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Table 2: Relative enthalpies (Hrel°) and relative Gibbs free energies
(Grel°) between the two most stable 1b·H+-catalyzed DA TSs leading to
opposite enantiomeric cycloadducts and predicted ee values based on
experiments, Balskus and Jacobsen recently demonstrated[14]
that macrocyclic lactones such as E,E,E-triene 6 undergo
stereoselective transannular DA reactions to furnish tricycles
such as 7 (Scheme 2c). The reason for the unexpected
enantioselectivities obtained for these reactions has now
been identified by DFT calculations.
the DGrel values.[a]
°
Dichloromethane solvent[b]
ee [%][d]
Exp. ee [%][d]
°[c]
°[c]
Entry
Substrate
Hrel
Grel
The Corey catalyst used in the calculations is 1b·H+,
protonated 1b, which was used in an early experimental
study.[1] In general, we limit our investigation to enantiose-
lectivities in DA reactions leading to the observed major
diastereomer (i.e. cis- or trans-fused bicycle, exo- or endo-
intermolecular DA adduct). Comprehensive sets of reactant–
1b complexes and plausible transition states (TSs) leading to
the two enantiomeric cycloadducts were located for each
reaction. Geometry optimizations and thermal corrections
were calculated by using B3LYP/6-31G(d) theory[15] and more
reliable single-point energies were calculated at the MPW1
K/6-31 + G(d,p) level of theory.[16,17] The polarizable contin-
uum model (PCM)[18] approximation was used to model the
dichloromethane solvent (e = 8.93).[19]
1
2
3
4
5
6
7
8
2
4
8
9
10
11
12
13
5.3
7.5
6.6
5.0
2.8
6.2
7.1
6.3
7.1
10.6
6.9
1.9
6.9
85
82
97
94
36
87
96
77
70[e]
53[e]
–
90[f]
80[f]
93[f,g]
86[f]
88[h]
9.4
5.09
8.13
[a] MPW1K/6-31+G(d,p)//B3LYP/6-31G(d)
+ B3LYP/6-31G(d) ther-
mal corrections. The reported values are in kJmolÀ1, calculated at
298.15 K. [b] Nonspecific solvent effect using the polarizable continuum
model. [c] Hrel° =H°(minor enantiomer)ÀH°(major enantiomer);
Grel° =G°(minor enantiomer)ÀG°(major enantiomer); [d] In all cases,
computational and experimental results give the same major enantiomer
(see Figure 1 for depictions of TSs leading to the major enantiomer.)
[e] This work. [f] Reference [5]. [g] The -CO2CH2CF3 group was used
experimentally. [h] Reference [2].
The Gibbs free energies (DGcomp) for formation of the
most stable reactant–LA complex for several dienophiles are
given in Table 1 together with the free energies of activation
Table 1: Gibbs free energies of formation (DGcomp) of the most stable
1b·H+ complexes of reactants and DA Gibbs free energies of activation
(DGa°) relative to these complexes.[a]
Gas phase
DGcomp
Dichloromethane solvent[b]
DGcomp
Substrate
DGa°
DGa°
2
4
9
12
13
À34.7
À23.2
À41.7
À16.1
À38.9
90.0
91.2
66.8
85.3
99.4
À28.0
À13.7
À33.9
À4.4
93.1
86.3
69.7
85.2
101.4
Figure 1. Schematic representation of the favored TS for each 1b·H+-
catalyzed DA reaction studied. The depicted diastereoselectivities
(cis or trans for triene precursors and endo or exo for dienophiles) and
p-enantiofacial selectivities are those favored experimentally
(LA=1b·H+).
À30.2
[a] MPW1K/6-31+G(d,p)//B3LYP/6-31G(d)
+
B3LYP/6-31G(d) ther-
mal corrections. Values reported in kJmolÀ1, calculated at 298.15 K.
[b] Nonspecific solvent effect by using the polarizable continuum model.
See Figure 1 for schematic transition structures.
ment with those observed experimentally (Table 2, entries 1
and 2, and 4–8). With one exception (Table 2, entry 5), the
predicted ee values are in good agreement with the exper-
imental values.[21]
(DGa°), which are relative to the precursor complex (or
include the diene for 2 and 13), for the most favorable DA
transition state.
These data clearly show that, for each system, the
numerical value of the free energy of complexation is
considerably smaller than the corresponding free energy
activation for the DA reaction. Assuming that the complex
formation is essentially barrierless, we conclude that the
complex formation is rapidly reversible on the DA reaction
timescale.[20] Consequently, DA enantioselectivities in these
LA-catalyzed DA reactions is determined solely by the
relative free energies of competing TSs, upon which we now
focus attention.
The essential features of Coreyꢀs pre-transition-state
assembly models are clearly evident in the TS geometries
(Figure 2). Thus, the lowest energy TSs[22] for the a,b-enals 8,
9, and 10 have the s-trans C C C O conformation[23] and the
= À =
boron center complexed to the oxygen atom through the lone
=
pair anti to the C C bond. This coordination mode, typified
by 9-TS (Figure 2a), is consistent with in the presence of a
formyl CH···OB hydrogen bond having an H···O distance of
2.47 , which lies within the range from 2.41 to 2.59 as
determined from X-ray crystal structures of aldehyde–boron
complexes.[24] The 3.38 separation between the formyl
carbon atom and C1’ of the exo-phenyl group at C5 might
signal a stabilizing p–p interaction postulated in the Corey
model.
Table 2 presents the relative enthalpies (Hrel°) and free
energies (Grel°) between the most favorable TSs leading to
each enantiomer for each system, and the ee values as
calculated from the Grel° values. Figure 1 presents schematic
representations of the predicted favored TSs. The predicted
p-enantiofacial selectivities are in complete qualitative agree-
The final feature of the Corey model—having the exo-
phenyl group at C5 hinder approach of the diene from the C5
7014
ꢀ 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2008, 47, 7013 –7017