Electron Transfer in Inorganic, Organic, and Biological Systems

17 Puzzles of Electron Transfer John R. M i l l e r

Downloaded by UNIV OF ARIZONA on December 16, 2012 | http://pubs.acs.org Publication Date: May 5, 1991 | doi: 10.1021/ba-1991-0228.ch017

Chemistry Division, Argonne National Laboratory, Argonne, IL 60439

After much progress several questions remain in our understanding of electron-transfer reactions, including a lack of clear understanding of the factors controlling the dependence of rate on distance. Distance dependence of long-distance electron-transfer rates is similar in a variety of experimental situations, such as rigid glasses, donors and acceptors bound to rigid spacer groups, monolayer assemblies, and proteins. But two puzzling cases in which the distance dependence is dramatically weaker have not been understood and interpreted. An even more serious lack of understanding exists for control of rate by orientation. In some cases rates depend strongly on solvent polarity, but in at least one other case the rates seem to be independent of polarity. Important energetic quantities such as free energy change and solvent reorganization energy are often difficult to obtain and are particularly difficult to predict because of inaccuracies of the dielectric continuum model. This chapter compiles a list of many of these problems, but makes no attempt to suggest the nature of their solutions.

^MAJOR PROGRESS HAS DRAMATICALLY CHANGED

o u r concepts of e l e c t r o n transfer reactions over the last several years b y d e f i n i n g the distances, e n ergetics, a n d e v e n orientations of electron donor a n d acceptor groups. T h i s chapter w i l l e m p h a s i z e the aspects of electron transfer (ET) that w e u n d e r stand poorly. M o s t of the m a n y recent successes of e l e c t r o n transfer are discussed elsewhere i n this v o l u m e . O t h e r chapters, p a r t i c u l a r l y that of B o l t o n a n d A r c h e r , offer an i n t r o d u c t i o n to electron transfer.

Experiment and Theory A l t h o u g h the past few years have seen explosive g r o w t h i n o u r k n o w l e d g e about electron-transfer processes, the p r o b l e m s or p u z z l e s i n v o l v i n g v e r y 0065-2393/91/0228-0265$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.

266

E T IN INORGANIC, O R G A N I C , A N D BIOLOGICAL SYSTEMS


basic questions about the electron-transfer process are still n u m e r o u s a n d substantial. L o n g - t e r m goals for u n d e r s t a n d i n g e l e c t r o n transfer c o u l d l e a d to t h e design of t r u l y useful m o l e c u l a r devices for p h o t o c h e m i c a l e n e r g y c o n v e r s i o n o r o t h e r e n e r g y - c h a n n e l i n g processes. Those goals w i l l r e q u i r e us to u n d e r s t a n d a n u m b e r of questions i n great detail. H o w e v e r , this c h a p t e r w i l l n o t focus o n details because t h e p u z z l e s about v e r y basic questions i n e l e c t r o n transfer are so n u m e r o u s . T h e basic " g o l d e n r u l e " expression for nonadiabatic electron-transfer rate processes (1-15) can b e u s e d to categorize these p u z z l e s .

(1) I n this expression, t h e rate (fc ) is a p r o d u c t of an e l e c t r o n i c c o u p l i n g b e t w e e n reactants a n d products ( H j , w h i c h depends strongly o n distance (r), o n orientation of the donor a n d acceptor m o l e c u l e s , a n d o n t h e F r a n c k - C o n d o n w e i g h t e d density o f states ( F C W D ) . I n e q 1, his Planck's constant d i v i d e d b y 2 ^ . T h e F C W D gives t h e p r o b a b i l i t y o f finding t h e d o n o r a n d acceptor groups a n d t h e s u r r o u n d i n g m e d i u m i n a n u c l e a r configuration such that a n e n e r g y l e v e l o f t h e p r o d u c t matches that o f t h e reactants. W h e n s u c h a m a t c h o f e n e r g y levels occurs there is a chance, p r o p o r t i o n a l to Η , for t h e e l e c t r o n to j u m p to t h e acceptor. T h e electronic c o u p l i n g decays r a p i d l y and e x p o n e n t i a l l y w i t h distance w h e n m a t e r i a l b e t w e e n t h e e l e c t r o n d o n o r and t h e e l e c t r o n acceptor is classically f o r b i d d e n to t h e e l e c t r o n . T h e ex p o n e n t i a l attenuation o f the rate w i t h distance occurs because t h e e l e c t r o n transfer is b y nature a n e l e c t r o n - t u n n e l i n g process. et

φ

2

T h e F r a n c k - C o n d o n w e i g h t e d d e n s i t y o f states contains most o f t h e d e p e n d e n c e o f the rate o n free e n e r g y change ( A G ) , t e m p e r a t u r e , solvent p o l a r i t y , a n d changes i n t h e structure of the donor a n d acceptor m o l e c u l e s w h e n t h e y a d d o r release a n e l e c t r o n . A c h i e v i n g a n u c l e a r configuration i n w h i c h e l e c t r o n transfer is a l l o w e d b y energy conservation often i n v o l v e s t h e r m a l activation, p a r t i c u l a r l y o f t h e solvent molecules i n a polar solvent. It m a y also i n v o l v e q u a n t u m m e c h a n i c a l motions of n u c l e i w i t h i n t h e d o n o r and acceptor groups themselves. S u c h a n " a c t i v a t e d " n u c l e a r configuration a c h i e v e d b y q u a n t u m m e c h a n i c a l motions is sometimes r e f e r r e d to as n u c l e a r tunneling. 0

T h i s chapter w i l l d i v i d e t h e puzzles i n t o those i n v o l v i n g e l e c t r o n i c c o u p l i n g , those i n v o l v i n g t h e F r a n c k - C o n d o n part of t h e p r o b l e m , a n d those d e p e n d e n t o n b o t h to such an extent that t h e y cannot b e classified.

Puzzles of Electronic Coupling Distance Dependence. E l e c t r o n - t r a n s f e r rates have b e e n m e a s u r e d as a f u n c t i o n o f distance i n rigid glasses (16-21), i n d i f u n c t i o n a l m o l e c u l e s


17.

MILLER

Puzzles of Electron

Transfer

267

i n w h i c h a r e l a t i v e l y r i g i d spacer group holds the d o n o r a n d acceptor apart (22-34), i n m o n o l a y e r assemblies (34-39), a n d i n proteins (40-46). W h e r e it has b e e n possible to accurately measure d e p e n d e n c e o n distance, it has always b e e n f o u n d that electron-transfer rates decayed e x p o n e n t i a l l y because of the exponential decrease of electronic c o u p l i n g w i t h distance.


i V ( r ) = i V ( r = 0) exp (~a(r

-

r )) 0

(2)

M a j o r questions about the distance d e p e n d e n c e r e m a i n . D o e s the at t e n u a t i o n p a r a m e t e r change α substantially as the nature of the m a t e r i a l b e t w e e n the d o n o r a n d acceptor group changes? A r e t h e r e o t h e r i m p o r t a n t factors i n f l u e n c i n g a ? W h a t , p r e c i s e l y , are the values of a , w h i c h c a n b e q u i t e i m p o r t a n t at l o n g distances because of the exponential nature of the process? G r e a t care is r e q u i r e d i n the m e a s u r e m e n t of α because distance d e p e n d e n c e of electron-transfer rates can also result from d i s t a n c e - d e p e n d ent factors i n F C W D . Solvent reorganization energy is d i s t a n c e - d e p e n d e n t , a n d the F C W D tends to b e m o r e strongly d i s t a n c e - d e p e n d e n t for w e a k l y exoergic reactions, w h i c h are the easiest to measure (17). A p p a r e n t v e r y large values of α have b e e n q u o t e d i n c o r r e c t l y (47), w h e n the actual d e p e n d e n c e of the rate p r e d o m i n a n t l y reflected the F r a n c k - C o n d o n t e r m s . T h i s e r r o r o c c u r r e d i n some w o r k o n glasses a n d i n early w o r k o n p r o t e i n s , w h e r e it s e e m e d that the rates w e r e d e c a y i n g u n u s u a l l y r a p i d l y w i t h d i s tance. T h i s d e p e n d e n c e was p r o b a b l y d u e m a i n l y to F r a n c k - C o n d o n effects. Values of a near 1.0 Â " have usually b e e n f o u n d i n r i g i d glasses, w i t h values slightly s m a l l e r 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 groups c o n n e c t e d b y r i g i d saturated spacer groups. T h e m o r e efficient t r a n s m i s s i o n of i n t r a m o l e c u l a r e l e c t r o n i c c o u p l i n g appears to result from the slightly greater efficiency of t h r o u g h - b o n d interactions, as c o m p a r e d to interactions that m u s t pass from one m o l e c u l e to another t h r o u g h regions i n w h i c h t h e r e are no c h e m i c a l bonds. E l e c t r o n i c c o u p l i n g appears to pass m u c h m o r e efficiently t h r o u g h conjugated IT systems b e t w e e n the d o n o r a n d acceptor groups (28-31, 48-50), a l t h o u g h it has not yet b e e n possible to characterize these w i t h a value for a . A w i d e range of data for glasses, i n t r a m o l e c u l a r e l e c t r o n transfer, e l e c t r o n transfer t h r o u g h p r o t e i n s , a n d some data for m o n o l a y e r assemblies appear to b e a c c o m m o d a t e d b y values of α b e t w e e n 0.6 a n d 1.2 A " w h e n the m a t e r i a l b e t w e e n the d o n o r a n d acceptor is m a i n l y saturated. T h e r e are, h o w e v e r , two i m p r e s s i v e anomalies i n w h i c h v e r y efficient transfer of e l e c t r o n i c c o u p l i n g has b e e n r e p o r t e d to occur over l o n g distances (small a). O n e of these cases involves e l e c t r o n transfer f r o m p h o t o e x c i t e d molecules to e l e c t r o n acceptors across a m o n o l a y e r assembly. M o e b i u s (39) r e p o r t e d data that can be i n t e r p r e t e d to give an α a p p r o x i m a t e l y 3 times smaller than that for most other experiments w i t h saturated spacer m a t e r i a l . A l t h o u g h this e x p e r i m e n t is approximately 10 years o l d , it has n e v e r b e c o m e 1

1


268

E T IN INORGANIC, ORGANIC, A N D BIOLOGICAL SYSTEMS


c o m p l e t e l y clear w h e t h e r a l l sources o f e x p e r i m e n t a l artifacts have b e e n r e m o v e d o r w h e t h e r some special feature of these assemblies leads to a v e r y weak attenuation of the electronic c o u p l i n g w i t h distance. A n o t h e r e x t r e m e l y i n t e r e s t i n g example is electron-transfer fluorescence q u e n c h i n g o f m e t a l complexes b o u n d to D N A (51). T h e s e e x p e r i m e n t s are at a n early stage; t h e i r i n t e r p r e t a t i o n is c o m p l e x a n d appears to b e fraught w i t h a n u m b e r o f difficulties. It is possible, h o w e v e r , to i n t e r p r e t t h e ex p e r i m e n t s as p r o v i d i n g e v i d e n c e for long-distance e l e c t r o n transfer t h r o u g h the D N A backbone w i t h a v e r y slow decay of the electronic c o u p l i n g . A n o t h e r curious question involves " h o l e t u n n e l i n g " . E x p e r i m e n t s i n r i g i d glasses have s h o w n that positive charge c a n b e transferred o v e r d i s tances s i m i l a r to those i n w h i c h electrons can b e transferred (19, 52-54). I n o u r laboratory w e m e a s u r e d distance d e p e n d e n c e for such processes a n d c o n c l u d e d that these hole-transfer processes p r o v i d e d excellent e v i d e n c e for the superexchange p i c t u r e first advanced for E T b y M c C o n n e l l (55), b u t that consideration o f t h e energetics also r e q u i r e d a n a d d i t i o n a l type of s u p e r exchange i n w h i c h a " h o l e " rather than an e l e c t r o n was t h e t u n n e l i n g q u a s i particle (19). M o r e recent experiments o n i n t r a m o l e c u l a r E T have d e m o n strated that these t w o processes c a n have almost exactly t h e same d e p e n d ence o n distance (25). It is not clear w h e t h e r this was a n accident o r w h e t h e r the factors affecting the t w o can i n d e e d b e almost i d e n t i c a l , so that i n g e n e r a l , at least for saturated h y d r o c a r b o n spacers, w e can expect hole t u n n e l i n g a n d e l e c t r o n t u n n e l i n g to have similar distance d e p e n d e n c e . Superexchange c a n also i n v o l v e ττ mediators (28-31, 49, 50, 56). Orientation Dependence. F o r i n t r a m o l e c u l a r e l e c t r o n transfer i n d i f u n c t i o n a l molecules i n v o l v i n g r i g i d spacers, i t has r e c e n t l y b e c o m e p o s sible to measure the effects o f the spatial orientation of donor, spacer, a n d acceptor groups o n electron-transfer rates. O r i e n t a t i o n effects are o f great t h e o r e t i c a l , a n d possibly practical, interest; t h e o r i e n t a t i o n c o u l d b e c o m e a p o w e r f u l c o n t r o l tool for d i r e c t i n g electron-transfer processes a n d d i s c r i m i n a t i n g against u n d e s i r a b l e E T paths. F o r m a n y E T reactions, the e l e c t r o n i c c o u p l i n g , Η , c a n b e e i t h e r positive o r negative, d e p e n d i n g o n angles. T h e r e f o r e there are, i n p r i n c i p l e , angles at w h i c h the c o u p l i n g c a n b e zero. A t such angles t h e electron-transfer rate c o u l d b e c o m e exceedingly s m a l l . T h e most s t r i k i n g example o f orientation d e p e n d e n c e has c o m e f r o m ex p e r i m e n t s i n M c L e n d o n ' s laboratory, i n w h i c h e l e c t r o n transfer occurs b e t w e e n t w o p o r p h y r i n molecules h e l d at a series of angles w i t h respect to one another (57, 58). A l t h o u g h there m a y be m o r e than one possible i n t e r p r e t a t i o n , a satisfactory one has b e e n advanced b y C l o s s (59). φ

I n t w o other cases, h o w e v e r , interpretations of the effects o f o r i e n t a t i o n are not available. O n e of these is a p o r p h y r i n - q u i n o n e (P—Q) m o l e c u l e separated b y t w o spacers g i v i n g different orientations b e t w e e n t h e Ρ a n d Q groups (60). I n t h e other case, b i p h e n y l a n d naphthalene groups attached


17.

MILLER

Puzzles of Electron

269

Transfer

to decalins a n d cyclohexane spacers show sizable (about a factor of 4) o r i entation effects o n t h e rates (61). A t present no theory appears able to e x p l a i n these results.

Puzzles About Franck-Condon Effects R e h m a n d W e l l e r (62) focused attention o n the q u e s t i o n of an " i n v e r t e d r e g i o n " p r e d i c t e d b y the M a r c u s theory (63, 64) a n d other electron-transfer theories. T h e r e was a decade of confusion a n d controversy about t h e nature o f the d e p e n d e n c e of electron-transfer rates o n the free energy change ( A G ) . M o r e r e c e n t l y , i n a series o f s t u n n i n g successes, the i n v e r t e d r e g i o n has b e e n clearly d e m o n s t r a t e d b y studies i n a n u m b e r o f different k i n d s o f systems (16, 17, 23, 26, 27, 45, 61, 65-77). R e c e n t w o r k has a d d e d an exclamation p o i n t to the success i n this area b y s h o w i n g that the t h e o r y a n d reorganization parameters that describe the d e p e n d e n c e of electron-transfer rates o n A G can p r o v i d e a quantitative d e s c r i p t i o n of the t e m p e r a t u r e d e p e n d e n c e o f electron-transfer reactions (78). F o r this aspect o f e l e c t r o n transfer, the results of one k i n d o f e x p e r i m e n t can b e u s e d to p r e d i c t t h e results o f a different a n d s e e m i n g l y q u i t e u n r e l a t e d k i n d o f e x p e r i m e n t . W e m i g h t c o n c l u d e that the F C W D is w e l l u n d e r s t o o d .


0

0

B u t w h e r e t h e r e are exclamation points, there are also q u e s t i o n m a r k s . O n e v e r y large question m a r k is raised b y results for d e p e n d e n c e o f rates o n A G i n W a s i e l e w s k i ' s laboratory (65). P h o t o e x c i t e d charge-separation electron-transfer rates i n a series of p o r p h y r i n - q u i n o n e c o m p o u n d s s h o w e d e v i d e n c e for b o t h a n o r m a l a n d an i n v e r t e d region. H o w e v e r , w h e n t h e relationship b e t w e e n rate a n d A G was investigated (65) i n t w o solvents, one q u i t e polar (butyronitrile) a n d the other v e r y n o n p o l a r (toluene), t h e r e 0

0

was n o noticeable difference i n the relationship b e t w e e n rate a n d A G ! T h e absence o f a solvent-polarity effect stands strongly i n contrast to t h e o r y a n d to t h e observations of large effects of solvent p o l a r i t y i n charge-shift reactions. 0

Solvent d e p e n d e n c e was also e x a m i n e d i n p o r p h y r i n - q u i n o n e c o m p o u n d s b y B o l t o n a n d co-workers (33, 34) a n d M a u z e r a l l a n d co-workers (79-81). I n those cases charge-separation reactions w e r e s t u d i e d for w h i c h solvent d e p e n d e n c e is expected to be weak because t h e free energy change a n d t h e solvent reorganization energy are i n p a r a l l e l b y i n c r e a s i n g solvent p o l a r i t y . T h e r e f o r e , a c c o r d i n g to d i e l e c t r i c c o n t i n u u m t h e o r y , o n l y changes i n t h e refractive indices o f the solvents are expected to l e a d to substantial changes i n t h e rates. T h e data from the B o l t o n group illustrate that this t h e o r y is not exact. T h i s q u e s t i o n o f w h e t h e r electron-transfer rates d e p e n d u p o n solvent p o l a r i t y is c o n n e c t e d to another one of o u r major p r o b l e m s : W e have a v e r y p o o r u n d e r s t a n d i n g o f the t h e r m o d y n a m i c s o f c r e a t i n g ions i n s o l u t i o n . I n charge-separation o r r e c o m b i n a t i o n reactions ( D + A ) ^ ( D + A " ) s u c h as those of W a s i e l e w s k i p r e v i o u s l y c i t e d , to k n o w the free e n e r g y change +


270

E T IN INORGANIC, O R G A N I C , A N D BIOLOGICAL SYSTEMS

for the process w e m u s t k n o w the solvation free energies of the ions o n the r i g h t side o f the the e q u a t i o n . T h o s e solvation energies can b e e s t i m a t e d as a f u n c t i o n of solvent p o l a r i t y a n d size of the ions b y use of t h e B o r n e q u a t i o n

(3)

so that t h e energetics o f charge separation a n d r e c o m b i n a t i o n as a f u n c t i o n of solvent p o l a r i t y can b e e s t i m a t e d b y use of the W e l l e r e q u a t i o n (82), w h i c h adds corrections to the d o n o r s oxidation p o t e n t i a l ( E / D ) D

+ 0

a

n

d *

n e

acceptor's


r e d u c t i o n p o t e n t i a l (£A/A-°).

AG ° = S

Here R

D A

e(E +

Electron Transfer in Inorganic, Organic, and Biological Systems

Recommend Documents