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 journalArticlepeer-review

4 Scopus citations


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
Issue number12
StatePublished - Sep 2000


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

ASJC Scopus subject areas

  • General Chemistry
  • Computational Mathematics


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