We present a theory that efficiently describes the quantum dynamics of an electronic excitation that is coupled to a continuous, highly structured phonon environment. Based on a stochastic approach to non-Markovian open quantum systems, we develop a dynamical framework that allows us to handle realistic systems where a fully quantum treatment is desired yet the usual approximation schemes fail. The capability of the method is demonstrated by calculating spectra and energy transfer dynamics of mesoscopic molecular aggregates, elucidating the transition from fully coherent to incoherent transfer.

Energy transfer in the photosynthetic FennaMatthews-Olson (FMO) complex of Green Sulfur Bacteria is studied numerically taking all three subunits (monomers) of the FMO trimer and the recently found eighth bacteriochlorophyll (BChl) molecule into account. The coupling to the nonMarkovian environment is treated with a master equation derived from non-Markovian quantum state diffusion. When the excited state dynamics is initialized at site eight, which is believed to play an important role in receiving excitation from the main light harvesting antenna, we see a slow exponential-like decay of the excitation. This is in contrast to the oscillations and a relatively fast transfer that usually occurs when initialization at sites 1 or 6 is considered. We show that different values of the electronic transition energies found in the literature can lead to large differences in the transfer dynamics and may cause additional * To whom correspondence should be addressed † Max-Planck-Institut

A master equation, derived from the non-Markovian quantum state diffusion (NMQSD), is used to calculate excitation energy transfer in the photosynthetic Fenna-Matthews-Olson (FMO) pigmentprotein complex at various temperatures. This approach allows us to treat spectral densities that contain explicitly the coupling to internal vibrational modes of the chromophores. Moreover, the method is very efficient, with the result that the transfer dynamics can be calculated within about one minute on a standard PC, making systematic investigations w.r.t. parameter variations tractable. After demonstrating that our approach is able to reproduce the results of the numerically exact hierarchical equations of motion (HEOM) approach, we show how the inclusion of vibrational modes influences the transfer.

Electronic-vibrational dynamics in molecular systems that interact with an environment involve a large number of degrees of freedom and are therefore often described by means of open quantum system approaches. A popular approach is to include only the electronic degrees of freedom into the system part and to couple these to a non-Markovian bath of harmonic vibrational modes that is characterized by a spectral density. Since this bath represents both intra-molecular and external vibrations, it is important to understand how to construct a spectral density that accounts for intra-molecular vibrational modes that couple further to other modes. Here, we address this problem by explicitly incorporating an intra-molecular vibrational mode together with the electronic degrees of freedom into the system part and using the Fano theory for a resonance coupled to a continuum to derive an "effective" bath spectral density, which describes the contribution of intra-molecular modes. We compare this effective model for the intra-molecular mode with the method of pseudomodes, a widely used approach in simulation of non-Markovian dynamics. We clarify the difference between these two approaches and demonstrate that the respective resulting dynamics and optical spectra can be very different.