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to molecular dimers of pentacene, a widely studied material that exhibits singlet fission in the crystal phase. We address a longstanding theoretical issue, namely whether singlet fission proceeds via two sequential electron transfer steps mediated by charge-transfer states or via a direct two-electron transfer process. We find evidence for a superexchange mediated mechanism, whereby the fission process proceeds through virtual charge-transfer states which may be very high in energy. In particular, this mechanism predicts efficient singlet fission on the sub-picosecond timescale, in reasonable agreement with experiment. We investigate the role played by molecular vibrations in mediating relaxation and decoherence, finding that different physically reasonable forms for the bath relaxation function give similar results. We also examine the competing direct coupling mechanism and find it to yield fission rates slower in …