Electron transfer via bridges

Abstract

In this paper we explore the energetic control of sequential and superexchange electron transfer (ET) mechanisms on the basis of quantum-mechanical simulations and calculations for long-range ET in DBA systems, where the donor (D) and the acceptor (A) are separated by a bridge (B). We studied ET dynamics in a Franck–Condon (FC) system characterized by three multi-dimensional displaced harmonic potential surfaces, where an initial single vibronic doorway state |α〉 (with energy Eα) in the DBA (≡D) electronic state is coupled to the mediating {|β〉} vibronic quasicontinuum of the D+B−A (≡B) electronic state, which in turn is coupled to the final {|γ〉} vibronic quasicontinuum of the D+BA− (≡A) electronic state. The level structure was described by the vibrational frequencies (for a four-mode harmonic system) and the energy gaps ΔGDB and ΔGDA between the origins of the corresponding electronic states (with nα=1–50, nβ=1000–2000, and nγ=1000–2000 states in the {|α〉}, {|β〉}, and {|γ〉} manifolds, respectively), while the couplings were characterized by the spectral densities and by the pair correlations (specified in terms of correlation parameters ηαα′ and ηββ′) between states belonging to the same manifold. The correlation parameters ηαα′ (α,α′=1–40) for the doorway-quasicontinuum coupling and ηββ′ (β,β′=150–190) for the interquasicontinuum coupling are considerably lower than unity (|ηαα′|⩽0.4 and |ηββ′|⩽0.3), obeying propensity rules with the highest values of |ηαα′| and |ηββ′| which correspond to a single vibrational quantum difference, while for multimode changes between α and α′ or between β and β′ very low values of |ηαα′| or |ηββ′| are exhibited. Radiationless transitions theory was applied for quantum-mechanical simulations based on the dynamcis of wave packets of molecular eigenstates for resonance (ΔGDB<Eα) and for off-resonance (ΔGDB>Eα) coupling. Resonance |α〉–{|β〉}–{|γ〉} coupling results in two-step sequential ET kinetics for all doorway states |α〉, manifesting phase erosion due to weakly correlated intercontinuum coupling, without the need of intermediate state phonon induced thermalization. Off-resonance |α〉–{|β〉} coupling in conjunction with {|β〉}–{|γ〉} resonance interactions results in unistep superexchange ET kinetics. The simulated sequential ET rates and the superexchange rate are in good agreement with the calculated quantum-mechanical rates obtained using the electronic couplings and FC densities. The energy-gap (ΔGDB) dependence of the simulated and the calculated ET rates from a single doorway state reveal a “transition” from sequential to superexchange ET with increasing ΔGDB. For a finite-temperature system, characterized by a fixed ΔGDB (>0) small energy gap, the thermally averaged rate from a canonical ensemble of doorway states will result in the superposition of both superexchange and sequential mechanisms.