Unveiling the Different Chemical Reactivity of Diphenyl Nitrilimine and Phenyl Nitrile Oxide in [3+2] Cycloaddition Reactions with (R)-Carvone through the Molecular Electron Density Theory.

The [3+2] cycloaddition (32CA) reactions of diphenyl nitrilimine and phenyl nitrile oxide with (R)-carvone have been studied within the Molecular Electron Density Theory (MEDT). Electron localisation function (ELF) analysis of these three-atom-components (TACs) permits its characterisation as carbenoid and zwitterionic TACs, thus having a different reactivity. The analysis of the conceptual Density Functional Theory ( DFT) indices accounts for the very low polar character of these 32CA reactions, while analysis of the DFT energies accounts for the opposite chemoselectivity experimentally observed. Topological analysis of the ELF along the single bond formation makes it possible to characterise the mechanisms of these 32CA reactions as cb- and zw-type. The present MEDT study supports the proposed classification of 32CA reactions into pdr-, pmr-, cb- and zw-type, thus asserting MEDT as the theory able to explain chemical reactivity in Organic Chemistry.

32CA reactions have been widely computationally studied using different DFT functionals, the B3LYP [1,2], MPWB1K [3] and M06-2X [4] being the most used. A comparative analysis of the relative energies in DCM of the stationary points associated with the two more favourable chemoselective reaction paths associated to the 32CA reactions of (R)-carvone 1 with diphenyl NI 2a and with phenyl NO 4a obtained using these functionals was performed. In addition, the B3LYP-D3 [5] and wB97XD [6] functionals, which are capable of capturing also long-range interactions, were also tested.
The total and relative energies are given in Table S1.
A comparative analysis of the relative energies obtained with the five functionals shows that the activation energies decrease in the order B3LYP>MPWB1K>M06-2X> wB97XD> B3LYP-D3, while the exothermic character of these reaction increases in the order B3LYP<B3LYP-D3>MPWB1K>M06-2X<wB97XD. A similar trend was observed in Diels-Alder reactions for the functionals B3LYP, MPWB1K and M06-2X [7]. Unlike the B3LYP functional, the MPWB1K, M06-2X, B3LYP-D3 and wB97XD functionals suggest a total chemoselectivity for the 32CA reaction of (R)-carvone 1 with diphenyl NI 2a, but for the 32CA reaction with phenyl NO 4a, the MPWB1K functional reduces the chemoselectivity, while the M06-2X and B3LYP-D3 functionals predicts the reaction to be non-chemoselective. It is interesting to note that the wB97XD functional even predicts an inverse chemoselectivity to that experimentally observed.
Consequently, none of the five functionals is able to predict completely the experimental outcomes for the two 32CA reactions. This finding is a consequence of the different nature of the TSs of the two 32CA reactions, a cb-type and a zw-type, which are differently considered for these functional. This comparative analysis also emphasized that the M06-2X, B3LYP-D3 and wB97XD functionals yield very low activation energies because they significantly underestimate the energies of the TSs [8]. Table S1. B3LYP/6-311G(d,p), MPWB1K/6-311G(d,p), M06-2X/6-311G(d,p), B3LYP-D3/6-311G(d,p) and wB97XD/6-311G(d,p) total, E in au, and relative energies, E in kcal·mol -1 , in DCM, of the stationary points associated to the more favourable chemoselective reaction paths of the 32CA reactions of diphenyl NI 2a and phenyl NO 4a with (R)-carvone 1. In order to characterise the most nucleophilic and electrophilic centers of diphenyl NI 2a and (R)-carvone 1, the nucleophilic Parr functions of diphenyl NI 2a and the electrophilic Parr functions of (R)-carvone 1 were analysed (see Figure S1) [9].  carbon having a slightly more nucleophilic character (see Figure S1). Note that the more nucleophilically activated C3 carbon corresponds to the less electronegative atom.

ELF topological analysis of the CC and CN bond formation along the 32CA reaction between diphenyl NI 2a and (R)-carvone 1.
In order to characterise the C-C and C-N bond formation along the 32CA reaction between diphenyl NI 2a and (R)-carvone 1, a topological analysis of the Electron Localisation Function (ELF) [10] of the structures of the IRC directly involved in the formation of the new C-C and CO single bonds was performed. These structures were selected by applying the Bonding Evolution Theory (BET) [11] along the IRC associated with the most favourable reaction path. The populations of the most relevant ELF valence basins, the C-C and C-O forming bond distances, global electron density transfer (GEDT) [12] and relative energies of the selected structures of the IRC are gathered in Table S2.
The electronic structure of S1-NI, d(N1C5) = 3.364 Å and d(C3C4) = 3.541 Å, which is the first structure of the reaction path, resembles that of the separated reagents.
Thus, at the NI framework, two V(N1) and V(C3) monosynaptic basins, integrating 3.33 e and 1.43 e, are observed, which can be associated with less than two N1 nitrogen lone increased to 3.28 e, 2.75 e and 3.13e, respectively. Note that after a slight depopulation along the reaction path, the V(N1) monosynaptic basin recovers almost its initial population of S1-NI(see Table S2). The most drastic depopulation is that experienced by    Table S3. monosynaptic basin can be associated with the C4 pseudoradical center demanded for the formation of C3C4 single bonds [12]. Note that at S2-NO, the non-bonding electron density at the C3 carbon has increased to 1.54e as the N2C3 and C3C3' bonding    Table S7. B3LYP/6-311G(d,p) electronic energies, E in a.u., enthalpies , H in a.u., entropies, S in cal·mol −1 ·K −1 , and Gibbs free energies, G in a.u., and relative electronic energies, ΔE in kcal·mol −1 , enthalpies, ΔH, in kcal·mol −1 , entropies, ΔS in cal·mol −1 ·K −1 , and Gibbs free energies, ΔG, in kcal·mol −1 ,computed at 0˚C in DCM, of the stationary points associated with the 32CA reaction of phenyl NO 4a with (R)-carvone 1.   Table S8. B3LYP/6-311G(d,p) electronic energies, E in a.u., enthalpies, H in a.u., entropies, S in cal·mol −1 ·K −1 , and Gibbs free energies, G in a.u., and relative electronic energies, ΔE in kcal·mol −1 , enthalpies, ΔH, in kcal·mol −1 , entropies, ΔS in cal·mol −1 ·K −1 , and Gibbs free energies, ΔG, in kcal·mol −1 ,computed at 25˚C in DCM, of the stationary points associated with the 32CA reaction of simplest NI 8 and simplest NO 9 with ethylene 6.