Chemistry Reference
In-Depth Information
Z
-isomers and pairs of permutation operators and rotation/reflection operators
results in a molecular symmetry group of larger size, however, may allow one to
derive the above mechanism in a more consistent manner.
4.3.8 Summary of the Dynamic Stereochemistry of Homomerous BAEs
Symmetry considerations, e.g., the molecular symmetry group approach, are very
powerful tools to derive and classify all possible types of conformations for
minima, transition states, and higher order saddle points. Permutation and
permutation-inversion operators may also be used to derive the mechanisms of
automerization and isomerization reactions of these conformations and the connec-
tivity of the various labeled versions of the minima and transition states. Thus, the
molecular symmetry group allows a systematic analysis of the conformational
space and dynamic stereochemistry of molecules. However, symmetry consider-
ations alone can only predict stationary points [
280
]. They cannot distinguish
minima, transition states, and higher order saddle points. Such a classification
requires calculations of the actual geometries and their vibrational frequencies or
experimental results on structures and their relative energies.
In theoretical studies, prior knowledge about symmetry allows one to introduce
symmetry constraints that reduce the degrees of freedom and therefore the number
of coordinates that have to be optimized. In the optimization of a transition state,
symmetry rules allow one to distinguish cases where a symmetry constrained
energy minimization will converge to the transition state from cases where a full
transition state search is necessary. A symmetry-constrained minimization is suffi-
cient when the transition vector is not totally symmetric, i.e., the transition state has
a higher symmetry than the structures along the pathways to reactants and products
[
270
]. This greatly facilitates calculations.
In view of the large number of possible mechanisms for automerizations and
isomerizations of BAEs predicted by the symmetry considerations, an illustrative
example based on a scenario of plausible assumptions about the conformational
type and symmetry of the minima and transition states may be instructive.
The following conformations have been observed experimentally in BAEs and
may be assumed to be (local) minima:
Twisted conformations t-
D
2
anti
-Folded conformations a-
C
2h
(
y
)
syn
-Folded conformations s-
C
2v
(
x
)
Twisted conformations have been observed, e.g., in the X-ray crystal structures
of bifluorenylidene (2)[
47
], and have been identified with the thermochromic and
photochromic B forms.
anti
-Folded conformations have been observed, e.g., in the
X-ray crystal structures of bianthrone (3)[
56
-
60
], and dixanthylene (4)[
70
,
71
].
syn
-Folded conformations have been observed in the X-ray crystal structure
of tetrabenzo[7,7
0
]fulvalene (8) and related BAEs [
61
,
76
], and have been identified
as the photochromic E form. The relatively small deviations of the conformations
