  Fullerenes, including C60, C70, and C60+, are widespread in space through
their characteristic infrared vibrational features (C60+ also reveals its
presence in the interstellar medium through its electronic transitions) and
offer great insights into the carbon chemistry and stellar evolution. The
potential existence of fullerene-related species in space has long been
speculated and recently put forward by a set of laboratory experiments of C60+,
C60H+, C60O+, C60OH+, C70H+, and [C60-Metal]+ complexes. The advent of the
James Webb Space Telescope (JWST) provides a unique opportunity to search for
these fullerene-related species in space. To facilitate JWST search, analysis,
and interpretation, an accurate knowledge of their vibrational properties is
essential. Here, we compile a VibFullerene database and conduct a systematic
theoretical study on those species. We derive a set of range-specific scaling
factors for vibrational frequencies, to account for the deficiency of density
functional theory calculations in predicting the accurate frequencies. Scaling
factors with low root-mean-square and median errors for the frequencies are
obtained, and their performance is evaluated, from which the best-performing
methods are recommended for calculating the infrared spectra of fullerene
derivatives which balance the accuracy and computational cost. Finally, the
recommended vibrational frequencies and intensities of fullerene derivatives
are presented for future JWST detection.
