<p>Weakly bound complexes of inert gas atoms with aromatic rings have received the attention because these are important for understanding the several solution- and condensed-phase properties. Extrapolated complete basis set (CBS) limit interaction energies for van der Waal complexes of benzene with He, Ne and Ar were calculated by using MP2 level and B2PLYPD3 and M06-2X functionals, employing aug-cc-pVTZ basis set. It was observed that as the size of inert gas increases, the interaction energy becomes more negative suggesting more stabilizing interaction. In sandwich complexes, the magnitude of CBS interaction energies was found to be double when compared to benzene complexes. The calculated vibrational stretching frequencies of cationic benzene complexes show red-shift, whereas almost same frequencies are found in sandwich complexes, with respect to benzene–X (X = He, Ne and Ar) complexes. However, in deuterated benzene–X complexes, the C–D stretching frequencies show a decrease in frequency value compared to benzene–X complexes and this may due to the presence of deuterated atom. Apart from that, the complexes, (benzene)⁺⁺–X dication and X–(benzene)⁺–X sandwich cation were also studied using MP2/aug-cc-PVTZ level. It is observed that the charge is increased when moving from (benzene)⁺–X to (benzene)⁺⁺–X complexes, the strength of interaction is increasing. Further, the nature of interaction present in benzene–X complexes was investigated by energy decomposition analysis using SAPT analysis. The SAPT analysis revealed that the contribution from dispersion terms is increasing when moving from He to Ar complexes.</p> Graphical abstract <p></p>