Solution of a torsional Schrödinger equation with a periodic potential of general form. The probability amplitude and probability density

Abstract

Analytic expressions for the probability density of states of a molecule with internal rotation and the probability of finding the state in the potential well are derived for the first time. Two methods are proposed for assigning conformers to potential wells. A quantitative measure of localization and delocalization of a state in the potential well is introduced. The rotational symmetry number is generalized to the case of asymmetric rotation. On the basis of the localization criterion, a model is developed for calculating the internal rotation contribution to thermodynamic properties of individual conformers with low rotational barriers and/or at a high temperature.