The Partition Functions and Energy Levels of Molecules with Internal Torsional Motions

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Abstract
The complete energy matrix is set up for external and (hindered) internal rotations of ``pseudo‐rigid'' molecules; i.e., molecules consisting of a rigid framework to which symmetric hindered rotators are attached. The reduced secular equation for the energy levels of such a molecule with one internal rotation is given explicitly. By using the perturbation method of Wilson, the partition function for this model is found, correct to the second order. Effects due to angular momentum couplings are included. A simple method for the calculation of thermodynamic contributions of hindered internal rotations is given. As an example, the application of the method to propylene is described; in this case, the coupling terms here included may amount to as much as 19 percent of the effect of the hindering potential on the thermodynamic contributions.