In this work, the hydrogenation of acetylene on the Pd 2 /g-C 3 N 4 catalyst is investigated by the Density Functional Theory (DFT) and Quantum Theory of Atoms in Molecules (QTAIM) calculations. The Prereactant (R), transition states (TSs), and the intermediates (IMs), involved in the hydrogenation process, are characterized from the point of view of energy and structure. The calculated energy barrier for the hydrogen transfer to the acetylene and ethylene are 6.77 and 12.28 kcal/mol, respectively which shows that the Pd 2 /g-C 3 N 4 catalyst has good selectivity for the conversion of acetylene to ethylene rather than ethane. Comparing the values of these energy barriers with those of the hydrogenation of acetylene on the Pd/g-C 3 N 4 catalyst (21.53 and 38.88 kcal/mol, respectively) shows that the increase in the number of the Pd atoms decreases the energy barriers of the hydrogenation reaction and increases the selectivity of the catalyst for the ethylene production.