Prediction of the electrophilic/nucleophilic character of the reagents
In order to determine the electrophilic/nucleophilic character of the reagents (hydroxyparthenolide 1 and nitrileimine 2), we calculated the electronic chemical potential μ, the hardness η, the nucleophilic index N and the electrophilic index ω. and are shown in Table 1.
Table 1 show that the electronic chemical potential of the nitrileimine 2 and hydroxyparthenolide 1 are similar; which implies that this reaction has a non-polar character. The nucleophilie and eletrophilie index of the nitrileimine 2, are 3.48 and 1.74 eV respectively and that of hydroxyparthenolide 1 are 3.01 and 1.44 eV respectively. Therefore, both reagents are classified as potent nucleophiles and potent eletrophiles, in addition these reagents have similar characteristics, so we will use charge transfers at the level of the transition state to classify them, the transfer of charge in the transition state will take place from the nitrileimine 2 to the hydroxyparthenolide 1, the fact that the hydroxyparthenolide 1 will participate as eletrophile and nitrileimine 2 will participate as nucleophile, as this reaction is non-polar, numerous studies show that the formation of the first bond in cycloaddtions reactions takes place on the most electrophilic center of ethylene derivative [55,32]. We have represented in figure 1 the eletrophilic Parr functions of dipolarophile (hydroxyparthenolide 1).
Figure 1 indicates that the Mulliken atomic spin densities of hydroxyparthenolide 1 are clustered on the exocyclic C1=C2 double bond, while almost no surface is noted around the endocyclic C3=C4 double bond. This result indicates that the C1=C2 double bond is the most reactive part of hydroxyparthenolide 1, which confirms the total chemoselectivity experimentally observed.
Hydroxyparthenolide 1 has two double bonds. Due to his chiral character, as well as the non-symmetry of the two reactants, 8 competitive reaction paths are possible. They are linked to the different chemo-, regio- and diastereofacial approaches. The formation of a single product P-4 indicates that this 32CA reaction exhibited chemo-, regio-, and diastereofacial-selective.
To interpret the deferent selectivities observed experimentally (chemo-, regio- and diastereo-facial), six approach modes associated to the chemoselective attack of the C1=C2 and C3=C4 double bonds of hydroxyparthenolide 1, and two regioisomeric approach modes of nitrileimine 2 and the attack on both sidesof the double bond C1=C2 of Hydroxyparthenolide1, the syn and the anti, were considered,six transition states TS, TS-1 to TS-6, and the corresponding cycloadducts were characterized and located.The relative energies, in gas phase and in DCM, are assigned in Scheme 2, while the total electronic energies are given in table S1.
The scheme 2 indicate that the activation energies of six reaction paths are: TS-1 (9.2 Kcal/mol), TS-2 (7.2 Kcal/mol), TS-3 (18.1 Kcal/mol), TS-4 (2.2 Kcal/mol),TS-5 (19.4 Kcal/mol) and TS-6 (16.9 Kcal/mol), indicating that reaction path 4 is kinetically more favored. It corresponds to the formation of the spirocycloadducts P-4.The six reaction paths having an exothermic character are as follows: P-1 (-53.4Kcal/mol), P-2 (-53.5 Kcal/mol), P-3 (-44.5 Kcal/mol), P-4(-3.7 Kcal/mol), P-5 (-37.8 Kcal/mol) and P-6 (-40.9 Kcal/mol), which shows that the product P-4 has a lesser exothermic character, consequently the productP-4 is obtained from a kinetic control.The use of dichloromethane as a solvent increases the activation energy of the six reaction paths by: TS-1 (3.9 Kcal/mol), TS-2 (3.9Kcal/mol), TS-3 (10.5Kcal/mol),TS-4 (3.5Kcal/mol),TS-5 (3.4 Kcal/mol) and TS-6 (5.9 Kcal/mol), and reduces the exothermic character by: P-1 (4.5Kcal/mol), P-2 (4.6 Kcal/mol), P-3 (2 Kcal/mol), P-5 (3.2Kcal/mol) and P-6 (8 Kcal/mol) while the exothermic character of the product P-4 increases by (17.9Kcal/mol), which shows that dichloromethane disadvantages this reaction.
We have shown in figure 2 the free energy profile of this reaction, the total of the thermodynamic values are exposed in Table S2. Taking into account the term TΔS increases enormously the relative free energies of Gibbs compared to the relative enthalpies between 11 and 15 kcal/mol, this increase is due to the entropy which disadvantages the bimolecular process.
The free Gibbs activation energies associated with the formation of the cycloducts P-1, P-2, P-3, P-4, P-5 and P-6 via TS-1, TS-2, TS-3,TS-4, TS-5 and TS-6 are 26.45, 23.92, 19.98, 18.24, 37.65 and 35.98 kcal/mol, respectively;the formation of these products are respectively exergonic at 31.42, 31.86, 23.42, 8.13, 15.02 and 13.60 kcal/mol. Consequently, these 32CA reactions being irreversible and the formation of the cycloaduct P-4 is more favorable, indicating that this cycloaddition raection is chemo-, stereo- and regiospecificity, which has been observed experimentally.
The geometries of the transition states associated with the six reaction paths are shown in Figure 3. A comparative analysis of the geometric parameters of the transition states localized in the gas phase and those found in DCM shows that the implicit consideration of the solvent in the optimizations geometry does not produce noticeable changes.
Important conclusions can be drawn from the geometric parameters of the transition states shown in Figure 3: i) the bond lengths clearly indicate that the new single bonds are formed in an asynchronous fashion ii) the inclusion of solvent effects makes the TSs slightly earlier and more asynchronous. Finally, the polar character of these zw32-like CA reactions was assessed by calculating the values of the GEDT at the corresponding TS.at TS-1, 0.08;at TS-2, 0.08;at TS-3, 0.04;at TS-4, 0.04;at TS-5, 0.1;and at TS-6, 0.03, these low values clearly indicate that these cycloaddition reactions have a nonpolar character.
ELF topological investigation
To reveal the description of the formation of the new single bonds along the more favorable reaction path of the cycloaddition reaction between hydroxyparthenolide and nitrilimine, An ELF topological investigation of selected points of the IRC curve. The populations of the most relevant ELF valence basins involved in the formation of the single bonds C-C and C-N of the selected structures are arranged in Table S3, while the positions corresponding ELF basin attractors are exposed in Figure 4.
In structure 1, we observe the presence of two monosynaptic basins V(N1)=3.55e and V(C3)=0.67e and five bisynaptic basins namely V(N1,N2)=1.95e, V(C1,C2)=1.72e, V'(C1,C2)=1.76e, V(N2,C3)=2.01e and V'(N2,C3)=3.96e, this structure corresponds to the separate reactants. During structure 2 until structure 22, we observe a decrease in the value of the monosynaptic basin V(N1) up to the value 3.46e, and the increase in the monosynaptic value V(C3), which will take thevalue V(C2)=1.01e in structure 22. In structure 23, we have the appearance of a monosynaptic basin carried by the nitrogen atom 2 V(N2)=0.81e, this value will increase to 2.08e in structure 33, in theStructures 33 and 34 show the appearance of a monosynaptic basin carried by carbon C2, which takes the value V(C2)=0.36e.The monosynaptic basins V(C2) and V(C3), will unify to form the first single bond with an electronic population V(C2,C3)=1.72e, once this bond is formed, we have the appearance ofa monosynaptic basin carried by carbon C1, V(C1)=0.13e, this increases during structures 37 up to 48, which will take the value V(C1)=0.41e in structure 49. In structure 50 the monosynaptic pools V(N1) and V(C1) will form the second single bond. During structures 51 to 60 there is a relaxation towards the final product.So from this study it can be concluded that the cycloaddition reaction between hydroxyparthenolide(1) and nitrilimine (2) follows an asynchronous mechanism.