Calculation of internal valence force constants for XY 6( Oh) octahedral molecules

Abstract

The valence force constants have been calculated in terms of simple dependent rectilinear internal co-ordinates for a series of XY 6 octahedral molecules that have been amply studied from a vibrational point of view, i.e. the hexafluorides of sulphur, selenium, molybdenum, tungsten and uranium. The calculations have been carried out using the most recent force constants in symmetry co-ordinates to appear in the literature and following Kuczera's treatment, according to which the indetermination of the internal valence force constants involved in redundancies can be solved by using the transformation F* R= W T WF R W T W, which he calls the pure vibrational force field. The results show that the eleven F R dependent constants are reduced to seven F* R independent constants, the same number as the F S independent force constants. This is because of the zero value of the ƒ′* dα constants and the relationships ƒ* dα= −ƒ″* dα ƒ* αα = −ƒ″* αα ƒ* α=−2ƒ′* αα−ƒ′″* αα that are obtained from the combination of the above mentioned F* R transformation and the sum rule in Kuczera's treatment. These latter relationships can be obtained from the interactions between the displacement coordinates with which they are associated. This has allowed individual values to be assigned to the bending, bending—bending and stretching—bending constants for the above mentioned molecules without the need for recourse to any model whatsoever.