Geometrical properties of the potential energy of the soft-sphere binary mixture

TL;DR

This paper investigates the geometric properties of the potential energy surface in a soft-sphere binary mixture, revealing a transition from minima to saddle points and questioning the relevance of the instability index in liquid dynamics analysis.

Contribution

It compares algorithms for locating stationary points on the PES and demonstrates the robustness of energy-based analysis over instability index plots, uncovering a geometric transition in the system.

Findings

Identification of a geometric transition from minima to saddle points.

Instability index K vs. temperature is algorithm-dependent.

System is closer to saddle points than minima above the glass transition.

Abstract

We report a detailed study of the stationary points (zero-force points) of the potential energy surface (PES) of a model structural glassformer. We compare stationary points found with two different algorithms (eigenvector following and square gradient minimization), and show that the mapping between instantaneous configuration and stationary points defined by those algorithms is as different as to strongly influence the instability index K vs. temperature plot, which relevance in analyzing the liquid dynamics is thus questioned. On the other hand, the plot of K vs. energy is much less sensitive to the algorithm employed, showing that the energy is the good variable to discuss geometric properties of the PES. We find new evidence of a geometric transition between a minima-dominated phase and a saddle-point-dominated one. We analyze the distances between instantaneous configurations and stationary points, and find that above the glass transition, the system is closer to saddle points than to minima.