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.

The vibrational spectrum of ice II was investigated using the CASTEP code based on first-principles density functional theory (DFT). Based on good agreement with inelastic neutron scattering (INS), infrared (IR), and Raman experimental data, we discuss the translation, libration, bending, and stretching band using normal modes analysis method. In the translation band, we found that the four-bond and two-bond molecular vibration modes constitute three main peaks in accordance with INS ranging from 117 to 318 cm⁻¹. We also discovered that the lower frequencies are cluster vibrations that may overlap with acoustic phonons. Whale et al. found in ice XV that some intramolecular vibrational modes include many isolated-molecule stretches of only one O–H bond, whereas the other O–H bond does not vibrate. This phenomenon is very common in ice II, and we attribute it to local tetrahedral deformation. The pathway of combining normal mode analysis with experimental spectra leads to scientific assignments.

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.