Free Internal Rotation of a Single Symmetric Top

Free Internal Rotation of a Single Symmetric Top. Although there are few examples of free internal rotation, it is instructive to consider this case first since restricted internal rotation has been generally considered as a perturbation of free internal rotation. The partition function for a single free internal rotation has been obtained by classical mechanics, and may be conveniently expressed by  

The symmetry number is the number of identical configurations into which the molecule can be transformed on internal rotation. In toluene, for example, crnt.m is 6, while in but-2-yne o-ib. is 3. Contributions to thermodynamic functions from a single free internal rotation are readily calculated from equation (17), and the practical equations are summarized in Table 4. A breakdown of a typical calculation for a molecule with free internal rotation is illustrated by data for toluene in Table 5. 

Free internal rotation has been assumed in thermodynamic calculations of nitromethane, toluene, aaa-trifluorotoluene, / -fluorotoluene, 2-picoline, 3-picoline, and but-2-yne. For all these molecules satisfactory agreement between calorimetric data and statistical calculations could be obtained only by assuming the internal rotation to be essentially unrestricted. 

Independent evidence for free rotation in nitromethane has come from an analysis of its microwave spectrum, which has shown that the potential barrier restricting internal rotation is only 25.2Jmol for thermodynamic purposes this barrier is eflFectively zero. The low barrier in nitromethane is believed to be due to the possession of 6-fold S3rm-metry about the internal rotation axis. A Fourier cosine series expansion of the restricting potential in the form  

Although 2-picoline and 3-picoline have 3-fold internal rotation symmetry, they can be considered to have local 6-fold symmetry. The essentially free rotation in but-2-yne determined from thermodynamic calculations has been confirmed by recent spectroscopic measurements. The small term is probably the result of the significant spectral separation between the methyl groups. Free rotation has also been postulated in dimethylcadmium.  

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