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Global Optimization of Morse Clusters by Potential Energy Transformations

University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
San Diego Supercomputer Center, University of California, San Diego, San Diego, California 92186-9784, USA
Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, I-10149 Torino, Italy
Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S.Marta, 3, I-50139 Firenze 185, Italy
jpkd1{at}cam.ac.uk
leary{at}sdsc.edu
locatell{at}di.unito.it
schoen{at}ing.unifi.it

The Morse potential is a simple model for the potential energy of atoms with a single parameter that determines the width of the potential well and allows a wide variety of materials to be modeled. Morse clusters are particularly important for applications, but their global optimization is also an extremely hard problem, highly relevant to methods that are to be applied to find the optimal configuration of a biomolecule. In particular, large values are very challenging and, until now, no unbiased global-optimization method has been able to detect all the (putative) global minima at = 14 for clusters with up to N = 80 atoms. In this paper we introduce some techniques for transforming the original Morse potential that allow us to increase considerably the efficiency in locating the known global minima and also to discover some new optimal clusters. These methods are promising candidates for application to the optimization of biomolecules.

Key words: Morse potential; global optimization; basin-hopping; two-phase local search
History: received July 2003; revised February 2004; accepted March 2004.