Chemistry Reference
In-Depth Information
4.3.4
Interconversions of the Twisted and
anti
-Folded Conformations
In conformational isomerization reactions, the starting geometry and the geometry
of the product correspond to different conformations and thus cannot be related by
any symmetry operations or permutations of the atom labels. Thus the only sym-
metry elements available for the transition state, as well as for the pathway
connecting it to the reactant and the product, are those common to reactant and
product conformations [
248
]. The transition vector is necessarily totally symmetric
with respect to the point group of the transition state [
270
]. The transition state is
not characterized by a higher order point group. All structures along the steepest
descent paths from the transition state to the reactant and product conformations
have the same point group. Thus, geometry optimizations of the transition state of a
conformational isomerization will always require a search for a transition state. A
symmetry constrained energy minimization will not converge to the transition state
[
270
].
The permutation-inversion operators corresponding to the point group symmetry
operators of the twisted conformation t-
D
2
and the
anti
-folded conformation a-
C
2h
(
y
) are listed in Table
19
together with their largest common subgroup.
The only common symmetry operators are:
E
, and (11
0
)(88
0
)(99
0
), leading to the
possible transition states listed in Table
20
. The highest possible point group
symmetry of the transition state for interconversion of twisted and
anti
-folded
conformations is
C
2
(
y
). A
C
2
axis along
y
, i.e., through the center of the
overcrowded regions, allows twisting of the central double bond and folding of
the tricyclic moieties in opposite directions (
anti
). The transition state may be
classified as a ta-
C
2
(
y
)orat-
C
2
(
y
) conformation (Table
4
). According to the
Hammond principle, twisting is expected to be more pronounced if the twisted
conformation has a higher energy than the
anti
-folded conformation.
Anti
-folding
will be more pronounced in the transition state if the twisted conformation is more
stable. However, these arguments go beyond pure symmetry considerations. In the
following analysis, the transition state will be labeled ta-
C
2
(
y
), irrespective of the
question whether twisting or folding is more dominant.
In addition to the
C
2
pathway, a
C
1
pathway via a ft-
C
1
transition state may be
considered.
The transition state ta-
C
2
(
y
) has a point group order
h
TS
= 2. Thus, there are
n
TS
= 8 versions of this transition state in the molecular symmetry group
G
16
. Four
versions have a
Z
-configuration and convert the two
Z
-versions of t-
D
2
(t
Z-P
and
t
Z-M
) into the two
Z
-versions of a-
C
2h
(
y
)(a
Z-RR
'
and a
Z-SS
'
). The other four
versions have an
E
-configuration and interconvert the corresponding
E
-versions
of the twisted and
anti
-folded conformations. The mechanism is shown schemati-
cally in Fig.
35
.
The ft-
C
1
transition state combines a twisted central ethylene bond with unequal
folding of the two moieties in opposite directions (
anti
). The lower symmetry
C
1
transition state (
h
TS
= 1) has
n
TS
= 16 versions, leading to a doubling of all
pathways as shown in Fig.
36
. The versions with
E
- and
Z
-configurations
