Simulating Electronically Nonadiabatic Dynamics via the Generalized Quantum Master Equation
An important group of chemical reactions are those that involve the transfer of energy within or between molecules. These types of reactions include vibrational and electronic relaxation, oxidation-reduction reactions, charge transfer, and optical response and are pertinent to many technologically- and biologically-relevant processes, such as in photovoltaics and photosynthetic systems. Quantum dynamical effects play a central role in these important processes that take place in molecular condensed phase systems. As a result, the simulation of quantum dynamics in such systems remains one of the most important challenges facing computational chemistry. Theoretically, Schrödinger's equation can simulate quantum dynamics for these systems. However, the exponential scaling of the computational cost with system dimensionality makes the numerically exact simulation of quantum dynamics in complex molecular systems non-feasible, with the important exception of a subclass of Hamiltonians whose form makes such an exact simulation possible. Because of this, many methods involving approximations have been proposed to simulate quantum dynamics in the condensed phase.
The generalized quantum master equation (GQME) is arguably the most general framework for simulating electronically nonadiabatic reduced dynamics, as it requires no approximations in its derivation and has the ability to capture the full electronic density matrix. The GQME-based methodology fills a gap which is not addressed by currently available methods for simulating electronically nonadiabatic dynamics. Methods based on Marcus theory, Fermi's golden rule, or the Redfield equation require assuming weak electronic coupling between donor and acceptor states while direct application of quasiclassical methods that can handle strong coupling, such as Ehrenfest, linearized semiclassical, or the mixed quantum-classical Liouville methods, often have decreasing reliability and/or computational feasibility with increasing simulation time. The GQME-based methodology allows one to restrict the dynamical input to short times via the memory kernel while providing a unified framework that can describe a wide range of electronic coupling strengths. As such, it capitalizes on the advantages of both alternative approaches without suffering from the corresponding disadvantages.
For a short video about my research, you can view my Lightning Talk from the 2020 Virtual Conference in Theoretical Chemistry.