Photochemistry and Photophysics of Coordination Compounds

18 V. Balzani et al.
Fig. 11 Free energy dependence of electron-transfer rate (i, initialstate;f ,finalstate)according
to the Marcus (a) and quantum mechanical (b) treatments.Thethreekinetic
regimes (normal, activationless, and “inverted”) are shown schematically in terms of
Marcus parabolas
The reorganizational energy λ can be expressed as the sum of two independent
contributions corresponding to the reorganization of the “inner” (bond
lengths and angles within the two reaction partners) and “outer” (solvent
reorientation around the reacting pair) nuclear modes:
λ = λi + λo . (20)
The electronic transmission coefficient κel is related to the probability of
crossing at the intersection region (Fig. 10). It can be expressed by the equation
κel = 2 � 1–exp � ��
– νel/2νN 2–exp � � , (21)
– νel/2νN
where
νel =
�
2 Hel� 2
h
� π 3
λRT
�1/2
, (22)
and Hel is the matrix element for electronic interaction (Fig. 10).
If Hel is large, νel ≫ νN, κel =1and
�
– ∆G ‡ �
kel = νN exp
(adiabatic limit) . (23)
RT