| This thesis focuses on the development of theoretical approaches toward the understanding of the complex nature of molecular aggregates. Applications are made to four-wave-mixing spectroseopies of the B820 Chlorophyll dimers and the B850 LH2 antenna in purple bacteria. Two types of theories are developed. The first type rigorously partitions the third-order polarization into a coherent and a sequential contribution. The latter is given by a sum of an exciton-hopping and a ground state (bleaching) terms, both expressed using the doorway-window representation. The theory includes effects of two-exciton states, static disorder, and coupling to a phonon bath with an arbitrary spectral density. It accounts for strong energetic disorder and applies when the disorder-induced exciton localization length is shorter than the phonon-induced exciton self-trapping length (polaron size) in the absence of disorder. Exciton transport is described by a master equation. Two-exciton states are expressed using Bethe ansatz, hence, the final expressions apply for a cyclic Frenkel-exciton model with the nearest-neighbor intermolecular interactions.;The second type of theory describes the combined effects of two-exciton resonances and exciton transport. It is derived using the nonlinear exciton equations (NEE), which follow explicitly the complete set of one-, two-, and three-point dynamical exciton variables relevant for the third-order response. The two-exciton state is calculated through an exciton-exciton scattering matrix. Effects of nuclear motions are incorporated through relaxation superoperators calculated perturbatively in exciton-phonon coupling. Thus the approach is limited to weak exciton-phonon coupling and is not sensitive to the detailed features of the spectral densities. A Green function expression for the third order response is obtained by solving the NEE using a truncation scheme based on factorizing the three-point relaxation kernels. These results set the stage for designing multidimensional spectroscopies of excitons and analyzing them using coherence-transfer pathways. New two-dimensional femtosecond resonant spectroscopic techniques which have the capacity to probe directly the excitonic couplings among chromophores are proposed. Model calculations illustrate that 2D techniques could fully characterize the system by providing information on intermolecular coupling constants. |
