Calculation of internal valence force constants for XY 5 trigonal bipyramidal molecules

Abstract

By using procedure of the pure vibrational force field proposed by Kuczera , the internal valence force constants for XY 5( D 3h) trigonal-bipyramidal molecules have been calculated. In particular, a detailed study has been carried out, comparing the most reliable empirical and ab initio force fields that have appeared in the literature for the PF 5 molecule. The results show that the twenty F R dependent constants are reduced to thirteen F * R independent constants, the same number as the F ° S independent symmetry force constants because of the fulfillment of the following relationships between the F * R constants: ⨍ *′ r α=−2⨍ * rβ = −2⨍ *′ rβ , ⨍ * α=−2⨍ * αα, ⨍ *′ αα=−2⨍ * αβ, ⨍ * dα =0, ⨍ * dβ =−⨍ *′ dβ and ⨍ * β + ⨍ *′ ββ= −2⨍ * ββ-2⨍ *″ ββ These constants are obtained from the F * R= W ′ WF R W ′ W transformation force fieldof the pure vibrational force field and from the sum rule in Kuczera's treatment. These latter relationships can be obtained from an analysis of the interactions between the displacement coordinates with which the F * R constants are associated. This has allowed individual values to be assigned to the bending, bending-bending and stretching-bending constants for the PF 5 molecule, without the need for recourse to any model whatsoever.