# Confronting theoretical results of localized and additional surface plasmon resonances in silver nanoparticles with EELS measurements

## TL;DR

This paper develops a quantum model to explain large energy blueshifts and additional surface plasmon resonances in silver nanoparticles, aligning theoretical predictions with experimental EELS measurements.

## Contribution

It introduces a new quantum model that accurately predicts surface plasmon resonance energies and explains large blueshifts in silver nanoparticles.

## Key findings

- Derived size-dependent energy and line broadening of localized surface plasmons.
- Proposed a generation mechanism for additional surface plasmon resonances.
- Achieved excellent agreement between theoretical calculations and experimental data.

## Abstract

Raza et al. recently observed the extraordinarily large energy blueshifts of localized surface plasmon resonances and additional surface plasmon resonances in silver nanoparticles encapsulated in silicon nitride, which are not fully understood yet. By using the quantum model consisting of two subsystems respectively for describing the center of mass and intrinsic motions of conduction electrons of a metallic nanosphere and a coupling occurred between the center of mass and conduction electrons outside the metallic nanosphere, we firstly deduced the general energy and line broadening size-dependence of localized surface plasmon resonances, which removes the divergent defect of usual 1/R size-dependence. Secondly, we proposed that the additional surface plasmon resonance in a metallic nanosphere originates from the transition of the first excited state to the ground state of the center of mass subsystem with energy levels corrected by degenerate state pairs of the system composed of the center of mass and intrinsic motions of conduction electrons. Then, we implemented this generation mechanism of additional surface plasmon resonances for silver nanoparticles encapsulated in silicon nitride and the calculated results are well consistent with experimental results. Furthermore, we obtained a new energy expression of localized surface plasmon resonances, with which we successfully explained the extraordinarily large energy blueshifts of localized surface plasmon resonances in few-nanometer silver nanoparticles encapsulated in silicon nitride. Finally, we calculated the localized and additional surface plasmon resonance energies of silver nanoparticles resting on carbon films and the calculated results perfectly explain the experimental measurements of Scholl et al..