Cluster Indexes and Vibrational Components in CF4

Abstract

The rotation-vibrational energies of the 10 lowest vibrational states for 12CF4, 13CF4, and 14CF4 have been calculated for J ≤ 70 from an anharmonic potential function fitted to all experimental data. It is shown that the rotation-vibrational states belonging to a certain vibrational state may be divided into vibrational components, equal in number to the degeneracy of the vibrational state. Each vibrational component is characterized by a symmetry D(J+Δ)g or D(J+Δ)u, in the point group O3, where Δ is a small integer. The correlation from O3 to Td then indicates the symmetries in Td of all the rotation-vibrational states present in the vibrational component for a given J. Each cluster of rotation-vibrational states is characterized by a cluster index τ, defined by means of the k-distribution of the computed wavefunctions. A table is presented allowing a prediction of the symmetry of any cluster from the τ value. All clusters within the manifold of rotation-vibrational states for a given vibrational component and a certain J value may be ordered into at the most three series of clusters, one consisting of 6-fold clusters, one of 8-fold clusters, and one of 12-fold clusters, the cluster index τ increasing from 0 upward within each series. In exceptional cases, even 24-fold clusters appear. Examples are given of the use of the cluster index to order series in which the energy bends as a function of the cluster index, and to split overlapping vibrational components.