Macroscopic quantum electrodynamics approach to multichromophoric excitation energy transfer. I. Formalism

In this study, we develop a theory of multichromophoric excitation energy transfer (MC-EET) in the framework of macroscopic quantum electrodynamics. The theory we present is general for studying the interplay between energy transfer and fluorescence in the presence of arbitrary inhomogeneous, dispersive, and absorbing media. The dynamical equations of MC-EET, including energy-transfer kernels and fluorescence kernels, allow us to describe the combined effects of molecular vibrations and photonic environments on excitation energy transfer. To demonstrate the universality of the MC-EET theory, we show that under specific conditions, the MC-EET theory can be converted to three representative theories. First, under the Markov approximation, we derive an explicit Förster-type expression for plasmon-coupled resonance energy transfer [Hsu et al., J. Phys. Chem. Lett. 8, 2357 (2017)] from the MC-EET theory. In addition, the MC-EET theory also provides a parameter-free formula to estimate transition dipole-dipole interactions mediated by photonic environments. Second, we generalize the theory of multichromophoric Förster resonance energy transfer [Jang et al., Phys. Rev. Lett. 92, 218301 (2004)] to include the effects of retardation and dielectric environments. Third, for molecules weakly coupled with photonic modes, the MC-EET theory recovers the previous main result in Chance-Prock-Silbey classical fluorescence theory [Chance et al., J. Chem. Phys. 60, 2744 (1974)]. This study opens a promising direction for exploring light-matter interactions in multichromophoric systems with possible applications in the exciton migration in metal-organic framework materials and organic photovoltaic devices.