Our theoretical study of stability and reactivity was carried out on six (06) molecules of a series of pyrimidine tetrazole hybrids (PTH) substituted with H, F, Cl, Br, OCH3 and CH3 atoms and groups of atoms using the density function theory (DFT). Analysis of the thermodynamic formation quantities confirmed the formation and existence of the series of molecules studied. Quantum chemical calculations at the B3LYP / 6-311G (d, p) level of theory determined molecular descriptors. Global reactivity descriptors were also determined and analyzed. Thus, the results showed that the compound PTH_1 is the most stable, and PTH_5 is the most reactive and nucleophilic. Similarly, the compound PTH_4 is the most electrophilic. The analysis of the local descriptors and the boundary molecular orbitals allowed us to identify the preferred atoms for electrophilic and nucleophilic attacks.