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

Y. Z. Xu, Q. Ouyang, J. G. Wu, J. A. Yorke, G. X. Xu, D. F. Xu, R. D. Soloway, J. Q. Ren

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1101-1108
Number of pages8
JournalJournal of Computational Chemistry
Volume21
Issue number12
StatePublished - Sep 2000

Fingerprint

Molecular Mechanics
Molecular mechanics
Fractals
Fractal
Saddlepoint
Molecules
Newton-Raphson method
Fractal Structure
Global Minimum
Self-similarity
Extremum
Energy
Singular Point

Keywords

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

ASJC Scopus subject areas

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

Cite this

Xu, Y. Z., Ouyang, Q., Wu, J. G., Yorke, J. A., Xu, G. X., Xu, D. F., ... Ren, J. Q. (2000). Using Fractal to Solve the Multiple Minima Problem in Molecular Mechanics Calculation. 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.

In: Journal of Computational Chemistry, Vol. 21, No. 12, 09.2000, p. 1101-1108.

Research output: Contribution to journalArticle

Xu, YZ, Ouyang, Q, Wu, JG, Yorke, JA, Xu, GX, Xu, DF, Soloway, RD & Ren, JQ 2000, 'Using Fractal to Solve the Multiple Minima Problem in Molecular Mechanics Calculation', Journal of Computational Chemistry, vol. 21, no. 12, pp. 1101-1108.
Xu YZ, Ouyang Q, Wu JG, Yorke JA, Xu GX, Xu DF et al. Using Fractal to Solve the Multiple Minima Problem in Molecular Mechanics Calculation. Journal of Computational Chemistry. 2000 Sep;21(12):1101-1108.
Xu, Y. Z. ; Ouyang, Q. ; Wu, J. G. ; Yorke, J. A. ; Xu, G. X. ; Xu, D. F. ; Soloway, R. D. ; Ren, J. Q. / Using Fractal to Solve the Multiple Minima Problem in Molecular Mechanics Calculation. In: Journal of Computational Chemistry. 2000 ; Vol. 21, No. 12. pp. 1101-1108.
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