  Singlet fission, a spin-allowed energy transfer process generating two
triplet excitons from one singlet exciton, has the potential to dramatically
increase the efficiency of organic solar cells. However, the dynamical
mechanism of this phenomenon is not fully understood and a complete,
microscopic theory of singlet fission is lacking. In this work, we assemble the
components of a comprehensive microscopic theory of singlet fission that
connects excited state quantum chemistry calculations with finite-temperature
quantum relaxation theory. We elaborate on the distinction between localized
diabatic and delocalized adiabatic bases for the interpretation of singlet
fission experiments in both the time and frequency domains. We discuss various
approximations to the exact density matrix dynamics and propose Redfield theory
as an ideal compromise between speed and accuracy for the detailed
investigation of singlet fission in dimers, clusters, and crystals.
Investigations of small model systems based on parameters typical of singlet
fission demonstrate the numerical accuracy and practical utility of this
approach.
