Multiexciton generation processes, in which multiple charge carriers are generated from a single photon, are of significant interest for achieving efficiencies beyond the Shockley-Queisser limit of conventional p-n junction solar cells. One well-studied multiexciton process is singlet fission, whereby a singlet exciton decays into two spin-correlated triplet excitons. In this talk I will present a newly developed computational approach to calculate the coupling terms and rates dominating this process from an ab initio Green’s function formalism based on many-body perturbation theory within the GW approximation and the Bethe-Salpeter equation approach. This method allowed the discovery of a new, purely-Coulombic, symmetry-allowed exciton decay mechanism involving a bright singlet exciton initial state and a final state consisting of two non-equivalent but nearly-degenerate triplets of nonzero, equal and opposite, center-of-mass exciton momenta. For such a process, the new method predicts a singlet-fission rate in very good agreement with available experimental data, indicating the importance of the studied decay channel in the process. This analysis elucidates the role of symmetry in singlet fission and shows that not only energy conservation, but inversion symmetry, the number of symmetry-inequivalent molecules in a unit cell, and the parity of each finite-momentum excited state play a central role in determining the singlet fission rates in crystals.