Valence Electron Density-Dependent Pseudopermittivity for Nonlocal Effects in Optical Properties of Metallic Nanoparticles

The peak positions of localized surface plasmonic resonance (LSPR) are strongly dependent on the sizes of metallic nanoparticles. TDDFT calculations have shown a remarkable size effect for metallic nanoparticles smaller than 1 nm, because it could account for fully nonlocal effects. Due to the high resource consumption of TDDFT, several semiquantum approaches have been proposed to reduce the computation time while addressing nonlocal effects, and it is still desirable to introduce new ideas into this area since physical origins of related fields are not completely known yet. In this work, we took account of both spilling out of s-band electrons and the screening effect of d-band electrons in the LSPR phenomena and developed a model using pseudopermittivity to describe several quantum mechanical effects that contribute to nonlocal effects in LSPR. With incorporation of machine learning, this model is capable of calculating the optical response of large nanostructures above the nanometer scale. Besides successful prediction for different metallic nanoparticle monomers, the tunneling effect occurring in dimers can also be well described by using the concept of pseudopermittivity. The employing of pseudopermittivity and machine learning is expected to achieve both high accuracy and high efficiency in quantum plasmonics. It provides a new ideology in the simulation of wave matter interactions.