Time-resolved optical spectroscopy is widely used to study vibrational and electronic dynamics by monitoring transient changes in excited state populations on a femtosecond timescale. Yet the fundamental cause of electronic and vibrational dynamics--the coupling between the different energy levels involved--is usually inferred only indirectly. Two-dimensional femtosecond infrared spectroscopy based on the heterodyne detection of three-pulse photon echoes has recently allowed the direct mapping of vibrational couplings, yielding transient structural information. Here we extend the approach to the visible range and directly measure electronic couplings in a molecular complex, the Fenna-Matthews-Olson photosynthetic light-harvesting protein. As in all photosynthetic systems, the conversion of light into chemical energy is driven by electronic couplings that ensure the efficient transport of energy from light-capturing antenna pigments to the reaction centre. We monitor this process as a function of time and frequency and show that excitation energy does not simply cascade stepwise down the energy ladder. We find instead distinct energy transport pathways that depend sensitively on the detailed spatial properties of the delocalized excited-state wavefunctions of the whole pigment-protein complex.

A theoretical description of femtosecond two-dimensional electronic spectroscopy of multichromophoric systems is presented. Applying the stationary phase approximation to the calculation of photon echo spectra and taking into account exciton relaxation processes, we obtain an analytic expression for numerical simulations of time- and frequency-resolved 2D photon echo signals. The delocalization of one-exciton states, spatial overlaps between the probability densities of different excitonic states, and their influences on both one- and two-dimensional electronic spectra are studied. The nature of the off-diagonal cross-peaks and the time evolution of both diagonal and off-diagonal peak amplitudes are discussed in detail by comparing experimentally measured and theoretically simulated 2D spectra of the natural Fenna-Matthews-Olson (FMO) photosynthetic light-harvesting complex. We find that there are two noncascading exciton energy relaxation pathways.

The Q y excitation energies of the 96 chlorophyll molecules in photosystem I of Synechococcus elongatus, both in and out of their protein environments, were obtained by using the semiempirical INDO/S method and the crystal structure geometries. The dipole-dipole approximation was used to calculate the coupling between the Q y states of chlorophylls; in the case of closely separated chlorophylls INDO/S dimer calculations were used to determine the couplings. The effective Hamiltonian for chlorophyll Q y excitations was constructed, enabling tentative assignment of red chlorophylls and calculation of the absorption spectrum of PSI.