Theory of Jahn Teller signatures in the infrared absorption of C$_{60}^{3-}$

Among the molecular superconductors, trivalent fullerides such as Cs$_{3}$C$_{60}$, with three folded degenerate HOMO and a fully ordered pressure induced superconductor-insulator are still intriguing. The orbital degeneracy of the fulleride ion C$_{60}^{-3}$ implies that besides a Jahn-Teller distorted state with S=1/2 and high-lying spin (S=3/2) excitation known from NMR, another undetected orbital excitation with S=1/2 should exist. Building upon accurate density hybrid functional theory calculations where properties such as the infrared (IR) spectrum and its Jahn-Teller features are well described, we extracted the {\sc ab-initio} orbital and spin spectrum of a C$_{60}^{-3}$ ion in different spin and orbital states including a new low lying L=2 S=1/2 excitation. Despite a Jahn-Teller distortion so small to be observable in its IR spectrum, this state is found to gain a large zero-point energy, placing it just above the L=1, S=1/2 ion ground state, and way below the L=0, S=3/2 high lying excitation. We can now elegantly explain the surprising early thermal disappearance of the low-temperature Jahn-Teller IR spectral features and splitting without a concurrent rise of spin susceptibility that would instead be required by population of the high spin S=3/2 excitation.