Despite a large number of experimental studies, the adsorption structure of benzene C6H6 on the (111) surface of platinum is still a matter of debate. In this study, results from first principles Density functional periodic calculations are presented, including the total energy and the simulation of vibrational spectra. Among the six high-symmetry adsorption modes for the molecule, the most stable one corresponds to a bridge site, the C-C bonds in benzene being rotated by 30degrees with respect to the atomic directions on the surface. The adsorption of the hollow site (rotated by 0degrees) is less stable by about 0.2 eV, Upon adsorption, the amplitude of the distortion of the molecule and the strength of its interaction with the surface are correlated since they are linked by the variation of the molecular HOMO-LUMO gap. The calculation of the vibrational spectra confirms the total energy results since the bridge structure that is rotated 30degrees is the only one that is able to reproduce all of the measured bands, and they suggest that the hollow structure could be a minority species. This analysis is consistent with the results obtained from scanning tunneling microscopy, but they contrast with the structure proposed from a low-energy electron diffraction experiment.