Chemistry Reference
In-Depth Information
t
^
-
D
2d
t
^
-
C
2v
(
d
)
t
^
-
C
s
(
d
)
Fig. 15 Three-dimensional projections of the orthogonally twisted conformations of
homomerous, heteromerous, and monosubstituted BAEs including their point group symmetry
operators
(
z
) the central ethylene group is confined to planarity. However, the two tricyclic
moieties may be twisted out-of-plane like a propeller blade and thus non-planar.
Orthogonally Twisted Conformations
An orthogonally twisted t
⊥
homomerous BAE may have
D
2d
symmetry. The point
group
C
2v
(
d
) is characteristic of orthogonally twisted heteromerous BAEs and
C
s
(
d
) of monosubstituted BAEs (Fig.
15
). Note that in disubstituted BAEs the
orthogonally twisted conformation has
C
2
symmetry and is chiral. The torsion
angles of the central ethylene group are no longer symmetry constrained to
90
.
The symmetry properties of such a conformation are identical to, e.g., ts
E-RPR
0
-
C
2
(
x
)orta
Z-RPR
0
-
C
2
(
y
) (see above). However, the pure ethylenic twist
ω
will be close
to 90
. Thus, the definitions of helicity (
P/M
) based on
as well as of
E/Z
and
syn
/
anti
will depend on the small deviation from 90
. In this situation it is better to label
the two enantiomeric conformations (
P
)or(
M
) based on the torsion angle
τ
(C
9a
-C
9
-
C
9
0
-C
9a
0
), which will be either close to +90
or close to
ω
90
and thus clearly
distinct (i.e., applying the concept of axial chirality; cf. Sect.
2.2
). From a symmetry
point of view, t
⊥
PM
-
S
4
is an interesting case. In this conformation, the two tricyclic
moieties are non-planar. They may, e.g., be propeller twisted with positive and
negative helicity, respectively, as indicated by the subscript
PM
. As a result, the
mirror planes
y
)of
D
2d
are lost. However, the two
non-planar moieties are still equivalent and symmetry related by
S
4
, and
S
4
3
. The
torsion angles of the central ethylene group are constrained to
˃
d
(
x
¼
y
) and
˃
d
(
x
¼
90
. The confor-
mation is achiral, but both tricyclic moieties are chiral with opposite helicity.
Twisted Conformations
The symmetric twisted conformations of homomerous BAEs are classified as t
P
-
D
2
and its enantiomer t
M
-
D
2
. Non-equivalent moieties in heteromerous BAEs lead to
