The photoabsorption spectra of a Xe atom encapsulated inside C$_{54}$, C$_{56}$, and C$_{58}$ fullerenes

The photoabsorption spectra of a Xe atom encapsulated inside C$_{54}$, C$_{56}$, and C$_{58}$ have been investigated using the time-dependent-density-functional-theory (TDDFT). The most stable isomers for these fullerenes are respectively, C$_{54}$ C$_{2v}$:540, C$_{56}$ C$_s$:864, and C$_{58}$ C$_{3v}$:1205. The stuctures of these fullerenes have been created using the Fullerene4.4 [1] package. The structures are then optimized using DMol$_3$ software. The absolute photoabsorption cross sections of C$_{54}$, C$_{56}$, C$_{58}$ and Xe@C$_{54}$, Xe@C$_{56}$, Xe@C$_{58}$ are evaluated using TDDFT. The results demonstrate that, except for the Xe atom inside C$_{58}$, which has similar confinement resonances as those of Xe@C$_{60}$, the Xe atoms inside C$_{54}$ and C$_{56}$ have totally different spectra. Because of this the measured spectra, with the loss of one or more pairs of C atoms, may be affected by the spectra of the Xe inside C$_{54}$ (or C$_{56}$, C$_{58}$). More discussions about the spectra of fullerenes and endohedral fullerenes will be presented at the conference.\\[4pt] [1] P. Schwerdtfeger et al J. Comput. Chem. 35 1508 (2013).