Due to its importance for the function of organic optoelectronic devices, accurate simulations of the singlet exciton diffusion are crucial to predict the performance of new materials. We present a protocol which allows for the efficient directional analysis of exciton transport with high-level ab initiomethods. It is based on an alternative to the frequently employed rate equation since the latter was found to be erroneous in some cases. The new approach can be used in combination with the master equation which is considerably faster than the corresponding Monte Carlo approach. The long-range character of the singlet exciton coupling is taken into account by an extrapolation scheme. The approach is applied to singlet exciton diffusion in those substances where these quantities are experimentally best established: naphthalene and anthracene. The high quality of the crystals, furthermore, diminish uncertainties arising from the geometrical structures used in the computations. For those systems, our new approach provides exciton diffusion lengths L for naphthalene and anthracene crystals which show an excellent agreement with their experimental counterparts. For anthracene, for example, the computed L value in a direction is computed to 58 nm while the experimental value is 60 ± 10 nm.
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