Fluctuation-induced acceleration of inter-ligand exciton transfer in bis(dipyrrinato)Zn(II) complex

where Ψ i and Ψ f are the initial and final states of the exciton transfer, and Ĥ is Hamiltonian of the system. 7 It is well understood, from both theoretical and experimental perspectives, that V strongly depends on the relative orientation between the chromophores that involve the exciton transfer. 1,[8][9][10][11][12] Hence, efforts have been made to control or accelerate the exciton transfer by tuning V on the basis of molecular-or aggregatestructure design. [13][14][15][16] From this point of view, V is seen as a static parameter that is determined by the chemical structure of material. In contrast, because the orientation of chromophores is subject to structural dynamics at finite temperature, V can vary with time reflecting the change in structure. 17 In fact, dynamical fluctuation in relative orientation of chromophores and the resulting distribution of electronic coupling have been reported in covalent organic frameworks. 18,19 Taking the dynamical effects in V into account, the exciton transfer dynamics can, in principle, differ from that is expected from V at the static geometry. However, the understanding of the effects of dynamic V on exciton transfer phenomena is still very limited from both points of view of qualitative mechanism interpretation and quantitative estimation of its impact.

a) Electronic mail: uratani@moleng.kyoto-u.ac.jp

In this context, the exciton transport in multinuclear dipyrrin complexes synthesized by Toyoda, Sakamoto and coworkers [20][21][22][23] provide much implication for us. These complexes constitute repetition of the unit Zn(dp) 2 (Figure 1a), where dp denotes dipyrrin chromophore. At the ground-state stable geometry, the two dps coordinated to Zn are orthogonal to each other, where the excitonic coupling between the dps is exactly zero due to the symmetry; 24 in principle, the exciton transfer between these two dps is unable to occur. On the contrary, it has been experimentally suggested that the exciton transfer between these two dps constitutes one of the exciton transfer paths. 20,23 In Ref. 23 the lower limit of rate constant for the exciton transfer is estimated as 5 × 10 10 s -1 based on the fluorescence quantum yield and lifetime of the dp chromophores. These results make us expect that the dynamical angular fluctuation between the two dps yield the nonzero excitonic coupling to enable the ultrafast exciton transfer.

In the present study, the mechanism of exciton-transfer acceleration via the dynamical fluctuation in V is clarified by the combined use of the non-adiabatic molecular dynamics (NA-MD) simulations, the exciton density analysis, and a simplified picture of exciton transfer based on a two-state model. The results demonstrate that V, which is zero at the groundstate stable geometry, becomes to have finite values via the dynamical fluctuation in the dihedral angle between the two dps, realizing ultrafast exciton transfer. The atomic displacement mode that works as the reaction coordinate is determined via regression analysis, clarifying that the dynamics along the reaction coordinate, which drives the exciton transfer, has the faster timescale compared to the fluctuation in the dihedral angle between the two dps. These results suggest the dynamical picture of exciton transfer phenomena in the present system, that is, the slow fluctuation in the dihedral angle between the two dps “turns on/off” the exciton transfer, which is driven by the fast nuclear motion along the reaction coordinate.

The NA-MD simulations were performed for Zn(dp) 2 complex (Figure 1a). Hereafter, we use the labels dp1 and dp2 to distinguish the two dp ligands in Zn(dp) 2 . Among several NA-MD strategies distinct in the levels of approximation to the quantum nature of nuclei, 26 surface hopping (SH) 27,28 approaches, in which the nuclear dynamics are treated as classical trajectories that can hop among different potential energy surfaces (PESs) to incorporate the non-adiabatic effects, have been well-established theoretical frameworks to study exciton transfer dynamics in molecular systems. [29][30][31][32][33][34][35][36] In the present study, the simulations were conducted in SH approach based on the fewest-switches algorithm (FSSH) 37 for 100 trajectories in total, where each trajectory was propagated for 250 fs. The energy-based decoherence correction 38 was applied with the decay parameter set to the commonly used value (0.1 au). The propagation of time-dependent electronic wavefunction and the calculations of non-a