Left panel: Schematic illustration of the oligothiophene(OT4)-fullerene (C60) complex considered in this work. Right panel: Illustration of the electron transfer process, with the LUMO orbitals of the OT4 and C60 moieties shown.
(a) Schematic illustration of the XT/CT potential crossing. Here, ε = ΔXT-CT is the vertical XT-CT gap at the XT equilibrium geometry (see Eq. (2)), is the CT reorganization energy (see Eq. (4)), ΔE = ΔXT-CT + λ is the energetic offset between the minima of the two diabatic potentials, and Δx is the phonon-induced shift of the equilibrium geometry. (b) Phonon-induced shifts Δx for the vibrational normal modes of the and fragments, respectively. Reprinted with permission from H. Tamura, I. Burghardt, and M. Tsukada, J. Phys. Chem. C 115, 10205 (2011). Copyright 2011 American Chemical Society.
Left panels: Successively broadened spectral densities, based upon a convolution of the original data shown in Fig. 2 with a Lorentzian envelope function as described in Secs. II B and IV A. Right panels: Corresponding XT state decay profiles. The magenta trace indicates the simulation result obtained with the original discretized spectral density of Fig. 2(b). While the oscillatory features beyond 50 fs tend to be washed out for the strongly broadened spectral densities, the decay on the shortest time scale (<50 fs) remains unaffected.
Time-evolving electronic coherence, see Eq. (9), accompanying the population transfer. Real and imaginary parts are shown separately, see the discussion in Sec. IV A. The simulations were carried out for Δ = 0.25Δ0.
Fragment spectral densities obtained by convolution of the original data shown in Fig. 2, separated for the and moieties. The fullerene fragment features a dominant contribution in the high-frequency region.
(a) Transfer profiles for the pure electronic case (red trace) giving rise to Rabi oscillations, and the case where the inter-fragment mode R is included as a single phonon mode (blue trace), as compared with the full dynamics (black trace) as in Fig. 4. (b) XT state decay for the fragment spectral densities of Fig. 5. The spectral density of the C60 moiety generates a very similar decay as the overall phonon distribution. The simulations were carried out for Δ = 0.25Δ0.
XT state decay including the dynamical effects of the inter-fragment coordinate R, as compared with a simulation for R fixed at the XT state equilibrium geometry (⟨ΔR⟩ = 0 a.u.). Due to the increase in the diabatic coupling as a function of the dynamics in R (see blue trace), the dynamics is increasingly anharmonic and coherent motions become less pronounced.
Simulations for different initial conditions of the inter-fragment coordinate R, given in terms of deviations ⟨ΔR⟩0 from the XT equilibrium geometry. The case ⟨ΔR⟩0 = −2 a.u. corresponds to the CT state minimum. The inset shows ⟨ΔR⟩(t).
Parameters, quoted in eV, for the and portions of the Hamiltonian, see Eqs. (2) and (3).
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