Quantum Mechanical Simulation of Vibration-Torsion-Rotation Levels of Methanol

Abstract

Two kinds of vibration-torsion-rotation Hamiltonians, referred as a model Hamiltonian and quantum mechanical Hamiltonian, are constructed to investigate the vibration-torsion-rotational interaction in methanol. The model Hamiltonian is based on the formulation of reduction of Hamiltonian in which the CO-stretching mode ऍ8, the large-amplitude torsion mode ऍ12 and the three degrees of freedom that correspond to the overall rotation of the molecule are considered simultaneously. This Hamiltonian is used to carry out an analysis of already published data for CH3OH with vco ऊ 1 घCO-stretching vibrational quantum numberङ, vt ऊ 4 घtorsional quantum numberङ, and J ऊ 5. The relative locations of the CO-stretch vibrational ground state and the fundamental state are well reproduced for torsional states with vt ऊ 4 and J ऊ 5. An eaeective potential energy surface that describes ऍ8 and ऍ12 modes is obtained from this analysis. The quantum mechanical Hamiltonian is partitioned in the form HA + HB + Hint by employing a body-aexed axis system and the Jacobi coordinates, where HA and HB are the rovibrational Hamiltonians of methyl group CH3 and asymmetric rotor OH, and Hint represents their interactions. This Hamiltonian is used to carry out a pure quantum mechanical simulation of the CO-stretching-torsion-rotational states using the the potential function obtained from the model Hamiltonian analysis. The present analyses show that a variety of resonance interactions can aaeect states for energies larger than 1100 cm ,1 .