Great advances have been made during the past two decades in characterization of molecular excitons and their quantum transitions in complex molecular environments. To this end, depending on the nature of systems and environments, the dynamics of excitons can be characterized by rates or more complete quantum dynamical description. For the calculation of rates of exciton transfer and decay, Fermi’s golden rule (FGR) has been widely and successfully used for various molecular systems. However, in its applications to complex molecular systems, there are some ambiguities and issues requiring further refinement and development of FGR. I will provide a short summary of our FGR-based theories of resonance energy transfer and nonradiative energy gap law behavior that can account for new quantum effects that were missing in previously established theories. Applications of some of these to light harvesting complexes and organic molecular aggregates are demonstrated as well. For transitions that go beyond simple rate description, (quantum) master equation has been successful in many cases. I will provide a general overview of these quantum approaches we have been pursuing such as polaron transformed quantum master equation. For driven quantum dynamical processes involving excitons such as in quantum control and quantum sensing, accurate dynamics calculation of quantum systems driven by time dependent Hamiltonian is essential. However, efficient implementations of such calculations are in general challenging and may incur artifacts if not done correctly. Magnus expansion provides a formally superior starting point in this respect since any finite truncation approximation remains unitary. I will present simple and straightforward general quantum propagators based on the Magnus expansion we have recently developed, and their applications for quantum dynamics calculations of driven exciton systems.
