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derived according to the rules of transition state symmetry, and tabulated. The point
group order
h
TS
, number of versions
n
TS
, connectivity
C
, and number of parallel
pathways
p
are determined. The point group symmetry of transient structures along
the pathways of steepest descent from the transition state to educt and product and
the symmetry species of the transition vector are checked for consistency. Impor-
tant mechanisms are discussed in detail, showing schematic projections for illus-
tration. In this analysis, it is assumed that the educt and product conformations are
bona fide minima and that the transition state derived by symmetry considerations is
a true transition state with one and only one imaginary vibrational frequency and
directly linked to the educt and product by pathways of steepest descent. The
possibility of higher order saddle points or intermediates will be pointed out
where relevant. Sect.
4.3
is focused on the symmetry aspects of the dynamic
stereochemistry of BAEs and their implications for the mechanisms of
automerizations. Energetic aspects were discussed, e.g., in the review [
3
] reporting
semiempirical calculations.
4.3.1 Degenerate Isomerizations of the
anti
-Folded Conformations
The permutation-inversion operators of the molecular symmetry group
G
16
of
homomerous BAEs are applied to the
anti
-folded conformation a-
C
2h
(
y
)in
Fig.
22
. The a
Z-RR
conformation serves as reference conformation (top left in
Fig.
22
). The respective permutation-inversion operators are given above the
schematic projections and the stereochemical descriptors identifying the
E
-or
Z
-
configurations and folding direction (
R
/
S
) of the tricyclic moieties are given below.
Using Fig.
22
, the permutation-inversion operators may be classified according
to their effect on the
anti
-folded conformation a-
C
2h
(
y
) into symmetry operators
having no effect on the structure apart from permuting labels of equivalent atoms,
operators inverting the folding of one or two moieties, and operators
interconverting
E
- and
Z
-configurations. Such a classification is shown in Table
8
.
Three types of dynamic processes are predicted by the classification of the
permutation-inversion operators:
1. Conformational inversion, i.e., simultaneous inversion of the folding directions
of both moieties, e.g., a
Z-RR
0
a
Z-SS
0
2.
E
,
Z
-isomerization with simultaneous inversion of the first moiety, e.g.,
a
Z-RR
0
a
E-SR
0
3.
E
,
Z
-isomerization with simultaneous inversion of the second moiety, e.g.,
a
Z-RR
0
a
E-RS
0
Any other process, e.g., inversion of only one moiety or
E
,
Z
-isomerization
without simultaneous inversion of a moiety, or with inversion of both moieties,
would lead to a different (
syn
-folded) conformation (cf. Sects.
4.3.6
and
4.3.7
).
The four permutation-inversion operators listed in Table
8
for each of the three
types of dynamic processes are the respective cosets. The cosets may be generated
by selecting one of the operators corresponding to the automerization and applying
