Global minimum potential energy conformations of small molecules

Costas D. Maranas, Christodoulos A. Floudas

Research output: Contribution to journalArticle

105 Citations (Scopus)

Abstract

A global optimization algorithm is proposed for finding the global minimum potential energy conformations of small molecules. The minimization of the total potential energy is formulated on an independent set of internal coordinates involving only torsion (dihedral) angles. Analytical expressions for the Euclidean distances between non-bonded atoms, which are required for evaluating the individual pairwise potential terms, are obtained as functions of bond lengths, covalent bond angles, and torsion angles. A novel procedure for deriving convex lower bounding functions for the total potential energy function is also introduced. These underestimating functions satisfy a number of important theoretical properties. A global optimization algorithm is then proposed based on an efficient partitioning strategy which is guaranteed to attain ε-convergence to the global minimum potential energy configuration of a molecule through the solution of a series of nonlinear convex optimization problems. Moreover, lower and upper bounds on the total finite number of required iterations are also provided. Finally, this global optimization approach is illustrated with a number of example problems.

Original languageEnglish (US)
Pages (from-to)135-170
Number of pages36
JournalJournal of Global Optimization
Volume4
Issue number2
DOIs
StatePublished - Mar 1 1994

Fingerprint

Global Minimum
Global optimization
Potential energy
Conformation
Global Optimization
Conformations
Molecules
Torsional stress
Torsion
Optimization Algorithm
Energy
Potential energy functions
Dihedral angle
Angle
Covalent bonds
Convex optimization
Bond length
Potential Function
Euclidean Distance
Independent Set

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this

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Global minimum potential energy conformations of small molecules. / Maranas, Costas D.; Floudas, Christodoulos A.

In: Journal of Global Optimization, Vol. 4, No. 2, 01.03.1994, p. 135-170.

Research output: Contribution to journalArticle

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