  We propose and illustrate a quantum hydrodynamic (QHD) model for the
description of plasmonic oscillations in the $\rm C_{60}$ molecule. Although
simpler than competing approaches such as time-dependent density functional
theory (TDDFT), the model contains the key ingredients to characterize
plasmonic modes, namely the Hartree, exchange and correlation potentials, as
well as nonlocal, nonlinear and quantum effects to the lowest order. A
variational technique is used to solve analytically the QHD model for the case
of breathing (monopolar) plasmonic oscillations, revealing a bulk mode near the
plasmon frequency. Numerical simulations of both the QHD equations and a TDDFT
model confirm the existence of this mode and highlight a second collective mode
at lower energy. Such monopolar modes may be measured experimentally using
electron energy loss spectroscopy.
