The hydrogen-disordered structure of ice III makes it difficult to analyze its vibrational spectrum theoretically. To clarify the contribution of hydrogen bonds (HBs), we constructed a 24-molecule supercell to mimic the real structure and performed first-principles density functional theory calculations. The calculated curve of phonon density of states showed good correspondence with the experimental data. Based on the theory of two kinds of HB vibrational modes, we analyzed the distributions of two-bond modes and four-bond modes. The energy splitting of these modes results in a flat vibrational band, which is a common phenomenon in high-pressure ice phases. These findings verified the general rule that there are two types of HB vibrations in ice, thereby furthering our understanding of HB interactions in water ice and their broad role in nature.
