Generalized valence force field force constants and mean-square amplitudes of vibration of some trigonal bipyramidal XY5 molecules calculated by the logarithmic steps method

Abstract

Normal-co-ordinate analysis has been carried out for some reputedly trigonal bipyramidal XY₅ molecules such as PF₅, AsF₅, SbF₅, VF₅, MoF₅, PCl₅, and SbCl₅. Complete sets of stretching, bending, and interaction force constants and mean-square amplitudes have been calculated from the generalized valence force field using the logarithmic steps method followed by blocking off. For SbF₅ and MoF₅, it is found that previous band assignments, and even the molecular symmetry should be revised. Examination of the stretching force constants and mean amplitudes of vibration shows that in the molecules of D_3h symmetry the axial bonds are longer than the equatorial and that the relative deviation between axial and equatorial bond lengths increases when for a given halide, the size of the central atom decreases, and when for a given central atom X, the size of the ligand atoms increases. The values for bond lengths derived from the stretching force constants using Badger's rule are in good agreement with those obtained by electron diffraction methods. The equatorial bond orders (according to Siebert) are significantly greater than the axial ones. Since, for symmetry reasons, axial π-bonding is necessarily stronger than equatorial π-bonding, a large difference will result in the nature of the respective σ-bonding. This π-bonding, which arises from the nephel-auxetic effect and back-donation, is more pronounced in the fluorides than in the chlorides.