Exciton dynamics at an interface between an electron donor, rubrene, and a C(60) acceptor is studied by nonadiabatic quantum molecular dynamics simulation. Simulation results reveal an essential role of the phenyl groups in rubrene in increasing the charge-transfer rate by an order-of-magnitude. The atomistic mechanism of the enhanced charge transfer is found to be the amplification of aromatic breathing modes by the phenyl groups, which causes large fluctuations of electronic excitation energies. These findings provide insight into molecular structure design for efficient solar cells, while explaining recent experimental observations.