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Table 17 Possible point groups and conformations of the transition state for
E
,
Z
-isomerization
with simultaneous inversion of helicity 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
),
(18)*, (1
0
8
0
)*, (11
0
88
0
)(99
0
)*, (18
0
81
0
)(99
0
)*}
t
⊥
-
D
2d
8
2
1
1
D
2
B
1
{
E
, (18)(1
0
8
0
), (11
0
88
0
)(99
0
)*, (18
0
81
0
)(99
0
)*} t
⊥
-
S
4
4 4 1 2
C
2
(
z
) B
{
E
, (18)(1
0
8
0
), (18)*, (1
0
8
0
)*} t
⊥
-
C
2v
(
d
)4 4 12
C
2
(
z
) A
2
{
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
)} 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
, (18)*} ft
⊥
-
C
s
(
d
)2 814
C
1
A”
{
E
,(1
0
8
0
)*} ft
⊥
-
C
s
(
d
0
)2 8 14
C
1
A”
{
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
])
Fig. 33 Schematic
mechanism of the
E
,
Z
-
isomerization with
simultaneous
enantiomerization of the
twisted conformation t-
D
2
via the orthogonally twisted
transition state t
⊥
-
D
2d
1'
1
t
^
P
1
1'
1'
1
t
t
Z-P
E-M
1
1'
t
1
^
M
1'
1
1'
t
t
Z-M
E-P
combining symmetry operators of the t-
D
2
conformation,
E
, (18)(1
0
8
0
), (11
0
)(88
0
)
(99
0
), and (18
0
)(81
0
)(99
0
), with operators corresponding to the process of
E
,
Z
-
isomerization, (18), (1
0
8
0
), (11
0
88
0
)(99
0
), and (18
0
81
0
)(99
0
). Table
18
lists all transi-
tion state conformations predicted by the molecular symmetry group theory,
including the symmetries of transient conformations along the steepest descent
paths and the symmetry species of the vibrational mode of the transition state,
which corresponds to the transition vector.
Combining the symmetry operators of t-
D
2
with the permutation operators
corresponding to this dynamic process results in a group that is isomorphous to
D
4
. However, there is no conformation with
D
4
symmetry. The permutation oper-
ators (18), (1
0
8
0
), (11
0
88
0
)(99
0
), and (18
0
81
0
)(99
0
) do not appear as symmetry oper-
ators in any conformation of an overcrowded bistricyclic aromatic ene (cf
.
Table
7
).
This is an unusual situation: the permutation-inversion operators corresponding to
