We show by means of density-functional-theory (DFT) calculations that dissociative adsorption bonding of imidazole is feasible on copper-oxide surfaces, but it differs considerably from that of 1,2,3-triazole and tetrazole (these three molecules can be seen as archetypal models of azole corrosion inhibitors). While for the latter two dissociative adsorption proceeds via the cleavage of the N-H bond leading to a strongly bonded molecule adsorbed upright on the surface with two N atoms, such a mode is unfavorable for imidazole due to its incompatible molecular geometry, because it has the two N atoms on opposite sides of the molecule. Instead, imidazole may adsorb dissociatively via either the cleavage of the C-H bond (in an upright adsorbed geometry) or the cleavage of the N-H bond in a lying down geometry; among the two possibilities, C-H dissociation is thermodynamically superior to the "lying down" N-H dissociation. Calculations further indicate that for triazole and tetrazole the C-H dissociative mode is also viable, because it is similar in stability to the N-H dissociative mode. However, there exists a notable difference between the two dissociation modes: while N-H dissociation of triazole and tetrazole is barrierless (or almost so) at oxygen vacancy sites on copper-oxide surfaces, the respective barrier for C-H dissociation of imidazole is 1.1 eV and is therefore kinetically hindered. We also investigate the C-H dissociation mode of imidazole on zinc and aluminum surfaces. We find that these are less reactive toward molecular C-H bond cleavage in most considered cases, with zinc being moderately less reactive and aluminum considerably less reactive than copper.