1,3 Dipolar cycloaddition reactions can be divided into three types: (1) those with the LUMO provided by the 1,3-dipole are collectively called LUMO-controlled reaction, (2) those with the HOMO provided by the 1,3-dipole are collectively called HOMO-controlled reaction, and (3) those wherein both of the above conditions occur are collectively called LUMO-HOMO controlled reaction. As can be seen in Tables 1, LUMO₁-HOMO₂ < LUMO₂-HUMO₁; therefore, 1,3-dipolar cycloaddition requires symmetry matching between the LUMO of the substituted chloroxime, which acts as the electron acceptor, and HOMO of the substituted isatin, which acts as the electron donor. The interaction between the two compounds leads to the formation of a σ bond, which reduces the energy of the system. Because the 1,3-dipole provides the LUMO for a LUMO-controlled reaction, a lower LUMO energy level for the chloroxime compound is more conducive to the reaction. Analysis of the data in Tables 1 and Table S2.1-S2.4 indicates that the LUMO energy levels of the substituted compounds increase in the order Ph < thiophene < n-Pr. Therefore, the LUMOs of phenyl-substituted compounds are more conducive to the progress of the reaction, which is consistent with the experimental results (For experimental data, see table1 and table S1).

When the chloroxime compound contains a substituted phenyl group, the LUMO energy level increases in the order Br < Cl < F < H < OCH₃ < CH₃ < Et, while the degree of difficulty of the reaction decreases in the order Br > Cl > F > H > OCH₃ > CH₃ > Et. According to the general law of organic pericyclic reactions, an electron-withdrawing group reduces the LUMO energy level of the dienophile. A 1,3-dipole substituted with an electron-withdrawing group has a lower LUMO energy level, which is consistent with the calculated results. Among the electron-withdrawing groups, F, Cl and Br were used to reduce the LUMO energy level of the reactant. On the other hand, the electron-donating groups OCH₃, CH₃, and Et increase the LUMO energy level of the reactant. F has a stronger electron-withdrawing effect than Cl and Br. However, in the 1,3-dipole, the 2p orbital electron of F is conjugated to the benzene ring because being in the same period, F and C have a similar 2p orbital radius. Consequently, the two orbitals can overlap better, which strengthens conjugation but weakens the induced electron-withdrawing ability of F. However, when the conjugate electron donor and induced electron-withdrawing abilities are combined, the latter is still exhibited by the F substituent.

When the substituent is a halogen, substitution at the meta position leads to a lower LUMO energy level, which is more conducive to the reaction, compared with substitution at the ortho or para position. When the substituent is an alkyl group, the LUMO energy level increases in the order ortho < meta < para, that is, having an ortho substituent is more conducive to the reaction. However, increasing the length of the alkyl chain increases the LUMO energy level, which is not conducive to the reaction.

In this reaction system, isatin provides the HOMO. Analysis of the theoretical data indicates that the HOMO energy levels of the different substituted compounds increase in the order Br < F < OCH₃ < H < CH₃. According to the general law of organic pericyclic reactions, an electron-donating group increases the HOMO energy level of dienes. Isatin compounds substituted with such a group have a higher HOMO energy level, which is in good agreement with the above calculated results. In addition, the energy level difference between LUMO₁ and HOMO₂ also reflects the degree of difficulty of the reaction to a certain extent. However, in the actual reaction, the degree of difficulty also depends on other factors, such as steric hindrance and symmetry matching of the orbitals.

Subsequently, we calculated the LUMO and HOMO energy levels of intermediates 1a’ and 2a’ using the 6-31G(d) basis set and M052X, M062X, and APFD functionals (see Supporting Information 2 for details). The results are in good agreement with the above conclusions, although there are a few differences in the relative numerical value, which is within the range of experimental error. The values calculated using the APFD functional are similar to those calculated using the B3LYP functional; however, those calculated using M052X and M062X functionals are different. This is mainly reflected in the higher LUMO energy level and lower HOMO energy level. Because there is no reference value for comparison, it is impossible to determine which functional is more suitable for calculations for this system. In terms of time consumption, using the same calculation parameters for the same compound, the functionals that are similar are B3LYP and APFD and M052X and M062X. However, the computing times using M052X and M062X are about twice as long as that using B3LYP. In summary, the conclusions obtained from the calculations of the frontier orbital energies for this system using the four functionals are completely consistent. Therefore, B3LYP is more economical and efficient for batch calculation of these compounds.

Finally, at the B3LYP/6-31G(d) level, we used PCM with triethylamine as the solvent to calculate the frontier orbital energy difference between1a’ and 2a’ , and the results are shown in Table S2.5-S2.8 of supporting information. Analysis of the data shows that the substituent effect is completely consistent with that in the gas phase. This proves that the use of triethylamine as the solvent only has a minor effect on the reaction. Specifically, the energy level difference for 1a’ in the solvent phase is basically close to that in the gas phase. However, owing to the induced electron-withdrawing ability of triethylamine, the calculated LUMO and HOMO energy levels of2a’ are slightly lower.

The ΔG of each reaction was calculated at the B3LYP/6-31G(d) level, as shown in Table 2. The magnitude of ΔG can be used to predict the difficulty or ease of the reaction. Among the phenyl, thiophene, and alkyl substituents, the phenyl group is the most favorable for the reaction. On the other hand, the alkyl group is not conducive to reaction progress, which is consistent with experimental data and the conclusion derived from frontier orbital theory discussed in section 3.1. For chloroxime compounds containing a substituted phenyl group, the ΔG and hence, difficulty, of the reaction, decreases in the order Et > H > OCH₃ > F > Cl > Br. Moreover, the effect of an ortho substituent is stronger than those of meta and para substituents, which basically agrees with the relevant law of organic reaction.

The M052X, M062X, and APFD functionals were also used to calculate the ΔG of the 36 reactions (see Supporting Information 3 for details). The ΔG values obtained using these three functionals are negative, indicating that the reactions can occur in the standard gaseous state. The APFD functional takes less computing time, although the ΔG regularity of each reaction is small. M052X and M062X calculations are time consuming and yield similar ΔG values that are basically consistent with the general law of organic reaction. For substituted 1areactants, the ΔG and hence, difficulty, of the reaction increases in the order Ph < thiophene < n-Pr. For chloroxime compounds containing a halogen-substituted phenyl group, the ΔG of the reaction is lower, that is, substitution with F, Cl, Br, or other halides is more conducive to the reaction. The effect is strongest when the substituent is in the ortho position. For reactant 2a , substitution with OCH₃ or other electron-donating groups is more conducive to the reaction. It can be concluded that if1a contains an electron-withdrawing group, an electron-donating group on 2a is more conducive to the reaction. According to the above analysis, the ΔG values calculated using B3LYP, M052X, and M062X are basically consistent with the general law of organic reaction.

Table 2. ΔG of the reactions under gas-phase condition.