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We show that the biomolecular exciton dynamics under the influence of slowpolarization fluctuations in the solvent cannot be described by approacheswhich are perturbative in the system-bath coupling. For this, we compareresults for the decoherence rate of the exciton dynamics of a resumedperturbation theory with numerically exact real-time path-integral results. Wefind up to one order in magnitude difference in the decoherence rate forrealistically slow solvent environments even in the weak coupling regime, whileboth results coincide for fast environmental noise. This shows explicitely thenonperturbative influence of the bioenvironmental fluctuations and might rendercurrent perturbative approaches to biomolecular exciton transport questionable.

Breakdown of perturbative weak coupling approaches for the biomolecular energy transfer