Dissecting the experimental vibrational density of states of liquids using instantaneous normal mode theory

Liquid dynamics play crucial roles in chemical and physical processes, ranging from biological systems to engineering applications. Yet, the vibrational properties of liquids are poorly understood when compared to the more familiar case of crystalline solids. Here, we report experimental neutron-scattering measurements of the vibrational density of states (VDOS) of water and liquid Fomblin in a wide range of temperatures. In the liquid phase, we observe a universal low-energy linear scaling of the experimental VDOS as a function of the frequency, which persists at all temperatures. Importantly, in both systems, we observe that the slope of this linear behavior grows with temperature. We confirm this experimental behavior using molecular dynamics simulations, and we explain it using instantaneous normal mode (INM) theory, whose predictions are in good agreement with the experimental and simulation data. Finally, we experimentally observe a sharp crossover at the melting point of water, below which the standard Debye's law is recovered. On the contrary, in Fomblin, we observe a gradual and continuous crossover indicating its glassy dynamics and proving that the low-frequency power-law scaling of the VDOS is a good probe for the nature of the solid-to-liquid transition. Our results experimentally confirm the validity of INM theory and the success of a normal mode approach to liquid dynamics, which could pave the way towards a deeper understanding of liquids and their properties in general.