Rotation–vibration interactions between the two lowest frequency modes in formaldehyde

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Abstract
Rotation–vibration interactions between the two lowest frequency normal modes of H2CO, the out-of-plane bend and the in-plane wag, are studied using classical trajectories. The dynamics is investigated for a range of rotational angular momenta, J, and energy values. Vibrational energy flow is elucidated by examining trajectories in several different canonical representations. The a-axis Coriolis term, which is quadratic in the normal coordinates, accounts for most of the coupling, as seen by comparing plots in the normal mode representation and one in which the Coriolis term has been subsumed into the zero-order Hamiltonian. In the former, the modes are more strongly coupled as the projection of J onto the body-fixed z axis increases; in contrast, the Coriolis adapted normal modes are more decoupled. Making use of the observed decoupling, the rovibrational Hamiltonian is reduced to an effective one degree-of-freedom rotational Hamiltonian whose dynamics depends on the vibrational excitation. Model spectra have been obtained using the semiclassical method of Gaussian wave packet propagation of Heller [J. Chem. Phys. 62, 1544 (1975)]. Semiclassical and full quantum results analogous to the observed classical dynamics are presented.