The adiabatic approximation as a diagnostic tool for torsion–vibration dynamics

Abstract

The adiabatic separation of large-amplitude torsional motion from small-amplitude vibrations is applied as an aid in interpreting the results of fully coupled quantum calculations on a model methanol Hamiltonian. Comparison is made with prior work on nitromethane [D. Cavagnat, L. Lespade, J. Chem. Phys. 106 (1997) 7946]. Even though the torsional potentials are very different, both molecules show a transition from adiabatic to diabatic behavior when the CH stretch is excited to ν CH = 4 or higher. In the adiabatic approximation, the effective torsional potentials for the various CH stretch vibrational states do not cross, but the CH vibrational amplitude moves from one bond to the next as a function of torsional angle. In the diabatic approximation, the effective torsional potentials do cross, but the distribution of the CH vibrational amplitude remains approximately constant in the vicinity of the crossing. The transition to diabatic behavior is promoted by the normal mode to local mode transition, and the relevant adiabatic and diabatic effective torsional potentials are determined by the torsion–vibration coupling. The torsion–vibration couplings in the four overtone manifolds considered (methanol OH, CH, nitromethane CH, and hydrogen peroxide OH) are large, reaching 265–500 cm −1 by ν XH = 6, and are of generally similar magnitude. The largest torsion–vibration couplings involve the first Fourier term in the torsional angle (cos γ for the CH stretch in methanol and the OH stretch in HOOH), whereas higher Fourier terms (cos2 γ in nitromethane and cos3 γ for the OH stretch of methanol) result in somewhat weaker coupling. Nonadiabatic matrix elements in methanol couple the torsional and vibrational energies and they exhibit a slow fall-off with coupling order.