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The Osme bond is defined as pairing a Group 8 metal atom as an electron acceptor in a noncovalent interaction with a nucleophile. DFT calculations with the ωB97XD functional consider MO₄ (M = Ru, Os) as the Lewis acid, paired with a series of π electron donors C₂H₂, C₂H₄, C₆H₆, C₄H₅N, C₄H₄O, and C₄H₄S. The calculations establish interaction energies in the range between 9.5 and 26.4 kJ/mol. Os engages in stronger interactions than does Ru, and those involving more extensive π-systems within the aromatic rings form stronger bonds than do the smaller ethylene and acetylene. Extensive analysis questions the existence of a true Osme bond, as the bonding chiefly involves interactions with the three O atoms of MO₄ that lie closest to the π-system, via π(C-C)→σ*(M-O) transfers. These interactions are supplemented by back donation from M-O bonds to the π*(CC) antibonding orbitals of the π-systems. Dispersion makes a large contribution to these interactions, higher than electrostatics and much greater than induction.