Exciton–vibrational coupling in the dynamics and spectroscopy of Frenkel excitons in molecular aggregates

The influence of exciton–vibrational coupling on the optical and transport properties of molecular aggregates is an old problem that gained renewed interest in recent years. On the experimental side, various nonlinear spectroscopic techniques gave insight into the dynamics of systems as complex as photosynthetic antennae. Striking evidence was gathered that in these protein–pigment complexes quantum coherence is operative even at room temperature conditions. Investigations were triggered to understand the role of vibrational degrees of freedom, beyond that of a heat bath characterized by thermal fluctuations. This development was paralleled by theory, where efficient methods emerged, which could provide the proper frame to perform non-Markovian and non-perturbative simulations of exciton–vibrational dynamics and spectroscopy. This review summarizes the state of affairs of the theory of exciton–vibrational interaction in molecular aggregates and photosynthetic antenna complexes. The focus is put on the discussion of basic effects of exciton–vibrational interaction from the stationary and dynamics points of view. Here, the molecular dimer plays a prominent role as it permits a systematic investigation of absorption and emission spectra by numerical diagonalization of the exciton–vibrational Hamiltonian in a truncated Hilbert space. An extension to larger aggregates, having many coupled nuclear degrees of freedom, becomes possible with the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method for wave packet propagation. In fact it will be shown that this method allows one to approach the limit of almost continuous spectral densities, which is usually the realm of density matrix theory. Real system–bath situations are introduced for two models, which differ in the way strongly coupled nuclear coordinates are treated, as a part of the relevant system or the bath. A rather detailed exposition of the Hierarchy Equations Of Motion (HEOM) method will be given in terms of a stochastic decoupling ansatz. This method has become the standard in exciton–vibrational theory and illustrative examples will be presented as well as a comparison with ML-MCTDH. Applications will be shown for generic model systems as well as for small aggregates mimicking those formed by perylene bisimide dyes. Further, photosynthetic antenna complexes will be discussed, including spectral densities and the role of exciton–vibrational coupling in two-dimensional electronic spectroscopy