  The non-radiative electron-relaxation dynamics in C$_{60}$ molecule is
studied after selective initial photoexcitations. The methodology includes
nonadibabtic molecular simulation combined with time-dependent density
functional theory (DFT) and semi-classical surface hopping approach. Results of
treating the DFT exchange-correlation (xc) interaction by the non-empirical
Perdew-Burke-Ernzerhof (PBE), hybrid PBE0, and hybrid Becke 3-parameter
Lee-Yang-Parr (B3LYP) functional are compared. Even though some differences in
the details are found, all three functionals produce qualitatively similar
unoccupied band structures in the ground state. The model-dependent differences
in the ultrafast population dynamics, including the occurrences of transient
entrapment of population, are studied systematically. The trend of the results
demonstrates a universal dependence on the structure of unoccupied band
offering a spectroscopic route to probe this structure. Results can be
verified, as well as the best xc model for quantitative accuracy can be
determined, by comparing with ultrafast transient absorption or time-resolved
photoelectron spectroscopy measurements. From the computational standpoint, the
study facilitates method optimization to simulate nonadiabatic relaxation
dynamics in technologically important fullerene derivatives.
