The reaction mechanism of the Aza-Diels-Alder (A-D-A) cycloaddition reaction between X2C=NNH2, where X = H, F, Cl, Br, and 1,3-butadiene catalyzed by a PHCl2 Lewis acid was characterized using density functional theory calculations. The influences of various substituents of X on the studied reaction were analyzed using the activation strain model (ASM), which is also termed as the distortion interaction model. Calculations showed that the smallest and largest values of the activation energies belong to the substituents of F and Br, respectively. The activation energy of the studied reactions was decreased within 8.6 kcal.mol(-1) in the presence of PHCl2 catalyst. Investigations showed that the pnicogen bonding is adequately capable I of activating the A-D-A reaction. The quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analysis were implemented to understand the nature of C4,cbut center dot center dot center dot CxIm and C1,cbut center dot center dot center dot NXIm the energy decomposition analysis (EDA) based on the ETS-NOCV scheme was used to characterize the nature of C4,Cbut center dot center dot center dot CXIm and C1,Cbut center dot center dot center dot NXIm bond. The results of the study mirror the fact that the PHCl2 Lewis acid may be suggested as a simple suitable catalyst for experimental studies on the A-D-A reactions.