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The infrared bar-spectrum of a single ammonia molecule encapsulated innano-cage C$_{60}$ fullerene molecule is modelled using the site inclusionmodel successfully applied to analyze spectra of CO$_2$ isotopologues isolatedin rare gas matrix. Calculations show that NH$_3$ can rotate freely on a sphereof radius 0.184 $\text{\AA}$ around the site centre of the nano-cage and spinfreely about its C$_3$ symmetry axis. In the static field inside the cagedegenerate $\nu_3$ and $\nu_4$ vibrational modes are blue shifted and split.When dynamic coupling with translational motion is considered, the spectralsignature of the $\nu_2$ mode is modified with a higher hindering barrier (2451cm$^{-1}$), an effective reduced mass (6.569 g.mol$^{-1}$) and a longertunneling time (55594 ps) for the fundamental level compared to gas-phasevalues (2047 cm$^{-1}$), (2.563 g.mol$^{-1}$) and (20.85 ps). As a result thismode is red shifted. Moreover, simulation shows that the changes in thebar-spectrum of the latter mode can be used to probe the temperature of thesurrounding media in which fullerene is observed.

Trapping effects on the vibration-inversion-rotation motions of an ammonia molecule encapsulated in C$_{60}$ fullerene molecule