A fast algorithm for particle simulations
Journal of Computational Physics
The order of Appel's algorithm
Information Processing Letters
Minimizing the Lennard-Jones potential function on a massively parallel computer
ICS '92 Proceedings of the 6th international conference on Supercomputing
Fast Global Optimization of Difficult Lennard-Jones Clusters
Computational Optimization and Applications
Equivalent formulations and necessary optimality conditions for the Lennard–Jones problem
Journal of Global Optimization
Minimal interatomic distance in Morse clusters
Journal of Global Optimization
A Cost Optimal Parallel Algorithm for Computing Force Field in N-Body Simulations
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Lower Bound for the Interatomic Distance in Lennard-Jones Clusters
Computational Optimization and Applications
Minimal inter-particle distance in atom clusters
Acta Cybernetica
New results for molecular formation under pairwise potential minimization
Computational Optimization and Applications
Improved bounds for interatomic distance in Morse clusters
Operations Research Letters
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In computer simulations of molecular conformation and protein folding, a significant part of computing time is spent in the evaluation of potential energy functions and force fields. Therefore many algorithms for fast evaluation of potential energy functions and force fields are proposed in the literature. However, most of these algorithms assume that the particles are uniformly distributed in order to guarantee good performance. In this paper, we prove that the minimum inter-particle distance at any global minimizer of Lennard-Jones clusters is bounded away from zero by a positive constant which is independent of the number of particles. As a by-product, we also prove that the global minimum of an n particle Lennard-Jones cluster is bounded between two linear functions. Our first result is useful in the design of fast algorithms for potential function and force field evaluation. Our second result can be used to decide how good a local minimizer is.