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Direct Use of the Gradient for Investigating Molecular Energy Surfaces

  • Chapter
Applications of Electronic Structure Theory

Part of the book series: Modern Theoretical Chemistry ((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).

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  1. Department of General and Inorganic Chemistry, Eötvös L. University, Budapest, Hungary

    Péter Pulay

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  1. University of California, Berkeley, USA

    Henry F. Schaefer III

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Pulay, P. (1977). Direct Use of the Gradient for Investigating Molecular Energy Surfaces. In: Schaefer, H.F. (eds) Applications of Electronic Structure Theory. Modern Theoretical Chemistry, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8541-7_4

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