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Direct Use of the Gradient for Investigating Molecular Energy Surfaces

  • Péter Pulay
Part of the Modern Theoretical Chemistry book series (MTC, volume 4)

Abstract

A great deal of chemical and spectroscopical processes involve the relative motion of atomic nuclei. For most low-energy processes the Born-Oppenheimer fixed-nuclei approximation is sufficient: the nuclear motion takes place on an effective potential surface which is the sum of the electronic energy and the nuclear repulsion as a function of the nuclear coordinates. One of the main fields of quantum chemical activity is the study of these surfaces. Complete characterization of a multidimensional potential surface is a very complex task. Often, however, the nuclear motion takes place in the vicinity of a reference configuration, and the surface can be adequately characterized by a power series expansion, i.e., by its derivatives with respect to the nuclear coordinates. Traditionally, these derivatives have been evaluated from a pointwise calculation of the energy, followed by a fitting procedure. This method has some serious drawbacks both in efficiency and in numerical accuracy. Indeed, Hartree(1) observes that “the differentiation of a function specified only by a table of values ... is a notoriously unsatisfactory process, particularly if higher derivatives than the first are required” (see Gerratt and Mills(2) for examples).

Keywords

Force Constant Polyatomic Molecule Integral Force Force Constant Matrix Harmonic Force Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • Péter Pulay
    • 1
  1. 1.Department of General and Inorganic ChemistryEötvös L. UniversityBudapestHungary

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