Average Structure

Like the equilibrium structure, the average structure has a well-defined physical meaning. The vibrational effects contained in the moments of inertia may be divided into harmonic s* (har) and anharmonic s*(anhar) contributions, which depend, respectively, on the quadratic and cubic part of the potential energy function. To evaluate the average structures, the moments of inertia for the average configuration, denoted by I* (a = a, b, c), are required. These may be obtained from the effective moments of inertia by correcting for the s* (har) effects:

Only a knowledge of the harmonic force constants is required to make this correction. For a diatomic molecule, eb(har) = -6h/8n 2&>e; and for the ground state, Ifc = - eb(har)/2. The average bond length is then calculated from

m XmY

In Table XIX, it is clear that (r) parameters change with isotopic substitution, but re parameters do not, as expected. The anharmonic part of the potential function has the effect of displacing the average configuration of a molecule from its equilibrium configuration, and (r) > re. Usually (r) > ro > re, and replacement of H by D, which significantly decreases the amplitude of vibration, causes a large shortening in (r). Average structures for excited vibra-tional states have also been evaluated; these clearly indicate the variation expected for a given vibrational excitation. This measure of the molecular structure is most meaningful for simple molecules. Two drawbacks are that a knowledge of the harmonic force constants is required, and if isotopic data are needed to evaluate the average structure, then the isotopic shrinkage effects just mentioned must be ignored or estimated. This introduces some ambiguity in the derived parameters.

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