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.
Gibbs free energy (ΔG).
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.