  We develop a new first-principles approach to predict and understand rates of
singlet fission with an ab initio Green's-function formalism based on many-body
perturbation theory. Starting with singlet and triplet excitons computed from a
GW plus Bethe-Salpeter equation approach, we calculate the exciton--bi-exciton
coupling to lowest order in the Coulomb interaction, assuming a final state
consisting of two non-interacting spin-correlated triplets with finite
center-of-mass momentum. For crystalline pentacene, symmetries dictate that the
only purely Coulombic fission decay from a bright singlet state requires a
final state consisting of two inequivalent nearly degenerate triplets of
nonzero, equal and opposite, center-of-mass momenta. For such a process, we
predict a singlet lifetime of 40 to 150 fs, in very good agreement with
experimental data, indicating that this process can dominate singlet fission in
crystalline pentacene. Our approach is general and provides a framework for
predicting and understanding multiexciton interactions in solids.
