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.

We extract the site energies and spectral densities of the Fenna-Matthews-Olson (FMO) pigment protein complex of green sulphur bacteria from simulations of molecular dynamics combined with energy gap calculations. Comparing four different combinations of methods, we investigate the origin of quantitative differences regarding site energies and spectral densities obtained previously in the literature. We find that different forcefields for molecular dynamics and varying local energy minima found by the structure relaxation yield significantly different results. Nevertheless, a picture averaged over these variations is in good agreement with experiments and some other theory results. Throughout, we discuss how vibrations-external or internal to the pigment molecules-enter the extracted quantities differently and can be distinguished. Our results offer some guidance to set up computationally more intensive calculations for a precise determination of spectral densities in the future. These are required to determine absorption spectra as well as transport properties of light harvesting complexes.

We present a scheme to express a bath correlation function (BCF) corresponding to a given spectral density (SD) as a sum of damped harmonic oscillations. Such a representation is needed, for example, in many open quantum system approaches. To this end we introduce a class of fit functions that enables us to model ohmic as well as superohmic behavior. We show that these functions allow for an analytic calculation of the BCF using pole expansions of the temperature dependent hyperbolic cotangent. We demonstrate how to use these functions to fit spectral densities exemplarily for cases encountered in the description of photosynthetic light harvesting complexes. Finally, we compare absorption spectra obtained for different fits with exact spectra and show that it is crucial to take properly into account the behavior at small frequencies when fitting a given SD.