A RANDOM MATRIX APPROACH TO ROTATION VIBRATION MIXING IN H2CO AND D2CO

In a previous study of highly excited states of H2CO, we found that ro tation-vibration mixing increases rapidly as a function of J for those states whose vibrational energy is greater than 6000 cm-1 [McCoy, Bur leigh, and Sibert, J. Chem. Phys. 95, 7449 (1991)]. The present work e lucidates the onset of this mixing in both H2CO and D2CO. In addition to Coriolis and centrifugal coupling, vibrational mixing between the n ormal modes is shown to have a strong influence on the breakdown of th e separation between rotation and vibration. The role of this latter e ffect is accurately modeled using a random matrix approach. An ensembl e of vibrational Hamiltonian matrices are defined whose matrix element s are chosen from distribution functions whose functional forms were d etermined by examining the matrix form of the original model Hamiltoni an. In adopting such an approach, the goal is not to attempt to predic t rotation-vibration mixing for a specific zero order state, but rathe r to model the distribution of rotation-vibration mixing for all the r otation-vibration states of a given J and within a total energy range E +/- DELTAE. The trends observed for these distributions as J and E a re increased are quantitatively reproduced using the random matrix app roach. Furthermore, the random matrix approach allows one to accuratel y reproduce the mixing with distribution functions defined with only a few parameters.