Theoretica chimica acta

, Volume 66, Issue 5, pp 333–340 | Cite as

Estimating the hessian for gradient-type geometry optimizations

  • H. Bernhard Schlegel


Optimization methods that use gradients require initial estimates of the Hessian or second derivative matrix; the more accurate the estimate, the more rapid the convergence. For geometry optimization, an approximate Hessian or force constant matrix is constructed from a simple valence force field that takes into account the inherent connectivity and flexibility of the molecule. Empirical rules are used to estimate the diagonal force constants for a set of redundant internal coordinates consisting of all stretches, bends, torsions and out-of-plane deformations involving bonded atoms. The force constants are transformed from the redundant internal coordinates to Cartesian coordinates, and then from Cartesian coordinates to the non-redundant internal coordinates used in the specification of the geometry and optimization. This method is especially suitable for cyclic molecules. Problems associated with the choice of internal coordinates for geometry optimization are also discussed.

Key words

Optimization methods geometry optimization gradients Hessian force constants 


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • H. Bernhard Schlegel
    • 1
  1. 1.Department of ChemistryWayne State UniversityDetroitUSA

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