Final state-selected spectra in unimolecular reactions: A transition-state- based random matrix model for overlapping resonances

Final state-selected spectra in unimolecular decomposition are obtained by a random matrix version of Feshbach’s optical model. The number of final states which are independently coupled to the molecular quasibound states is identified with the number of states at the dividing surface of transition state theory ~TST!. The coupling of the transition state to the molecular complex is modeled via a universal random matrix effective Hamiltonian which is characterized by its resonance eigenstates and provides the correct average unimolecular decay rate. The transition from nonoverlapping resonances which are associated with isolated Lorentzian spectral peaks, to overlapping resonances, associated with more complex spectra, is characterized in terms of deviations from a x-like distribution of the resonance widths and the approach to a random phase-distribution of the resonance scattering amplitudes. The evolution of the system from a tight transition state to reaction products is treated explicitly as a scattering process where specific dynamics can be incorporated. Comparisons with recently measured final state-selected spectra and rotational distributions for the unimolecular reaction of NO2 show that the present model provides a useful new approach for understanding and interpreting experimental results which are dominated by overlapping resonances. © 1995 American Institute of Physics.