VIBRATIONAL COHERENCE IN NONADIABATIC DYNAMICS

In this paper we explore temporal vibrational coherence effects in non adiabatic radiationless transitions between two electronic states in a large molecule or in the condensed phase, accounting explicitly for t he role of the (intramolecular and/or medium) vibrational quasicontinu um of the final slates. Our treatment of the time evolution of the wav e packet of states and of coherence effects in the nonradiative popula tion probabilities of the reactants and the products rests on the diag onalization of the Hamiltonian of the entire multimode system, with su pplementary information being inferred from the effective Hamiltonian formalism. New features of the vibrational Franck-Condon quasicontinuu m, which originate from weak, but finite, correlations between off-dia gonal coupling terms, were established. The state dependence of the of f-diagonal couplings V-s alpha between the doorway states manifold {\s ]} and the quasicontinuum {\alpha]} was quantified by the correlation parameters eta(ss') = [Vs alphaValpha s']/[(V-s alpha(2)][V-s'alpha(2) ]](1/2), where [] denotes the average over the relevant energy range. Calculations were conducted for a Franck-ConcIon four-mode system cons isting of n(s) = 100 doorway states and n(alpha) = 3000 quasicontinuum states. The correlation parameters for all pairs of doorway states ar e considerably lower than unity (\eta(ss')\ less than or similar to 0. 4), obeying propensity rules with the highest values of \eta(ss')\ cor responding to a single vibrational quantum difference, while for multi mode changes between \s] and \s'] very low values of \eta(ss')\ are es tablished. Quantum beats in the population probabilities of products a nd reactants in nonadiabatic dynamics are characterized by an upper li mit for their modulation amplitudes xi congruent to (Gamma/Delta E)eta (for Delta E/2 pi Gamma greater than or equal to 1), where Gamma is t he decay width of the doorway states and Delta E is their energetic sp acing. These low xi values originate from a small (similar to Gamma/De lta E) contribution to the off-diagonal matrix elements of the nonradi ative decay matrix in conjunction with low correlation parameters, The amplitudes of the quantum beats in nonradiative temporal dynamics pro vide dynamic information on the larger correlation parameters eta(ss') Our theoretical and numerical analysis was applied for temporal coher ence effects in nonadiabatic electron transfer dynamics in a Franck-Co ndon quasicontinuum of Mulliken charge transfer complexes [K. Wynne, C . Reid, and R. M. Hochstrasser, J. Chem. Phys. 105, 2287 (1996)]. This accounts for the ''preparation'' (signature of coherent excitation), for thr low amplitudes of coherent temporal modulation of reactants an d products (xi congruent to 0.05-0.06 determined by the eta(ss') param eters) and for the dominating contributions' to temporal coherence (su bjected to propensity rules). (C) 1997 American Institute of Physics.