### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 83-90 |

Number of pages | 8 |

Journal | Journal of Global Optimization |

Volume | 11 |

Issue number | 1 |

State | Published - 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Global mmimizers
- Leunard-Jones cluster
- Minimum inter-particle distance

### ASJC Scopus subject areas

- Management Science and Operations Research
- Global and Planetary Change
- Applied Mathematics
- Control and Optimization

### Cite this

**Minimum Inter-Particle Distance at Global Minimizers of Lennard-Jones Clusters.** / Xue, Guoliang.

Research output: Contribution to journal › Article

*Journal of Global Optimization*, vol. 11, no. 1, pp. 83-90.

}

TY - JOUR

T1 - Minimum Inter-Particle Distance at Global Minimizers of Lennard-Jones Clusters

AU - Xue, Guoliang

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

KW - Global mmimizers

KW - Leunard-Jones cluster

KW - Minimum inter-particle distance

UR - http://www.scopus.com/inward/record.url?scp=0003090779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0003090779&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0003090779

VL - 11

SP - 83

EP - 90

JO - Journal of Global Optimization

JF - Journal of Global Optimization

SN - 0925-5001

IS - 1

ER -