Chemistry Reference
In-Depth Information
Figure 1.3. Neutral TTF molecule with the Cartesian coordinate system used for
the determination of its symmetry operations. C, S and H are represented by black,
medium grey and light grey balls, respectively.
where
E
represents the identity operator (from German
Einheit
),
C
2
(
x
)
,
C
2
(
y
)
,
C
2
(
z
) stand for proper rotations of
π
degrees (rotations of order 2) with respect
to the
x
-,
y
- and
z
-axes, respectively,
σ
yz
are planes of symmetry with
respect to the
xy
-,
xz
- and
yz
-planes, respectively (from German
Spiegel
), and
i
is
an inversion operation with its centre at the origin of the coordinate system. The full
set of such symmetry operations leads to the
D
2
h
point group (see Appendix A for
the symmetry operations of other point groups of interest). Table 1.3 classifies some
of the molecules from Table 1.1 according to their corresponding point groups. The
table is divided into three blocks. The topmost one contains the special groups
C
∞
v
and
D
∞
h
, characteristic of asymmetric and symmetric linear molecules, respec-
tively, and the groups containing high-order axes, such as
I
h
. The second block
refers to point groups containing no proper or improper axes of rotation, such as
C
s
, and finally the third block contains those groups containing proper axes of
rotation.
In Table 1.3 we have assumed that molecules belonging to the groups with
proper axes of rotation (third block) are planar (
σ
xy
,
σ
xz
,
σ
xy
applies). This is not strictly true
since molecules tend to deform in space in order to accommodate to the 3D crystal
structure. One of the most notable examples is BEDT-TTF, which is illustrated
in Fig. 1.4, where the dimer structure of the monoclinic phase of neutral BEDT-
TTF is shown. From the figure we observe that the molecules are non-planar, the
angles formed between the planes containing the central carbon-carbon bond and
the four neighbouring sulfur atoms (TTF core) with the planes containing the four
more external sulfur atoms (half TTF core and ethylenedithia groups) are 166.6
and 162.6 degrees, respectively. However, the most remarkable non-planarity is
observed for the outer (CH
2
)
2
groups. Upon oxidation of BEDT-TTF these angles
become larger, as will be discussed in Section 1.5.
PTCDA represents a further example of non-planarity. When chemisorbed on
an Ag(111) surface the carboxylic oxygen atoms become 0.018 nm closer to the
