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In-Depth Information
Table 16 Possible point groups and conformations of the transition state for enantiomerization of
the twisted conformation t-
D
2
Group of permutation-inversion operators
n
TS
Cp
a
b
TS
h
TS
{
E
, (18)(1
0
8
0
), (11
0
)(88
0
)(99
0
), (18
0
)(81
0
)(99
0
),
E
*,
(18)(1
0
8
0
)*, (11
0
)(88
0
)(99
0
)*, (18
0
)(81
0
)(99
0
)*}
p-
D
2h
8
2
1
1
D
2
A
u
{
E
, (18)(1
0
8
0
), (11
0
)(88
0
)(99
0
), (18
0
)(81
0
)(99
0
)} t-
D
2
4 4 1 2
D
2
A
{
E
, (18)(1
0
8
0
),
E
*, (18)(1
0
8
0
)*} p-
C
2v
(
z
) 4 412
C
2
(
z
)A
2
{
E
, (11
0
)(88
0
)(99
0
),
E
*, (11
0
)(88
0
)(99
0
)*} p-
C
2v
(
y
)4 412
C
2
(
y
)A
2
{
E
, (18
0
)(81
0
)(99
0
), (18)(1
0
8
0
)*, (11
0
)(88
0
)(99
0
)*} s-
C
2v
(
x
) 4 412
C
2
(
x
)A
2
{
E
, (18)(1
0
8
0
), (11
0
)(88
0
)(99
0
)*, (18
0
)(81
0
)(99
0
)*} pt-
C
2h
(
z
)4 4 12
C
2
(
z
)A
u
{
E
, (11
0
)(88
0
)(99
0
), (18)(1
0
8
0
)*, (18
0
)(81
0
)(99
0
)*} a-
C
2h
(
y
)4 412
C
2
(
y
)A
u
{
E
, (18
0
)(81
0
)(99
0
),
E
*, (18
0
)(81
0
)(99
0
)*} p-
C
2h
(
x
) 4 412
C
2
(
x
)A
u
{
E
, (18)(1
0
8
0
)} t-
C
2
(
z
) 2 8 1 4
C
2
(
z
)A
{
E
, (11
0
)(88
0
)(99
0
)} ta-
C
2
(
y
)2 814
C
2
(
y
)A
{
E
, (18
0
)(81
0
)(99
0
)} ts-
C
2
(
x
) 2 814
C
2
(
x
)A
{
E
,
E
*} p-
C
s
(
yz
) 2 814
C
1
A
00
{
E
, (18)(1
0
8
0
)*} f-
C
s
(
xz
) 2 814
C
1
A
00
{
E
, (11
0
)(88
0
)(99
0
)*} s-
C
s
(
xy
) 2 814
C
1
A
00
{
E
, (18
0
)(81
0
)(99
0
)*} a-
C
i
2 8 1 4
C
1
A
u
{
E
} ft-
C
1
1 16 1 8
C
1
A
a
Point group symmetry along pathway from transition state to reactant or product, i.e., maximum
common subgroup of transition state and reactant or product
b
Symmetry species of the mode of the transition vector (using the conventional setting of the
transition state point group [
279
])
respectively, as shown in the schematic mechanism in Fig.
31
. The connectivity is
C ¼
1).
Starting from the twisted conformation, the twist (and hence the non-planarity)
of the structure is reduced to reach the planar transition state. Increasing the twist in
the opposite direction leads to the other enantiomer. All transient structures along
the pathway have
D
2
symmetry as the initial and final conformation. The transition
vector of p-
D
2h
leading to twisted conformations has A
u
symmetry. Note that the
planar conformation has also been considered as a transition state of the inversion
of the
anti
-folded conformation a-
C
2h
(
y
) and/or the inversion of the
syn
-folded
conformation s-
C
2v
(
x
). However, the corresponding transition vectors would have
different symmetries (Table
10
). The conformation p-
D
2h
can be a transition state
only in one of the three processes. Due to the extreme overcrowding, p-
D
2h
is most
likely a higher order saddle point and the enantiomerization process will have a
lower symmetry transition state.
The
anti
-folded conformation a-
C
2h
(
y
) and the
syn
-folded conformation s-
C
2v
(
x
) are possible transition states with lower symmetry (
h
TS
¼
1, and there is only one pathway (
p ¼
4
versions of these transition states. They may interconvert the
Z
- and
E
-versions of t-
D
2
in mechanisms with connectivities
C
4). There are
n
TS
¼
¼
1 and two parallel pathways (
p
¼
2), as
shown in Fig.
32
.
In the first mechanism (Fig.
32a
), the two tricyclic moieties of the twisted
conformation are folded in opposite directions (
anti
) and the twist of the central
