Self-Consistent Diagrammatic Theory of Energy Migration and Trapping on Spherical Nanoparticles

Abstract We present, for the first time, a comprehensive theoretical model that elucidates multistep energy migration, including its remigration in the donor ensemble, followed by nonradiative excitation transfer to acceptors, on a finite-radius spherical nanoparticle labeled with both donors and acceptors. Using a three-body diagrammatic method, we derive the most general expressions for donor fluorescence decay and emission anisotropy decay. These expressions account for the intricate dynamics of energy transfer processes within the nanoparticle environment. To validate our theoretical framework, we performed extensive Monte Carlo simulations on a representative donor–acceptor system positioned on a spherical nanoparticle. These simulations thoroughly evaluate the model predictions across varying donor and acceptor configurations. The theoretical predictions and Monte Carlo results show excellent agreement, demonstrating the model’s accuracy in capturing the complex dynamics of energy migration and transfer. This study advances our understanding of energy transfer in nanoscale systems and highlights the power of combining theoretical modeling with Monte Carlo simulations to predict the optical properties and dynamics of nanoparticle-based donor–acceptor assemblies, and shows a clear advantage over the simplified model based on Padé approximant.