Coherence length determination of meso-meso linked porphyrin arrays based on forward-backward pair trajectory analysis

We investigated the excitation energy transfer process of meso-meso linked zinc(II) porphyrin arrays using the on-the-fly filtered propagator path integral method. Details of the dynamics such as coherence length of a porphyrin array are estimated by analysis of the characteristics of forward-backward pair trajectories. Upon examination of the convergence of the reduced density matrix with respect to the subset of Hilbert space trajectories, we determine the number of porphyrin units that form collective coherent states, that is, the coherence length. Simulation results show that the coherence length of zinc(II) porphyrin arrays is up to 4 units, which agrees excellently with experimental observations. On the other hand, the energy bias provided by the energy-accepting 5,15-bisphenylethynylated zinc(II) porphyrin reduces the degree of coherence which becomes negligible for an array with more than for porphyrin units. Considering conformational inhomogeneity, we found that the experimentally determined coherence length is the result of electronic and environmental influence rather than the structure disorder. Temperature dependence is also discussed.