A random matrix approach to rotation–vibration mixing in H2CO and D2CO

Abstract

In a previous study of highly excited states of H2CO, we found that rotation–vibration mixing increases rapidly as a function of J for those states whose vibrational energy is greater than 6000 cm−1 [McCoy, Burleigh, and Sibert, J. Chem. Phys. 95, 7449 (1991)]. The present work elucidates the onset of this mixing in both H2CO and D2CO. In addition to Coriolis and centrifugal coupling, vibrational mixing between the normal modes is shown to have a strong influence on the breakdown of the separation between rotation and vibration. The role of this latter effect is accurately modeled using a random matrix approach. An ensemble of vibrational Hamiltonian matrices are defined whose matrix elements are chosen from distribution functions whose functional forms were determined by examining the matrix form of the original model Hamiltonian. In adopting such an approach, the goal is not to attempt to predict rotation–vibration mixing for a specific zero order state, but rather to model the distribution of rotation–vibration mixing for all the rotation–vibration states of a given J and within a total energy range E±ΔE. The trends observed for these distributions as J and E are increased are quantitatively reproduced using the random matrix approach. Furthermore, the random matrix approach allows one to accurately reproduce the mixing with distribution functions defined with only a few parameters.