Roto-torsional Levels for Symmetric and Asymmetric Systems: Application to HOOH and HOOD Systems

Abstract

Two pictures of separation of torsional mode in intramolecular dynamics are given for the treatment of hindered rotations of molecular systems like ABCD, which present a large amplitude motion associated with the torsional mode. The energy profile (torsional potential) is described by a dihedral angle and the chosen coordinates are based on orthogonal local vectors. Our model consists of two linear rigid rotors AB and CD that rotate around the Jacobi vector connecting the centers of mass of the diatoms AB and CD. We have used two procedures to calculate the roto-torsional energy levels. The first, referred to bi-rotor, uses the Hamiltonian as function of the azimuth angles of the AB and CD rotors. In the second one, referred to roto-torsion, we separate the internal rotation (torsional mode) from the overall rotation around the Jacobi vector. For the cases where the two moments of inertia are equal, e.g. HOOH, conservation of both energy and angular momentum for a system viewed as involving either torsion plus external rotation or interaction of two rotors requires correlation of levels with symmetries τ = 1 and 4 with zero or even values of the external rotation angular momentum quantum number k in units of $\hbar$. Conversely, torsional energy levels that belong to the τ = 2 and 3 symmetries, correlate with odd values of k. In HOOD the two rotors have different moments of inertia, and this causes further level splitting for τ = 2 and 3 only. Here we apply the two procedures to understanding the roto-torsional levels for HOOH and HOOD molecules.