Direct Use of the Gradient for Investigating Molecular Energy Surfaces

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


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).


Force Constant Polyatomic Molecule Integral Force Force Constant Matrix Harmonic Force Constant 
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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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