The contribution to the entropy for a methyl rotor depends on the reduced moment of inertia and the barrier to internal rotation.Using ethane (CH3-CH3) as an example we can compute the contribution to entropy of the methyl internal rotation. We will use results calculated at HF/6-31G* and a temperature of 298.15K and determine the contribution to the entropy three different ways:
|Free internal rotation||7.5||12.0||14.2||17.1|
At low temperatures the harmonic oscillator is a good approximation, and at very high temperatures the free rotor is a better approximation.
The reduced moment of inertia for a methyl group varies depending on the rest of the molecule. In the ethane example it is 1.55 amu Å2. The moment of inertia for a methyl attached to an infinitely heavy mass will be about 3 amu Å2 . For example, in (E)-1,3-pentadiene the methyl rotor reduced moment of inertia is 2.987 amu Å2
See also the discussion on internal rotation in section I.D. A brief description of the thermochemical quantities and methods.