The term "wolfium bond" is employed to denote attractive interactions between group 6 elements and electron-rich moieties. A theoretical investigation of the wolfium bond involving the compounds WnF4O or WnF2O, where Wn represents Cr, Mo or W, and π systems such as C2H2, C2H4 and C6H6, was conducted using density functional theory (DFT) at the ωB97XD/aug-cc-pVTZ level of theory. Interaction energies range from -3.74 to -10.86 kcal/mol upon formation of the π-Wn bond. The electrostatic contributions to the interaction energy were found to be dominant. Notably, the WnF4O system exhibits greater stability than its WnF2O counterpart, with the exception of the CrFxO system. The charge transfer between the interacting molecules lies between 0.0114 and 0.0946e in magnitude. The predominant type of orbital interaction is πC-C→BD*Wn-O. Our theoretical investigation revealed the presence of weak, but significant, wolfium bonds between group 6 elements and electron-rich π systems.