For liquid water in the far-infrared spectrum, phonons of molecular vibrations constitute two bands with a narrow gap at around 30 meV. Interestingly, there are two distinct peaks for ice in this gap. We demonstrated that the two peaks come from two kinds of translational modes. Considering different O–O–O bending constants, we yielded two frequencies based on the ideal model of ice Ic. These two kinds of vibrational modes do not exist in liquid water due to the collapse of the rigid tetrahedral structure. Thus, a window remains for ice resonance absorption with minimum energy loss in liquid water. A new method to decompose gas hydrates was proposed by supplying two terahertz radiation energies at ∼6.8 and 9.1 THz. This is also applicable to flow assurance in gas pipelines, aircraft deicers, and so on. Experimental measurements are expected to verify this finding along with the rapid development of a THz laser.

Despite its simple molecular structure, water is still a mystery to scientists. For the atomic and molecular vibrational modes of ice, as is well known, there are two kinds of vibrations: intra-molecular O—H stretching vibration and H—O—H bending vibration within the molecules and three kinds of molecular spatial rotations. However, thirty years ago, a high flux inelastic neutron scattering experiment showed that there are two distinct characteristic peaks in the far-infrared molecular translational vibration region of many ice phases. The origins of these peaks have not been determined till now. In this work, based on the CASTEP code, a first-principles density functional theory plane wave programme, the vibrational spectra as well as the vibrational normal modes of a series of ice phases are investigated. Two kinds of intrinsic hydrogen bond vibrational modes are first found in hydrogen-ordered ice Ic. Then it is found to be a general rule among ice family. Based on the ideal model, we prove that the two vibrational modes can be classified as four-bond vibration and two-bond vibration. There are many coupling modes in-between due to tetrahedral structure deformation under high pressure. Besides, there are also some optical vibrational modes with lower energy in the translational region, such as cluster vibrations and inter-plane vibrations. In Ice VII/VIII and XV/VI, each of which consists of two sublattices, there exist non-hydrogen bond vibrations. These molecular translational vibrations can explain all the far-infrared vibrational spectrum of ice phase, which makes up the last piece of the jigsaw puzzle for the molecular vibration theory of ice. The two vibrational modes do not exist in liquid water due to the collapse of the rigid tetrahedral structure. Thus, a window remains for ice resonance absorption with minimum energy loss in water. This theory is expected to be applicable to industrial deicing, food thawing, gas hydrate mining, and biomolecule frozen molding, etc.

Based on first-principles density functional theory, we investigated the relationship between the vibrational normal modes and the spectrum of the newest laboratory-prepared ice phase, an empty clathrate hydrate structure from gas hydrate named ice XVII. A 48-molecule supercell was designed to mimic the hydrogen-disordered structure. Despite its much lower density than ice Ih, its phonon density of states shows features very similar to those of that phase. In our previous studies of ice Ic and ice XIV, we found two basic hydrogen bond vibrational modes in these hydrogen-ordered ice phases, which contribute two sharp hydrogen bond peaks in the translation region. In this study, we found that this rule also holds in the hydrogen-disordered phase ice XVII. A water molecule vibrating along its angle bisector possesses strong energy, because this vibrational mode involves oscillation against four bonded neighbors. In contrast, a water molecule vibrating perpendicular to its angle bisector has low energy because this mode involves only two of the molecule's hydrogen bonds. This is an evidence in hydrogen-disordered ice and strengthens our proposal that the existence of two basic hydrogen bond vibrational modes is a general rule among ice family. Figure 5. Smoothed probability density distribution of bond angles of ice XVII (blue) and ice Ih (black). Inset: Normal mode at 1647 cm −1 . This vibrational mode is mainly contributed by water molecules with large bond angles, which are highlighted in gold.

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.

It is always difficult to assign the peaks of a vibrational spectrum in the far-infrared region. The two distinct peaks seen in many ice phases are still a mystery to date. The normal modes of ice XV were calculated using the CASTEP code based on first-principles density functional theory. On the basis of vibrational modes analysis, we divided the translational modes into three categories: four-bond vibrations, which have the highest energy levels; two-bond vibrations, which have medium levels of energy; and relative vibrations between two sublattices, which have the lowest energy. Whale et al. found that some intramolecular stretching modes include the isolated vibration of only one O–H bond, whereas the others do not vibrate in ice XV. We verified this phenomenon in this study and attributed it to local tetrahedral deformation. Analysis of normal modes, especially in the translation and stretching band of ice XV, clarified the physical insights of the vibrational spectrum and can be used with other ice phases.