Quantum dynamics of methanol: Hamiltonian, representation and intensity considerations

Abstract

Employing a body-fixed axis system and Jacobi coordinates, a model for the vibration–torsion–rotation Hamiltonian of the CH 3OH molecule with large-amplitude internal motions has been derived. This Hamiltonian is expressed in terms of Jacobi coordinates and is partitioned in the form H A+ H B+ H int, where H A and H B are the rovibrational Hamiltonians of methyl group CH 3 and asymmetric rotor OH, and H int represents their interactions. The resulting Hamiltonian is used to carry out a pure quantum mechanical calculation for this kind of molecule or to construct the potential surface using observed data. The detailed discussion of the Hamiltonian is presented for the model with a rigid methyl group and a rigid OH, which describes five lower frequency vibrational modes and pure rotation in the molecule. We discuss the advantages of body-fixed Jacobi form of the Hamiltonian and solution strategies for practical programming. The properties of labels of the energy states, potential function and dipole moments are investigated according to the molecular symmetry group G 6 of methanol. Finally, the developed formulation is used to calculate the energy levels of CO-stretching–torsion–rotation for lower rotational excitation ( J⩽5). Comparison of the calculated results with experimental ones is presented.