Chemistry Reference
In-Depth Information
6.8 Application: Linear and Circular Dichroism
Selection rules are of primary importance in spectroscopy, where they provide direct
evidence concerning the nature of excited states. As an application, we study the
linear and circular dichroism of tris-chelate transition-metal complexes [
14
]. The
prototype is a divalent ruthenium complex with three 2
,
2
-bipyridyl ligands, which
is an important chromophore for energy conversion. In this section we shall describe
the charge transfer and intra-ligand transitions of this type of complex. The linear
dichroism (LD) spectrum measures the absorption of the chromophore under plane-
polarized incident light for different orientations of the polarization with respect to
the molecular frame. This requires that the molecules should be embedded in an
oriented phase, such as a crystalline host. Circular dichroism (CD) measures the
difference in absorption between left and right circularly polarized light. Since this
is based on the intrinsic helicity of the molecule, it can be performed in non-oriented
medium, such as a solution.
As always, we start the treatment by making a simple sketch of the structure.
Two sets of Cartesian axes are relevant. In the usual octahedral coordinate system
the
x,y,z
-axes coincide with the metal-ligand bond directions, assuming that the
ligator atoms form a perfect octahedron. In addition, in Fig.
3.6
of Chap.
3
aprimed
x
,y
,z
-coordinate system was introduced, which is adapted to the tris-chelate ge-
ometry. The
z
-axis is along the threefold direction, and the
x
axis is oriented along
a twofold axis, coinciding with the bisector of the positive
x
and the negative
y
axes. Next, we determine the point group, which in the present case is
D
3
.This
is a rotational group, which implies that the molecule is chiral. The figure shows
the
-enantiomer.
7
Thirdly, we define the functional basis. The relevant orbitals
are the metal
t
2
g
orbitals, which are fully occupied in the Ru
2
+
ground state, and
the frontier orbitals on the ligand. For conjugated bidentate ligands, such as 2
,
2
-
bipyridyl (bipy) or 2
,
4-pentanedionate (also named “acetylacetonate”, acac
−
), the
frontier orbitals are of
π
-type. The essential parts of these orbitals are the contribu-
tions on the ligator atoms. These are either symmetric or antisymmetric with respect
to the twofold axis through the bidentate ligand, as shown in Fig.
6.5
. Following
Orgel, we denote them as
χ
-or
ψ
-type, respectively [
15
]. The standard techniques
of characters and projection operators yield SALCs for all these basis sets. The re-
sults are shown in Table
6.4
.Forthe
e
-irrep the components are labelled as
e
θ
and
e
, following the standard canonical format. As a splitting field we use the twofold
axis along
x
. Finally, we also include in the table the symmetries of the transi-
tion dipoles, which are the operators for the optical transitions. This completes the
groundwork for the symmetry analysis.
7
In tris-chelate complexes
refers to a right-handed (
dextro
) helix. A left-handed helix (
lævo
)is
denoted as
Λ
.
