Internal Rotation in Completely Asymmetric Molecules. IV. Energy Contributions from the α Dependence of the Torsional Kinetic Energy

For molecules with asymmetric internal rotors, the reduced moment of inertia for the torsional motion depends explicitly upon $\alpha$ , the angle of internal rotation. General expressions have been obtained for this dependence from a model which considers one degree of internal freedom for molecules with one part planar and the other with a plane of symmetry. The formulas are functions only of the inertial parameters of the molecule. For those cases where the $\alpha$ dependence is small, the results are expanded in trigonometric series. In this case the $\alpha$ dependence of the torsional kinetic energy may be expressed as a variation in the effective potential hindering the internal motion. Torsional coefficients have been calculated for some representative molecules.