Accurate ab initio calculations at the B3LYP/6-311+G** level have been performed on anionic and neutral structures of 4,5-dihydro-5-oxo-[1,2,4]triazolo[1,5-a]pyrimidine, 4,7-dihydro-7-oxo-[1,2,4]triazolo[1,5-a]pyrimidine, and 4,5-dihydro-7-amino-5-oxo-[1,2,4]triazolo[1,5-a]pyrimidine compounds. The quality of the theoretical results has been tested against the experimental X-ray structures for the three most stable neutral forms, yielding very good agreement. The electronic properties of the anionic forms have been evaluated by means of the atoms in molecules theory (AIM) and electrostatic potential analyses, allowing the rationalization of the coordination mode preferences observed experimentally for the anions. Moreover, a theoretical study of the tautomerism for the neutral forms has also been made, by energetic, geometrical and NMR chemical shift (GIAO method) calculations. The results gave the protonated forms at the N₄ atom as the most stable ones, corroborated by the experimental geometries and the NMR data. In addition, the preferred coordination mode at the N₃ atom, against N₁ or the carbonyl oxygen, is also discussed.