Computational Chemistry Comparison and Benchmark DataBase Release 22 (May 2022) Standard Reference Database 101 National Institute of Standards and Technology | |
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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:100K | 298.15K | 500K | 1000K | |
---|---|---|---|---|
Harmonic oscillator | 0.7 | 6.1 | 10.0 | 15.6 |
Free internal rotation | 7.5 | 12.0 | 14.2 | 17.1 |
Hindered rotor | 0.7 | 6.8 | 11.2 | 16.1 |
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.