Hydroxamic acids, best known as iron chelators, have recently been widely used as a key functional group of potential therapeutics targeting at zinc-bound matrix metalloproteinases involved in cancers. To investigate the optimal structural variations of hydroxamic acids that confer the maximal selectivity for zinc over iron for rational design of cancer drugs, we have first performed calculations of hydroxamic acids in the absence of metal ions employing density functional, Moller-Plesset, and coupled cluster theories. Herein we report the high-level ab initio calculations of hydroxamic acids that offer new insights into the intricate structures of acetohydroxamic acid. The results suggest that in the gas phase acetohydroxamic acid exists in the E- and Z-keto forms and the Z-iminol form that are in equilibrium, whereas the deprotonated acetohydroxamic acid exists in the nitrogen-deprotonated Z-keto form and the C-hydroxy oxygen-deprotonated Z-iminol form that are in resonance. Substitution of the nitrogen proton of acetohydroxamic acid by a methyl group does not change the structures and relative stability of the neutral and deprotonated acetohydroxamic acid in different configurations and tautomers.