A theoretical investigation on the dimerization and trimerization of formaldehyde molecules has focused on the singlet potential energy surface. Based on the possible reaction pathways, twelve transition states, three intermediates, and eight final products are obtained. All of the stationary points structures are calculated at the DFT/B3LYP method with the 6-311++G (3df, 3pd) basis set. In the present study, the CCSD/6-311++G (3df, 3pd) level of calculations was used to determine the precise energies of all species in the single point format on the B3LYP method optimized structures. The thermodynamic parameters were obtained using the DFT method. Our results show that among the obtained adducts six adducts have negative values in the Gibbs free energy. Also, the catalytic effect of formaldehyde was explored in the formation of 2-hydroxyacetaldehyde.

: For (Z)-(Z)-N-(λ5-phosphanylidene) formohydrazonic formic anhydride Aza-Wittig reaction and Mumm rearrangement are studied using both density functional and coupled cluster theories. For this propose, two different products starting from one substrate are considered that are competing with each other. The obtained products, P1 and P2, are thermodynamically favorable. The product of the aza-Wittig reaction, P1, is more stable than the product of Mumm rearrangement (P2). For the mentioned products, just one reliable pathway is separately propose based on unimolecular reaction. Therefore, the rate constants based on RRKM theory in 300-600 K temperature range are calculated. Results show that the P1 generation pathway is a suitable path due to low energy barriers than the path P2. The first path has three steps with three transition states, TS1, TS2, and TS3. The P2 production path is a single-step reaction. In CCSD level, the computed barrier energies are 14.55, 2.196, and 10.67 kcal/mol for Aza-Wittig reaction and 42.41 kcal/mol for Mumm rearrangement in comparison with the corresponding complexes or reactant. For final products, the results of the computational study have good agreement with experimental predictions.