Vibrational coherence in nonadiabatic dynamics

M. Bixon*, Joshua Jortner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


In this paper we explore temporal vibrational coherence effects in nonadiabatic radiationless transitions between two electronic states in a large molecule or in the condensed phase, accounting explicitly for the role of the (intramolecular and/or medium) vibrational quasicontinuum of the final states. Our treatment of the time evolution of the wave packet of states and of coherence effects in the nonradiative population probabilities of the reactants and the products rests on the diagonalization of the Hamiltonian of the entire multimode system, with supplementary information being inferred from the effective Hamiltonian formalism. New features of the vibrational Franck-Condon quasicontinuum, which originate from weak, but finite, correlations between off-diagonal coupling terms, were established. The state dependence of the off-diagonal couplings V between the doorway states manifold {|s〉} the quasicontinuum {|α〉} was quantified by the correlation parameters ηss′=〈VV αs′〉/[〈V2 〉〈V2 s′α〉]1/2, where 〈〉 denotes the average over the relevant energy range. Calculations were conducted for a Franck-Condon four-mode system consisting of ns=100 doorway states and nα=3000 quasicontinuum states. The correlation parameters for all pairs of doorway states are considerably lower than unity (|ηss′|≲0.4), obeying propensity rules with the highest values of |ηss′| corresponding to a single vibrational quantum difference, while for multimode changes between |s〉 and |s′〉 very low values of |ηss′| are established. Quantum beats in the population probabilities of products and reactants in nonadiabatic dynamics are characterized by an upper limit for their modulation amplitudes ξ≅(Γ/ΔΕ) η (for ΔΕ/2πΓ≥ 1), where Γ is the decay width of the doorway states and ΔΕ is their energetic spacing. These low ξ values originate from a small (-Γ/ΔΕ) contribution to the off-diagonal matrix elements of the nonradiative decay matrix in conjunction with low correlation parameters. The amplitudes of the quantum beats in nonradiative temporal dynamics provide dynamic information on the larger correlation parameters ηss′. Our theoretical and numerical analysis was applied for temporal coherence effects in nonadiabatic electron transfer dynamics in a Franck-Condon quasicontinuum of Mulliken charge transfer complexes [K. Wynne, G. Reid, and R. M. Hochstrasser, J. Chem. Phys. 105, 2287 (1996)]. This accounts for the "preparation" (signature of coherent excitation), for the low amplitudes of coherent temporal modulation of reactants and products (ξ≅0.05-0.06 determined by the ηss′ parameters) and for the dominating contributions to temporal coherence (subjected to propensity rules).

Original languageEnglish
Pages (from-to)1470-1482
Number of pages13
JournalJournal of Chemical Physics
Issue number5
StatePublished - 1 Aug 1997


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