Chemistry Reference
In-Depth Information
Table 11 Possible point groups and conformations of the transition state for
E
,
Z
-isomerization
with simultaneous inversion of one moiety of the
anti
-folded conformation a-
C
2h
(
y
)
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
)*}
-
c
-
d
t
⊥
-
D
2d
8
2
2
C
2
(
y
)
{
E
, (18)(1
0
8
0
), (11
0
88
0
)(99
0
)*,
(18
0
81
0
)(99
0
)*}
-
d
t
⊥
-
S
4
4
4
2
1
C
1
{
E
, (18)(1
0
8
0
), (18)*, (1
0
8
0
)*}
-
d
t
⊥
-
C
2v
(
d
)
4
4
2
1
C
1
{
E
, (11
0
)(88
0
)(99
0
), (18)(1
0
8
0
)*,
(18
0
)(81
0
)(99
0
)*}
a-
C
2h
(
y
)
e
4
4
2
1
C
2h
(
y
)
1
{
E
, (11
0
)(88
0
)(99
0
)}
ta-
C
2
(
y
)
e, f
2
8
2
2
C
2
(
y
) A
f-
C
s
(
xz
)
e
{
E
, (18)(1
0
8
0
)*}
C
s
(
xz
)
0
2
8
2
2
A
00
{
E
, (18)*}
ft
⊥
-
C
s
(
d
)
2
8
2
2
C
1
{
E
,(1
0
8
0
)*}
ft
⊥
-
C
s
(
d
0
)
A
00
2
8
2
2
C
1
a-
C
i
e
{
E
, (18
0
)(81
0
)(99
0
)*}
2 8 2 2
C
i
A
g
{
E
} ft-
C
1
1 16 2 4
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
])
c
There is no integer
p
which would satisfy (
4
)
d
The point group along the pathway does not correspond to any non-degenerate representation of
the transition state point group
e
For a-
C
2h
(
y
), ta-
C
2
(
y
), f-
C
s
(
xz
), and a-
C
i
there is no pathway for
E
,
Z
-isomerization without
leaving this point group
f
See Sect.
4.3.7
of parallel pathways, point group symmetry of transient structures along the
pathways, and the symmetry species of the transition vector.
For the transition state t
⊥
-
D
2d
,(
4
) leads to a contradiction. There is no integer
solution
p
for
C
4. This implies that t
⊥
-
D
2d
may be excluded
as a possible transition state. For the conformations t
⊥
-
D
2d
, t
⊥
-
S
4
and t
⊥
-
C
2v
(
d
),
the largest subgroups shared with the reactant and product conformation, a-
C
2h
(
y
),
are
C
2
(
y
),
C
1
, and
C
1
, respectively. These are the highest possible symmetries
along the respective pathways. The transition vector of the transition states has to be
symmetric with respect to the symmetry operators of the pathway, and
anti
-sym-
metric with respect to all other symmetry operators of the transition state confor-
mation. However, in the above cases, there is no (non-degenerate) representation
with this symmetry species. Thus, the conformations t
⊥
-
D
2d
, t
⊥
-
S
4
, and t
⊥
-
C
2v
(
d
)
do not qualify as transition states for the
E
,
Z
-isomerization with inversion of one
moiety in a direct single step process. They may be higher order saddle points or
intermediates (local minima), or transition states of pathways with multiple steps,
performing the process in question, or transition states of pathways with a
bifurcation.
¼
2,
n
TS
¼
2 and
n
¼
