Density of states of one-dimensional hindered internal rotors and separability of rotational degrees of freedom

Analytical formulas for the density-of-states and sum-of-states functions of internal one-dimensional hindered rotors are developed and analyzed. Quantum effects are taken into account via the inverse Laplace transform of the classical rotational partition function corrected for quantum effects by the method of Fitter and Gwinn. Density-of-states and partition functions of i-C3H7, n-C4H10, n-C5H12, and sec-C4H9 are calculated under a separability assumption with internal hindered rotors treated either classically or classically with corrections for quantum effects. Results are compared with those obtained in a full treatment with explicit accounting for interaction between internal and external (overall) rotations. It is demonstrated that separability of the rotational degrees of freedom can be assumed in most cases with reasonable accuracy, the main source of disagreement between the two approaches being not the separability assumption but the approximation of a complex torsional potential with a simpler sinusoidal function.