Plasmonic-Quantum and Emitter's Finite-Size Effects in Plasmon-Emitter Coupling: A QHT-DFT Hybrid Approach.

We implement a hybrid scheme that combines time-dependent density functional theory (TDDFT) with quantum hydrodynamic theory (QHT). Using TDDFT, we capture the transition charge density of a p-nitroaniline (PNA) molecule, which translates into a realistic field distribution used to excite the QHT-treated plasmonic systems. This facilitates the investigation of plasmonic quantum effects and the emitter's spatial extent in plasmon-emitter interactions. As a result, we compare the emission properties of the PNA and a point dipole (PD) in plasmonic dimer gaps. Significant discrepancies are observed in both the oscillator strengths of the emission rates and the spectral positions of the prominent modes in the PNA- and PD-based models when the dimer gap size is smaller than approximately 3.2 nm. These discrepancies are attributable to the spatial extent of the PNA molecule. The gap at which quantum-tunneling-induced emission quenching begins is observed to be three times larger in the PNA-based system than in the PD-based one. We study these phenomena by progressively introducing the quantum effects, starting from the local response approximation, moving to the nonlocal Thomas-Fermi hydrodynamic theory, and ultimately extending to the full QHT.