The ro-vibrational spectroscopy of CH5+

I shall present methods for computing ro-vibrational energy levels of floppy molecules and results for CH₅⁺.   Ro-vibrational energy levels of CH5⁺ are determined by fixing stretch coordinates, using a simple product basis, exploiting symmetry, and carefully parallelizing the calculation.   They are compared with the experimental ground state combination differences of Asvany et al. [Science, 347 1346 (2015)].    If the assignment of Asvany et al. is correct, there are important differences between the levels we compute and those observed.   We propose a different assignment of the experimental levels that reduces the maximum error from 34 to 2 cm^-1.  The new assignment can only be correct if states of both parities exist in the experiment.   Although, ro-vibrational levels of   CH₅⁺   cannot be associated with individual vibrational states, they do occur in blocks separated by gaps.