A fresh look at the vibrational and thermodynamic properties of liquids within the soft potential model

Haichen Xu; Matteo Baggioli; Tom Keyes

doi:10.1063/5.0158089

A fresh look at the vibrational and thermodynamic properties of liquids within the soft potential model

J Chem Phys. 2023 Oct 21;159(15):154501. doi: 10.1063/5.0158089.

Authors

Haichen Xu^{1

2

3}, Matteo Baggioli^{2

3}, Tom Keyes⁴

Affiliations

¹ University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China.
² Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
³ Shanghai Research Center for Quantum Sciences, Shanghai 201315, China.
⁴ Chemistry Department, Boston University, Boston, Massachusetts 02215, USA.

PMID: 37846955
DOI: 10.1063/5.0158089

Abstract

Contrary to the case of solids and gases, where Debye theory and kinetic theory offer a good description for most of the physical properties, a complete theoretical understanding of the vibrational and thermodynamic properties of liquids is still missing. Liquids exhibit a vibrational density of states (VDOS) which does not obey Debye law, and a heat capacity which decreases monotonically with temperature, rather than growing as in solids. Despite many attempts, a simple, complete and widely accepted theoretical framework able to formally derive the aforementioned properties has not been found yet. Here, we revisit one of the theoretical proposals, and in particular we re-analyze the properties of liquids within the soft-potential model, originally formulated for glasses. We confirm that, at least at a qualitative level, many characteristic properties of liquids can be rationalized within this model. We discuss the validity of several phenomenological expressions proposed in the literature for the density of unstable modes, and in particular for its temperature and frequency dependence. We discuss the role of negative curvature regions and unstable modes as fundamental ingredients to have a linear in frequency VDOS. Finally, we compute the heat capacity within the soft potential model for liquids and we show that it decreases with temperature, in agreement with experimental and simulation data.