  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..
