The constitutional isomers and tautomers of oxadiazolones, as well as their mono- and disulfur analogues, were calculated at the B3LYP/aug-cc-pVDZ level. Four groups of 30 molecules each were considered: oxadiazolone, oxadiazolthione, thiadiazolone, and thiadiazolthione isomers. The compounds were categorized into six groups according to permutations of three heteroatoms in the five-membered ring. Additionally, each of the constitutional isomer was considered to have five tautomers conserving stable five-membered ring: two NH tautomers, two rotameric OH (or SH) forms and one CH2 tautomer. It appeared that the largest difference between oxadiazolone O and S analogues is produced by the kind of chalcogen atom in the ring, which is strained when the O atom is in the ring while much less strained when the S-atom, of much larger van der Waals radius, is built into the ring. The external chalcogen is only modifying the general energetic factors. The comparison of energetics of analogous groups of molecules with thiadiazole and oxadiazole rings is done in details as well as differences resulting from different external chalcogen atoms are discussed as well. The presence of water surrounding was mimicked with the IEF-PCM implicit water model which did not change general isomer relative stability picture, but for some special cases indicated an extra stability of the forms with external OH or SH groups. The aromaticity monitored by the structural HOMA aromaticity index shows that the systems are not additionally stabilized by pi-electron delocalization. The fair linear correlation between the aromaticity indices of oxadiazolones and oxadiazolthiones shows that the pi-electron system in the studied systems is not sensitive to change of the external chalcogen group.