Chemistry Reference
In-Depth Information
p
-
D
2h
t
-
D
2d
^
(
1
8)(1'8')
C
2
(z)
(18)(1'8')
C
2
(z)
(11')(88')*
s
h
(
xy
)
1
8
8
1
9
9
'
9
(
1
1')(88')(99')
C
2
(y)
(18')(81')(9
9
')
C
2
(x)
(18')(81')(99')
C
2
(x)
1
'
(11')(88')(99')
C
2
(y)
9'
8'
8
'
1'
E
*
s
v
(yz)
(18)(1'8')* s
v
(xz)
(1'8')* s
d
(x=-y)
(18)* s
d
(x=y)
t
-
D
2
a
-
C
2h
(
y
)
s
-
C
2v
(
x
)
(18)(1'8')
C
2
(z)
(11')
(88')
(99')
C
2
(y)
1
1
8
1
8
8
9
9
9'
9
(1
8
')(81')
(99')
C
2
(x)
9
'
1'
(11')(88')
(99')*
s
v
(xz)
9'
(11')(88')
(99')
C
2
(y)
(18')(81')
(99')
C
2
(x)
1'
1'
8'
8'
8'
(18)(1'8')*
s
h
(y)
(18)(1'8')*
s
v
(xz)
Fig. 21 Rotation axes, reflection planes and corresponding permutation-inversion operators in the
conformations p-
D
2h
, t
⊥
-
D
2d
, t-
D
2,
a-
C
2h
(
y
), and s-
C
2v
(
x
) of representative BAEs. The rotation-
reflection axis
S
4
of
D
2d
is oriented along the
z
-axis; the symmetry center
i
of
D
2h
and
C
2h
is at the origin
symmetry element at all. Furthermore, the permutation-inversion operators of the
molecular symmetry group apply to all conformations (possibly creating new
versions of the conformation with different orientation and labeling of the mole-
cular framework; see below), while the point group operators are defined only if
they are present in the respective point group of a specific conformation.
In accordance with the conventions customary in vibrational spectroscopy [
281
],
the
z
-axis may be chosen to go through the atoms C
9
and C
9
0
(and possibly also
through X and Y). The
y
-axis may be chosen to go through the centers of the fjord
regions and the
x
-axis to pass through the center of the double bond and perpen-
dicular to the mean plane of the molecule. Thus, the
yz
-plane would be the mean
plane of the molecule and a projection down the
x
-axis onto this plane should
always give a figure close to the schematic 2D representation shown in Fig.
1
, i.e.,
with the first moiety up in the positive direction of the
z
-axis and atoms 1 and 1
0
on
the left side, in the negative direction of the
y
-axis. Figure
21
illustrates the
orientation of the molecule and the permutation-inversion operators corresponding
to symmetry axes and reflection planes for the planar
D
2h
symmetric conformation
p of bifluorenylidene (2), the orthogonally twisted
D
2d
symmetric conformation t
⊥
of dixanthylene (4), the twisted
D
2
symmetric conformation t of bifluorenylidene
