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The pseudopericyclic character of a group of cycloaddition reactions is theoretically investigated with the quantum theory of atoms in molecules of Bader at B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p) levels of theory. The analysis of the topology of the Laplacian of the charge density, inverted Delta2rho(r), along the reaction coordinate sets out a clear cut between pericyclic and pseudopericyclic processes and also allows one to account for intermediate cases.

The distinct role of the Cu(I) in the Huisgen dipolar cycloaddition of azides to alkynes (denoted as CuAAC) is disclosed by following the evolution of the topology of the Laplacian of the electronic charge density, ∇(2)ρ(r), and its gradient vector field, ∇∇(2)ρ(r), along the reaction coordinate with several density functionals (wB97XD, LCwPBE, M06-2X, M06-L, B3LYP) and the 6-311++G(d,p) basis set. Remarkably, in view of the topology of ∇(2)ρ(r) and ∇∇(2)ρ(r), the mechanism appears to be diverse (asynchronous concerted or stepwise) depending on the reaction conditions. Overall, the catalyst orchestrates first the formation of the external N-C and subsequently the internal one by following alternatively a pericyclic-like or a pseudopericyclic-like mechanism. The role of the catalyst is envisaged as transforming the type of the mechanism from pericyclic to pseudopericyclic, and thence eventually facilitating the process. The mononuclear process (CuAAC) is concerted (with L = CH3CN) with all the functionals tested (i.e., wB97XD, LCwPBE, M06-2X, M06-L), except for the B3LYP who rendered a stepwise mechanism. Nevertheless, with L = H2O and CH3OH attached to the copper, the process becomes asynchronous concerted. Interestingly, upon introduction of the second Cu (Cu2AAC) at our best theory level (i.e., LCwPBE/6-311++G(d,p)), all the processes considered turned out to be concerted except for the 1,4-Cu2AAC which is predicted to be stepwise, with an extremely low enthalpy for the ring-contraction process (0.18 kcal/mol). This fact is explicated by the stability of the intermediate, which is in turn rationalized by the hole within the valence shell of the carbon attached to the Cu and the position of the (3, -3)LP, of the internal N, toward it. Furthermore, due to the tiny energy difference between the stepwise dinuclear and concerted mononuclear mechanisms (0.39 kcal/mol), we argue that the concurrence of both processes (CuAAC and Cu2AAC) is feasible.

New density functional theory (DFT) calculations show that the nature of the mechanism for the classical copper-catalyzed cycloaddition of azide to terminal alkynes--widely known as the CuAAC reaction--also depends on the ligands attached to Cu(I). Further, the topological evolution of the charge density, ρ (r), the laplacian of ρ (r), ∇²ρ(r), and its gradient field along the reaction coordinate shed light on the regioselectivity of the process. The performance of most suitable functionals for DFT calculations in this kind of system was tested.

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