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The theoretical description and the properties of Frenkel excitons innon-covalently bonded molecular aggregates are reviewed from a multi-excitonperspective of dissipative quantum dynamics. First, the photophysical andquantum chemical characterization of the monomeric dye building blocks isdiscussed, including the important aspect of electron-vibrational couplingwithin the Huang-Rhys model. Supplementing the model by the Coulombicinteractions between monomers, the description of aggregates in terms ofexcitonic or vibrational-excitonic bands follows. Besides of giving rise tocomplex absorption and emission line shapes, exciton-vibrational interaction isresponsible for energy and phase relaxation and thereby limits the size ofcoherent excitations in larger aggregates. Throughout, emphasis is put on theelectronic three-level model as a minimum requirement to describe nonlinearspectroscopies including effects of two-exciton states such as excited stateabsorption and exciton-exciton annihilation. The experimentally observedcharacteristics of stationary absorption and fluorescence spectra of aggregatesas well as their temperature dependence are discussed. Examples for ultrafastspectroscopic experiments including pump-probe studies, photon echo andtwo-dimensional spectroscopy are presented and results on the size of coherencedomains and on intra- and interband relaxation are given. Finally, experimentalsignatures for exciton-exciton annihilation and their analysis with respect tothe mobility of excitons are described.

Quantum Dynamics and Spectroscopy of Excitons in Molecular Aggregates