To find out the most favorable reaction path, which might be important to help clarify, the reaction diastereoselectivity of [3+2] reactions observed in experiments, we further analyzed the reactions from both thermodynamics and kinetics point of view. As shown in Figure 6 and Table S1, all reactions are exothermic reaction, the energy difference between products and reactants are about or more than ­20 kcal/mol. Therefore, all these [3+2] reactions are thermodynamically favorable. From the kinetic point of view, the energy barrier from of TS1 to TS8 are 3.2, 10.7, 16.8, 13.2, 6.8, 6.9, 19.7 and 20.9 kcal/mol respectively and the reaction starting from CR1 that resulted the syn product reveals to be the most probable reaction path with the lowest energy barrier of 3.2 kcal/mol (path1 in Figure 6), which is about 3.7 kcal/mol lower than the lowest energy barrier that resulted in the anti products (path6 in Figure 6). Such energy barrier differences might be the reason that result in the diastereoselectivity observed in experiments, i.e. syn:anti=72:28. After the formation of intermediate structures M, with the departure of the catalyst Cu(OTf)2 , we can finally get the [3+2] products.
We need to keep in mind that we start all our calculations from one enantiomer of the C complex. Therefore, from the mirror of CR1 and CR8, we can find another eight reaction paths with similar reaction paths but lead to the enantiomer products. For instance, from the mirror of CR1, we can finally get the P5 product, which is the enantiomer of P1. Therefore, these reactions are diastereoselectivity but not enantioselectivity according to our present results.
Potential Energy Surfaces of [3+2] Cycloaddition without Cu(OTf)2
To figure out the role of Cu(OTf)2 molecule played in the whole cycloaddition process, we have also investigated the reaction paths without the Cu(OTf)2 catalyst. Starting from structures that similar to CR1 to CR8, namely R1 to R8, we optimize the relevant reactants and transition states as shown in Figure 8 and Figure 9.
Figure 8. The UB3LYP+D3 optimized eight initial structures for the [3+2] cycloaddition that without the Cu(OTf)2catalyst. Also shown are relevant bond lengths (in angstrom).
Figure 9. The UB3LYP+D3 calculated potential energy profiles that start from two reactants R1’ and R5’ that without Cu(OTf)2molecule (in kcal/mol). Also shown are the relevant bond lengths of reactants, transition states and products (in angstrom).
Several important conclusions can be drawn from a glance of these results: (1) Without the Cu(OTf)2 molecule, the reactant, transition state and products of R1/R5 (TS1’/TS5’) [P1/P5], R2/R6 (TS2’/TS6’) [P2/P6], R3/R7 (TS3’/TS7’) [P3/P7] and R4/R8 (TS4’/TS8’) [P4/P8] are exact enantiomers with nearly the same energies and same bond lengths as expected; (2) The lowest energy barriers of the [3+2] cycloaddition is somewhat larger than the Cu(OTf)2 catalyzed reactions, 8.0 kcal/mol vs 3.2 kcal/mol (path1 in Figure 6 and path1’ in Figure 9); (3) The energy barrier difference that lead to syn and anti products is smaller than the Cu(OTf)2 catalyzed reactions, 2.4 kcal/mol (path2’ minus path1’ in Figure 9) vs 3.7 kcal/mol (path6 minus path1 in Figure 6), which indicates that the Cu(OTf)2 catalyzed reactions tend to have improved diastereoselectivity of the products.
Specifically, we take a closer look at the path1’ and compare this reaction path with the Cu(OTf)2 catalyzed path1. In comparison with transition state structure of path1, the C1­C3 has similar bond lengths of 2.11 Å. The C2­N4 bond in TS1’, however, is much shorter than that in TS1, 2.63 Å vs 3.17 Å. Similar phenomenon has been found in other species: the C­C bonds are similar to the Cu(OTf)2 catalyzed reactions but the C­N bonds are much shorter. To find out whether the mechanism of such [3+2] reactions without Cu(OTf)2 follow similar concerted asynchronous mechanism, we have also calculated the IRC paths starting from the TS’ to both forward and reverse directions.
The calculated IRC path that corresponds to path1’ is shown in the left panel of Figure 10 while all other paths are shown in Figure S8­S14. The IRC
Figure 10. The energies along the IRC path that connecting R1 and P1 (left panel) and the Mayer bond order analysis of C1­C3, C2­C4 and C2­C3 bonds along the IRC path (right panel). Also shown is LOL analysis of three typical structures along the IRC path.
energies that start from the initial reactant to transition state is similar to the Cu(OTf)2, with a somewhat higher energy barrier of about 8.0 kcal/mol. However, the IRC path from transition state to the [3+2] product P1 is totally different from previous one. The energies decreased sharply and lead directly to the P1 products. There is no shoulder from the TS to the final [3+2] products as the Cu(OTf)2 catalyzed reaction, which imply a concerted synchronous cycloaddition mechanism. Similarly, we have conducted the Mayer bond order analysis along the IRC path as depicted in the right panel of Figure 10. It is obvious from the right panel of Figure 10 that the decrease of the C2­C3 bond order and the increase of C2­N4, C2­C3 bond order happen at nearly the same coordinate of ­5 amu1/2Bohr. This fact further seconded the concerted synchronous cycloaddition mechanism. The IRC paths and corresponding Mayer bond order analysis of other configurations (R2­R8) can be found in Figure S8­S14 and all these reactions follow a similar concerted synchronous cycloaddition mechanism as R1. No concerted asynchronous mechanism as the Cu(OTf)2 catalyzed reactions is found.