Unveiling the effect of electron tunneling on the plasmonic resonance of closely spaced gold particles.

Recent experimental techniques enable the nanoparticles' (NPs) ensembles to be made with an angstrom-level of interparticle gap widths. The theoretical description of their optical properties becomes more challenging because of the nonnegligible quantum mechanism (QM) effects such as electron tunneling and nonlocal screening. To demonstrate the microscopic mechanism of QM effects and quantitatively elucidate their impact on a variety of surface plasmon resonance (SPR) models of gold particle oligomers, in this work we performed a theoretical study on closely spaced Au cluster dimers and NP oligomers by the first-principles approach, and the classical or quantum-corrected electromagnetic models (CEM or QCM), respectively. Through the first-principles calculation on a series of AuN dimers with different interparticle distances d and N, we depicted the variation of the possibility of direct electron tunneling (DET) across the junction constructed by two nearest NPs with d and N, and found that it exactly follows an exponential decay and the decay rate linearly varies with 1/N. The impact of the QM effect on the SPR models excited along the dimer axis is much more profound than those perpendicular to the dimer axis. CEM/QCM calculations on strongly coupled NP dimers and symmetric and asymmetric trimers demonstrated the evolution of their optical properties with variable NP sizes, gap separations and light polarization, as well as the QM effect on the major SPR modes. The side-by-side comparison between the results from time-dependent density functional theory and CEM/QCM models sheds light on understanding the origin of a variety of SPR models of gold NP oligomers and the QM effect on those modes, and makes a connection between the calculations of small cluster and large NP oligomers.