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

TL;DR

This paper analyzes how the potential energy surfaces of Lennard-Jones clusters evolve with size, revealing structural complexity and proposing methods to simplify the landscape for better global optimization.

Contribution

It introduces the use of monotonic sequence basins and explores landscape transformations to address the complexity of energy surfaces in Lennard-Jones clusters.

Findings

Number of local minima increases exponentially with cluster size.

Disconnectivity graphs reveal size-dependent topographical features.

Landscape transformation aids in understanding global optimization challenges.

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.