Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids

Abstract

We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using a combination of Newton-Raphson and eigenvector-following techniques. Numerical results are presented for a 256-atom supercell representation of a binary Lennard-Jones system. We then derive analytical formulae for the number of stationary points as a function of both system size and the Hessian index, using a framework based upon weakly interacting subsystems. This analysis reveals a simple relation between the total number of stationary points, the number of local minima, and the number of transition states connected on average to each minimum. Finally we calculate two measures of localisation for the displacements corresponding to Hessian eigenvectors in samples of stationary points obtained from the Newton-Raphson-based geometry optimisation scheme. Systematic differences are found between the properties of eigenvectors corresponding to positive and negative Hessian eigenvalues, and localised character is most pronounced for stationary points with low values of the Hessian index.

16 pages, 2 figures

Cited by in corpus (15)

• Characterizing the network topology of the energy landscapes of atomic clusters
• Kinetic Analysis of Discrete Path Sampling Stationary Point Databases
• Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface
• Are there localized saddles behind the heterogeneous dynamics of supercooled liquids?
• Thermodynamic-Dynamic Interrelations in Glass-Forming Polymer Fluids
• Exploring the energy landscape of XY models
• Network of inherent structures in spin glasses: scaling and scale-free distributions
• Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: Geodesic pathways through the potential energy landscape
• Properties of Kinetic Transition Networks for Atomic Clusters and Glassy Solids
• Potential Energy Landscape of the Two-Dimensional XY Model: Higher-Index Stationary Points
• Spatial structure of unstable normal modes in a glass-forming liquid
• An Inversion-Relaxation Approach for Sampling Stationary Points of Spin Model Hamiltonians
• The Angell Plot from the Potential Energy Landscape Perspective
• Revisiting the single-saddle model for the $\beta$-relaxation of supercooled liquids
• Energy Landscapes for Digital Alchemy