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accessible to the molecule, i.e., if a molecule can adopt a twisted and an
anti
-folded
conformation, or a twisted and a
syn
-folded conformation, or an
anti
-folded and a
syn
-folded conformation. In all three cases, the molecular symmetry group (the
smallest group containing all permutation-inversion operators of each two of the
above three point groups) is
D
2h
(or higher). However, the conclusion that the
planar (
D
2h
) conformation is the transition state of the enantiomerization of a
twisted conformation or the transition state for conformational inversion of an
anti
-folded or
syn
-folded conformation is not valid. The planar conformation may
not be accessible at all under the given experimental conditions.
Permutation-inversion operators corresponding to feasible isomerizations or
inversions of a molecule should not be confused with the reaction mechanism of
such a process, i.e., the transition state or a description based on the continuous
trajectory of atoms leading from educts to products. They only describe the
outcome of the process [
255
]. For example, dixanthylene (4) was found to be
anti
-folded in the solid state, and is thermochromic, implying a thermally populated
twisted conformation (the B form) (cf. Sects.
2.3
and
2.5
)[
3
]. On the basis of the
existence of both an
anti
-folded and a twisted conformation, one may predict that
conformational inversion is feasible. This was indeed shown by DNMR [
170
]. How-
ever, this does not prove that the planar conformation is involved as a transition
state (or in any other way) in the thermochromic process or in the conformational
inversion. Such mechanistic conjectures are not justified.
4.3 Dynamic Stereochemistry of Homomerous BAEs
The molecular symmetry group of unsubstituted homomerous BAEs with feasible
E
,
Z
-isomerizations is
G
16
(order
h
MSG
¼
16). The point groups for planar, orthog-
onally twisted, twisted,
anti
-folded,
syn
-folded, and various mixed conformations
have been defined in the first column of Table
4
. For simplicity, in the following
discussion only the experimentally observed, highly symmetric conformation types
a-
C
2h
(
y
), s-
C
2v
(
x
), and t-
D
2
will be considered as minima, i.e., as educts and
products. The planar conformation is expected not to be a minimum energy
conformation in BAEs. The dynamic stereochemistry of the planar conformation
and the orthogonally twisted conformation will not be analyzed. (For a discussion
of the dynamic stereochemistry of p-
D
2h
ethylene (C
2
H
4
) and t
⊥
-
D
2d
diborane
(B
2
H
4
) see [
254
].) However, all conformations will be considered as potential
transition states.
In Sects.
4.3.1
to
4.3.3
, all degenerate isomerization processes of the three main
conformations a-
C
2h
(
y
), s-
C
2v
(
x
) and t-
D
2
are derived by an analysis of the effect
of the permutation-operators of the molecular symmetry group
G
16
on the labeled
versions of the respective conformations. In Sects.
4.3.4
to
4.3.7
, all conformational
isomerization processes interconverting the conformations a-
C
2h
(
y
), s-
C
2v
(
x
), and
t-
D
2
are discussed. For the automerizations and the isomerizations, all possible
transition state point groups and conformations for direct one step mechanisms are
