Angewandte
Chemie
À1
À
by about 30 kcalmol . Rotation of the N C(O) bond in the
imine molecule with trans geometry gives rise to two
conformations, s-cis and s-trans (Scheme 2). The s-cis confor-
that of the neutral imine and protonated enamine. Gas-phase
B3LYP calculations indicated that protonation of the imine
was energetically more favorable by 6.29 kcalmolÀ1 (includ-
ing the zero-point energies) than protonation of the enamine.
Conversely, calculations on the THF-solution phase indicated
that protonation of the enamine was more favorable by
1.67 kcalmolÀ1 (including the zero-point energies).
The chirality of the reaction products indicates that attack
of the enamine predominantly occurs on the si face of the
imine. The enamine intermediates generated from diaryl
prolinols 1–3 possess bulky substituents on the carbon atom
neighboring the proline nitrogen atom, and thus, the face of
the enamine opposite the bulky substituent will approach the
si face of the imine in the most energetically favorable
reaction path to yield the Mannich adduct. We thus consider
Scheme 2. Conformations of the imine and the enamine molecules.
mer was found to be an energy minimum, and the s-trans
À
conformer corresponded to the transition state for N C(O)
bond rotation. For the enamine molecule, syn and anti
geometries were located as energy minima. The anti structure
of the enamine was slightly lower in energy than the syn
conformer by circa 0.7 kcalmolÀ1. Hereafter, we consider the
trans s-cis conformation of the imine and the anti structure of
the enamine.
À
that the C C bond forms between the si face of the
N-protonated imine and the face of the enamine opposite
the methyl group in our model calculation. Postulating such a
reaction path, we explored the potential energy surface along
À
The Mannich reaction proceeds in the presence of a
Brønsted acid, and, hence, we examined protonation sites in
the imine and enamine molecules. The imine molecule has
three possible sites for protonation (Scheme 2): 1) the nitro-
gen atom on the imine, 2) the oxygen atom on the carbonyl
group syn with respect to the nitrogen atom of the imine, and
3) the oxygen atom on the carbonyl group anti with respect to
the nitrogen atom of the imine. Not only in the gas phase but
also in the THF-solution phase (the polarized continuum
model[14]), B3LYP calculations indicated that the most
favorable protonation site on the imine was the nitrogen
atom (Table 3). Protonation also possibly occurs on the
nitrogen atom of the enamine molecule. We compared the
energy of the N-protonated imine and neutral enamine with
the reaction coordinate for C C bond formation in the
À
Mannich reaction. C C bond formation was found to be
unlikely to occur between neutral imine and protonated
enamine molecules. On the other hand, the protonated imine
and neutral enamine were found to form a C C bond between
À
them to yield the Mannich products. The imine molecule has
three possible sites for protonation (Table 3), and we also
calculated the Mannich products protonated by three differ-
ent modes that correspond with the protonation of the imine.
The Mannich product protonated on the nitrogen atom of its
imine moiety was found to be more stable by about
20 kcalmolÀ1 than the O-protonated Mannich products
(Figure 1).
The reaction of the N-protonated imine and neutral
enamine resulting in the N-protonated Mannich product was
found to be highly exothermic with a large negative reaction
energy: the exothermicities calculated by using the B3LYP
level were À38.82and À31.12kcalmol À1 in the gas phase and
in the THF-solution phase, respectively (including the zero-
point energies). By starting from the N-protonated Mannich
product (Figure 1a), we explored the reaction coordinate for
Table 3: Structures and relative energies (in kcalmolÀ1) of protonated
imine.[a]
À
the C C bond formation, and we found that the energy of the
adduct of the N-protonated imine and neutral enamine simply
À
increased as the C C bond was lengthened (Figure 2). In
addition, we optimized the structure of the adduct of the
N-protonated imine and neutral enamine with the length of
À
the newly formed C C bond fixed at 3.0 . In Figure 3, the
energy of the model system is plotted against the dihedral
À
angle of the newly formed C C bond. This energy profile
indicates three energy-minimum structures, A–C, for the
model system. According to B3LYP energy evaluations, the
energy differences between these 3 rotamers were calculated
to be less than 2kcalmol À1, with rotamer A being the most
energetically preferable.
Even after taking the basis-set superposition error
(BSSE)[15,16] into account, the energy profile in Figure 2did
not suggest a distinct transition state along the reaction
Protonation site
N
O (syn)
O (anti)
gas phase
0.00
(0.00)
0.00
8.02
(7.78)
7.50
9.56
(9.07)
10.69
(9.69)
solution phase (THF)[b]
(0.00)
(6.50)
[a] The gas-phase structures are shown. Values in parentheses include
zero-point energies. [b] Calculated with the polarized continuum model.
The solution-phase structures optimized with the polarized continuum
model (solvent=THF) did not differ significantly from the gas-phase
structures (see the Supporting Information).
À
coordinate for this C C bond-formation process. Accord-
ingly, B3LYP calculations suggested that the reaction of the
N-protonated imine and neutral enamine should occur readily
Angew. Chem. Int. Ed. 2008, 47, 9053 –9058
ꢀ 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
9055