Electron Transfer in Weakly Interacting Systems - ACS Publications

5 Electron Transfer in Weakly Interacting Systems NORMAN SUTIN and BRUCE S. BRUNSCHWIG

Downloaded by EMORY UNIV on March 28, 2016 | http://pubs.acs.org Publication Date: September 27, 1982 | doi: 10.1021/bk-1982-0198.ch005

Brookhaven National Laboratory, Department of Chemistry, Upton, NY 11973

A recently proposed semiclassical model, in which an electronic transmission coefficient and a nuclear tunneling factor are introduced as corrections to the classical activated-complex expression, is described. The nuclear tunneling corrections are shown to be important only at low temperatures or when the electron transfer is very exothermic. By contrast, corrections for nonadiabaticity may be significant for most outer-sphere reactions of metal complexes. The rate constants for the Fe(H2O)6 -Fe(H2O)6 , Ru(NH ) 2+-Ru(NH ) 3+ and Ru(bpy) 2+-Ru(bpy) 3+ electron exchange reactions predicted by the semiclassical model are in very good agreement with the observed values. The implications of the model for optically-induced electron transfer in mixed-valence systems are noted. 2+

3

6

3

6

3

3+

3

The study of electron transfer reactions i n s o l u t i o n i s characterized by a strong i n t e r p l a y of theory and experiment* Theory has suggested systems for study, and experiments have suggested modifications to the theory* Although a number of theories have been proposed (1-13), there i s general agreement that the crux of the e l e c t r o n transfer problem i s the fact that the equilibrium nuclear configuration of a species changes when i t gains or loses an electron* In the case of a metal complex, t h i s configuration change involves changes i n the metal-ligand and i n t r a l i g a n d bond lengths and angles as w e l l as changes i n the v i b r a t i o n s and orientations of the surrounding solvent d i p o l e s . In view of these configuration changes, the rate constants for electron transfer reactions are determined by nuclear as w e l l as e l e c t r o n i c factors* The f i r s t factor depends on the difference i n the nuclear configurations of the reactants and products; the smaller t h i s difference, the more rapid the reaction* The second 0097-6156/82/0198-0105$08.75/0 © 1982 American Chemical Society Rorabacher and Endicott; Mechanistic Aspects of Inorganic Reactions ACS Symposium Series; American Chemical Society: Washington, DC, 1982.


106

MECHANISTIC ASPECTS OF INORGANIC REACTIONS

f a c t o r i s a f u n c t i o n of the e l e c t r o n i c i n t e r a c t i o n of the two r e a c t a n t s ; the l a r g e r t h i s i n t e r a c t i o n , the more r a p i d the electron transfer* Since the e l e c t r o n i c i n t e r a c t i o n of the two r e a c t a n t s becomes more f a v o r a b l e w i t h decreasing s e p a r a t i o n , the most f a v o r a b l e c o n f i g u r a t i o n f o r e l e c t r o n t r a n s f e r i s g e n e r a l l y one i n which the two r e a c t a n t s are i n c l o s e p r o x i m i t y . Opposing t h i s i s the coulombic work r e q u i r e d t o b r i n g s i m i l a r l y - c h a r g e d reactants together, and ultimately the e l e c t r o n - e l e c t r o n r e p u l s i o n s * Consequently, i n b i m o l e c u l a r r e a c t i o n s the e l e c t r o n t r a n s f e r occurs over a range of separation d i s t a n c e s , each w i t h i t s own t r a n s f e r p r o b a b i l i t y , and i t i s necessary t o i n t e g r a t e w i t h respect to the s e p a r a t i o n d i s t a n c e i n order to o b t a i n the r a t e constant f o r the r e a c t i o n : 00

ο I n t h i s equation g ( r ) i s the e q u i l i b r i u m r a d i a l d i s t r i b u t i o n f u n c t i o n f o r a p a i r of r e a c t a n t s ( 1 4 ) , g(r)4wr2

(*a) (4b)

w(o)

-

z

z

e 2

2 3 D o ( l + Βσ/Γ)

(5)

s

The above expression f o r has been derived from f r e e volume c o n s i d e r a t i o n s (17) as w e l l as from the forward and reverse r a t e s of d i f f u s i o n - c o n t r o l l e d r e a c t i o n s (18); the expression f o r w i s v a l i d when the r a d i i of a l l the ions are equal. The r e l a t i o n between the above f o r m u l a t i o n and eq 1 may be seen from the following considerations. I f most of the c o n t r i b u t i o n to the observed r a t e comes from e l e c t r o n t r a n s f e r over a small range of r values then k

-

^52

or giôke^r")

(6)

where r i s the value of r corresponding to the maximum value of the integrand and or i s the range of r values over which the r a t e is appreciable (19)« For t y p i c a l outer-sphere reactions σ ^ r = 6-8 R and, provided that the r e a c t i o n does not border on the nonadiabatic, or ~ 2 SI Under these c o n d i t i o n s the r a t e constants c a l c u l a t e d from eq 4 and 1 w i l l not d i f f e r significantly. We next consider the expression f o r i n the c l a s s i c a l formalism. According to the Franck-Condon principle, i n t e r n u c l e a r d i s t a n c e s and nuclear v e l o c i t i e s do not change during the a c t u a l e l e c t r o n t r a n s f e r . This requirement i s i n c o r p o r a t e d i n t o the c l a s s i c a l e l e c t r o n - t r a n s f e r t h e o r i e s by p o s t u l a t i n g that the e l e c t r o n t r a n s f e r occurs a t the i n t e r s e c t i o n of two p o t e n t i a l energy s u r f a c e s , one f o r the r e a c t a n t s

Rorabacher and Endicott; Mechanistic Aspects of Inorganic Reactions ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

MECHANISTIC ASPECTS OF

108

(precursor complex) and the other f o r the products (successor complex). This Is i l l u s t r a t e d i n F i g u r e 1. The Franck-Condon p r i n c i p l e i s obeyed since the nuclear c o n f i g u r a t i o n s and energies of the reactants and products are the same at the i n t e r s e c t i o n . I t i s f u r t h e r assumed that the e l e c t r o n t r a n s f e r occurs w i t h u n i t p r o b a b i l i t y i n the i n t e r s e c t i o n r e g i o n , that i s , the r e a c t i o n i s assumed to be a d i a b a t i c . In terms of the surfaces i n Figure 1, AB> e l e c t r o n i c c o u p l i n g of the i n i t i a l and f i n a l s t a t e s , i s assumed to be l a r g e enough so that the system remains on the lower potential energy surface on passing through the i n t e r s e c t i o n r e g i o n , but small enough so that i t may be neglected in calculating the height of the potential barrier ( AB « t h ) * Under these c o n d i t i o n s the r a t e constant f o r the conversion of the precursor to the successor complex i s independent of the magnitude of the e l e c t r o n i c coupling and depends only on the nuclear f a c t o r

H

t n e

H


INORGANIC REACTIONS

E

v

n

exp(-(AGi

n

(7)

+ AG* )/RT) ut

where v i s the e f f e c t i v e (nuclear) frequency w i t h which the system crosses the b a r r i e r and AGj and AG are the c o n t r i b u t i o n s of the i n n e r - s h e l l and o u t e r - s h e l l ( s o l v e n t ) r e o r g a n i z a t i o n s to the f r e e energy b a r r i e r . The effective frequency (8) and the r e o r g a n i z a t i o n energies f o r an exchange r e a c t i o n are given by n

n

v

2

in AGj

+ *

n

o u t

2

o l l

t MW

) 1/2 (8)

Δ

the d i f f u s i o n - c o n t r o l l e d r a t e constant, as AG° becomes more negative. However i f κ i s small then k -* Κ ^ κ ν as AG° becomes more negative (AG* 0 ) . Thus κ can be obtained i f r a t e s a t u r a t i o n below the d i f f u s i o n l i m i t i s observed. (Care must be e x e r c i s e d i n t h i s case, too, since r a t e s a t u r a t i o n below the d i f f u s i o n l i m i t may be observed f o r other reasons, i n c l u d i n g a p r e e q u i l i b r i u m change on one of the r e a c t a n t s (41,42), s u b s t i t u t i o n c o n t r o l (43), e t c . ) Values of and κ obtained using the f i r s t three procedures are presented i n Table I I I . On the b a s i s of Newton's c a l c u l a t i o n s (37), the F e ( H 2 0 ) 6 - Fe(H20)6 exchange at r = 6.4 A i s n o n a d i a b a t i c . On the other hand, c a l c u l a t i o n s f o r the C r ( H 2 0 ) 5 - Cr(H20)£ exchange performed by Hush (4) i n d i c a t e that t h i s exchange i s a d i a b a t i c . I n c o n t r a s t to the Fe(H20)g2+ - Fe(H20)5^+ exchange i n which the two o x i d a t i o n s t a t e s d i f f e r by an e l e c t r o n i n a t2g o r b i t a l , in the C r ( H 2 0 ) 5 - C r ( H 2 0 ) 6 exchange the two o x i d a t i o n s t a t e s d i f f e r by an eg e l e c t r o n . E v i d e n t l y the e l e c t r o n i c c o u p l i n g i n the l a t t e r exchange, but not the former, i s c o n s i d e r a b l y enhanced by mixing i n the o r b i t a l s of the i n t e r v e n i n g water molecules. Based on d i r e c t 4d - 4d o v e r l a p (37), the R u ( N H 3 ) e - Ru(NH3)e exchange is barely adiabatic (43,44) while the Ru(bpy)3 Ru(bpy)3 exchange i s h i g h l y nonadiabatic1 Presumably i t i s the d e r e a l i z a t i o n of the metal t2g e l e c t r o n d e n s i t y onto the π* o r b i t a l s of the b i p y r i d i n e l i g a n d s that makes the R u ( b p y ) 3 - Ru(bpy)3^+ exchange so r a p i d . Estimates of the magnitude of the e l e c t r o n i c c o u p l i n g provided by the IT* - π* i n t e r a c t i o n of the two r e a c t a n t s are c o n s i s t e n t w i t h t h i s i n t e r p r e t a t i o n (43). Table I I I a l s o i n c l u d e s values of H ^ B and κ estimated from the properties of the intervalence band observed for mixed-valence diruthenium complexes. Coupling by the pyrazine i n these complexes i s very strong and i s p a r t i c u l a r l y s t r i k i n g when compared w i t h the coupling provided by the through-space I n t e r a c t i o n of two ruthenium centers at comparable r as η

2+

2+

3+

3+

2+

3 +

2+

2+

3+

2+


3+


6

3

Ru(NH )

Ru(bpy)

3

5

14

6.4

- 6.5

6.4

5

5

3

a

d Estimated assuming e l e c t r o n t r a n s f e r through the ir* o r b i t a l s of the b i p y r i d i n e r i n g system.

Estimated assuming e l e c t r o n t r a n s f e r by d i r e c t 4d-4d o v e r l a p .

36,48,49

c

- 3000

36,45

43

43

36,46,4^

Most of the e l e c t r o n i c i n t e r a c t i o n i s through the Η atoms of the l i g a n d s ( 4 4 ) .

6.9

1.0

0.2

- id

c

36,37

4

37

Reference

D

3

400

87

d

D

2

< 10-*

0.2

- 1

- 10"

κ

F u r t h e r d e t a i l s of some of the c a l c u l a t i o n s are g i v e n i n ( 3 6 ) .

5

C

- 20-100

0

67b

- 180

31

cm~l

-HAB

a

3

[ (NH )RuN^Q^NRu(NH ) 5 ] 5+

3

3

10.8

3 +

3 +

3 +

3 +

[ ( NH ) R u ^ ^ ^ _ ^ N R u ( NH ) 5 ] 5+

|Ru(bpy)3

6

6

6

12.3

2 +

3

|Ru(NH )

2 +

2

|Cr(H 0)

2 +

2

|Fe(H 0)

2 +

[ ( N H ) R u N ^ ^ - C - ^ ^ R u ( N H ) ] 5+

3

6

Cr(H 0)

2

6

2

Fe(H 0)

k

r

Table I I I . Estimates of E l e c t r o n i c Coupling M a t r i x Elements and A d i a b a t i c i t y F a c t o r s



120

INORGANIC REACTIONS

2+

manifested i n the Ru(NH3)£ - Ru(NH3)6^+ exchange. Coupling of the ruthenium centers by the A ^ ' - b i p y r i d i n e group i s strong enough f o r the i n t r a m o l e c u l a r e l e c t r o n exchange to be a d i a b a t i c . Introduction of a -CH2" group between the two pyridine r i n g s reduces the c o u p l i n g so that the e l e c t r o n t r a n s f e r becomes nonadiabatic. For many purposes % R may be approximated by (38,39) H

AB

=

H

AB

19

« Ρ ^ ' ί ™ »

where HJJp i s the value of % B at r • σ. The values of $' are ~ 1.7 ir-t f o r the F e ( H 2 0 ) 6 - F e ( H 2 0 ) 6 exchange at r ~ σ (37), 2.5 i " f o r the C r ( H 2 0 ) - Cr(H20) exchange at r - σ J£) and ~ 1.0 f o r two p a r a l l e l aromatic r i n g s such as anthracene and i t s r a d i c a l anion (39). An important c o n c l u s i o n that can be drawn from the above d i s c u s s i o n i s that most outer-sphere e l e c t r o n t r a n s f e r r e a c t i o n s of metal complexes are, at best, m a r g i n a l l y a d i a b a t i c and that the r e a c t i o n w i l l r a p i d l y become nonadiabatic w i t h i n c r e a s i n g separation of the r e a c t a n t s . I n view of these c o n s i d e r a t i o n s , eq 11 can be i n t e g r a t e d to give (50)


2+

1

3+

2 +

3 +

6

4πΝσ

w(o) RT

2

exp

9

6

κ(σ)Γ νη(σ) exp η

(AG* + A G o t ( o ) ) U0) RT n

U

20003» which i s v a l i d provided that σ » 1/$'. I n s p e c t i o n of eq 20 shows that the e f f e c t i v e or f o r a nonadiabatic reaction i s 1/2$'. Thus f o r $» » 1.7 i " , or f o r a nonadiabatic r e a c t i o n i s ^ 1 / 5 that f o r an a d i a b a t i c r e a c t i o n at comparable σ. We next reconsider the systems i n Table I i n the l i g h t of eq 20. The r e s u l t s of the c a l c u l a t i o n s are presented i n Table IV which i n c l u d e s the c l a s s i c a l and experimental r e s u l t s . The r a t e constants f o r the R u ( N H 3 ) $ - Ru(NH3)$ and R u ( b p y ) 3 Ru(bpy)3^+ exchanges calculated from the semlclassical expressions are i n much b e t t e r agreement w i t h the observed values than are the r a t e constants given by the c l a s s i c a l expressions. On the other hand, the agreement w i t h the observed value of the Fe(H 0)6 ~ ( 20)6 exchange i s much poorer f o r the semlclassical calculation. However, good agreement can be obtained f o r t h i s system, too, i f the EXAFS value of Ad° (0.11 i (51)) r a t h e r than the c r y s t a l l o g r a p h i c value (0.14 & (20)) i s used. (Use of the smaller Ad° value lowers the i n n e r - s h e l l r e o r g a n i z a t i o n b a r r i e r l e a v i n g more room f o r n o n a d i a b a t i c i t y ; use of the c r y s t a l l o g r a p h i c value of Ad° leads to a c a l c u l a t e d r a t e constant that i s much lower than the observed value i f κ ^ 10~ .) Unfortunately the smaller value of Ad° cannot be used w i t h confidence at t h i s time s i n c e recent EXAFS measurements y i e l d a Ad value c l o s e r to the c r y s t a l l o g r a p h i c value (52). C l e a r l y the 1

2+

2 +

F e

H

3+

2+

3 +

2

2



s c

a

, M-l s-1

M"

1

s-1

6

2 +

4.2

0.96C

3 +

- 3

/

1.3 χ Ι Ο

2

Fe(H 0) 6

2 +

/

3 +

b C l a s s i c a l c a l c u l a t i o n using eq 4,5 and 7-10.

2 +

/

3 +

4.2 χ 108

9

8

4.3 χ 103

8.6 χ 1 0

3

8.0 χ 1 0

3

Ru(bpy)

2.8 χ 105

7.4 χ 1 0

3

Ru(NH )

Rate Constants f o r Exchange Reactions at 25 °C

Comparison of S e m l c l a s s i c a l and C l a s s i c a l C a l c u l a t i o n s of

a S e m l c l a s s i c a l c a l c u l a t i o n using eq 20 together w i t h eq 5, 9,10 and 13-16.

^bsd,

kc^b, M-l s-1

k

Table IV·



122 2

3

1

l a s t word on the F e ^ O ^ " * " - FeiR^O^ " * exchange has been w r i t t e n .

not

yet


Conclusions The above d i s c u s s i o n shows that very good agreement of observed and c a l c u l a t e d exchange r a t e constants can be obtained u s i n g the s e m l c l a s s i c a l formalism* In the bimolecular r e a c t i o n s discussed i n t h i s paper the r e a c t a n t s were t r e a t e d as hard spheres and an outer-sphere mechanism was assumed. I f the e l e c t r o n i c i n t e r a c t i o n of the r e a c t a n t s i s very weak, then the c o u p l i n g may be i n c r e a s e d through interpénétration of the i n n e r - c o o r d i n a t i o n s h e l l s of the r e a c t a n t s (36,43,44); i n the l i m i t t h i s may g i v e r i s e to an inner-sphere mechanism. Under e i t h e r of these c o n d i t i o n s the observed r a t e s can be l a r g e r than those c a l c u l a t e d from the outer-sphere model. The s e m l c l a s s i c a l formalism reduces to the classical formalism when the e l e c t r o n t r a n s f e r i s a d i a b a t i c and n u c l e a r t u n n e l i n g e f f e c t s are neglected. When these c o n d i t i o n s are not s a t i s f i e d , the s e m l c l a s s i c a l formalism g i v e s r e s u l t s f o r exchange r e a c t i o n s that are i d e n t i c a l over the e n t i r e temperature range w i t h those given by the f u l l quantum-mechanical treatment (13)* The s e m l c l a s s i c a l formalism a l l o w s f o r the d i f f e r e n t time-scales c h a r a c t e r i z i n g the e l e c t r o n t r a n s f e r process (Table I I ) i n a n a t u r a l manner* The f a s t e s t motion, that of the e l e c t r o n s (ν£&)> d e f i n e s the p o t e n t i a l energy surfaces f o r the r e a c t i o n * The slower nuclear processes ( i n t h i s d i s c u s s i o n , the solvent motion) take place on the surface and d e f i n e a c l a s s i c a l b a r r i e r for the r e a c t i o n A G * By c o n t r a s t , the f a s t e r n u c l e a r processes (here, the inner-sphere motion) are not r e q u i r e d to remain on the s u r f a c e ; r a t h e r they can tunnel through the b a r r i e r AGi (T). F i n a l l y , the slower of the e l e c t r o n hopping (v &) and the average nuclear ( v ) frequencies becomes a p r e f a c t o r i n the r a t e expression* out

n

e

n

Nonequilibrium e f f e c t s * I n a p p l y i n g the v a r i o u s formalisms, a Boltzmann d i s t r i b u t i o n over the v i b r a t i o n a l energy l e v e l s of the i n i t i a l s t a t e i s assumed* The r a t e constant c a l c u l a t e d on the b a s i s of the e q u i l i b r i u m d i s t r i b u t i o n , kgq, i s the maximum p o s s i b l e value of k^* I f the e l e c t r o n t r a n s f e r i s very r a p i d then the assumption of an e q u i l i b r i u m d i s t r i b u t i o n over the energy l e v e l s i s not v a l i d , and i t i s more a p p r o p r i a t e to t r e a t the nuclear f l u c t u a t i o n s i n terms of a steady-state r a t h e r than an e q u i l i b r i u m formalism* Although a r i g o r o u s treatment of t h i s problem has not yet appeared, i n t u i t i v e l y i t seems that s i n c e the slowest nuclear fluctuation w i l l g e n e r a l l y be a solvent orientâtional motion, k ^ w i l l equal keq when v » k^ and w i l l tend to v when v « kgq (a simple treatment g i v e s l/kejt 1/ v + l/k^). These c o n s i d e r a t i o n s are o u t

o u t

o u t

m

o u t



5.

SUTIN A N D BRUNSCHWIG

Electron

Transfer in Interacting Systems

123

u n l i k e l y to be important f o r most bimolecular r e a c t i o n s since the r e a c t i o n s w i l l become d i f f u s i o n c o n t r o l l e d before they become subject to solvent r e o r i e n t a t i o n c o n t r o l . However, the above considerations will be important in calculating the a c t i v a t i o n - c o n t r o l l e d r a t e constants f o r r e a c t i o n s that are c l o s e to or at the d i f f u s i o n - c o n t r o l l e d l i m i t and i n c a l c u l a t i n g the r a t e s of very r a p i d " i n t r a m o l e c u l a r " e l e c t r o n t r a n s f e r r e a c t i o n s . A n o n e q u i l i b r i u m d i s t r i b u t i o n of nuclear c o n f i g u r a t i o n s can, of course, be d e l i b e r a t e l y produced by o p t i c a l e x c i t a t i o n of the system. In t h i s case the s t a t e immediately formed possesses the inner-sphere and the solvent c o n f i g u r a t i o n of the i n i t i a l s t a t e but the e l e c t r o n i c c o n f i g u r a t i o n of the f i n a l s t a t e (Figure 1 ) . R e l a x a t i o n to the nuclear c o n f i g u r a t i o n appropriate to the f i n a l s t a t e r e q u i r e s both inner-sphere and solvent r e o r g a n i z a t i o n . The former w i l l occur r a p i d l y , the l a t t e r only r e l a t i v e l y s l o w l y . Consequently, the i n i t i a l l y formed s t a t e w i l l f i r s t r e l a x to an intermediate state having the inner-sphere configuration appropriate to the f i n a l e l e c t r o n i c c o n f i g u r a t i o n , but w i t h a solvent c o n f i g u r a t i o n which i s s t i l l appropriate to the i n i t i a l electronic configuration. At t h i s stage solvent r e l a x a t i o n to the f i n a l s t a t e competes w i t h back e l e c t r o n - t r a n s f e r to the i n i t i a l s t a t e . The quantum y i e l d f o r the formation of the f i n a l s t a t e w i l l be approximately equal to v / ( K V + v ) which i s « 1 when κ ~ 1. T h i s type of e x p l a n a t i o n can account f o r the low y i e l d s (< 10%) of the e l e c t r o n i c isomer formed a f t e r o p t i c a l e x c i t a t i o n i n the i n t e r v a l e n c e band of c e r t a i n mixed-valence systems (53). Although formation of the f i n a l s t a t e w i l l be favored i f the e l e c t r o n i c c o u p l i n g i s very weak (κ « 1 ) , the i n t e n s i t y of the i n t e r v a l e n c e t r a n s i t i o n w i l l a l s o be very weak under these c o n d i t i o n s . To summarize, i n t h i s a r t i c l e we have discussed some aspects of a s e m l c l a s s i c a l e l e c t r o n - t r a n s f e r model (13) i n which quantum-mechanical e f f e c t s a s s o c i a t e d w i t h the inner-sphere are allowed f o r through a nuclear t u n n e l i n g f a c t o r , and e l e c t r o n i c f a c t o r s are i n c o r p o r a t e d through an e l e c t r o n i c transmission c o e f f i c i e n t or a d i a b a t i c i t y f a c t o r . We focussed on the v a r i o u s time s c a l e s that c h a r a c t e r i z e the e l e c t r o n t r a n s f e r process and we presented one example to i n d i c a t e how c o n s i d e r a t i o n s of the time scales can be used i n understanding nonequilibrium phenomena. o u t

i n

Q u t

Acknowledgments. The authors wish to acknowledge very h e l p f u l d i s c u s s i o n s w i t h Drs. C. Creutz and R. A. Marcus. T h i s research was supported by the O f f i c e of B a s i c Energy Sciences of the U . S. Department of Energy.



124


Literature Cited 1. Marcus, R. A. Annu. Rev. Phys. Chem. 1964, 15, 155. 2. Marcus, R. A. J. Chem. Phys. 1965, 43, 679. 3. Hush, N. S. Trans. Faraday Soc. 1961, 57, 557. 4. Hush, N. S. Electrochim. Acta 1968, 13, 1005. 5. Kestner, R. N.; Logan, J.; Jortner, J. J. Phys. Chem. 1974, 78, 2148. 6. Dogonadze, R. R.; Kuznetsov, A. M.; Levich, V. G. Electrochim. Acta 1968, 13, 1025. 7. German, E. D.; Dvali, V. G., Dogonadze, R. R.; Kuznetsov, A. M. Elektrokimiya 1976, 12, 639. 8. Dogonadze, R. R. In "Reactions of Molecules at Electrodes", Hush, N. S., Ed.; Wiley-Interscience: New York, 1971; Chapter 3, p 135. 9. Van Duyne, R. P.; Fischer, S. F. Chem. Phys. 1974, 5, 183. 10. Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975, 63, 4358. 11. Efrima, S.; Bixon, M. Chem. Phys. 1976, 13, 447. 12. Chance, B., DeVault, D. C., Frauenfelder, Η., Marcus, R. Α., Schrieffer, J. B., Sutin, N. Eds. "Tunneling in Biological Systems"; Academic Press: New York, 1979. 13. Brunschwig, B. S.; Logan, J.; Newton, M. D.; Sutin, N. J. Am. Chem. Soc. 1980, 102, 5798. 14. Friedman, H. L. Pure. Appl. Chem. 1981, 53, 1277-1290. 15. Debye, P. Trans. Electrochem. Soc. 1942, 82, 265. 16. Brown, G. M.; Sutin, N. J. Am. Chem. Soc. 1979, 101, 883. 17. Fuoss, R. M. J. Am. Chem. Soc. 1958, 80, 5059. 18. Eigen, M. Z. Phys. Chem. (Frankfurt am Main) 1954, 1, 176. 19. Reynolds, W. L.; Lumry, R. W. "Mechanisms of Electron Transfer"; Ronald Press: New York, 1966. 20. Hair, N. J.; Beattie, J. K. Inorg. Chem. 1977, 16, 245. 21. Stynes, H. C.; Ibers, J. A. Inorg. Chem. 1971, 10, 2304. 22. Zalkin, Α.; Templeton, D. H.; Ueki, T. Inorg. Chem. 1973, 12, 1641. 23. Baker, J.; Engelhardt, L. M.; Figgis, Β. N.; White, A. H. J. Chem. Soc., Dalton Trans. 1975, 530. 24. Silverman, J.; Dodson, R. W. J. Phys. Chem. 1952, 56, 846. 25. Meyer, T. J.; Taube, H. Inorg. Chem. 1968, 7, 2369. 26. Young, R. C.; Keene, F. R.; Meyer, T. J. J. Am. Chem. Soc. 1977, 99, 2468. 27. Holstein, T. Philos. Mag. 1978, 37, 49. 28. Sutin, N. Annu. Rev. Nucl. Sci. 1962, 12, 285. 29. Creutz, C.; Sutin, N. J. Am. Chem. Soc. 1977, 99, 241. 30. Beitz, J. V.; Miller, J. R. J. Chem. Phys. 1979, 71, 4579. 31. Ballardini, R.; Varani, G.; Indelli, M. T.; Scandola, F.; Balzani, V. J. Am. Chem. Soc. 1978, 100, 7219. 32. Brunschwig, B.; Sutin, N. J. Am. Chem. Soc. 1978, 100, 7568.



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33. Bock, C. R.; Connor, J. Α.; Guitierrez, A. R.; Meyer, T. J.; Whitten, D. G.; Sullivan, B. P.; Nagle, J. K. Chem. Phys. Lett. 1979, 61, 522. 34. Nagle, J. K.; Dressick, W. J.; Meyer, T. J. J. Am. Chem. Soc. 1979, 101, 3993. 35. Bock, C. R.; Connor, J. Α.; Gutierrez, A. R.; Meyer, T. J . ; Whitten, D. G.; Sullivan, B. P.; Nagle, J. K. J. Am. Chem. Soc. 1979, 101, 4815. 36. Sutin, N. In "Inorganic Reactions and Methods", Zuckerman, J. J. Ed.; Springer-Verlag: West Berlin, in press. 37. Newton, M. D. Int. J. Quant. Chem., Symp. 1980, 14, 363. 38. Hopfield, J. J. Proc. Natl. Acad. Sci. U.S.A. 1974, 71, 3640. 39. Buhks, E.; Jortner, J. FEBS Lett. 1980, 109, 117. 40. Hush, N. S. Prog. Inorg. Chem. 1967, 8, 391. 41. Marcus, R. A.; Sutin, N. Inorg. Chem. 1975, 14, 213. 42. Hoselton, Μ. Α.; Drago, R. S.; Wilson, L. J . ; Sutin, N. J. Am. Chem. Soc. 1976, 98, 6967. 43. Creutz, C.; Sutin, N. In "Inorganic Reactions and Methods", Zuckerman, J. J . , Ed.; Springer-Verlag: West Berlin, in press. 44. Newton, M. D. this volume. 45. Rieder, K.; Taube, H.; J. Am. Chem. Soc. 1977, 99, 7891. 46. Tom, G. M.; Creutz, C.; Taube, H. J. Am. Chem. Soc. 1974, 96, 7827. 47. Creutz, C.; Inorg. Chem. 1978, 17, 3723. 48. Creutz, C.; Taube, H. J. Am. Chem. Soc. 1973, 94, 1086. 49. Piepho, S. B.; Krausz, E. R.; Schatz, P. N. J. Am. Chem. Soc. 1978, 100, 2996. 50. Marcus, R. A. Int. J. Chem. Kin. 1981, 13, in press. 51. Sham, T. K.; Hastings, J. M.; Perlman, M. L. J. Am. Chem. Soc. 1980, 102, 5904. 52. Sham, T. K. personal communication. 53. Creutz, C.; Kroger, P.; Matsubara, T.; Netzel, T. L.; Sutin, N. J. Am. Chem. Soc. 1979, 101, 5442. RECEIVED April 21,

19 82.


General Discussion—Electron Transfer in Weakly Interacting Systems Leader: Robert Balahura

DR. DAVID McMILLIN (Purdue U n i v e r s i t y ) : I n view o f a l l o f t h i s , would you comment on t h e d i f f e r e n c e s between t h e s e l f exchange r a t e constants f o r t h e c o b a l t hexaammine, t r i s e t h y l 3+ 2+ enediamine, and sepulchrate complexes ( i . e . , Co(NH^), ' , 3+ 2+ 3+ 2+ Co(en) , and Co(sep) )? I f t u n n e l i n g can be f a i r l y e f f e c t i v e , what do you f e e l i s r e s p o n s i b l e f o r d r a m a t i c a l l y changing t h e self-exchange r a t e constant o f c o b a l t i n these three c l o s e l y r e l a t e d amine complexes? 9

9


3

DR. SUTIN: The c o b a l t systems t h a t you mention d i f f e r from t h e i r o n and ruthenium systems I d i s c u s s e d i n t h a t t h e e l e c t r o n t r a n s f e r i s a l s o accompanied by a s p i n change: t h e c o b a l t ( I I I ) complexes a r e low-spin and the c o b a l t ( I I ) complexes are h i g h - s p i n . Thus, t h e e l e c t r o n t r a n s f e r i s s p i n f o r b i d d e n and should n o t occur s i n c e H^g = 0 . I t becomes allowed through s p i n - o r b i t c o u p l i n g which mixes t h e e x c i t e d - s t a t e and grounds t a t e wave f u n c t i o n s o f t h e complexes. The extent o f m i x i n g o f the wave f u n c t i o n s i s very important f o r i t determines t h e de gree o f a d i a b a t i c i t y o f t h e r e a c t i o n . Recent c a l c u l a t i o n s show the a d i a b a t i c i t y f a c t o r f o r t h e c o b a l t hexaammine exchange t o be v e r y s m a l l [Buhks, E.; Bixon, M.; J o r t n e r , J . ; Navon, G. Inorg.Chem. 1979, 18, 2014]. Another f a c t o r i n t h e c o b a l t systems i s t h a t t h e e l e c t r o n t r a n s f e r i n v o l v e s t h e e* antibonding o r b i t a l s . As a conse quence, t h e n u c l e a r c o n f i g u r a t i o n s o f the inner-spheres o f t h e c o b a l t ( I I ) and c o b a l t ( I I I ) complexes w i l l be very d i f f e r e n t . In t h e hexaammines t h e c o b a l t ( I I ) - n i t r o g e n and t h e c o b a l t ( I I I ) n i t r o g e n d i s t a n c e s d i f f e r by 0.18-0.20 A . This may be compared w i t h t h e f e r r o u s / f e r r i c couple, f o r which Ad = 0.14 8, o r t h e hexaammine ruthenium couple, f o r which Ad i s o n l y 0.04 8. In t h e c o b a l t system one thus has l a r g e inner-sphere b a r r i e r s and s m a l l a d i a b a t i c i t y f a c t o r s . I n some systems t h e e l e c t r o n t r a n s f e r may proceed v i a t h e e x c i t e d s t a t e s o f cob a l t ( I I ) o r c o b a l t ( I I I ) present i n thermal e q u i l i b r i u m w i t h t h e ground s t a t e s . Although such e x c i t e d - s t a t e r e a c t i o n s would be more a d i a b a t i c , t h e p r e e q u i l i b r i u m constants f o r forming t h e e x c i t e d s t a t e s a r e g e n e r a l l y not very f a v o r a b l e . I think that each c o b a l t system i s unique i n regard t o t h e mix o f e x c i t e d s t a t e s , inner-sphere b a r r i e r s , and a d i a b a t i c i t y . V a r i a t i o n s i n these f a c t o r s could g i v e r i s e t o r a t h e r dramatic r a t e changes. DR. HENRY TAUBE ( S t a n f o r d U n i v e r s i t y ) : These c o b a l t sys tems now appear t o be l e s s i n t e r e s t i n g than we had o r i g i n a l l y believed. Much o f t h e l i t e r a t u r e data upon which our i n t e r e s t



5.

in

these

systems was

Electron

based


now

127

appear to be wrong.

Firstly, 3+ 2+ the p u b l i s h e d self-exchange r a t e constant f o r Co(NH^)^ ' i s , I am q u i t e c e r t a i n , i n c o r r e c t . I f you examine S t r a n k s paper c r i t i c a l l y , there i s no b a s i s f o r d i s m i s s i n g the observed r a t e as being due t o a term which has a simple f i r s t - o r d e r dependence 1


on

Co(NH ) 3

3 + 6

[ B i r a d a r , N.

S.;

S t r a n k s , D.

R. ; Vaidya, M.

S.

Trans. Faraday Soc. 1962, 58, 2421]. We have now returned t o a measurement of t h i s system. Secondly, the l i t e r a t u r e value f o r the c o b a l t ( I I ) - n i t r o g e n 3+ 2+ d i s t a n c e i n Co(NH~), ' i s i n c o r r e c t . The d i f f e r e n c e between 3+ 2+ 3+ 2+ the CoCNHg)^ ' and Co(en)g * self-exchange r a t e constants can almost be accounted f o r simply by the Franck-Condon f a c t o r . As f o r the d i f f e r e n c e observed f o r the s e p u l c h r a t e complex, t h a t may have to do w i t h s t r a i n i n the l i g a n d . A student of mine has done some c a l c u l a t i o n s c o n s i d e r i n g the f a c t t h a t the l i g a n d i t s e l f may change the p r e f e r r e d d i s t a n c e and change the frequencies. This could account f o r a l a r g e p a r t of the d i f ference between the self-exchange r a t e constants f o r the s e p u l chrate and t r i s e t h y l e n e d i a m i n e complexes. f

DR. RICHARD PIZER (Brooklyn C o l l e g e ) : I n A l a n Sargeson s l a b o r a t o r y , molecular-mechanics c a l c u l a t i o n s have been done, p r i n c i p a l l y by Dr. Rodney Geue, on the e l e c t r o n t r a n s f e r s e l f 3+ 2+ 3+ 2+ exchange r a t e constants of Co(sep) ' , Co(en)~ ' , and 3+ 2+ CoiNHg)^ ' . We see no d i f f e r e n c e between the behavior of the l a t t e r two complexes, supporting Dr. Taube*s v i e w p o i n t . These c a l c u l a t i o n s a l s o support the n o t i o n t h a t the f a s t e l e c t r o n t r a n s f e r i n the s e p u l c h r a t e couple i s due t o r e l e a s e of i n t e r n a l l i g a n d s t r a i n i n the t r a n s i t i o n s t a t e . DR. SUTIN: Various values f o r the c o b a l t - n i t r o g e n d i s tances i n the hexaammines have been r e p o r t e d . P a r t of t h i s v a r i a t i o n i s almost c e r t a i n l y due t o l a t t i c e (counter-ion) effects. Recent l i t e r a t u r e values f o r the Co-N d i s t a n c e s i n Co(NH^)^

are

fairly

c l o s e , ranging

only

from

8

1.96

[Her-

l i n g e r , A. W. ; Brown, J . N. ; Dwyer, Μ. Α.; Pavkovic, S. F. Inorg. Chem., 1981, 20, 2366] t o 1.98 8 [Iwata, M. Acta C r y s t . *977, B33, 59]. I understand t h a t Freeman has very r e c e n t l y 2^ obtained a value of 2.16 8 f o r the Co-N d i s t a n c e i n Co(NH^), 2* The d i f f e r e n c e between the Co-N d i s t a n c e s i n Co(NH ), and 3+ ο Co(NH ) thus appears t o be about 0.18-0.20 A, which i s v e r y s i m i l a r to the value r e p o r t e d by Stynes and Ibers [Stynes, H.C.; 6

0

3

6


128


I b e r s , J . A. Inorg. Chem. 1971, 10, 2304] and t o the Ad value f o r the sepulchrates reported by Sargeson [Sargeson, A. M. Chem. B r i t . 1979, 15, 2 3 ] . DR. EPHRAIM BUMS ( U n i v e r s i t y o f Delaware): There i s a d i f f e r e n c e o f three orders o f magnitude between the s e l f - e x 3+ 2+ 3+ 2+ change r a t e constants o f F e ( H 0 ) , ' and Ru(NH ), while ζ ο 8 the r a t i o o f t h e i r Franck-Condon f a c t o r s i s 10 . The c o r r e s 3+ 2+ ponding r a t e constant f o r Mn(ELO), i s close to that f o r 3+2+ FeiH^O)^ * d e s p i t e the f a c t t h a t the d i f f e r e n c e between t h e i r Franck-Condon f a c t o r s i s 10** (these estimates being based on the d i f f e r e n c e i n m e t a l - l i g a n d d i s t a n c e s ) . One cannot f i t the 12f o l d d i f f e r e n c e i n the C o ( H 0 ) and C o ( N H ) selfexchange r a t e constants t o the r a t i o o f the Franck-Condon f a c 9

o

0


9

3 + , 2 +

2

6

3 + , 2 +

3

6

3

t o r s which i s 10 . I would l i k e t o suggest t h a t there may be many aquo compounds o f the t r a n s i t i o n metal ions i n which the self-exchange r a t e constants which have been reported do not represent outer-sphere processes. DR. SUTIN: I t h i n k t h a t t h i s i s always a problem w i t h ex change r e a c t i o n s i n v o l v i n g aquometal i o n s . The manganese system bears out what Dr. Taube s a i d : we have t o be sure o f the numbers which we a r e attempting t o i n t e r p r e t . I n t h i s regard, I b e l i e v e t h a t the manganese self-exchange r a t e constant which you r e f e r r e d t o was not measured d i r e c t l y . There a r e only a few r e a c t i o n s i n v o l v i n g aquometal ions t h a t can be c o n f i d e n t l y c h a r a c t e r i z e d as outer-sphere. One 3+ 2+ example i n the Fe /V redox r e a c t i o n , i n which the e l e c t r o n t r a n s f e r i s f a s t e r than the l o s s o f water molecules from the metal centers. This i s the type o f c r i t e r i o n f o r an outersphere r e a c t i o n w i t h which one f e e l s comfortable. 3+ 2+ The mechanism o f the Fe * exchange i s c e r t a i n l y open 3+ 2+ to q u e s t i o n ; however, the s i m i l a r i t i e s o f the Fe and 3+ 2+ Φ Fe /V r e a c t i o n s (both o f which e x h i b i t AS = -25 eu) suggest t h a t there i s no dramatic mechanistic d i f f e r e n c e f o r e l e c t r o n t r a n s f e r i n these two systems. Although such comparisons must be made w i t h c a u t i o n , I know o f no strong evidence r e q u i r i n g 3+ 2+ the Fe ' exchange t o be inner-sphere. DR. NOEL HUSH ( U n i v e r s i t y o f Sydney): I t i s very p l e a s i n g t o t h i n k t h a t we now have a general d e s c r i p t i o n o f outer-sphere e l e c t r o n t r a n s f e r which we may b e l i e v e t o be g e n e r a l l y c o r r e c t . I t i s a l s o very s a t i s f y i n g t h a t a l a r g e body o f experimental 9



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129

i n f o r m a t i o n i s thereby systematized and i t s general f e a t u r e s understood. I t h i n k i t i s unique i n chemistry t h a t such complicated r e a c t i o n s can be understood s e m i q u a n t i t a t i v e l y i n q u i t e simple p h y s i c a l terms. And I b e l i e v e i t i s a great achievement t h a t t h i s very accurate experimental i n f o r m a t i o n has been acquired and t h a t i t i s p o s s i b l e t o make such d i r e c t s u c c e s s f u l compari son w i t h theory. I t i s a t t h i s stage t h a t we should now b e g i n to look i n t o the d e t a i l s and ask j u s t the s o r t s of questions t h a t Dr. S u t i n i s r a i s i n g — e.g., the importance of nuclear t u n n e l i n g or of electronic nonadiabaticity. These a r e , as we might say, the f i n e s t r u c t u r e of the problem. F i r s t , i n c o n s i d e r i n g the question of whether or not i n a p a r t i c u l a r case we do have an outer-sphere process, we need to know a c c u r a t e l y such q u a n t i t i e s as bond d i s t a n c e s . I have brought some data ( s h o r t l y to be published) from Dr. J . K. Beattie s laboratory i n Sydney, which show t h a t i n the 3+ 2+ Οο(ΟΗ^)^ * complex ions the d i f f e r e n c e between the lengths of the c o b a l t ( I I ) - and c o b a l t i l l l ) - ! ^ bonds i s very l a r g e . f

This r u l e s out, I would t h i n k completely, a dominant outersphere mechanism f o r t h a t system, because the observed r a t e i s j u s t too f a s t to be compatible w i t h t h i s . The self-exchange r e a c t i o n must almost c e r t a i n l y proceed most favourably v i a an inner-sphere mechanism. More data of t h i s k i n d are e v i d e n t l y needed. 3+ 2+ As f o r the Οο(ΝΗ^)^ ' , exchange, which has been thought to be a problem f o r many y e a r s , I t h i n k P r o f e s s o r Taube s p o i n t i s correct. I t now appears t h a t the r a t e i s not as slow as i t has p r e v i o u s l y been thought t o be. Thus, i t may w e l l prove to be e x p l i c a b l e i n terms of the u s u a l theory. On the q u e s t i o n of o b t a i n i n g estimates of the e l e c t r o n i c n o n a d i a b a t i c i t y f a c t o r , you h i n t e d a t , but I d o n t t h i n k ex p l i c i t l y mentioned, one approximate approach. That i s the method used by Dogonadze and German [German, E. D.; Dogonadze, R. R. I z v . Akad. Nauk SSSR, Ser. Khim. 1973, 2155; Chem.Abstr. 1974, 80, 30998a], who compared the e n t r o p i e s of a c t i v a t i o n of a number of self-exchanges of d i f f e r e n t charge types, 1-2, 2-3, 3-4 and so on. The l a r g e s t c o n t r i b u t i o n t o the entropy of a c t i v a t i o n , apart from some s m a l l terms, comes from the work terms, which depend on the product of the charges, Z^Z^, times a dielectric factor. I f one p l o t s a c t i v a t i o n e n t r o p i e s f o r homogeneous t r a n s f e r i n water, one obtains roughly a s t r a i g h t line. The slope corresponds t o an average i n t e r - i o n d i s t a n c e of ca 7 8, which i s c l o s e t o t h a t u s u a l l y assumed. Although t h i s i s not c o n c l u s i v e , i t does s t r o n g l y suggest t h a t depar t u r e s from e l e c t r o n i c a d i a b a t i c i t y are f a i r l y s m a l l i n outer1

f



130


INORGANIC REACTIONS

sphere r e a c t i o n s . That i s , one does indeed g e n e r a l l y have r e a c t i o n s which are e s s e n t i a l l y e l e c t r o n i c a l l y a d i a b a t i c . Of course, f u r t h e r work i s necessary t o get accurate estimates of s m a l l nonadiabatic e f f e c t s . One f i n a l p o i n t should be noted. T h e o r e t i c a l d i s c u s s i o n s of e l e c t r o n t r a n s f e r processes have focused almost e n t i r e l y on outer-sphere processes. When we have an inner-sphere mechanism, or s u f f i c i e n t e l e c t r o n i c i n t e r a c t i o n i n a dynamically trapped mixed-valence complex to produce a l a r g e s e p a r a t i o n between upper and lower p o t e n t i a l s u r f a c e s , the usual w e a k - i n t e r a c t i o n approach has t o be abandoned. Thus a d e t a i l e d knowledge of a p o t e n t i a l surface which i s not d e s c r i b a b l e as an i n t e r s e c t i o n surface of perturbed harmonic s u r f a c e s , f o r example, i s r e quired. For t h i s purpose, d e t a i l e d c a l c u l a t i o n s w i l l be r e quired. The theory of these processes w i l l be l i n k e d more c l o s e l y to those of atom t r a n s f e r s , where the motion i s nor m a l l y e s s e n t i a l l y confined t o a lower p o t e n t i a l s u r f a c e . Recent t h e o r e t i c a l work i n my l a b o r a t o r y has been concerned w i t h the l a t t e r [ C r i b b , P. H. ; Nordholm, S.; Hush, N. S. Chem.Phys. 1978, 29, 31; i b i d . , 43; i b i d . 1979, 44, 315]. R e v e r t i n g t o outer-sphere processes, one should bear i n mind t h a t the observed spread of r e a c t i o n r a t e s f o r these i s very l a r g e i n d e e d — i n f a c t , i t i s on the order of magnitude of the age of the universe i n seconds! So I t h i n k t h a t Dr. S u t i n i s doing very w e l l i n e x p l a i n i n g i t . DR. SUTIN: When you say t h a t I e x p l a i n i t , I have, of course, drawn h e a v i l y on aspects of the models which you have contributed. DR. ARTHUR WAHL (Washington U n i v e r s i t y i n S t . L o u i s ) : I would l i k e t o make a few comments concerning the experimental evidence f o r e l e c t r o l y t e and s o l v e n t e f f e c t s on e l e c t r o n t r a n s f e r r e a c t i o n s . I might s t a r t by reminding you of some o l d work which was p u b l i s h e d i n 1967 showing the e f f e c t s of v a r i o u s 3- 4c a t i o n s on the r a t e of the Fe(CN)^ self-exchange r e a c t i o n [Campion, R. J . ; Deck, C. F. ; K i n g , P., J r . ; Wahl, A. C. Inorg. Chem. 1967, 6, 672]. The c a t i o n e f f e c t was tremendous—spanning two o r three orders of magnitude—and occurred a t low concen tration levels. Many e l e c t r o n t r a n s f e r r e a c t i o n s a r e , of course, s t u d i e d a t q u i t e h i g h e l e c t r o l y t e c o n c e n t r a t i o n s , and e f f e c t s of t h i s type, even w i t h what are u s u a l l y i n e r t e l e c t r o l y t e s , can be important. We t h i n k t h i s e f f e c t i s due mainly t o i o n a s s o c i a t i o n , so t h a t i o n p a i r s , t r i p l e t s , e t c . , are i n v o l v e d as r e actants . Similar e f f e c t s occur f o r e l e c t r o n t r a n s f e r between c a t i o n s , the r e a c t i o n s being c a t a l y z e d by anions. We have i n vestigated the oxidation of t r i s ( 4 , 7 - d i m e t h y l b i p y r i d y l ) y


Electron


5.


131


osmium(II) by the corresponding f e r r i c complex i n a c e t o n i t r i l e [ S t a l n a k e r , N. D. ; Solenberger, J . C ; Wahl, A. C. J . Phys. Chem. 1977, 81, 601]. Here the e f f e c t s of p e r c h l o r a t e and hexafluorophosphate ions are d i f f e r e n t . Both c a t a l y z e the r e a c t i o n much more than one c a l c u l a t e s from a c t i v i t y - c o e f f i c i e n t effects. We p o s t u l a t e again t h a t the e f f e c t s are due t o i o n association. An i o n p a i r , having a s m a l l e r charge (+2) than the +3 r e a c t a n t would r e a c t more r a p i d l y w i t h the +2 r e a c t a n t . This i n v e s t i g a t i o n has been extended by Tom Braga, who measured the temperature e f f e c t of the k i n e t i c s and made c o n d u c t i v i t y measurements t o determine the e q u i l i b r i u m constants f o r i o n a s s o c i a t i o n , K^, a t a number of temperatures [Braga, T., Ph.D. D i s s e r t a t i o n ; Washington U n i v e r s i t y : S t . L o u i s , 1979]. From data f o r the analogous c o b a l t ( I I I ) complex w i t h p e r c h l o r a t e and hexafluorophosphate as anions, he found a s s o c i a t i o n constants of about 900 and 300, w i t h d i s t a n c e s of c l o s e s t approach of 5 or 6 Â, r e s p e c t i v e l y . These values seem reasonable. For the i r o n ( I I ) compound w i t h the hexafluorophosphate or p e r c h l o r a t e , the i o n a s s o c i a t i o n constants were too s m a l l t o measure (< ~ 50). K i n e t i c measurements f o r the same o s m i u m ( I I ) - i r o n ( I I I ) r e a c t i o n were made a t a number of temperatures. At 25 C the intercept 1

M

a t zero

1

s (=

kj).

different.

The

c o n c e n t r a t i o n i s about 5 χ

slopes of the curves i n C10^

and PF^

10** are

of the r a t e constant and the e q u i l i b 10 9 rium constant, k^K^, are 1.0 χ 10 and 2.5 χ 10 , r e s p e c t i v e l y . D i v i s i o n of these values by the measured e q u i l i b r i u m constants g i v e s the r a t e constants f o r r e a c t i o n s i n v o l v i n g i o n p a i r s . The

two

k

The

electrolyte

9 z

products

1

values are e s s e n t i a l l y the same, about 1 χ 10^ M

-1 s , 20 times l a r g e r than k^ f o r the r e a c t i o n between the 2+ and 3+ i o n s . The simple, c l a s s i c a l Marcus model gives p r e d i c t i o n s t h a t are one to two orders of magnitude too l a r g e f o r both k- and k. 9

Φ

The

temperature

dependence i s q u i t e s m a l l : ΔΗ

Φ

~ 0, AS

=

Φ

-27 ± 10 eu, AS2 — -18 i 10 eu. These values seem reasonable. F u r t h e r evidence f o r the i o n - p a i r formation has come from 19 3+ F-NMR s t u d i e s of the a s s o c i a t i o n of PF^ w i t h the Cr(phen)^ complex [ T r i e g a a r d t , D. M. ; Wahl, A. C , work i n p r o g r e s s ] . An i n c r e a s e i n the l i n e width and a s h i f t i n the l i n e p o s i t i o n 3+ w i t h i n c r e a s i n g [CrCphen)^ ] , has been observed. The system i s i n the fast-exchange l i m i t , and the measured values depend on the degree of i o n a s s o c i a t i o n and on the l i n e width of the




132

f l u o r i n e i n the i o n p a i r . I f the same parameters determined from the c o n d u c t i v i t y measurements a r e used, the data a t the lower concentrations can be represented q u i t e w e l l , but the c a l c u l a t e d curve f a l l s w e l l below the data f o r the higher concen trations. To represent these d a t a , d i f f e r e n t a c t i v i t y c o e f f i c i e n t c o r r e c t i o n s need t o be made and the r e s u l t i n g e q u i l i b r i u m constant v a l u e s , although not u n i q u e l y determined, a r e roughly a few hundred, i n agreement w i t h the c o n d u c t i v i t y r e s u l t s . We have i n v e s t i g a t e d t h e ferrocene/ferrocenium i o n exchange to determine the e f f e c t s o f d i f f e r e n t s o l v e n t s on e l e c t r o n transfer rates. There i s probably o n l y a v e r y s m a l l work term and very l i t t l e i n t e r n a l rearrangement i n t h i s system. Thus the r a t e s should r e f l e c t mostly the s o l v e n t r e o r g a n i z a t i o n about the r e a c t a n t s , t h e outer-sphere e f f e c t . We measured the exchange r a t e s i n a number o f d i f f e r e n t s o l v e n t s and d i d not f i n d the dependence on the macroscopic d i e l e c t r i c constants p r e d i c t e d by the simple model [Yang, E. S.; Chan, M.-S.; Wahl, A. C. J . Phys. Chem. 1980, 84, 3094]. Very l i t t l e d i f f e r e n c e was found f o r d i f f e r e n t s o l v e n t s , i n d i c a t i n g e i t h e r t h a t the formalism i s i n c o r r e c t o r t h a t the m i c r o s c o p i c values o f the d i e l e c t r i c constants a r e not the same as the macroscopic ones. In more recent work, we have i n v e s t i g a t e d another exchange system, R u ( h f a c )

0 , 3

~

[Chan, M. -S.; Wahl, A. C. J . Phys. Chem.,

submitted f o r p u b l i c a t i o n ] . F o r t h i s r e a c t i o n , we found the expected dependence on t h e macroscopic values o f the d i e l e c t r i c constants. An e x c e p t i o n occurs f o r chloroform i n which i o n a s s o c i a t i o n may be u n u s u a l l y l a r g e . L i and Brubaker have i n v e s t i g a t e d the chromium(0,l) b i p h e n y l exchange and have found a similar relationship [ L i , T. T.-T; Brubaker, C. Η., J r . Organomet. Chem., i n p r e s s ] . Thus, the p r e d i c t e d dependence does h o l d i n some cases, b u t i t does not h o l d i n o t h e r s . DR. RICHARD DODSON (Brookhaven N a t i o n a l L a b o r a t o r y ) : F o r 3+ + many years there has been d i s c u s s i o n o f whether the T l , T l e l e c t r o n exchange occurs i n a s i n g l e , two-equivalent step o r 2+ i n two s u c c e s s i v e one-equivalent steps i n v o l v i n g T l as an intermediate. In informal discussions accompanying this Conference, i n t e r e s t has been expressed concerning t h i s type o f system. I would l i k e t o summarize some experimental evidence which seems t o provide a compelling answer. The q u e s t i o n i s : Does t h e e l e c t r o n exchange mechanism i n v o l v e the r e p r o p o r t i o n a t i o n - d i s p r o p o r t i o n a t i o n r e a c t i o n rep resented as i n r e a c t i o n 1? The apparent answer i s t h a t i t 3+ + 2+ T1 + T l J 2T1 k (1) rep, d i s , rep J

does

n o t . The observed

exchange

r e a c t i o n i s many orders o f


5.

Electron


magnitude

too f a s t


reaction i n 2+ view o f what has been l e a r n e d about the p r o p e r t i e s o f T l There a r e three p i e c e s o f work which speak r a t h e r d e c i s i v e l y to t h i s q u e s t i o n . I ' l l o u t l i n e one o f them and mention t h e other two. An important r e a c t i o n i n our approach t o the problem i s the r e d u c t i o n o f t h a l l i c i o n by f e r r o u s i o n , as shown i n reaction (2),


Tl

3 +

t o be accounted

133

+ 2Fe

2 +

J

Tl

+

+ 2Fe

f o r by t h i s

3 +

Κ

(2)

χ 2

which was s t u d i e d v e r y b e a u t i f u l l y i n the e a r l y 1950* s by Ashurst and Higginson [Ashurst, K. G. ; Higginson, W. C. E. J . Chem. Soc. 1953, 3044]. They found t h a t the progress o f t h e r e a c t i o n i s diminished as products accumulate and, s p e c i f i c a l l y , that i r o n ( I I I ) retards the reaction. And the c o n c l u s i o n was very p e r s u a s i v e t h a t the r e a c t i o n occurs i n two steps i n v o l v i n g 2+ Tl as an i n t e r m e d i a t e . Thus, t h e f i r s t step i s represented i n r e a c t i o n ( 3 ) . The second, and v e r y r a p i d , step i s g i v e n Tl

3 +

+ Fe

2 +

J

+ Fe

3 +

T l + Fe

3 +

Tl

2 +

k

p

k_

Κ

r

χ

(3)

i n reaction (4). Tl

2 +

+ Fe

2 +

+

+

k

(4)

£

The r a t e parameters t h a t can be e x t r a c t e d from t h e thermal k i n e t i c s , k^ and the r a t i o k^^/k^, a r e not q u i t e enough f o r present purposes. Nevertheless, Ashurst-Higginson mechanism can problem. What we wanted e v e n t u a l l y work t o do s o — w e r e the s p e c i f i c s t a n t s f o r the r e p r o p o r t i o n a t i o n

the f i r s t serve as

reaction of the t h e key t o the

t o o b t a i n — a n d we used t h i s forward and reverse r a t e con reaction, ^ p ^àis' ^ a n a

Electron Transfer in Weakly Interacting Systems - ACS Publications

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