the water vapor state the stretching bands of INTs move to lower frequencies by a shift of about 340 cm-1 with respect to those of gaseous water molecule (around 3657 and 3756 cm-1, respectively, according to ref 45). It can be explained by the fact that formation of a hydrogen bond causes a reduction of the force

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Figure 3. Comparison of the IR spectra of (a) pentagonal, (b) hexagonal, and (c) heptagonal INT and that of (d) conventional hexagonal ice phase for the vibrational frequencies between 100 and 500 cm-1.

Figure 4. Same as Figure 3 for frequencies between 500 and 800 cm-1.

constant of the covalent O-H bond and a corresponding shift to lower frequency for the O-H stretching vibration. For the same reason, the stretching bands of INTs move to higher frequency with a shift of about 50 cm-1 with regard to those of ice-Ih (around 3260 and 3380 cm-1, respectively, predicted by the SCC-DFTB-D method) because the hydrogen-bond networks of INTs are not as strong as those of ice-Ih. Another remarkable signature shown in this high-frequency region is the broad band consisting of two couple peaks that

are centered at about 3690 and 3710 cm-1, respectively, with an absorption intensity ratio of about 1:3. This band is slightly shifted toward higher frequency with increasing size of the n-gonal water ring of INTs. Similar bands also appear in the IR spectra of liquid water confined in rigid cylinders and CNTs, and Martı´ attributed them to the effect of confinement.21,50 Resonant Raman Spectra. The SCC-DFTB-D method was applied to calculate the vibrational resonant Raman spectra of INTs. Figure 7 shows the resonant Raman spectra of pentagonal,

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Feng et al.

Figure 5. Same as Figures 3 and 4 for frequencies between 1450 and 1650 cm-1.

Figure 6. Same as Figures 3-5 for frequencies between 3200 and 3800 cm-1.

hexagonal, and heptagonal INTs for vibrational frequency between 0 and 300 cm-1. The signatures in the low-frequency domain of resonant Raman spectra of the three INTs are significantly distinct. The vibration of pentagonal INT presents a single sharp band, while that of heptagonal INT showed a broad band. The bands for pentagonal and heptagonal INTs are both centered at about 20 cm-1. In contrast, the band for the hexagonal INT is shifted to a higher frequency of about 80 cm-1 and is accompanied by two weaker shoulders located at 45 and 130 cm-1, respectively.

The microscopic interpretation of this band has been the subject of controversy for a long time. Walrafen46 argued that it should be related to the hydrogen-bond network and associated with the bending of the hydrogen-bonded O‚‚‚O‚‚‚O unit. Further confirmation of the hydrogen-bonding source for this band derives from isotopic measurements and theoretical predictions.50 Such a low-frequency feature is also observed in the spectra of dense nonassociated liquids, so an alternative interpretation is to attribute this band to the nonbonded “cage effects” induced by neighboring water molecules.51,52

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Figure 7. Comparison of the resonant Raman spectra of (a) pentagonal, (b) hexagonal, and (c) heptagonal INT for frequencies between 0 and 300 cm-1.

4. Summary and Conclusions Using the SCC-DFTB method with empirical dispersion energy correction we optimized the geometry structures of n-gonal INTs, n ) 5-7, under the confinement within zigzag SWNTs. Each water molecule in the optimized INTs was hydrogen bonded to its four nearest-neighbor water molecules in a tetracoordinate configuration, and all water molecules constituted a novel cylindrical ice phase with ordered hydrogenbond network, which was weaker than that of conventional hexagonal ice. In addition, we revealed that the unique crystalline structures of INTs were due mainly to the steric hindrance effect induced by the confining CNT rather than the ordinary OH/π interaction between INT and CNT. We then calculated IR spectra of three n-gonal INTs based on the optimized models and compared them with that of iceIh. It was revealed that hydrogen bonds play a prominent role in the signatures in the IR spectra of INTs. In the low-frequency domain between 100 and 500 cm-1 a series of intermolecular vibrational bands exist, including a very weak band at about 220-240 cm-1 which corresponds to stretching of the hydrogen bond or the restricted translation of two hydrogen-bonded water molecules. Two librational bands are observed around 560 and 700 cm-1 both of which originate from the restricted rotations of hydrogen-bonded water molecules with constraints imposed by hydrogen bonds. In the middle-frequency region the bending vibrational bands of the intramolecular H-O bond can be observed around 1540 cm-1 for INTs, which are moved to lower frequencies by a 40 cm-1 shift, compared to the corresponding bands for ice-Ih. In the high-frequency domain the symmetric and asymmetric stretching vibrational bands of the intramolecular H-O-H bond are located around 3330 and 3420 cm-1 for INTs, and these stretching bands are moved to higher frequencies by about a 340 cm-1 shift, referred to those of iceIh. Both the red and blue shifts of the intramolecular vibrational bands for INTs can be derived from the fact that the hydrogenbond networks of INTs are weaker than those of ice-Ih. The resonant Raman spectrum calculations were also performed for three n-gonal INTs in the low-frequency region

between 0 and 300 cm-1. The bands observed at 20 cm-1 for pentagonal and heptagonal INT and 80 cm-1 for hexagonal INT may be due to the bending of the hydrogen-bonded O‚‚‚O‚‚‚O unit or the nonbonded “cage effects” of the neighboring water molecules. For both IR and resonant Raman spectra pentagonal and heptagonal INT present quite similar signatures in terms of vibrational frequencies and relative absorption intensities of vibrational bands while hexagonal INT shows some features different from them. Despite the possible deviations of vibrational frequencies and absorption intensities of the bands predicted by the SCCDFTB-D method, our theoretical calculations of the energies, geometry structures, and signatures in vibrational IR and resonant Raman spectra are expected to benefit the structural and spectral analyses of INTs both theoretically and experimentally. Moreover, further applications of the SCC-DFTB-D method to the behavior of water under confinement within nanoscale Q1D channels as well as other relevant systems will provide valuable quantitative and qualitative insight into various novel properties of those complexes. Acknowledgment. The work described in this paper is supported by the Research Grants Council of Hong Kong SAR [project no. CityU103305], the Major State Research Development Program (grant no. 2004CB719903), and the National Natural Science Foundation of China. References and Notes (1) Saito, R.; Dresselhaus, G.; Dresslhaus. M. S. Physical Properties of Carbon Nanotube; Imperial College Press: London, 1998. (2) Ugarte, D.; Stoeckli, T.; Bonard, J. M.; Chatelain, A.; de Heer, W. A. Appl. Phys. A. 1998, 7, 101. (3) Franks, F. In Water: A ComprehensiVe Treatise; Franks, F., Ed.; Plenum Press: New York, 1972. (4) Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Sciences of Fullerenes and Carbon Nanotubes; Academic Press: San Diego, 1996. (5) Sanson, M. S. P.; Biggin, P. C. Nature 2001, 414, 156. (6) Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Nature 2001, 414, 188.

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