Properties of random state manifolds with applications to intramolecular vibrational redistribution

Abstract

We investigate spectral properties of random manifolds, which consist of a bright state coupled to mutually uncoupled dark states for an equal but otherwise arbitrary distribution of the couplings. Both Poisson and Wigner distributions of the energy spacings of the dark states are taken into account. The Poisson spacing model is solved exactly. The average spectrum is Lorentzian. The average dilution factor comes out to be a function alone of the mean coupling strength normalized to the mean neighbor spacing of the dark states. A simple expression for the explored fraction of the available phase space is obtained. Numerical studies indicate that the normalized coupling even controls the whole distribution of the dilution factor for the Poisson model. For weak mean coupling strength a secondary peak occurs in this distribution for both the Poisson and the Wigner model. A perturbational analysis shows that this peak leads back to accidental resonances of the bright state with single dark states. A simple tier model is suggested for treating the intermixing of vibrational dark basis states in molecules. Results are compared with experimental data.