6.8 Application: Linear and Circular Dichroism
145
Fig. 6.7 Allowed intra-ligand transitions from χ -toψ -type ligand orbitals for tris-chelate complexes with D 3 symmetry. The circular dichroism has a lower right-circularly polarized (rcp) band
and an upper left-circularly polarized (lcp) band. This gives the CD spectrum the appearance of the
first derivative of a Gaussian curve, with a negative part at longer wavelength and a positive part at
shorter wavelength
We designate these dipole moments as µ
A , µ
B , µ
C . These vectors can be expressed in a row notation for the primed x ′ ,y ′ ,z ′ coordinate system as follows:
µ
A = μ
0,
1
√
3
,
√
2
√
3
µ
B = μ
−
1
2
, −
1
2
√
3
,
√
2
√
3
µ
C = μ
1
2
, −
1
2
√
3
,
√
2
√
3
(6.109)
The scalar products between these orientations are equal to 1/2, which corresponds
to angles of 60 ◦ . Each of the three transitions gives rise to an excited state. In D 3
symmetry these states transform as A 2 + E. The composition of these exciton states 8
is as follows:
1 A 2
=
1
√
3
(χ A → ψ A )
1 + (χ B → ψ B )
1 + (χ C → ψ C )
1
1 E θ
=
1
√
2
−(χ B → ψ B )
1 + (χ C → ψ C )
1
1 E ǫ
=
1
√
6
2(χ A → ψ A )
1 − (χ B → ψ B )
1 − (χ C → ψ C )
1
(6.110)
8 The excitation creates an electron-hole pair, which can move from one ligand to another. This is
called an exciton.