Partition Function for Internal Rotation in Methanol and Similar Molecular Models

Abstract

Methanol falls outside the range of variables within which the internal rotator partition function and its required derivatives have been dependably calculated by the relatively simple methods of Pitzer and Gwinn. For such cases, Ivash, Li, and Pitzer have proposed a detailed, general formulation of potential extreme accuracy. It is shown here that their partition function, obtained by integration over functions which are not unique for the model, can have two formally different values. Elimination of an ambiguity from their derivation leads back to an earlier and simpler method developed empirically by Halford, without, however, establishing this method for the general case. A very simple derivation, which obviously gives answers of readily determined accuracy for a widely distributed set of special cases, is presented. It is shown that the Ivash-Li-Pitzer formulation gives accurate answers under specifiable conditions. It is also deduced that a considerable extension of the Pitzer-Gwinn Tables, at a high level of accuracy, sufficient to cover all likely cases of interest, is possible without serious increase in the detail of calculation. Such an extension would solve the general case in a practical sense.