### Abstract

This article presents an approach using fractal to solve the multiple minima problem. We use the Newton-Raphson method of the MM3 molecular mechanics program to scan the conformational spaces of a model molecule and a real molecule. The results show each energy minimum, maximum point, and saddle point has a basin of initial points converging to it in conformational spaces. Points converging to different extrema are mixed, and form fractal structures around basin boundaries. Singular points seem to involve in the formation of fractal. When searching within a small region of fractal basin boundaries, the self-similarity of fractal makes it possible to find all energy minima, maxima, and saddle points from which global minimum may be extracted. Compared with other methods, this approach is efficient, accurate, conceptually simple, and easy to implement.

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

Pages (from-to) | 1101-1108 |

Number of pages | 8 |

Journal | Journal of Computational Chemistry |

Volume | 21 |

Issue number | 12 |

State | Published - Sep 2000 |

### Fingerprint

### Keywords

- Conformer
- Fractal basin boundaries
- MM3
- Molecular mechanics
- Pentential surface

### ASJC Scopus subject areas

- Chemistry(all)
- Safety, Risk, Reliability and Quality

### Cite this

*Journal of Computational Chemistry*,

*21*(12), 1101-1108.

**Using Fractal to Solve the Multiple Minima Problem in Molecular Mechanics Calculation.** / Xu, Y. Z.; Ouyang, Q.; Wu, J. G.; Yorke, J. A.; Xu, G. X.; Xu, D. F.; Soloway, R. D.; Ren, J. Q.

Research output: Contribution to journal › Article

*Journal of Computational Chemistry*, vol. 21, no. 12, pp. 1101-1108.

}

TY - JOUR

T1 - Using Fractal to Solve the Multiple Minima Problem in Molecular Mechanics Calculation

AU - Xu, Y. Z.

AU - Ouyang, Q.

AU - Wu, J. G.

AU - Yorke, J. A.

AU - Xu, G. X.

AU - Xu, D. F.

AU - Soloway, R. D.

AU - Ren, J. Q.

PY - 2000/9

Y1 - 2000/9

N2 - This article presents an approach using fractal to solve the multiple minima problem. We use the Newton-Raphson method of the MM3 molecular mechanics program to scan the conformational spaces of a model molecule and a real molecule. The results show each energy minimum, maximum point, and saddle point has a basin of initial points converging to it in conformational spaces. Points converging to different extrema are mixed, and form fractal structures around basin boundaries. Singular points seem to involve in the formation of fractal. When searching within a small region of fractal basin boundaries, the self-similarity of fractal makes it possible to find all energy minima, maxima, and saddle points from which global minimum may be extracted. Compared with other methods, this approach is efficient, accurate, conceptually simple, and easy to implement.

AB - This article presents an approach using fractal to solve the multiple minima problem. We use the Newton-Raphson method of the MM3 molecular mechanics program to scan the conformational spaces of a model molecule and a real molecule. The results show each energy minimum, maximum point, and saddle point has a basin of initial points converging to it in conformational spaces. Points converging to different extrema are mixed, and form fractal structures around basin boundaries. Singular points seem to involve in the formation of fractal. When searching within a small region of fractal basin boundaries, the self-similarity of fractal makes it possible to find all energy minima, maxima, and saddle points from which global minimum may be extracted. Compared with other methods, this approach is efficient, accurate, conceptually simple, and easy to implement.

KW - Conformer

KW - Fractal basin boundaries

KW - MM3

KW - Molecular mechanics

KW - Pentential surface

UR - http://www.scopus.com/inward/record.url?scp=0347746698&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347746698&partnerID=8YFLogxK

M3 - Article

VL - 21

SP - 1101

EP - 1108

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

IS - 12

ER -