Random matrix treatment of intramolecular vibrational redistribution. II. Coriolis interactions in 1-butyne and ethanol

Abstract

A random matrix methodology has been applied to simulate the molecular eigenstate resolved infrared spectra of the 1-butyne ν16 band and the ethanol ν14 band. In these methyl C–H stretch bands, each rotational transition is fragmented into a clump of molecular eigenstates. The frequencies and intensities of these discrete features carry information about the rate and mechanism of the intramolecular vibrational redistribution (IVR) which would follow the coherent excitation of the zero-order state. The simulations include anharmonic and Coriolis x-, y-, and z-type interactions. These interactions mix the bright state with the bath and also mix the bath states with each other. Since the vibrational identities of the bath states are assumed to be sufficiently mixed, the vibrational parts of the coupling matrix elements are treated stochastically following the development in Paper I of this series [J. Chem. Phys. 98, 6665 (1993)]. The rotational parts of the matrix elements are treated dynamically based on the known rotational quantum number dependence of the Coriolis effect. A stochastic treatment cannot expect to reproduce the detailed line positions and intensities of the experimental spectra, therefore three measures of IVR are used as the basis for comparison of the simulation with experiment. The measures are the dilution factor φd, the interaction width Δε, and the effective level density ρeffc. In the presence of multiple coupling mechanisms (near the best fit to the ethanol ν14 band), the correlations between φd and Δε and the bright-bath Coriolis coupling mechanisms follow the expected trends. It was also found that ρeffc is sensitive to the x, y Coriolis coupling among the bath states. The results were not sensitive to the z-type Coriolis coupling among the bath states in the region of the ethanol simulation, but ρeffc was sensitive to it in the simulation of the 1-butyne ν16 band. Best-fit coupling parameters were obtained for both simulated bands. The rms bright-bath z-type Coriolis coupling was found to be 0.028±0.005 cm−1 which is about three times the value obtained from a naive approach which neglects the interaction of the multiple coupling mechanisms. A direct count vibrational level density, ρvib, provided good agreement with the experiments when a full treatment of the torsional modes was included and a 20% enhancement of the density from neglected diagonal anharmonicities was added. A method of quantifying the conservation of the rotational quantum number, K, is provided by the inequalities, ρvib≤ρeffc≤(2J+1)ρvib. For 1-butyne, ρeffc is closer to ρvib than for ethanol indicating that K is more nearly conserved. While this work treats only anharmonic and Coriolis coupling, the random matrix formalism provides the ability to treat a wide variety of coupling schemes.