Chemistry Reference
In-Depth Information
The three vectors of the ligand positions can be expressed in a row notation for the
primed
x
,y
,z
coordinate system as:
R
A
=
ρ(
1
,
0
,
0
)
R
B
=
ρ
2
,
√
3
2
,
0
1
−
(6.93)
√
3
ρ
2
,
0
1
2
,
R
C
=
−
−
The transfer term then becomes:
μ
e
(t
2
g
)
ψ
A
=−
→
e
κ
R
A
=
κ
μ
A
(6.94)
where the parameter
κ
is an overlap factor which indicates what fraction of the
charge is actually transferred:
√
2
H
π
E
ψ
−
ψ
A
=−
|
H
|
e
(t
2
g
)
κ
E
t
2
g
=−
(6.95)
E
ψ
−
E
t
2
g
Note that the transfer term is always polarized in the direction of the transferred
charge.
This parametrization can now be used to calculate the transfer term for the rele-
vant trigonal transitions. The Hamiltonian operator is of course totally symmetric, so
allowed interactions can take place only between orbitals with the same symmetry,
and are independent of the component; hence:
e
(t
2
g
)
|
H
|
e
(ψ)
=
√
3
H
π
e
θ
(t
2
g
)
(6.96)
√
3
H
π
e
θ
(ψ)
=
|
H
|
Symmetry prevents interaction between the
a
1
(t
2
g
)
and
a
2
(ψ)
orbitals. The
metal-ligand
π
acceptor interaction will thus stabilize the
e
-component of the
t
2
g
shell, while leaving the
a
1
-orbital in place, as shown in the simple orbital-energy
diagram in the left panel of Fig.
6.6
. We can now calculate the transfer term for the
e
a
2
orbital transitions. In each case only one component needs to be
calculated. The interaction element in this case is obtained from Eq. (
6.96
) and the
transfer fraction reads:
→
e
and
e
→
3
2
κ
√
3
H
π
E
ψ
−
−
E
t
2
g
=
(6.97)
The transfer-dipole element is given by:
6
2
ψ
A
ψ
C
=
1
1
6
[
1
2
μ
A
ψ
B
ψ
C
2
ψ
A
ψ
B
−
−
|
μ
|
−
−
4
μ
A
+
μ
B
+
μ
C
]=
(6.98)
