Calculation of internal valence force constants for XY 4 ( Td) tetrahedral molecules

Abstract

Valence force constants have been calculated in terms of simple dependent rectilinear internal coordinates for a series of XY 4 tetrahedral molecules that have been studied from a vibrational point of view. These molecules include the tetrahydrides of carbon, silicon, germanium and tin, and the tetrafluorides of carbon, silicon and germanium. Using the most recent and reliable force constants in symmetry coordinates, the pure vibrational force field has been arrived at by applying Kuczera's treatment. The results show that the seven F R dependent constants are reduced to five F * R independent constants; the same occurs for the F 0 S independent force constants. The relationships f * rα = − f *′ rα and f *′ αα = − f * α − 4 f * αα are obtained from the sum rule in Kuczera's treatment. On the basis of Wilson's S vectors and from the interactions between the displacement coordinates, a method is proposed here to obtain the above relationships. This allows individual values to be assigned to the bending, bending—bending and bending—stretching force constants for the above-mentioned molecules, without the need for recourse to any model whatsoever. Likewise, in each case we have attempted to obtain an empirical function to fit the force constant values dependent on the bond lengths. This method allows us to some extent to predict the values of the force constants for some tetrahydride molecules of this group, which has not yet been studied experimentally.