We present a model for the relaxation dynamics in perylene bisimide dimers, which is based on ab initio electronic structure and quantum dynamics calculations including effects of dissipation. The excited-state dynamics proceeds via a mixing of electronic states of local Frenkel and charge-transfer characters, which becomes effective upon a small distortion of the dimer geometry. In this way, it is possible to explain the fast depopulation of the photoexcited state, which we characterize by femtosecond transient absorption measurements. The combined theoretical and experimental analysis hints at a trapping mechanism, which involves nonadiabatic and dissipative dynamics in an excited-state vibronic manifold and provides an atomistic picture that might prove valuable for future design of photovoltaic materials.