### Abstract

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.

Original language | English (US) |
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Title of host publication | Proceedings of the 6th International Conference on Supercomputing, ICS 1992 |

Publisher | Association for Computing Machinery |

Pages | 409-416 |

Number of pages | 8 |

ISBN (Electronic) | 0897914856 |

DOIs | |

State | Published - Aug 1 1992 |

Event | 6th International Conference on Supercomputing, ICS 1992 - Washington, United States Duration: Jul 19 1992 → Jul 24 1992 |

### Publication series

Name | Proceedings of the International Conference on Supercomputing |
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Volume | Part F129617 |

### Other

Other | 6th International Conference on Supercomputing, ICS 1992 |
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Country | United States |

City | Washington |

Period | 7/19/92 → 7/24/92 |

### ASJC Scopus subject areas

- Computer Science(all)

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## Cite this

*Proceedings of the 6th International Conference on Supercomputing, ICS 1992*(pp. 409-416). (Proceedings of the International Conference on Supercomputing; Vol. Part F129617). Association for Computing Machinery. https://doi.org/10.1145/143369.143443