Chemistry Reference
In-Depth Information
Fig. 6.6
Allowed CT transitions from the
t
2
g
shell to
ψ
-or
χ
-type ligand acceptor orbitals for
tris-chelate complexes with
D
3
symmetry
Here, we have made use of the fact that the sum of the three dipole vectors vanishes.
The effective transfer term thus becomes:
3
8
κ
μ
A
μ
e
(t
2
g
)
e
(ψ)
=
→
(6.99)
In the Wigner-Eckart formalism, this matrix element is written as:
e
(t
2
g
)
|
μ
x
|
e
(ψ)
=
E
|
EθE
e(t
2
g
)
e(μ)
e(ψ)
(6.100)
The coupling coefficient in this equation is equal to 1
/
√
2. We can thus identify the
reduced matrix element as:
√
3
2
κμ
A
e(t
2
g
)
e(μ)
e(ψ)
=
(6.101)
All other
e
e
transfer terms can then be obtained by simply varying the coupling
coefficients. We give one more example of a transition that requires an operator
which is
μ
y
polarized:
→
e
θ
(t
2
g
)
e
(ψ)
=
√
8
κ
ψ
C
ψ
C
1
ψ
B
2
ψ
A
ψ
B
|
μ
|
−
|
μ
|
−
−
1
√
8
κ(
μ
B
−
=
μ
C
)
(6.102)
The vector
μ
B
−
μ
C
in this expression is directed in the
μ
y
d
irection, as required
by the selection rule. Moreover, the length of this vector is
√
3
μ
⊥
:
2
μ
⊥
2
3
μ
⊥
2
(
μ
B
−
μ
C
)
·
(
μ
B
−
μ
C
)
=
−
2
μ
B
·
μ
C
=
(6.103)
