The hydrogen-disordered structure of ice, Ic, makes it difficult to analyze the vibrational normal modes in the far-infrared region (i.e., the molecular translation band). To clarify the origin of the energy-splitting of hydrogen bond vibrations in this area, a 64-molecule supercell was constructed and calculated using first-principles density functional theory. The results were in good agreement with inelastic neutron scattering experiments and our previous study of a hydrogen-ordered ice Ic model. Assisted by analytic equations, we concluded that the origin of the two hydrogen bond peaks in real ice Ic is consistent with that of hydrogen-ordered ice Ic: the peaks originate from two kinds of normal mode vibration. We categorize the four peaks in the far-infrared region recorded from inelastic neutron scattering experiments as the acoustic peak, the superposition peak, the two-hydrogen bond peak and the four-hydrogen bond peak. We conclude that the existence of two intrinsic hydrogen bond vibration modes represents a general rule among the ice family, except ice X.

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.

It is difficult to investigate the hydrogen-bonding dynamics of hydrogen-disordered ice VI. Here, we present a comparative method based on our previous study of its counterpart hydrogen-ordered phase, ice XV. The primitive cell of ice XV is a 10 molecule unit, and the vibrational normal modes were analyzed individually. We constructed an 80 molecule supercell of ice VI to mimic the periodic unit and performed first-principles density functional theory calculations. As the two vibrational spectra show almost identical features, we compared the molecular translation vibrations. Inspired by the phonon analysis of ice XV, we found that the vibrational modes in the translation band of ice VI are classifiable into three groups. The lowest-strength vibration modes represent vibrations between two sublattices that lack hydrogen bonding. The highest-strength vibration modes represent the vibration of four hydrogen bonds of one molecule. The middle-strength vibration modes mainly represent the molecular vibrations of only two hydrogen bonds. Although there are many overlapping stronger and middle modes, there are only two main peaks in the inelastic neutron scattering (INS) spectra. This work explains the origin of the two main peaks in the far-infrared region of ice VI and illustrates how to analyze a hydrogen-disordered ice structure.

It was reported that a scanning tunneling microscopy (STM) study observed the adsorption geometry of a water monomer and a tetramer on NaCl(100) film. Based on first-principles density functional theory (DFT), the adsorption behavior of water on the NaCl surface was simulated with CASTEP code. The results showed that the water monomer almost lay on the NaCl(001) surface with one O–H bond tilted slightly downward. This was quite different from the STM observations. In fact, the experimental observation was influenced by the Au(111) substrate, which showed an upright form. A recent report on observations of two-dimensional ice structure on Au(111) substrate verified our simulations. However, the water tetramer formed a stable quadrate structure on the surface, which was consistent with observation. The intermolecular hydrogen bonds present more strength than surface adsorption. The simulations presented a clearer picture than experimental observations.

It is difficult to theoretically study the vibrational spectrum of hydrogen-disordered ice XII compared with its hydrogen-ordered counterpart, ice XIV. We constructed a 24-molecule supercell of ice XII to mimic its real structure. We focused on hydrogen bond (HB) vibrational modes in the translation band using first-principles density functional theory (DFT). Our simulated results were in good agreement with inelastic neutron scattering experiments. We found that the optical vibrational modes of HBs are composed of three main components. These are cluster vibrations in the lowest-frequency region, four-bond HB vibrations in the highest-frequency region, and two-bond modes in between. Although the experimentally recorded curve of ice XII is smooth in the translation region, our results support the proposal that two types of intrinsic HB vibrational modes are common in the ice family.