Chemistry Reference
In-Depth Information
central double bond is reversed. The two parallel pathways differ in the folding
directions of the two moieties. The transient structures along the pathways have
C
2
(
x
) symmetry. A mode with imaginary frequency of A
2
symmetry corresponds to
the transition vector leading to the twisted conformations. Note that s-
C
2v
(
x
) has
also been considered as transition state for the conformational inversion of the
anti
-
folded conformation (transition vector B
2
, Fig.
24b
). Also note the analogy of this
mechanism with the conformational inversion of the
syn
-folded conformation via a
twisted transition state (Fig.
28a
). Only the roles of minima and transition states are
interchanged.
E
,
Z
-Isomerization with Simultaneous Inversion of Helicity of the Twisted
Conformation
The possible point groups of the transition states for the
E
,
Z
-isomerization with
simultaneous inversion of helicity may be generated by combining the 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 the operators (18)*, (1
0
8
0
)*, (11
0
88
0
)(99
0
)*, and (18
0
81
0
)(99
0
)* interchanging
reactants and products. Note that the two sets of operators combined give the point
group
D
2d
. This is the highest possible point group for a transition state for
E
,
Z
-
isomerization with simultaneous inversion of helicity of the t-
D
2
conformation.
Table
17
enumerates all possible groups of operators, the transition state con-
formations and point groups, the point group order
h
TS
, number of versions
n
TS
,
connectivity
C
, number of parallel pathways
p
, the symmetry of transient structures
along the pathways, and the symmetry species of the transition vector.
The transition state with the highest point group order (
h
TS
¼
8) is t
⊥
-
D
2d
.
There are
n
TS
¼
2 versions of this transition state: t
⊥
P
and t
⊥
M
. Each of the two
“enantiomeric” labeled versions of the transition state interconverts two versions of
the twisted conformation as shown in the schematic mechanism in Fig.
33
. The
connectivity is
C
1).
Starting from the twisted conformation t
Z-P
, the twist of the central double bond
is increased to 90
at the transition state. Further twisting leads to the product, t
E-M
.
Transient structures along the pathway have
D
2
symmetry. The transition vector of
t
⊥
-
D
2d
has B
1
symmetry. In the case of a higher order saddle point, deformations
along imaginary modes with A
2
and B
2
symmetry lead to possible lower symmetry
transition states t
⊥
-
S
4
and t
⊥
-
C
2v
(
d
). In t
⊥
-
S
4
the two tricyclic moieties are
non-planar (e.g., propeller twisted), while in t
⊥
-
C
2v
(
d
) the two moieties are planar
and mutually orthogonal, but no longer symmetry equivalent.
¼
1 with one pathway each (
p
¼
E
,
Z
-Isomerization of the Twisted Conformation Without Inversion
of Helicity
The point groups of transition states for the
E
,
Z
-isomerization of the twisted
conformation without simultaneous inversion of the helicity are constructed by
