Capturing Plasmon-Molecule Dynamics in Dye Monolayers on Metal Nanoparticles Using Classical Electrodynamics with Quantum Embedding

A multiscale hybrid quantum/classical approach using classical electrodynamics and a collection of discrete three-level quantum systems is used to simulate the coupled dynamics and spectra of a malachite green monolayer adsorbed to the surface of a spherical gold nanoparticle (NP). This method utilizes finite difference time domain (FDTD) to describe the plasmonic response of the NP within the main FDTD framework and a three-level quantum description for the molecule via a Maxwell/Liouville framework. To avoid spurious self-excitation, each quantum molecule has its own auxiliary FDTD subregion embedded within the main FDTD grid. The molecular parameters are determined by fitting the experimental extinction spectrum to Lorentzians, yielding the energies, transition dipole moments, and the dephasing lifetimes. This approach can be potentially applied to modeling thousands of molecules on the surface of a plasmonic NP. In this paper, however, we first present results for two molecules with scaled oscillator strengths to reflect the optical response of a full monolayer. There is good agreement with experimental extinction measurements, predicting the plasmon and molecule depletions. Additionally, this model captures the polariton peaks overlapped with a Fano-type resonance profile observed in the experimental extinction measurements. This technique can be generalized to any nanostructure/multichromophore system, where the molecules can be treated with essentially any quantum method.