Partition function free rotor

The above treatment has made some assumptions, such as harmonic frequencies and sufficiently small energy spacing between the rotational levels. If a more elaborate treatment is required, the summation for the partition functions must be carried out explicitly. Many molecules also have internal rotations with quite small barriers, hi the above they are assumed to be described by simple harmonic vibrations, which may be a poor approximation. Calculating the energy levels for a hindered rotor is somewhat complicated, and is rarely done. If the barrier is very low, the motion may be treated as a free rotor, in which case it contributes a constant factor of RT to the enthalpy and R/2 to the entropy. 

V rotation barrier, partition function of the free rotor. ... 

In most quantum chemical program packages, these equations are used only to calculate the temperamre dependence of thermodynamic properties. Internal free and hindered rotation contributions to the partition functions are normally neglected or implicitly use the pseudo-vibration approach for the internal rotor. 

In molecules or radicals, such as ethyl, internal rotations around bonds such as CH3—O—CH2 occur. Accordingly, the partition function for a free rotor is defined as... 

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