Which resonances in small metallic nanoparticles are plasmonic?

We use time-dependent density functional theory to examine the character of various resonances corresponding to peaks in the optical response of small metallic nanoparticles. Each resonance has both "sloshing" and "inversion" character. The sloshing mode is an oscillation in the occupation of the shells nearest the Fermi energy, transferring charge back and forth from below the Fermi level to above it. It results in oscillation in charge density near the surface of the particle. Inversions monotonically move charge from occupied to unoccupied states, and result in oscillation in charge density in the core of the particle. We also discuss the dependence of the optical response on the size of the simulation grid, noting that the character of resonances appears stable with respect to changes in simulation size, even though the details of the spectrum change. This makes a reliable characterization possible. We consider what characteristics are important in deciding that a resonance is plasmonic.