Chemistry Reference
In-Depth Information
The exciton states on both chromophores are interchanged by the twofold axis
and can be recombined to yield a symmetric and an antisymmetric combination,
denoted as
A
and
B
, respectively. One has:
√
2
|
Ψ
1
+|
Ψ
2
1
|
Ψ
A
=
√
2
|
Ψ
2
1
|
Ψ
B
=
Ψ
1
−|
The corresponding transition dipoles are oriented along the positive
y
- and neg-
ative
z
-direction, respectively:
√
2
μ
0
,
cos
α
2
,
0
μ
A
=
√
2
μ
0
,
0
,
sin
α
2
μ
B
=
−
The dipole-dipole interaction is given by
1
4
π
0
cos
α
R
12
V
12
=
(9)
For
α<π/
2, the dipole orientation is repulsive. As a result, the in-phase cou-
pled exciton state
state.
Finally, we also calculate the magnetic transition dipoles, using the expressions
from Sect.
6.8
:
|
Ψ
A
will be at higher energy than the out-of-phase
|
Ψ
B
iπν
√
2
(
r
1
×
iπνμ
√
2
R
12
sin
α
m
A
=
μ
1
+
r
2
×
μ
2
)
=
2
(
0
,
1
,
0
)
iπ
ν
√
2
(
r
1
×
iπνμ
√
2
R
12
cos
α
2
(
0
,
0
,
1
)
These results are now combined in the Rosenfeld equation to yield the rotatory
strength of both exciton states:
m
B
=
μ
1
−
r
2
×
μ
2
)
=
πνμ
2
2
R
A
=
R
12
sin
α
