3 Nuclear and Electronic Factors
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in Electron Transfer Distance Dependence of Electron-Transfer Rates Norman Sutin Chemistry Department, Brookhaven National Laboratory, Upton, NY 11973
The factors that determine the distance dependence of electron-transfer rates are discussed in terms of current models. These models are used to analyze recent data on intramolecular electron-transfer rates in bridged systems. It is found that, in certain systems, the distance dependence of the nuclear factor is larger than that of the electronic factor, although the opposite is true in other systems. Theoretical models are available for calculating the dependence of the nuclear factor on separation distance, and a great deal of progress has been made in deriving expressions describing the distance dependence of the electronic factor. Despite these achievements, there is still considerable uncertainty regarding the values of certain of the key parameters to be used in calculating the magnitudes of the electronic coupling elements in complex systems.
R . E C E N T S T U D I E S O F M O D E L C O M P O U N D S (1-8) a n d naturally o c c u r r i n g systems (9-21) have l e d to a d e e p e r u n d e r s t a n d i n g of the factors d e t e r m i n i n g the distance d e p e n d e n c e of electron-transfer rates. T h e s e studies have s h o w n that the nuclear a n d electronic factors b o t h decrease w i t h i n c r e a s i n g separation of the redox sites. T h i s finding is i n accord w i t h theoretical p r e d i c t i o n s (22-28). T h i s chapter presents some recent results o n the distance d e p e n d e n c e of optical a n d t h e r m a l electron-transfer rates. It i n c l u d e s examples of h o w studies of m o d e l systems can p r o v i d e i n f o r m a t i o n about the d e t a i l e d electron-transfer pathways i n c o m p l e x , naturally o c c u r r i n g systems. 0065-2393/91/0228-0025$06.00/0 © 1991 American Chemical Society
In Electron Transfer in Inorganic, Organic, and Biological Systems; Bolton, J., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1991.
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E T IN INORGANIC, ORGANIC, A N D BIOLOGICAL SYSTEMS
Theoretical Framework T h e focus o f this chapter w i l l b e i n t r a m o l e c u l a r e l e c t r o n transfer at r o o m t e m p e r a t u r e . F i r s t , the f o r m a l i s m that w i l l b e u s e d is o u t l i n e d . N u c l e a r t u n n e l i n g corrections w i l l b e n e g l e c t e d ; such corrections are not large unless the t e m p e r a t u r e is l o w or the activation process involves changes i n h i g h f r e q u e n c y modes. I n the absence of such effects, the first-order rate constant for i n t r a m o l e c u l a r e l e c t r o n transfer b e t w e e n a d o n o r a n d an acceptor site can be expressed as the p r o d u c t of an electronic transmission coefficient K ,
Downloaded by STANFORD UNIV GREEN LIBR on July 31, 2012 | http://pubs.acs.org Publication Date: May 5, 1991 | doi: 10.1021/ba-1991-0228.ch003
E L
an effective n u c l e a r v i b r a t i o n f r e q u e n c y v
n
that destroys the activated c o m
p l e x configuration, a n d a n u c l e a r factor κ
η
(eq 1) (22,
k = κ ν κ 6ΐ
η
29-33) (1)
η
T h e electron-transfer reaction is adiabatic ( κ
~ 1 ) w h e n the p r o b a b i l i t y o f
βΙ
e l e c t r o n transfer i n the activated c o m p l e x is h i g h , a n d nonadiabatic ( K
G1
<
>
is nonadiabatic) w h e n v K v e l
n
e l
n
