13C-substituted C60+: Predictions of the rotational spectra

C${}_{60}^{+}$ has recently been identified as the carrier of some of the diffuse interstellar bands (Campbell et al., 2015). Unfortunately, this ion has no dipole moment and therefore no rotational spectrum. We investigate the situation where one of the carbon atoms in this ion is substituted by a ¹³C-atom. This shifts the center of mass away from the center of charge, resulting in a non-zero dipole moment and thus opening the possibility of rotational spectroscopy in the microwave region. That the population of the singly substituted species is comparable to that of the parent isotopologue increases the expected intensity. One complication is that the Jahn-Teller effect may distort the molecule. We use density functional theory to consider this possibility and the rotational properties of the different isomers that would result.