Chemistry Reference
In-Depth Information
H
ence
, the transfer-dipole length for this
y
-polarized transition also measures
√
3
/
8
κ
, which is exactly the same as for the
x
-polarized transition, given in Eq.
(
6.99
). This is expected since the corresponding coupling coefficients,
E
|
EθE
and
, are equal.
Using the transfer model, we can also express the reduced matrix elements for
the
e
→
a
2
channel. Even though there is no overlap between these orbitals, they do
give rise to a transfer-term intensity. Orbital interaction does indeed delocalize the
e(t
2
g
)
orbitals over the ligands. The dipole operators, centred on the complex origin,
will then couple the
e(ψ)
and
a
2
(ψ)
ligand-centred orbitals. Hence, we write:
Eθ
|
EE
μ
e
(t
2
g
)
a
2
(ψ)
=−
e
(ψ)
a
2
(ψ)
e
(t
2
g
)
|
H
|
e
(ψ)
→
|
μ
|
E
ψ
−
E
t
2
g
3
2
κ
e
(ψ)
a
2
(ψ)
=
|
μ
|
(6.104)
The dipole matrix element in this expression can easily be evaluated:
e
(ψ)
a
2
(ψ)
=
3
√
2
2
ψ
A
ψ
C
1
ψ
B
ψ
C
ψ
A
ψ
B
|
μ
|
−
−
|
μ
|
+
+
1
3
√
2
(
2
μ
A
−
=
μ
B
−
μ
C
)
1
√
2
μ
A
=
(6.105)
The total transfer term is obtained by combining Eqs. (
6.104
) and (
6.105
):
√
3
2
κ
μ
A
μ
e
(t
2
g
)
→
a
2
(ψ)
=
(6.106)
A final task is to calculate the transition-moments between the corresponding multi-
electronic states based on the orbital-transition moments obtained. In the tris-chelate
complex under consideration, a
1
A
1
→
1
E
state transition can be associated with
1
A
1
corresponds to the closed-shell ground
each allowed orbital-transition. The
state, based on the
(t
2
g
)
6
e
transitions will
give rise to a twofold-degenerate
1
E
state. As an example, the
θ
states are written in
determinantal notation as follows, where we write only the orbitals that are singly
occupied:
configuration. Both the
e
→
a
2
and
e
→
√
2
e
(t
2
g
)α
a
2
(ψ)β
−
e
(t
2
g
)β
a
2
(ψ)α
a
2
)
=
1
1
E
θ
(e
→
e)
=
2
e
θ
(t
2
g
)α
e
θ
(ψ)β
−
e
θ
(t
2
g
)β
e
θ
(ψ)α
−
1
(6.107)
1
E
θ
(e
→
e
(t
2
g
)α
e
(ψ)β
+
e
(t
2
g
)β
e
(ψ)α
