Knowledge Bank

A POS (points-on-a-sphere) repulsive potential was used to model the effect of anharmonic terms on the bending eigenvalues of octahedral molecules. The POS potential is $$V_{pos} = K {\Sigma_{i>j} {\Sigma}} {\left( \frac{1}{q_{ij}} \right)}^{n}$$ where K and n are freely varying parameters and $qij$ is the inter-nuclear distance between ligand atoms i and j which are constrained to move on the surface of a sphere of radius R(M-X bond length). The entire bending potential surface was expanded to fourth order in octahedral symmetry coordinates and the coefficients of this expansion were solved for in terms of the POS parameter n. Eigenvalues were calculated for the potential surface formed by omitting all anharmonic terms which coupled modes of different symmetries. The effect of the cross term coupling on the eigenvalues was estimated. As concrete examples the locations of hot band transitions for $SF6$ and $UF6$ were predicted for the following range of the parameter $n,4\le n\le \le 7$.