Effects of inter-fullerene $\pi $-band mixings in the photoexcitation of hybrid plasmons in the C$_{60}$@C$_{240}$ molecule

We perform a detailed study of the ground state electronic structure of a two-layer fullerene onion molecule C$_{60}$@C$_{240}$. Calculations are carried out in a quantum mechanical framework of local density approximation (LDA) where the onion's ion-core of sixty C$^{4+}$ ions from C$_{60}$ and two hundred and forty of those from C$_{240}$ is smeared into a classical jellium distribution [1]. Significant inter-fullerene mixing between the bands of single-node radial symmetry, the $\pi $-bands, is found. We then compute the photoionization from all the levels of the system using a time-dependent version of LDA at photon energies where the ionization is dominated by the inter-layer hybridization of collective plasmon resonances [2]. It is determined, by comparing the isolated fullerene cross sections with the cross section of the onion system for both $\pi $ and $\sigma $ (having nodeless radial waves) symmetry, that the $\pi $-band mixing is predominantly responsible for the production of plasmon hybrids.\\[0pt] [1] M.E. Madjet, H.S. Chakraborty, J.-M. Rost, and S.T. Manson, \textit{J. Phys.} B \textbf{41}, 105101 (2008);\\[0pt] [2] M.A. McCune, R. De, M.E. Madjet, H.S. Chakraborty, and S.T. Manson, \textit{J. Phys.} B Fast Track Comm. \textbf{44}, 241002 (2011).