Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Recent advances in global optimization
A discrete-continuous algorithm for molecular energy minimization
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Parallel two-level simulated annealing
ICS '93 Proceedings of the 7th international conference on Supercomputing
Minimum Inter-Particle Distance at Global Minimizers of Lennard-Jones Clusters
Journal of Global Optimization
Minimal inter-particle distance in atom clusters
Acta Cybernetica
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The Lennard-Jones potential energy function arises in the study of low-energy states of proteins and in the study of cluster statics. This paper presents a mathematical treatment of the potential function, deriving lower bounds as a function of the cluster size, in both two and three dimensional configurations. These results are applied to the minimization of a linear chain, or polymer, in two-dimensional space to illustrate the relationship between energy and cluster size. An algorithm is presented for finding the minimum-energy lattice structure in two dimensions. Computational results obtained on the CM-5, a massively parallel processor, support a mathematical proof showing an essentially linear relationship between minimum potential energy and the number of atoms in a cluster. Computational results for as many as 50000 atoms are presented. This largest case was solved on the CM-5 in approximately 40 minutes at an approximate rate of 1.1 32-bit gigaflops.