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.