Photochemistry and Photophysics of Coordination Compounds

Photochemistry and Photophysics of Coordination Compounds 23
transfer can be expressed as a function of the spectroscopic and photophysical
properties of the two molecular components:
k F en = 8.8 × 10–25 K2 Φ
JF =
n4r6 JF
(32)
ABτ � F(ν)ε(ν)/ν 4 dν
� F(ν)dν
, (33)
where K is an orientation factor which accounts for the directional nature
of the dipole–dipole interaction (K 2 =2/3 for random orientation), Φ and τ
are the luminescence quantum yield and lifetime of the donor, respectively,
n is the solvent refractive index, rAB is the distance (in ˚A) between donor
and acceptor, and JF is the Förster overlap integral between the luminescence
spectrum of the donor, F � ν � , and the absorption spectrum of the acceptor,
ε � ν � ,onanenergyscale(cm –1 ). With a good spectral overlap integral and
appropriate photophysical properties, the 1/r6 AB distance dependence allows
energy transfer to occur efficiently over distances largely exceeding the molecular
diameters. The typical example of an efficient coulombic mechanism
is that of singlet–singlet energy transfer between large aromatic molecules,
a process used by nature in the “antenna” systems of the photosynthetic apparatus
[72]:
∗
A(S1)–L–B(S0) → A(S0)–L– ∗ B(S1). (34)
4.4.2
Exchange Mechanism
The exchange (also called Dexter-type [73]) mechanism requires orbital overlap
between donor and acceptor, either directly or mediated by the bridge
(through-bond), and its rate constant, therefore, decreases with increasing
distance:
k D 4π2 � en
en = H
h
�2 JD , (35)
where
H en = H en �
(0) exp – βen � �
rAB – r0
2
�
(36)
� � � � �
F ν ε ν dν
JD = � � � � � � . (37)
F ν dν ε ν dν
The exchange interaction can be regarded (Fig. 13) as a double electrontransfer
process, one electron moving from the LUMO of the excited donor
to the LUMO of the acceptor, and the other from the acceptor HOMO to
the donor HOMO. Therefore, the attenuation factor β en for exchange energy