In [A•H + •B] clusters, the dispersion interactions between the two tethered molecular fragments have not been extensively studied. To assess the necessity for dispersion corrections, we took the H 5 O 2 + ion as an example and investigated the dependence of vibrational frequencies on dispersion interaction corrections. The dispersion interaction corrections are taken into account with the Becke-Johnson D3 correction scheme and the results are in Table . We find that for the frequency of the PTM in H 5 O 2 + , dispersion interaction corrections can lead to a blue shift of about 100 cm -1 . This shift is not negligible, however, it also causes the frequency to diverge from the reference value of CCSD(T), which may indicate that the original ωB97X with the aug-cc-pVDZ basis set benefits from a delicate error cancellation and adding dispersion corrections breaks the balance and introduces larger errors to the electronic parts. Furthermore, as noted by Ref. 49, the inclusion of dispersion with most functionals could yield large errors for hydrogen bonded systems. Consequently, we did not incorporate dispersion interaction corrections in our calculations.