Statistical thermodynamics of bond torsional modes

We present a formalism for treating torsions in complex molecules with nonsymmetry-related multiple minima along the internal rotation coordinate. We also present a comparison of rectilinear and curvilinear methods for estimating the moment of inertia of an internal rotor, and we find that they sometimes differ considerably. We point out that the usual method of estimating the free rotor limit of the moment of inertia may sometimes be inaccurate by an order of magnitude. We present an approach called the Cw-single-frequency approximation that provides a good compromise of accuracy and economy of information cost, in that it provides reasonably accurate partition functions for most systems over a wide range of temperature without requiring extra Hessians or information about saddle points.