Revisiting the question of what instantaneous normal modes tell us about liquid dynamics

Author:

Jin Sha123ORCID,Fan Xue45ORCID,Baggioli Matteo123ORCID

Affiliation:

1. School of Physics and Astronomy, Shanghai Jiao Tong University 1 , Shanghai 200240,

2. Wilczek Quantum Center, Shanghai Jiao Tong University 2 , Shanghai 200240,

3. Shanghai Research Center for Quantum Sciences 3 , Shanghai 201315,

4. College of Materials, Shanghai Dianji University 4 , Shanghai 201306,

5. Materials Genome Institute, Shanghai University 5 , Shanghai 200444,

Abstract

The lack of a well-defined equilibrium reference configuration has long hindered a comprehensive atomic-level understanding of liquid dynamics and properties. The Instantaneous Normal Mode (INM) approach, which involves diagonalizing the Hessian matrix of potential energy in instantaneous liquid configurations, has emerged as a promising framework in this direction. However, several conceptual challenges remain, particularly related to the approach’s inability to capture anharmonic effects. In this study, we present a set of “experimental facts” through a comprehensive INM analysis of simulated systems, including Ar, Xe, N2, CS2, Ga, and Pb, across a wide temperature range from the solid to gas phase. First, we examine the INM density of states (DOS) and compare it to the DOS obtained from the velocity auto-correlation function. We then analyze the temperature dependence of the fraction of unstable modes and the low-frequency slope of the INM DOS in search of potential universal behaviors. Furthermore, we explore the relationship between INMs and other properties of liquids, including the liquid-like to gas-like dynamical crossover and the momentum gap of collective shear waves. In addition, we investigate the INM spectrum at low temperatures as the system approaches the solid phase, revealing a significant fraction of unstable modes even in crystalline solids. Finally, we confirm the existence of a recently discussed cusp-like singularity in the INM eigenvalue spectrum and uncover its complex temperature-dependent behavior, challenging current theoretical models.

Publisher

AIP Publishing

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