In order to study the exciton transfer dynamics, we employ the time non-local quantum master equation to calculate the reduced density matrix with time evolution in pentacene and tetracene crystals. Firstly, we assign the parameters for the three-state models (the four-state model with parameters are described in the Supporting Information). We consider two pentacene molecules with the same site energies, i.e., ϵ 1 = ϵ 2 . The energy gap between the singlet excited states and the triplet-pair state is 850 cm -1 , thus, we have ϵ 1 -ϵ 3 = ϵ 2 -ϵ 3 = 850 cm -1 . Moreover, we assume the Holstein vibrational mode with frequency Ω H = 1013 cm -1 and Peierls mode of frequency Ω P = 177 cm -1 , respectively. We also assign the electronic coupling of two singlet states U 12 = 150 cm -1 and the vibronic coupling strength λ 12 = 50 cm -1 . Based on the ab-initio calculations, we assign the weak electronic couplings between singlet and triplet-pair states, U 13 = U 23 = 6 cm -1 . We set λ 13 = λ 23 = 150 cm -1 . The intramolecular vibration is linearly coupled to the electronic states, the corresponding vibronic coupling strengths are set to κ 1 = -300 cm -1 , κ 2 = -200 cm -1 and κ 3 = 300 cm -1 , respectively. According to the