Concept of the Equilibrium Structure

The equilibrium structure of a molecule is conceived as the hypothetical vibrationless state, i.e. the state in which all intramolecular modes of vibration are imagined as frozen at the minima of their potential energy curves. This concept, and indeed the entire concept of a potential energy surface which arises from the electronic structure of a molecule, depends on the Born-Oppenheimer approximation which is virtually always made in studies of molecular structure. 

The effects of break-down of the Bom-Oppenhemer approximation have been considered in a series of papers by Bunker. r values for the bond lengths of light diatomic molecules are not quite constant when determined in the conventional way for different isotopic species e.g. HCl and DCl). The differences are of the order 10 A, and for this reason no further consideration will be given to the validity of the Bom-Oppenheimer approximation. Apart from the fact that other errors are invariably more important in the determination of molecular structure for polyatomic molecules, it does not seem possible to take account of the effect for polyatomic molecules at present. 

Because it is to a hi degree of approximation isotopically independent, the equilibrium structure is important in molecular structure studies. As later sections show, all definitions of structural parameters in terms of some vibrationally averaged observed quantity are not isotopically independent, and this leads to problems in evaluating and in quoting structural parameters. Another reason for seeking the equilibrium structure is that it is this hypothetical vibrationless state which is predicted by ab initio wave-function calculations, and thus the experimental scientist should if possible provide r values of intemuclear distance parameters as test data for the theoretical chemist. 

3 Operational Definitrans of Bond Lmgfii Electron Diffiraction 

In an electron diffraction experiment the data are obtained as an average over the vibrational motions of the molecule at a particular temperature. If multiple scattering effects are neglected (see Chapter 1, p. 23), so that only scattering terms from pairs of atoms are included, the electron diffraction intensity depends on the nuclear probability distribution Pair) for each pair of atoms i and j in the molecule. 

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GAMESS . The vibrational data obtained in this way should, however, be used with care, since many weakly bonded systems exhibit large-amplitude motions (especially when simple hydrides are involved) which cannot be accurately modelled at the harmonic level. Indeed, the very concept of the equilibrium structure of such complexes, while formally valid, loses much of its significance, and a much larger section of the surface must be sampled than is customary for ordinary molecules. Appropriate techniques for evaluating vibrational wavefunctions beyond the harmonic level have been reviewed by Le Roy et and very recently by Briels et a/. and the interested reader is referred to these. 

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