Revisiting the phonon theory of liquid heat capacity: Low-frequency shear modes and intramolecular vibrations

Modeling the heat capacity of liquids presents fundamental difficulties due to the strong intermolecular particle interactions and large diffusivelike displacements. Based on the experimental evidence that the microscopic dynamics of liquids closely resemble those of solids, a phonon theory of liquid thermodynamics has been developed. Despite its success, the phonon theory of liquids relies on the questionable assumption that low-frequency shear excitations are propagating in nature and follow a Debye density of states. Furthermore, the same framework does not capture the contribution of intramolecular vibrations, which play a significant role in molecular liquids. In this work, we revisit the phonon theory of liquid heat capacity, introducing alternative approaches to model low-frequency shear modes. In particular, we consider the recently proposed idea of treating such modes as purely kinetic, and we propose an approach based on identifying those low-frequency excitations as overdamped liquidlike modes with a linear in frequency density of states. Moreover, we complete the theory by incorporating the effects of intramolecular vibrations. By comparing the theoretical predictions from these different approaches with the available data for the heat capacity of several liquids, we present a comprehensive evaluation of the original model and our proposed extensions. Although all approaches perform well at low temperatures, our results indicate that modeling low-frequency modes as overdamped liquidlike excitations yields the most accurate agreement with the data in the whole temperature range. Conversely, we demonstrate that treating these excitations as purely gaslike leads to significant inaccuracies, particularly at high temperatures.