Semi-empirical equilibrium molecular structure of benzene has been determined previously from experimental rotational constants and calculated vibrational corrections at the coupled cluster level of theory. In this work we have tested several types of simulations (see ESI for details) at the PBEh-3c level of theory. From WS+MD simulations we have computed vibrational corrections to rotational constants to be B e -B 0 = 0.192 ± 0.01 m -1 and C e -C 0 = 0.083 ± 0.004 m -1 . 12 C 6 1 H 6 benzene is an oblate symmetric top molecule, thus the A = B rotational constants cannot be obtained directly from experiment. For the C-constant our vibrational correction is in reasonable agreement with the reference theoretical value of 0.14 m -1 obtained at the very high level. Further, experimental vibrational IR spectra of benzene were taken from NIST Chemistry WebBook and compared with calculated in this work, see Figure . The averaged IR spectra from SWS-AT+MD and WS+MD reproduce all experimental bands. MBS-AT+MD underestimates intensity for the overtones in the 1700-2000 cm -1 range (not shown in the harmonic and VPT2 plots). It is interesting to discuss the C-H stretching region, corresponding to vibrations with highest Debye temperature in benzene. In MBS-AT+MD the position of the corresponding peak at 3260 cm -1 is essentially the same as in the harmonic approximation (3262 cm -1 ). This is explained by underestimation of vibrational amplitudes in the classical MD treatment (see discussion of Equation ). WS+MD results in larger anharmonic shift with the peak maximum at 3223 cm -1 . In SWS-AT+MD at both temperatures (0 and 300 K) this band is at 3185 cm -1 , the closest to the experimental value at about 3058 cm -1 . Notably, the MD models qualitatively correctly predict frequencies in the C-H stretching region around 3000 cm -1 , whereas in VPT2 calculation we obtained an unrealistically large anharmonic shift of 409 cm -1 for one of the modes. This VPT2 artifact probably arises from resonances, which have been discussed earlier. Overall, WS and SWS demonstrate a better agreement with experimental data in comparison to other tested methods.