  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.
