Determination of Barrier Heights from Low-Temperature Heat-Capacity Data

A method is presented by which barrier heights, in potential functions hindering the internal rotation of methyl groups, or spectroscopically inactive vibrational frequencies, can be obtained solely from thermal data for the solid phase. The observed heat capacities are analyzed in terms of contributions from the lattice vibrations, the internal vibrations, the expansion of the lattice, and the internal rotation. At low temperatures, the hindered rotation can be treated as torsional oscillation with a frequency related to the barrier height. It is shown that barrier heights derived by this method are in accord with those estimated from comparison of gas-phase entropies, but can be determined with greater precision than such values.