Ro-torsional energy correlation between the high barrier and free-internal-rotor limits: The case of the skew chain molecule HSOH

Abstract

Skew-chain molecules, such as HSOH, exhibit exotic behavior due to coupling of torsion and rotation. In particular, the torsional tunneling splittings vary cyclically in magnitude with axial rotational quantum number, K, with a period depending on the ratio of the moments of inertia for their end moieties. Although successfully modeled using a variety of approaches (algebraic, reduced-dimensional, and full-dimensional) a conceptual understanding of this cyclic variation for HSOH has not been presented. We do this here, using the reduced-dimension Generalized Semi-Rigid Bender (GSRB) approach to establish the correlation between states at the free-rotor (zero-barrier) limit and those at the more physical high-barrier limit. In this context we present the symmetries and appropriate quantum numbers for the states in these two limiting cases. We show that the cyclic variation of the magnitude of the torsional splittings originates in the energy level-structure in the zero-barrier limit combined with the correlation to the high-barrier limit. This allows us to give a simple recipe for calculating the period of this cyclic variation in any such skew-chain molecule, based only on the moments of inertia of the two end moieties.