Comparative Analysis of Hydrogen Bond Vibrations in Ice VIII and VII

May 22, 2019 - According to a report, the existence of two characteristic hydrogen bond (H-bond) peaks in the translational band of ice does not occur...
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Article Cite This: J. Phys. Chem. C 2019, 123, 14880−14883

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Comparative Analysis of Hydrogen Bond Vibrations in Ice VIII and VII Yue Gu,† Xu-Liang Zhu,† Lu Jiang,† Jing-Wen Cao,† Xiao-Ling Qin,† Shu-Kai Yao,‡ and Peng Zhang*,† †

School of Space Science and Physics, Shandong University, Weihai 264209, China School of Materials Engineering, Purdue University, West Lafayette, Indiana 47906, United States

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‡

ABSTRACT: According to a report, the existence of two characteristic hydrogen bond (H-bond) peaks in the translational band of ice does not occur in high-pressure ice VIII. To test this, a comparative analysis of ice VII and VIII was conducted. We demonstrated that the two intrinsic H-bond vibration modes found in ice Ic are also fundamental in these two phases. However, the peaks are merged with non-H-bond modes due to a large red shift of the H-bonds. A 64-molecule supercell was constructed to mimic the hydrogen-disordered structure of ice VII. Using first-principles density functional theory, the phonon density of states and vibrational normal modes of ice VII and VIII were analyzed. The primitive cell of ice VIII contains only four molecules, resulting in a relatively small number of normal modes. This simplicity facilitates the analysis of ice VII, which is structurally similar to ice VIII. Interestingly, the characteristic ice modes reported by Whale et al., such as “rigid network modes” in the translational band and “isolated O−H” vibrational modes in the stretching band, were also found in this work. Examples were illustrated in detail, and specifically we attributed the isolated O−H vibrations to lattice deformation of the local tetrahedral structure. K.17 It can be considered the most robust phase as it is metastable over a wide range of temperature and pressure. The structure of ice VII consists of two interpenetrating cubic Ic lattices with no interconnecting H-bonds between sublattices.5 As in the majority of ice phases, the hydrogen atom positions of ice VII are disordered; however, it is the only ice phase that can be ordered by simple cooling. At about 275 K, ice VII undergoes a disorder−order transition to ice VIII, in which the ordering of hydrogens in the two sublattices is antiparallel.18 As the ordered-phase equivalent of ice VII, ice VIII also has two interpenetrating but non-bonded sublattices, but is tetragonal in crystal form due to the hydrogen-ordering process, which causes a slight distortion of the cubic ice VII structure. The primitive cell of ice VIII contains only four water molecules. The hydrogen disorder in ice VII severely complicates the theoretical analysis of its lattice vibrations. However, because the oxygen atoms of ice VII and ice VIII have the same lattice position, a comparative analysis may facilitate characterization

1. INTRODUCTION Water is one of the most common materials on earth and is described as the “solvent of life”. The solid state of water, ice, has more than 17 experimentally established crystalline phases differing in their crystal structure or ordered−disordered hydrogen arrangement.1−10 In recent years, the discoveries of the s-II clathrate structure, named ice XVI,10 and the s-I lattice, ice XVII,11 have inspired intense curiosity regarding the nature of H-bonding in these ice phases. Among the ice family, many phases show a characteristic pair of H-bond peaks in the far-infrared region of the vibrational spectra, with the notable exceptions being ice VII and VIII. Li et al. detected only one H-bond peak in ice VIII.12,13 On the basis of the first-principles density functional theory (DFT) method, we revealed that the two H-bond modes in this phase are merged with non-H-bond vibration modes. This finding verified our speculation that the two distinct peaks are from two intrinsic H-bond vibration modes, which is a general rule among ice phases and is due to the local tetrahedral structure.14−16 Ice VII, one of the high-pressure phases of ice, can be produced from liquid water above 3 GPa by cooling to ambient temperature or by decompressing ice VI below 95 © 2019 American Chemical Society

Received: April 17, 2019 Revised: May 20, 2019 Published: May 22, 2019 14880

DOI: 10.1021/acs.jpcc.9b03606 J. Phys. Chem. C 2019, 123, 14880−14883

Article

The Journal of Physical Chemistry C

calculated spectra, they appear at 503 cm−1 (PDOS)/502 cm−1 (normal modes) and 593 cm−1 (PDOS)/583 cm−1 (normal modes), that is, showing a considerable blue shift. These peaks are not observed in the INS and PDOS spectrum of ice VII because the primitive cell of ice VIII contains only four molecules and thus has 4 × 3 × 3 − 3 = 33 optical normal modes in all. Regarding the 573 optical normal modes of ice VII, the nondegenerate modes overlap into a single broad band. In 1989, an INS experiment first identified two distinct triangle peaks at 28.2 and 37.7 meV in the translational band of ice Ih, which were later also found in many other phases.13,25 Based on a series of investigations, we proposed that there are two types of intrinsic H-bond vibrational modes responsible for these two peaks in the translational region, and this model has been verified in ice Ic, XIV, and XVI.14−16 Subject to the B−F rules in all ice phases, each water molecule is H-bonded with four neighboring molecules to form a tetrahedral geometry. In a so-called four-bond mode, one molecule vibrates along the direction of the angle bisector, taking oxygen as the vertex. In this case, four H-bonds oscillate together, which increases the frequency. In contrast, in a two-bond mode, the vibrational direction of the central molecule is perpendicular to that of the four-bond mode, and only two Hbonds vibrate along this direction while the other two remain static. This kind of mode presents a lower frequency. These two categories of intrinsic H-bond modes in the translational region are responsible for the two peaks. However, Li et al. reported that only one H-bond peak exists in ice VIII. Herein, we demonstrate that the two-H-bonds theory is still valid in ice VII and VIII. Whale et al. found that the three lowestwavenumber modes in the translation region of ice XV were caused by the vibrations of the two rigid networks against each other and named these modes “rigid-network modes”.26 Hbonds do not stretch or bend in this kind of mode. We also observed this phenomenon in ice VII and ice VIII, which will be discussed later. The six normal modes of H-bonds in ice VIII in the translational band are shown in Figure 2, and the total numbers of each of the three kinds of mode (two-bond, fourbond, and rigid-network modes) in ice VII and ice VIII are compared in Figure 3. There are nine normal modes in this region of ice VIII. The three modes at 174 and 177(1)(2) cm−1 represent the relative motion between sublattices without H-bond stretching, similar to the rigid-network modes of Whale et al. The other six modes, as shown in Figure 2, can be classified into two groups. In the modes at 160(1)(2) and 205(1)(2) cm−1, all of the molecules vibrate perpendicular to the molecular angle bisector. However, in the modes at 237 and 254 cm−1, the molecules stretch along the angle bisector, hence four H-bonds are involved. According to our classification criteria, 160(1)(2) and 205(1)(2) cm−1 belong to the two-bond category and 237 and 254 cm−1 are typical four-bond modes, as described in the study of ice Ic.14 We mimicked the PDOS spectrum for these nine modes, as shown in Figure 3a. The peaks resemble the four weak peaks at 152, 174, 203, and 231 cm−1 in Figure 1, in which the two strongest modes merge due to dispersion. Li and Ross proposed that the strong peak of ice VIII at 36 meV was absent from the experimental INS spectrum.12 In fact, the translational H-bond peaks are considerably red-shifted under high pressure. According to our calculations, the two opposed interpenetrating cubic ice lattices that constitute the ice VIII

of the intrinsic vibration modes in these two phases. Herein, we report a computational study of the lattice vibrations of ice VII and compare the calculated vibrations with the H-bond vibrations reported in our previous study of ice VIII.19 New evidence is presented to support the validity of the “two-Hbonds” theory.

2. COMPUTATIONAL METHODS Because of its hydrogen-disordered structure, ice VII does not have a periodic repeated unit. To mimic the real structure, we constructed an ice VIII supercell containing 64 molecules and rearranged the hydrogen atoms randomly in accordance with the Bernal−Fowler (B−F) rules.20 Because of the large size of the unit cell, there are 64 × 3 × 3 − 3 = 573 optical normal vibrational modes. The geometrical optimization and phonon calculations were conducted with the CASTEP code.21 For the exchange−correlation functional, the RPBE22 of the generalized gradient approximation was selected for this work based on our experience. The energy and self-consistent field (SCF) tolerances were set as 1 × 10−9 eV/atom for geometrical optimization with norm-conserving pseudopotentials. The energy cutoff was set at 830 eV and the K-point mesh was 3 × 3 × 2 for ice VII. The environmental pressure of geometrical optimization was set at 2.4 GPa. To count the number of different H-bond translational modes, we compiled a customized program. For singlemolecule vibrations, the program classifies the main vibration vector of oxygen as either a two-bond mode or four-bond mode. In addition, the program distinguishes the relative motions between the two sublattices of ice VII and ice VIII. 3. RESULTS AND DISCUSSION As depicted in Figure 1, the phonon density of states (PDOS) spectrum of ice VII is smoother than that of VIII. Such is also the case for the two inelastic neutron scattering (INS) spectra. The most notable feature is that the two sharp peaks in the librational region of VIII disappear in that of VII. In the INS spectrum, these two peaks are observed at 57.5/55.0 and 68.0/ 68.0 meV (i.e., 464/444 and 548/548 cm−1).23,24 In our

Figure 1. Simulated vibrational spectra of ice VII and ice VIII. The upper curve is the PDOS spectrum of ice VII and the lower curve is that of ice VIII. The four main bands of the PDOS spectra from left to right correspond to translation, libration, bending, and stretching, respectively. 14881

DOI: 10.1021/acs.jpcc.9b03606 J. Phys. Chem. C 2019, 123, 14880−14883

Article

The Journal of Physical Chemistry C

Figure 4. Representative modes of ice VII. (a) Two-bond mode, (b) four-bond mode, (c) rigid-network mode, and (d) “isolated” stretching mode. Typical molecules taking part are colored gold.

Figure 2. Six normal modes of H-bonds in ice VIII. The frequencies of each vibrational mode are labeled under the corresponding picture. The arrows represent the vibrational direction of the atoms and the dotted lines indicate the H-bonds.

crystal present a high density of 1.42 kg/cm3. However, the Hbond length in the inner sublattice elongates from 1.799 to 2.038 Å. Therefore, the vibrational frequencies are red-shifted dramatically and overlap with non-H-bond phonons. We consider the experimental peak at 26.7 meV (215 cm−1) as the strong H-bond peak and the peak at 20.7 meV (167 cm−1) as the weak peak, in good agreement with the observed Raman peaks at 214 and 172 cm−1.24,27 The weak peak of ice VIII is derived from the joint contribution of the two-bond modes and rigid-network modes, and the peak valley is relatively high due to multiple overlapped phonons. Because of the hydrogen-disordered structure of ice VII, all of the vibration modes are nondegenerate. That is, the three kinds of H-bond modes discussed above may have different peak wavenumbers, giving rise to a smooth spectral curve. Herein, three typical structures of ice VII are shown in Figure 4a−c to illustrate the dynamic motions of two-bond, fourbond, and rigid-network modes, respectively. The arrows showing the main vibrating molecules in the mode at 190 cm−1 indicate that the vibrational direction is perpendicular to the angle bisector. This is thus a two-bond mode. The mode at 219 cm−1, in which the molecules vibrate along the angle

bisector, is classified as a four-bond mode. In the rigid-network mode at 161 cm−1, the lengths of all of the H-bonds are almost constant. Using our in-house program, we classified the modes in the range from 160 to 260 cm−1 into the three categories, as shown in Figure 3b. The curves of the different modes overlap in ice VII, consistent with the spectrum shown in Figure 1, in which the strongest peak is at 194 cm−1. Details of the normal modes in the libration, bending, and stretching bands of ice VIII can be found in our previous work.19 Comparative analysis confirms that the normal modes in VIII replicate the main features of VII. Most interestingly, in this study we observed “isolated” stretching modes in ice VII, as reported in ice XV. In these kinds of modes, one of the covalent O−H bonds of a water molecule vibrates while the other is static.26 However, no such modes occur in ice VIII. An example of such a mode in ice VII at 3385 cm−1 is shown in Figure 4d. There is a slight structural deformation in the transition from ice VIII to VII. We attribute this phenomenon to the low symmetry or hydrogen-disordered structure of the latter.

Figure 3. Total number of two-bond modes (red), four-bond modes (blue), and rigid-network modes (green) in (a) ice VIII and (b) ice VII. 14882

DOI: 10.1021/acs.jpcc.9b03606 J. Phys. Chem. C 2019, 123, 14880−14883

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The Journal of Physical Chemistry C

(9) Salzmann, C. G.; Radaelli, P. G.; Mayer, E.; Finney, J. L. Ice XV: a new thermodynamically stable phase of ice. Phys. Rev. Lett. 2009, 103, 105701. (10) Falenty, A.; Hansen, T. C.; Kuhs, W. F. Formation and properties of ice XVI obtained by emptying a type sII clathrate hydrate. Nature 2014, 516, 231−233. (11) del Rasso, L.; Celli, M.; Ulivi, L. New porous water ice metastable at atmospheric pressure obtained by emptying a hydrogenfilled ice. Nat. Commun. 2016, 7, 13394. (12) Li, J.; Ross, D. K. Evidence for two kinds of hydrogen bond in ice. Nature 1993, 365, 327−329. (13) Li, J. Inelastic neutron scattering studies of hydrogen bonding in ices. J. Chem. Phys. 1996, 105, 6733−6755. (14) Yuan, Z.-Y.; Zhang, P.; Yao, S.-k.; Lu, Y.-B.; Yang, H.-Z.; Luo, H.-W.; Zhao, Z.-J. Computational assignments of lattice vibrations of ice Ic. RSC Adv. 2017, 7, 36801−36806. (15) Zhang, K.; Zhang, P.; Wang, Z.-R.; Zhu, X.-L.; Lu, Y.-B.; Guan, C.-B.; Li, Y. DFT simulations of the vibrational spectrum and hydrogen bonds of ice XIV. Molecules 2018, 23, 1781. (16) Wang, Z.-R.; Zhu, X.-L.; Jiang, L.; Zhang, K.; Luo, H.-W.; Gu, Y.; Zhang, P. Investigations of the hydrogen bonds and vibrational spectra of clathrate ice XVI. Materials 2019, 12, 246. (17) Klotz, S.; Besson, J. M.; Hamel, G.; Nelmes, R. J.; Loveday, J. S.; Marshall, W. G. Metastable ice VII at low temperature and ambient pressure. Nature 1999, 398, 681−684. (18) Vaks, V. G.; Zinenko, V. I. On the theory of the phase transition ice VII-ice VIII. Solid State Commun. 1981, 39, 643−645. (19) Yao, S.-K.; Zhang, P.; Zhang, Y.; Lu, Y.-B.; Yang, T.-L.; Sun, B.G.; Yuan, Z.-Y.; Luo, H.-W. Computing analysis of lattice vibrations of ice VIII. RSC Adv. 2017, 7, 31789−31794. (20) Bernal, J. D.; Fowler, R. H. A theory of water and ionic solution, with particular reference to hydrogen and hydroxyl ions. J. Chem. Phys. 1933, 1, 515−548. (21) Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. I. J.; Refson, K.; Payne, M. C. First principles methods using CASTEP. Z. Kristallogr. 2005, 220, 567−570. (22) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 7413−7421. (23) Li, J.-C.; Burnham, C.; Kolesnikov, A. I.; Eccleston, R. S. Neutron spectroscopy of ice VIII in the region of 20-500 meV. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 9088−9094. (24) Kolesnikov, A. I.; Li, J.-C.; Ross, D. K.; Sinitzin, V. V.; Barkalov, O. I.; Bokhenkov, E. L.; Ponyatovskii, E. G. Inelastic incoherent neutron scattering study of D2O and H2O ice VIII in the range 2-140 meV. Phys. Lett. A 1992, 168, 308−312. (25) Li, J. C.; Ross, D. K.; Howe, L.; Hall, P. G.; Tomkinson, J. Inelastic incoherent neutron scattering spectra of single crystalline and polycrystalline ice Ih. Phys. B 1989, 156−157, 376−379. (26) Whale, T. F.; Clark, S. J.; Finney, J. L.; Salzmann, C. G. DFTassisted interpretation of the Raman spectra of hydrogen-ordered ice XV. J. Raman Spectrosc. 2013, 44, 290−298. (27) Wong, P. T. T.; Whalley, E. Raman spectrum of ice VIII. J. Chem. Phys. 1976, 64, 2359−2366.

4. CONCLUSIONS Assisted by first-principles DFT calculations, the vibrational spectra and normal modes of ice VII and VIII were compared. Although a characteristic pair of H-bond peaks has been found in many phases of ice, Li et al. concluded that only the weak Hbond peak in the translational region exists in ice VIII based on INS experiments. In this computational work, we demonstrated that: (1) the two categories of H-bond modes also exist in ice VIII due to the local tetrahedral structure; (2) the two peaks are difficult to observe due to the overlapping of multiple non-H-bond modes; and (3) the H-bond lengths in the sublattice of ice VIII elongate dramatically, shifting the strong H-bond peak to a similar position to that of the weak peak seen in ice Ih. The latter finding confirmed that the two intrinsic Hbond modes are fundamental in all ice phases. We also found non-H-bond vibration modes in the translational band, similar to those reported by Whale et al. in ice XV. These are relative motions between two sublattices. Meanwhile, “isolated” vibration modes in the stretching band were also seen in ice VII but not VIII. We have previously demonstrated their existence in ice XIV and XVI. Isolated modes seem to be a third category of intramolecular vibration modes in addition to symmetric and antisymmetric stretching. We attribute their existence to lattice deformation of the local tetrahedral structure of ice VII.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86 13869010580. ORCID

Peng Zhang: 0000-0002-1099-6310 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The numerical calculations were conducted on the supercomputing system in the Supercomputing Center, Shandong University, Weihai.

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REFERENCES

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DOI: 10.1021/acs.jpcc.9b03606 J. Phys. Chem. C 2019, 123, 14880−14883