  Photoionization of two buckyonions, C$_{60}$@C$_{240}$ and C$_{20}$@C$_{60}$,
is investigated by means of time-dependent density-functional theory (TDDFT).
The TDDFT-based photoabsorption spectrum of C$_{60}$@C$_{240}$, calculated in a
broad photon energy range, resembles the sum of spectra of the two isolated
fullerenes, thus illustrating the absence of strong plasmonic coupling between
the fullerenes which was proposed earlier. The calculated spectrum of the
smaller buckyonion, C$_{20}$@C$_{60}$, differs significantly from the sum of
the cross sections of the individual fullerenes because of strong geometrical
distortion of the system. The contribution of collective electron excitations
arising in individual fullerenes is evaluated by means of plasmon resonance
approximation (PRA). An extension of the PRA formalism is presented, which
allows for the study of collective electron excitations in multishell
fullerenes under photon impact. An advanced analysis of photoionization of
buckyonions, performed using modern computational and analytical approaches,
provides valuable information on the response of complex molecular systems to
the external electromagnetic field.
