Protonated methane (CH + 5 ) is a strongly nonrigid molecular system. Its vibrational spectra and molecular structure and dynamics were extensively investigated. The availability of experimental data makes this highly flexible system a good test target for assessing theoretical vibrational spectra. We have done a series of simulations in different variants (WS, SWS and MBS) similar to those for benzene, as described above. Technical details are provided in ESI. Experimental vibrational spectra of CH + 5 were measured earlier using action spectroscopy , monitoring the yield of the OCOH + cation according to the reaction