Pseudo-permittivity in simulation of nonlocal effects in optical properties of metallic nanoparticles - Chen, Chao (2018)
Metallic nanoparticles exhibit localized surface plasmonic resonance (LSPR) with peak energy dependent on particle size. Under the frame of classical electrodynamics, this size effect would diminish for nanoparticles whose dimension is much shorter than the wavelength of incident light, and quasistatic approximation can be applied. By the prediction of ab initio, however, remarkable LSPR peak shift with size variation can be observed for metallic nanoparticles with radius less than 10 nm, indicating the failure of classical approach at nanometer and sub-nanometric scale. In this work, we systematically studied three quantum effects (s-band electron spilling out, d-band electron screening and surface atom relaxation) that may cause failure of classical electromagnetic models in contrast simulations. We also proposed a machine learning enhanced semi-classical semi-quantum approach, valence electron density dependent pseudo-permittivity model. This new model describes ground state valence electron densities by incorporating s-band electron spilling out effect and d-band screening effect into shell region and core region of metallic nanoparticles and successfully predicted different trends in size dependent peak shifts in LSPR for dissimilar metallic nanoparticles. The core-shell description of nanoparticles can also be used to explain quantum tunneling effect, and has good prediction of charge transfer plasmons in dimer systems. For very large plasmonic systems, our model can be accelerated by machine learning algorithms without losing accuracy. The optical spectra got from this model show excellent agreements with ab initio calculations, and the extrapolation of LSPR energies to nanometer scale also agrees classical electrodynamics. The employ of core-shell model and machine learning approach are expected to eliminate the long-existing contradiction of accuracy and efficiency in quantum plasmonics, providing a new ideology in simulation of wave-matter interactions for manometer and sub-nanometric scaled metallic nanostructures.