Superposition of quantum and classical rotational motions in $Sc2C2@C84$ fullerite

The superposition of the quantum rotational motion (tunneling) of the encapsulated $Sc2C2$ complex with the classical rotational motion of the surrounding $C84$ molecule in a powder crystal of $Sc2C2@C84$ fullerite is investigated by theory. Since the quantum rotor is dragged along by the $C84$ molecule, any detection method which couples to the quantum rotor (in casu the $C2$ bond of the $Sc2C2$ complex) also probes the thermally excited classical motion (uniaxial rotational diffusion and stochastic meroaxial jumps) of the surrounding fullerene. The dynamic rotation-rotation response functions in frequency space are obtained as convolutions of quantum and classical dynamic correlation functions. The corresponding Raman scattering laws are derived, and the overall shape of the spectra and the width of the resonance lines are studied as functions of temperature. The results of the theory are confronted with experimental low-frequency Raman spectra on powder crystals of $Sc2C2@C84$ [M. Krause et al, Phys. Rev. Lett. 93, 137403 (2004)]. The agreement of theory with experiment is very satisfactory in a broad temperature range.