Random coupling models for intramolecular dynamics. I. Mathematical approach

Intramolecular dynamics in large molecules is modeled as a problem involving random coupling between manifolds of molecular levels. The random coupling model (RCM) is based on the rapid variations observed in coupling matrix elements involving highly excited bound molecular states, and on the high density of such states encountered in large molecules. The finite time and energy scales involved in real experimental situations lead to the observation that the time evolution and spectral properties characterizing the system do not depend on the detailed arrangement of states and their coupling elements but rather on low order moments of the distribution characterizing these coupling elements. This provides the basis for an approach based on ensemble averages. The coupling V is taken as a superposition V=u+v of a smoothly varying component u=〈V〉 and a randomly varying (in state space) component v=V−〈V〉. We introduce a diagrammatic expansion and averaging method to evaluate the diadic Green’s function for problems involving absorption line shapes, and a similar approach for the evaluation of the tetradic Green’s function used in calculations of time evolution. With these methods, we study the time evolution in systems involving discrete states and quasicontinuous manifolds. The solution is relevant for multiphoton excitation of large molecules, and for intramolecular electronic and vibrational transitions. We also study the effect of random coupling in absorption line shapes involving interference between resonances or interference between a resonance and a background absorptions. The mechanism for coherence erosion resulting from the random behavior of the coupling is elucidated.