Theoretica chimica acta

, Volume 69, Issue 4, pp 265–279 | Cite as

Gradient extremals

  • David K. Hoffman
  • Ross S. Nord
  • Klaus Ruedenberg
Dynamics

Abstract

Gradient extremals on N-dimensional energy hypersurfaces V=V(x1x n ) are curves defined by the condition that the gradient ∇V is an eigenvector of the hessian matrix ∇∇V. For variations which are restricted to any (N−1) dimensional hypersurface ∇V(x1x N ) = V0= constant, the absolute value of the gradient ∇V is an extremum at those points where a gradient extremal intersects this surface. In many, though not all, cases gradient extremals go along the bottom of a valley or along the crest of a ridge. The properties of gradient extremals are discussed through a detailed differential analysis and illustrated by an explicit example. Multidimensional generalizations of gradient extremals are defined and discussed.

Key words

Potential energy surfaces Reaction paths 

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References

  1. 1.
    Similar results were also reported by Müller, K (1980) Angew Chem Int Ed Engl 19:1Google Scholar
  2. 2.
    Pancir J (1975) Collect Czech Chem Commun 40:1112Google Scholar
  3. 3.
    Basilevsky MV, Shamov AG (1981) Chem Phys 60:347Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • David K. Hoffman
    • 1
  • Ross S. Nord
    • 1
  • Klaus Ruedenberg
    • 1
  1. 1.Ames Laboratory-USDOE and Department of ChemistryIowa State UniversityAmesUSA

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