Evaluation of the Zeta-Sums for Rotation-Vibration Interaction in Axially Symmetrical Molecules

Abstract

It is shown that the contribution of a set of equivalent nuclei to the zeta‐sum for the fundamental vibrations of any symmetry species in a molecule possessing only one multiple axis of symmetry is zero unless the nuclei are situated on the axis. In the latter case the contribution of the set of equivalent nuclei to the zeta‐sum in any species is one unit for every degree of freedom the set contributes to that species. With the help of these theorems a table is worked out from which the zeta‐sums can be determined immediately for any axially symmetrical molecule of known structure. Use of the table is illustrated with several simple examples.