Electronic energy transfer in model photosynthetic systems: Markovian vs. non-Markovian dynamics

A simple numerical algorithm for solving the non-Markovian master equation in the second Born approximation is developed and used to propagate the traditional dimer system that models electronic energy transfer in photosynthetic systems. Specifically, the coupled integro-differential equations for the reduced density matrix are solved by an efficient auxiliary function method in both the energy and site representations. In addition to giving exact results to this order, the approach allows us to access the range of the reorganization energy and decay rates of the phonon auto-correlation function for which the Markovian Redfield theory and the second-order approximation is useful. For example, the use of Redfield theory for lambda > 10 cm(-1) in Fenna-Mathews-Olson (FMO) type systems is shown to be fundamentally inaccurate.