Evolution of the Potential Energy Surface with Size for Lennard-Jones Clusters

Abstract

Disconnectivity graphs are used to characterize the potential energy surfaces of Lennard-Jones clusters containing 13, 19, 31, 38, 55 and 75 atoms. This set includes members which exhibit either one or two `funnels' whose low-energy regions may be dominated by a single deep minimum or contain a number of competing structures. The graphs evolve in size due to these specific size effects and an exponential increase in the number of local minima with the number of atoms. To combat the vast number of minima we investigate the use of monotonic sequence basins as the fundamental topographical unit. Finally, we examine disconnectivity graphs for a transformed energy landscape to explain why the transformation provides a useful approach to the global optimization problem.

arXiv comment13 pages, 8 figures, revtex

References in corpus (6)

• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• The double-funnel energy landscape of the 38-atom Lennard-Jones cluster
• On the Thermodynamics of Global Optimization
• Thermodynamics and the Global Optimization of Lennard-Jones clusters
• Connected Network of Minima as a Model Glass: Long Time Dynamics
• Structural relaxation in Morse clusters: Energy landscapes

Cited by in corpus (47)

• A Doubly Nudged Elastic Band Method for Finding Transition States
• Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique
• Phase changes in 38 atom Lennard-Jones clusters. I: A parallel tempering study in the canonical ensemble
• Reversible self-assembly of patchy particles into monodisperse icosahedral clusters
• New Tetrahedral Global Minimum for the 98-atom Lennard-Jones Cluster
• Entropic effects on the Size Evolution of Cluster Structure
• Identifying "communities" within energy landscapes
• Entropic effects on the structure of Lennard-Jones clusters
• Magic number behavior for heat capacities of medium sized classical Lennard-Jones clusters
• Basin Hopping with Occasional Jumping
• Thermodynamics and equilibrium structure of Ne_38 cluster: Quantum Mechanics versus Classical
• Does the potential energy landscape of a supercooled liquid resemble a collection of traps?
• Modelling the structure of clusters of C_60 molecules
• Identifying structural patterns in `disordered' metal clusters
• An Infinite Swapping Approach to the Rare-Event Sampling Problem
• Composition-induced structural transitions in mixed rare-gas clusters
• Phase changes in selected Lennard-Jones X_{13-n}Y_n clusters
• Minima Hopping Guided Path Search: An Efficient Method for Finding Complex Chemical Reaction Pathways
• Group Leaders Optimization Algorithm
• Energy landscape of relaxed amorphous silicon
• The Dynamics of Structural Transitions in Sodium Chloride Clusters
• Energy landscapes, structural topologies and rearrangement mechanisms in clusters of dipolar particles
• Simulating structural transitions by direct transition current sampling: the example of LJ38
• The effect of compression on the global optimization of atomic clusters
• From Sticky-Hard-Sphere to Lennard-Jones-Type Clusters
• Sampling diffusive transition paths
• Superposition Enhanced Nested Sampling
• Methods to locate Saddle Points in Complex Landscapes
• Visualising energy landscapes through manifold learning
• Rare-Event Sampling: Occupation-Based Performance Measures for Parallel Tempering and Infinite Swapping Monte Carlo Methods
• Robustness of "cut and splice" genetic algorithms in the structural optimization of atomic clusters
• Finding reaction pathways with optimal atomic index mappings
• Close-Packing of Clusters: Application to Al_100
• Funnels in Energy Landscapes
• Dynamics in the Metabasin Space of a Lennard-Jones Glass Former: Connectivity and Transition Rates
• Computationally Efficient Characterization of Potential Energy Surfaces Based on Fingerprint Distances
• Taming the rugged energy landscape: Techniques for the production, reordering, and stabilization of selected cluster inherent structures
• A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network
• Doped rare gas clusters up to completion of first solvation shell, CO2-(Rg)n, n = 3-17, Rg = Ar, Kr, Xe
• Global Optimization on an Evolving Energy Landscape
• Funnel Hopping Monte Carlo: An efficient method to overcome broken ergodicity
• Theoretical study of the finite temperature spectroscopy in van der Waals clusters. III Solvated Chromophore as an effective diatomics
• On the efficient Monte Carlo implementation of path integrals
• Nested Sampling for Exploring Lennard-Jones Clusters
• Non-empirical weighted Langevin mechanics for the potential escape problem: parallel algorithm and application to the Argon clusters
• Mapping the metastability of Lennard-Jones clusters by the maximum vibrational frequency
• Homogeneous Connectivity of Potential Energy Network in a Solidlike State of Water Cluster