Green Hydrothermal Synthesis of 5-Phenyl-1H-tetrazole through Cycloaddition [3 + 2] Using Co(II) as Catalyst: Statistical Optimization by Response Surface Methodology (RSM) and DFT Calculations

5-Phenyl-1H-tetrazole (5-PHTA) and its derivatives exhibit relevant properties in pharmacology, corrosion, and coordination chemistry. In this work, a new methodology was proposed to obtain 5-PHTA under hydrothermal conditions using the [3 + 2] cycloaddition reaction between C₆H₅CN and NaN₃, with Co-(CH₃COO)₂·4H₂O as the catalyst and water as the solvent. This new method is an ecological and economical alternative that utilizes water instead of traditional organic solvents, such as DMSO, DMF, ethyl acetate, and <i>n</i>-hexane, for the synthesis and purification of 5-PHTA, reducing the E-factor and carbon footprint. The yield of the reaction was optimized by applying the statistical technique RSM on variables <i>A</i> (molar ratio C₆H₅CN/NaN₃), <i>B</i> (molar ratio Co²⁺/NaN₃), and <i>C</i> (reaction time), where the coordinates <i>A</i> = 2.09, <i>B</i> = 0.48, and <i>C</i> = 6.29 h produced a maximum yield of 81%. 5-PHTA structure was confirmed by single-crystal X-ray diffraction, ¹H-NMR, elemental analysis, FT-IR, and UV-vis. DFT calculations (B3LYP/def2-TZVP) were performed at 433.150 K and 1.45 atm, using water as the reaction solvent. The results demonstrate the crucial role of Co-(II) as a catalyst, via the formation of intermediates that are both kinetically and thermodynamically favored relative to the tested free-catalyst systems.