Four Aspects of the Distance Dependence of Electron-Transfer Rates

9 Four Aspects of the Distance Dependence of

Mechanistic Aspects of Inorganic Reactions Downloaded from pubs.acs.org by IOWA STATE UNIV on 01/04/19. For personal use only.

Electron-Transfer Rates EPHRAIM BUHKS-University of Delaware, Physics Department, Newark, DE 19711 RALPH G. WILKINS-New Mexico State University, Department of Chemistry, Las Cruces, NM 88003 STEPHAN S. ISIED-Rutgers University, The State University of New Jersey, Department of Chemistry, New Brunswick, NJ 08903 JOHN F. ENDICOTT-Wayne State University, Department of Chemistry, Detroit, MI 48202

In many biological systems, the electron transport chains involve some key steps in which electrons appear to move readily over large distances between prosthetic groups located at relatively fixed sites in membranes or in proteins. Such long range electron transfer processes are difficult to investigate in detail using simple, well-defined substances. Approaches to the problem of the distance dependence of electron transfer processes must include delineation of the theoretical concepts pertinent to such processes, identification of the important features of the processes manifested in well-defined biological moieties, and the modelling of selected aspects of these processes in "simple" coordination complexes. We have solicited four short essays from four different investigators to represent the approaches and concerns involved in dealing with long range electron transfer. In Part A, Buhks demonstrates how the temperature dependence of the electron transfer rate constant can be used to determine (i) the range of vibrational modes participating in electron transfer, (ii) the electron-phonon coupling, and ( i i i ) the spatial separation between donor and acceptor centers. In Part B, Wilkins reports on the slow (k = 2.7 x

0097-6156/82/0198-0213$06.25/0 © 1982 American Chemical Society

214

MECHANISTIC ASPECTS OF INORGANIC REACTIONS

-3

-1

10 s ) intramolecular disproportionation rate of a metastable (semi-met) form of octameric hemerythrin. In the (semi-met) form, each prot e i n subunit contains a mixed valence [Fe(II) -Fe(III)] binuclear iron s i t e which, upon electron rearrangement within the octamer, leads to [ F e ( I I ) ] or [ F e ( I I I ) ] at each binuclear iron s i t e . The square antiprismatic packing arrangement, inferred for the octamers and the subunit structures, leads to an estimated 2.8-3.0 nm separation between adjacent binuclear iron s i t e s . In Part C, Isied describes electron transfer between Ru(II) and Co(III) centers separated by polypeptide chains differing i n length and r i g i d ity. The observed electron transfer rate tends to decrease with an increase i n the number of amino acid residues i n the polypeptide linkage, and temperature dependencies are observed to vary considerably with the nature of the amino acids. In Part D, Endicott describes some studies of the intermolecular quenching of electronic excited states. The quenching rates may be useful as sensitive probes for the electronic coupling between d-orbital donors and acceptors. The inferred electronic matrix elements exhibit a O

O

2

distance dependence(k

2

q

Vo2

exp[-11R];

R in nm)

similar to that predicted t h e o r e t i c a l l y , but the rapid decrease of the rate constant with increasing donor-acceptor separation can be modified by enhanced electronic interactions formulated as charge transfer forces involving coordinated ligands.

Part A. Quantum-Mechanical Theory of Diffusion Independent Electron Transfer i n Biological Systems by Ephraim Bunks (University of Delaware) A number of publications i n recent years have demonstrated an active interest i n the theoretical aspects of electron transfer (ET) processes i n biological systems (1-9). This interest was stimulated by the extensive experimental information regarding the temperature dependence of ET rates measured over a broad range of temperatures (10-16). The unimolecular rate of cytochromes oxidation i n Chromatium (10-12), for example, exhibits the Arrhenius type dependence and changes by three orders of

9.

BUHKS ET AL.

magnitude

Distance Dependence

of Electron-Transfer

Rates

215

over the temperature range 100-300K, w h i l e below 100K

the mean l i f e t i m e (~10 other hand, one o f the p h o t o s y n t h e s i s , a step quinone, depends weakly

^ s ) i s temperature independent. On the steps o f charge s e p a r a t i o n i n bacterium i n v o l v i n g ET from b a c t e r i o p h e o p h y t i n t o on temperature (13). I t s mean l i f e t i m e

(~10 *^s) decreases by a f a c t o r o f 2 when t h e temperature i s decreased from 300K t o 83K (14). T h i s type o f b e h a v i o r , charac t e r i s t i c o f a c t i v a t i o n l e s s p r o c e s s e s , was a l s o observed f o r the back ET r e a c t i o n from quinone t o c h l o r o p h y l l , f o r which the mean «2 l i f e t i m e (~10 s ) i n c r e a s e s by a f a c t o r o f 3-4 as the tempera t u r e i s i n c r e a s e d from 150 t o 300K, b u t i s temperature indepen dent below 150K (15, 16). The t r a n s i t i o n p r o b a b i l i t y f o r multiphonon, n o n a d i a b a t i c ET can be formulated i n terms o f f i r s t - o r d e r p e r t u r b a t i o n t h e o r y , i . e . , by means o f t h e Fermi golden r u l e , as (2) 2

W = (2π/*)|ν| 0(Δε)

(1)

In t h i s e x p r e s s i o n , V i s the one e l e c t r o n - t w o c e n t e r i n t e r a c t i o n m a t r i x element, and decreases e x p o n e n t i a l l y w i t h the d i s t a n c e R between donor and acceptor centers ( 1 , 2, 6-9), V = V e"

a R

(2)

o

As estimated f o r molecular c r y s t a l s ( 8 ) , V

q

= 10** cm * and α =

10 nm The f u n c t i o n G i n eq 1 i s the Franck-Condon f a c t o r which accounts f o r the c o n t r i b u t i o n o f n u c l e a r degrees o f freedom and represents t h e thermal average o f t h e o v e r l a p i n t e g r a l s between n u c l e a r wavefunctions w i t h r e s p e c t t o c o n s e r v a t i o n o f energy, and i s g i v e n by (2, 3, 8, 9) 0(As) = ( 2 n H )

_1

- Φ

β

(

0

)

Ο

ί

Δ

ε

^ e*

( t )

dt

(3)

where Ht)

2 = /ρ(ω)| (ω)[(ν(ω) + l ) e

Ρ(ω) = p (u>) + l s

k

6(u>-u>) k

i u , t

iuit

+ v(u>)e" ]du>

(4) (5)

Eq 3 takes i n t o account the c o n t r i b u t i o n s o f : ( i ) continuum o f normal v i b r a t i o n a l modes o f a s o l v e n t c h a r a c t e r i z e d by a d e n s i t y of s t a t e s ρ (ω) w i t h reduced e q u i l i b r i u m displacement Δ (ω); and s s (ii.) l o c a l v i b r a t i o n a l modes w i t h corresponding f r e q u e n c i e s {u^} and reduced displacements {Δ^}; Δε i s the energy gap between the f i n a l and i n i t i a l e l e c t r o n i c s t a t e s f o r ET processes and v(u>) = [exp(]Au)/kgT) - 1]

1

i s the e q u i l i b r i u m phonon o c c u p a t i o n number.


216

The temperature dependence o f ET r a t e s between cytochrome-c and t h e r e a c t i o n center i n Chromatium ( F i g u r e 1 ) , f i t t e d t o eqs 3-5 ( 8 ) , demonstrated t h a t , u n l i k e many redox r e a c t i o n s i n i n o r g a n i c chemistry, ET i n b i o l o g i c a l systems i s c h a r a c t e r i z e d by l a r g e c o n f i g u r a t i o n a l changes o f t h e h i g h frequency mode (Hu^ ~

500 cm *) and modest c o n f i g u r a t i o n a l changes due t o c o u p l i n g 1

w i t h the p o l a r medium (Jiu> ~ 100-300 cm" f o r i c e ) . s I n an (average) s i n g l e mode approximation, t h e FranckCondon f a c t o r , eqs 3-5, can be s i m p l i f i e d and i t takes t h e w e l l known form ( 2 , 4, 7-9) 1

G = (Hw)" exp(-S

coth χ - p x ) I ( S / s i n h x )

(6)

p

where χ = Ηω/21^Τ, S = (ΔΓ/2, ρ = Δε/*ω, and Ιρ i s t h e m o d i f i e d B e s s e l f u n c t i o n s o f order p. A t h i g h temperatures (Jlu) « r a t e becomes, V

2k-T), eq 6 reduces so t h a t t h e

%

2

= (27t/H) ( 4 7 t E k T ) " | V | e x p ( - E / k T )

m

s

B

a

B

(7)

where t h e a c t i v a t i o n energy i s E and

E

2

a

= (p - S ) Hu)/4S

(8)

= S]£u) i s the r e o r g a n i z a t i o n energy.

g

tures

(Jiu> »

21^Τ),

A t low tempera

eq 6 y i e l d s t h e tempe rature-independent

Poisson d i s t r i b u t i o n , r e s u l t i n g i n the f o l l o w i n g expression f o r the r a t e , W

2

L T

= (27l/H)|V| e~

S

p

S /(p!)tfu>

A t s u f f i c i e n t l y l a r g e ρ t h i s may be r e c a s t energy gap law, W

L T

= (2TI/H)|V|

2

(9) i n t h e form o f an

%

(27ip)" exp (-S-γρ)

(10)

where ν = l n ( p / s ) - 1. A t r a n s i t i o n temperature, T , between t h e Arrhenius and q

tempe rature-independent r a t e forms may be d e f i n e d by t h e equa t i o n W ( T ) = W , and i s on t h e order o f kgT = ]4ω/4 f o r the H T

Q

LT

o

s t r o n g c o u p l i n g (S»l) case ( 7 ) . F o r t h e s p e c i a l , a c t i v a t i o n l e s s case, f o r which ρ = S, kgT £ Ηω/2 ( 6 ) . o

9.

Distance Dependence of Electron-Transfer

BUHKS E T A L .

10

6

ι

1—I I I I I I

1 11 m ι

Rates

217

I I I I III

10"

•* 1 0 ' m

10

%

I mil

10' 10

10

%

ι 1

ι ι

11

ml 10

10 *

%

T E M P E R A T U R E (°K) Figure 1. Theoretical fit of the temperature dependence of the rate of cytochrome oxidation in Chromatium. Experimental data are taken from Ref. 10. The details for the calculations are given in Ref. 8. Conditions: E , 2000 cm' ; fio> , 200 cm' ; ϋΔω, 200 cm' ; E , 18500 cm' ;**** 500 cm' ; and V , 90 cm' . 8

1

c

1

1

1

0

1

1


218

A c t i v a t i o n l e s s ET processes ( 1 , 4, 6, 9) are d e s c r i b e d by two d i a b a t i c p o t e n t i a l energy surfaces c r o s s i n g a t the minimum of the i n i t i a l s u r f a c e . This l i m i t i s c h a r a c t e r i z e d by a r a t e which decreases w i t h i n c r e a s i n g temperature a t h i g h Τ (negative apparent a c t i v a t i o n energy) W

2

HT

= (2n/H)|V| (47tE k T)" s

%

At low temperature, the a c t i v a t i o n l e s s temperature independent (see F i g u r e 2 ) , W

2

LT

(11)

B

= (2n/Jl)|V| (2πρ)"

ET

processes

become

%

(12)

Eqs 2 and 12 can be a p p l i e d to the data f o r a c t i v a t i o n l e s s ET processes t o g i v e a rough estimate of the e l e c t r o n exchange i n t e r a c t i o n and the s p a t i a l s e p a r a t i o n of donor and acceptor 1

centers i n b i o l o g i c a l systems (1., 2, 6-9) : V = 4 cm R = 1.0 nm f o r pheophytin-quinone e l e c t r o n exchange;

and and

V = 10 cm and R = 1.9 nm f o r ET i n the q u i n o n e - c h l o r o p h y l l system. These estimates of donor-acceptor s e p a r a t i o n are i n good agreement w i t h the r e s u l t s of magnetic measurements (17). P a r t B. 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 Reactions i n the R e s p i r a t o r y P r o t e i n , Hemerythrin by Ralph G. W i l k i n s (New Mexico S t a t e U n i v e r s i t y ) Hemerythrin i s a r e s p i r a t o r y p r o t e i n i s o l a t e d from s i p u n c u l i d s (marine worms). A l l s i p u n c u l i d s examined have, i n the coelomic f l u i d , e r y t h r o c y t e s loaded w i t h the p r o t e i n which i n most species so f a r examined i s octameric, but sometimes t r i meric (18, 19) and i n one i n s t a n c e d i m e r i c and t e t r a m e r i c (20, 21). From the r e t r a c t o r muscle of Themiste z o s t e r i c o l a , the p r o t e i n has been c h a r a c t e r i z e d as a monomer (22). The monomer (23) and the subunits of the t r i m e r (24) and octamer (25) are remarkably s i m i l a r i n t e r t i a r y s t r u c t u r e , having a M.W. of about 13,500 d a l t o n s . Each subunit contains one b i n u c l e a r i r o n s i t e . There i s no p o r p h y r i n r i n g and the i r o n s are coordinated o n l y t o amino a c i d s , some of which, as w e l l as probably an oxy group, form the b i n d i n g atoms (26). We have been i n v e s t i g a t i n g the o x i d a t i o n - r e d u c t i o n r e a c t i o n s of the b i n u c l e a r i r o n s i t e i n the p r o t e i n m a t r i x (27-32). The methemerythrin form contains both i r o n s i n the +3 o x i d a t i o n s t a t e and can be reduced i n two steps (by d i t h i o n i t e i o n (27, 31), reduced methylviologen, and photochemically u s i n g a r i b o f l a v i n / E D T A mixture (28)) t o the deoxy form i n which both i r o n s are i n the +2 o x i d a t i o n s t a t e . The intermediate (semimet),., i n which one i r o n i s +3 and the other i r o n +2, has been

9.

BUHKS E T A L .


Rates

temperature (°K) Figure 2. Theoretical prediction for the temperature dependence of the electron transfer rate for activated and for activationless processes. Solid lines are calculated for a continuum of vibrational modes; dotted lines represent the single-mode approximation (6, S). Upper curve: ΔΕ, -2000 cm' ; P, 20; and S, 20. Lower curves: Δ Ε , -800 cm' ; P, 8; and S, 20. 1

1

219

MECHANISTIC ASPECTS OF

220

INORGANIC REACTIONS

thoroughly c h a r a c t e r i z e d (31) i n c l u d i n g EPR s p e c t r a a t l i q u i d helium temperatures (30, 32). Another d i s t i n c t semi-met form i s obtained by one-electron o x i d a t i o n of the deoxy form by Fe(CN)

6

(29).

T h i s , the

chemical b e h a v i o r a l

(semi-met)

0

form, has

s p e c t r a l and

d i f f e r e n c e s from those of (semi-met)

R

(28,

30, 31). The two forms, w i t h p r o t e i n from Themiste z o s t e r i c o l a , undergo spontaneous s p e c t r a l changes (28, 31) and complete l o s s of EPR s i g n a l (30) by a f i r s t - o r d e r r a t e process, w i t h a r a t e constant independent of p r o t e i n c o n c e n t r a t i o n . This change i s a s c r i b e d t o a remarkable i n t r a m o l e c u l a r d i s p r o p o r t i o n a t i o n pro cess w i t h i n the octamer: [Fe(III)Fe(II)]

8

+ [Fe(II)Fe(II)] [Fe(III)Fe(III)] 4

4

(13)

The s t r u c t u r e s are known f o r the octamer from P h a s c o l o p s i s g o u l d i i and Themiste dyscritum (33, 34). The e i g h t i d e n t i c a l subunits are packed as a "square donut" w i t h f o u r subunits i n each of two l a y e r s . The b i n u c l e a r i r o n u n i t s are a t corners of an almost r e g u l a r square a n t i p r i s m w i t h d i s t a n c e s of 2.8-3.0 nm between adjacent b i n u c l e a r i r o n c e n t e r s . The d i s p r o p o r t i o n a t i o n -3 -1 r a t e constant f o r r e a c t i o n 13 i s 2.7 χ 10 s a t 25C and pH 8.2. This value can, t h e r e f o r e , be assigned to e l e c t r o n t r a n s f e r over the 2.8-3.0 nm d i s t a n c e s , making the reasonable assumption t h a t the s t r u c t u r e of octameric p r o t e i n from Themiste z o s t e r i c o l a i s s i m i l a r t o those from the other p r o t e i n s . A num ber of redox r e a c t i o n s of the semi-met forms are c o n t r o l l e d by t h i s d i s p r o p o r t i o n a t i o n (29, 31). Semi-met forms of hemerythrin from P h a s c o l o p s i s g o u l d i i and Themiste dyscritum a l s o d i s p r o p o r t i o n a t e and a t r a t e s comparable t o those f o r semi-met from Themiste z o s t e r i c o l a (31). There i s c u r r e n t l y much i n t e r e s t i n e l e c t r o n t r a n s f e r pro cesses i n metal complexes and b i o l o g i c a l m a t e r i a l (1-16, 35). Experimental data f o r e l e c t r o n t r a n s f e r r a t e s over long d i s tances i n p r o t e i n s are s c a r c e , however, and the semi-methemer y t h r i n d i s p r o p o r t i o n a t i o n system appears t o be a r a r e a u t h e n t i c example of slow e l e c t r o n t r a n s f e r over d i s t a n c e s of about 2.8 nm. I r o n s i t e and conformational changes may a l s o attend t h i s process and the t u n n e l i n g d i s t a n c e s from i r o n - c o o r d i n a t e d h i s t i dine edges t o s i m i l a r p o s i t i o n s i n the adjacent i r o n s may be reduced from the 3.0 nm v a l u e . The f i r s t - o r d e r r a t e constant i s some 5-8 orders of magnitude s m a l l e r than those f o r e l e c t r o n t r a n s f e r i n v o l v i n g some heme p r o t e i n s f o r which r e a c t i o n d i s tances of 1.5-2.0 nm appear e s t a b l i s h e d (35). Although semi-met forms of myohemerythrin (the monomeric p r o t e i n from Themiste z o s t e r i c o l a muscle) can be obtained i n a s i m i l a r manner t o the octamer (32), the i n t r a m o l e c u l a r d i s p r o p o r t i o n a t i o n p a t h i s o b v i o u s l y now u n a v a i l a b l e t o them. In

9.

BUHKS ET AL.


221

Rates

agreement w i t h t h i s , i t i s observed t h a t (semi-metmyo)^ changes to

(semi-metmyo)

and

R

the

l a t t e r disproportionates

by

second-

order r e v e r s i b l e k i n e t i c s : 2[Fe(III)Fe(II)] χ [Fe(II)Fe(II)] + [Fe(III)Fe(III)] The

(14)

forward and reverse second-order r a t e constants f o r r e a c t i o n 1

1

1

1

14 are 0.89 M" s" and 9.4 M" s" , r e s p e c t i v e l y , a t 25C and pH 8.2, where most of these experiments were c a r r i e d out. Full d e t a i l s of these experiments (32) and d i s c u s s i o n of a l l the r e s u l t s above are contained i n r e f s (27-32). Since the p r o t e i n can be found i n a number of o l i g o m e r i c forms (18-22), i t i s p o s s i b l e to study the e f f e c t of t e r t i a r y s t r u c t u r e on the i n t r a molecular e l e c t r o n t r a n s f e r process. I t i s a l s o apparent t h a t the p r o t e i n matrix confers unique behavior on the i r o n b i n u c l e a r s i t e , missing from simpler i r o n complexes. P a r t C. Dynamics of E l e c t r o n T r a n s f e r Across by Stephan S. I s i e d (Rutgers U n i v e r s i t y )

Polypeptides

E l e c t r o n t r a n s p o r t i n many b i o l o g i c a l systems takes p l a c e w i t h the a i d of p r o t e i n molecules (MW è 5,000) having p r o s t h e t i c groups t h a t are only a few percent by weight of the p r o t e i n . These p r o s t h e t i c groups are u s u a l l y one or more metal ions (e.g., Fe, Cu), a m e t a l l o p o r p h y r i n , a f l a v i n , or a quinone. These observations have l e d to many questions concerning the r o l e of the p r o t e i n and the d i f f e r e n t polypeptides surrounding the p r o s t h e t i c group i n the e l e c t r o n t r a n s f e r process. Further more, the l o c a t i o n of these p r o s t h e t i c groups w i t h i n the p r o t e i n ( i . e . , how b u r i e d or exposed the p r o s t h e t i c groups are w i t h i n the p r o t e i n ) have a l s o r a i s e d questions concerning the p a r t i c i p a t i o n of neighboring peptide s i d e chains i n the e l e c t r o n t r a n s f e r pathway (36, 37). In order to probe these e f f e c t s , a number of s t u d i e s on the k i n e t i c s of e l e c t r o n t r a n s f e r between s m a l l molecule redox reagents and p r o t e i n s , as w e l l as p r o t e i n - p r o t e i n 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 , have been c a r r i e d out (38-41). The s t u d i e s on r e a c t i o n s of s m a l l molecules w i t h e l e c t r o n t r a n s f e r p r o t e i n s have pointed to some s p e c i f i c i t y i n the e l e c t r o n t r a n s f e r pro cess as a f u n c t i o n of the nature of the l i g a n d s around the s m a l l molecule redox reagents, e s p e c i a l l y the hydrophobicity of these 3+ ligands. Thus, f o r example, [Co(phen)^] and r e l a t e d redox reagents are thought to penetrate the hydrophobic surface of the 2p r o t e i n much b e t t e r than [Fe(EDTA)] reagents, and, t h e r e f o r e , t o have access to d i f f e r e n t e l e c t r o n t r a n s f e r mechanisms (42). Although the above s t u d i e s have been important i n p r o b i n g some of the features of these p r o t e i n e l e c t r o n t r a n s f e r reac-

MECHANISTIC ASPECTS OF

222

t i o n s , they g e n e r a l l y s u f f e r from the with intermolecular electron transfer centers. These disadvantages i n c l u d e steps (eqs 15-17) i n v o l v e d , which can e l e c t r o n t r a n s f e r step (eq 16):

!

A + Β

AB

S

t

AB

A"V

K = iffl T

T

INORGANIC REACTIONS

disadvantages a s s o c i a t e d i n s m a l l molecule redox the m u l t i p l e elementary mask the d e t a i l s of the

(15) (16)

k

+ 3 Α Β Product (17) In these r e a c t i o n s , Κ i s the e q u i l i b r i u m q u o t i e n t f o r the f o r mation of the p r e c u r s o r complex, k i s the r a t e f o r e l e c t r o n t r a n s f e r w i t h i n the p r e c u r s o r complex, and k^ i s the r a t e of d i s s o c i a t i o n of the successor complex. I n t e r m o l e c u l a r r e a c t i o n s i n v o l v i n g p r o t e i n s are f u r t h e r complicated s i n c e one i s d e a l i n g w i t h l a r g e p r o t e i n s c o n t a i n i n g n e u t r a l , a c i d i c , b a s i c , hydrophobic, and hydrophilic side chains. The m u l t i p l i c i t y of mechanisms p o s s i b l e i n such l a r g e molecules makes d e t a i l e d mechanistic s t u d i e s very d i f f i c u l t . I t has long been acknowledged (44-47) t h a t , i f one could i s o l a t e and study the 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 step (eq 16), many ambiguities i n the e l e c t r o n t r a n s f e r r e a c t i o n could be c i r cumvented, and one c o u l d , t h e r e f o r e , study the f a c t o r s t h a t a f f e c t the r a t e of e l e c t r o n t r a n s f e r d i r e c t l y , uncomplicated by s u b s t i t u t i o n and other processes. I n a p p l y i n g t h i s p r i n c i p l e t o p r o t e i n s , one would i d e a l l y l i k e t o modify a p r o t e i n a t one s p e c i f i c s i t e w i t h a number of r e l a t e d , s u b s t i t u t i o n - i n e r t , i n o r g a n i c redox reagents, and then study the 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 step as a f u n c t i o n of a wide v a r i e t y of v a r i a b l e s (e.g., the redox p o t e n t i a l and h y d r o p h o b i c i t y of the redox reagent). Such a study i s extremely d i f f i c u l t t o c a r r y out w i t h l a r g e p r o t e i n s , and none has been reported thus f a r . We have, however, found out t h a t horseheart cytochrome c i s amenable t o m o d i f i c a t i o n a t a s i n g l e s i t e by the [(NH^)^Ru way

] group and such a d e t a i l e d study i s c u r r e n t l y under

i n our l a b o r a t o r y (43). E l e c t r o n - T r a n s f e r i n Simple B i n u c l e a r Complexes. I n t r y i n g to understand the e l e c t r o n t r a n s f e r mediation e f f e c t s of peptide bonds and amino a c i d s i d e chains on r a t e s of e l e c t r o n t r a n s f e r i n simple systems t h a t are amenable t o d e t a i l e d i n v e s t i g a t i o n , we have designed and synthesized a s e r i e s of complexes which c o n t a i n w i t h i n a s i n g l e molecule two d i f f e r e n t o x i d i z i n g agents — b o t h of which are i n e r t to s u b s t i t u t i o n . The s e r i e s of com plexes we have synthesized i s represented s c h e m a t i c a l l y by the general s t r u c t u r e I .

9.


BUHKS ET A L .

Rates

223

Peptide

A v a r i e t y o f amino a c i d and peptide m o i e t i e s have been i n s e r t e d i n between these two o x i d i z i n g agents, M and M . The s e l e c t i v e r e d u c t i o n o f one o f the two metal centers a l l o w s us t o form p r e c u r s o r complexes which c o n t a i n w i t h i n a s i n g l e molecule an o x i d i z i n g agent and a reducing a g e n t — b o t h i n e r t t o s u b s t i t u tion. Rates o f e l e c t r o n t r a n s f e r i n these p r e c u r s o r complexes can then be measured u n a f f e c t e d by s u b s t i t u t i o n o r i s o m e r i z a t i o n r e a c t i o n s n o t d i r e c t l y p e r t i n e n t t o the e l e c t r o n t r a n s f e r s t e p . I f one maintains the same environment around the metal i o n c e n t e r , no change i n the d r i v i n g f o r c e and i n n e r and outer sphere r e o r g a n i z a t i o n energies around the donor and acceptor metal ions i s expected. This a l l o w s us t o focus on the d e t a i l e d d i f f e r e n c e s between the d i f f e r e n t amino a c i d and peptide b r i d ging l i g a n d s . The s e t o f metal donor and acceptor ions t h a t has so f a r f

proved u s e f u l f o r peptide s y n t h e s i s i s the [(ΝΗ~) ϋο***-] and II the [(Oh^HNH^^Ru -] group as acceptor and donor, respec t i v e l y . This same s e t o f metal ions has p r e v i o u s l y been used t o study e l e c t r o n t r a n s f e r i n a number o f r e l a t e d organic b r i d g i n g l i g a n d s (44-47) and i s represented by s t r u c t u r e I I : ς

Amino A c i d or [H 0(NH ) Ru 2

3

II

Peptide

4

I H

-0-Co (NH ) ] 3

5 +

5

II The C o ( I I I ) - R u ( I I I ) complexes were s y n t h e s i z e d as shown i n Scheme I (48, 49). These complexes were p u r i f i e d by chroma tography and c h a r a c t e r i z e d by HPLC, elemental a n a l y s i s , UV-Vis s p e c t r a , and e l e c t r o c h e m i c a l p r o p e r t i e s . 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 Rates. Experiments were c a r r i e d out under i n e r t atmosphere by reducing a known concen2+ 2+ t r a t i o n o f the complexes w i t h [Ru(NH )^] o r Eu . The v a r i a t i o n o f r a t e constants w i t h temperature was s t u d i e d over a range o f twenty degrees a t f o u r d i f f e r e n t temperatures. The a c t i v a t i o n parameters AH^ and AS^ were obtained u s i n g eq 18: 3

k =

e

-AH*/RT

AS*/R e

(18)

MECHANISTIC

224

ASPECTS O F INORGANIC

ΝΗ

+

(1) [(NH3)5Co(OH2)]

(2)

Ç Ο

II

3 χ

NH3

C. Co(NH3)5 CH Ο

3 χ

/

CH

C

I

,Co(NH3)5 Ο

R1

Ο

π Boc-NH

C

x

I

N

OA

CH

A = Active Ester Anhydride or Symmetric

R2

R1

Ο Boc-NH

Mild Base

C \

/

CH \

CH

π 2+

R1 /

0-Co(NH3)5 \

NH

/

C

ι

II

R2

Ο

Ο +

(3)

II

— •

π3+

Ο "ΝΗ

+

Ί3+

Ο

R 3+

REACTIONS

95% Τ FA

NH3

C CH

3+

R1 CH NH

0-Co(NH3)5 C

I

II

R2

Ο

Ο (4)

(CF3S03)HN

II

-C-OA

Mild Base

3+ Ο ?2 II ,^ -Q, ,CH ,NH ,C NH C C H 0-Co(NH3)5| Ο II

CF3SO3HN

V

X

II

1

Ο

(5)

V

'

Ri

1. trans-[Ru(NH3)4S03(OH2)] 2. HBF4 3. H2O2

m

Ο (04S)-Ru-N

R2

II

-C

Ο

PH NH Λ C CH 0-Co(NH3)5 (BF )3 W

v

NH

V

4

II

Ο

I

R1 ÇH3O

Ru = Ru(NH3)4

Boc = C H 3 - C - O - C -

CH

Scheme I

3

9.

BUHKS ET AL.


Rates

225

The r a t e constants and a c t i v a t i o n parameters f o r a s e r i e s o f C o ( I I I ) - R u ( I I ) complexes separated by G l y , Phe, P r o , and G l y G l y , GlyPhe, ProPro are shown i n Table I . This s e r i e s o f r a t e con s t a n t s i s compared t o the r a t e constant and a c t i v a t i o n para meters f o r the parent compound ( I I I ) w i t h an i s o n i c o t i n a t e b r i d g i n g l i g a n d . I n the parent compound I I I , the l i g a n d s around

trans- [ H 0 ( O T ) R u 2

3

4

I 3 C

—]

C

0—Co

i A X

4+ (NH ) ] 3

5

III the metal ions are i d e n t i c a l t o those i n the r e s t o f the s e r i e s , except w i t h no amino a c i d or peptide s e p a r a t i n g the donor and acceptor metal i o n s . Influence of the Amino A c i d Linkages on Intramolecular E l e c t r o n - T r a n s f e r Rates. There i s a s i g n i f i c a n t drop i n the 2 r a t e (>10 ) when one amino a c i d i s i n t e r v e n i n g between the C o ( I I I ) and R u ( I I ) c e n t e r s . The nature of the amino a c i d ( i . e . , r i g i d , f l e x i b l e , hydrophobic, h y d r o p h i l i c ) does not a f f e c t the r a t e constant o r a c t i v a t i o n parameters s i g n i f i c a n t l y (Table I ) . A s m a l l increase i n the r a t e constant, however, between the two f l e x i b l e amino a c i d s ( G l y and Phe) and the r i g i d amino a c i d P r o , i s observed. I n s e r t i n g the second amino a c i d between the c o b a l t and ruthenium centers f u r t h e r decreases the r a t e constant f o r i n t r a molecular e l e c t r o n t r a n s f e r s l i g h t l y . A l l the d i p e p t i d e s stud ied so f a r have lower r a t e s of e l e c t r o n t r a n s f e r than the amino a c i d complexes. The r a t e constant f o r e l e c t r o n t r a n s f e r i n the f l e x i b l e d i p e p t i d e s GlyGly and GlyPhe decrease by a f a c t o r o f 3-4 from t h a t f o r the corresponding amino a c i d , w h i l e the r a t e constant f o r the r i g i d d i p e p t i d e ProPro decreases by a f a c t o r o f s i x t e e n from the corresponding p r o l i n e amino a c i d . The r e s u l t s i n Table I suggest t h a t the nature o f the peptide m a t e r i a l ( i . e . , the amino a c i d s i d e chains) may not be o f great s i g n i f i cance i n determining the r a t e of e l e c t r o n t r a n s f e r . Large d i f f e r e n c e s , however, are observed i n the temperature dependence of the r a t e o f e l e c t r o n t r a n s f e r ( i . e . , i n the a c t i v a t i o n param eters). The f l e x i b l e d i p e p t i d e GlyGly has a much s m a l l e r tem perature dependence than the other two d i p e p t i d e s s t u d i e d . I t i s too e a r l y t o draw any conclusions about the i n s e n s i t i v i t y o f the r a t e constants t o the nature o f the d i p e p t i d e . D i f f e r e n c e s among the peptides seem t o be revealed more i n the temperature dependencies o f the r a t e constants f o r intramolecu l a r e l e c t r o n t r a n s f e r than i n the magnitude of the r a t e constant itself. Work i s i n progress on the s y n t h e s i s o f other d i - , t r i - , and t e t r a - p e p t i d e s s e p a r a t i n g C o ( I I I ) and R u ( I I ) i n order to examine the temperature dependence o f the i n t r a m o l e c u l a r r a t e

226


Table I. Intramolecular Electron Transfer Rates and Activation Parameters* Complex

Bridge

k SEC ~

1

AH* KCAL/MOL

AS* E.U.

ProPro-lso

6.4 χ 10-6

18.6

-19.7

GlyPhe-lso

8.6 χ 10~6

20.7

-12.2

* Medium 1 M HTFA

9.

BUHKS ET AL.


Rates

227

constant as a f u n c t i o n o f the s t r u c t u r e and conformation o f the peptide chain. A systematic study o f the above r a t e s and t h e i r temperature dependencies should a l l o w systematic understanding of the e f f e c t s o f the amino s i d e chains on p o t e n t i a l e l e c t r o n t r a n s f e r pathways. P a r t D. Experimental Probes o f the E l e c t r o n i c Component o f Donor-Acceptor I n t e r a c t i o n s i n Bimolecular Reactions by John F. E n d i c o t t (Wayne State U n i v e r s i t y ) One expects the impact o f the e l e c t r o n i c m a t r i x element, eqs 1 and 2, 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 t o be manifested i n a v a r i a t i o n i n t h e r e a c t i o n r a t e constant w i t h : (1) donor-accep t o r s e p a r a t i o n ; (2) changes i n s p i n m u l t i p l i c i t y between reac t a n t s and products; (3) d i f f e r e n c e s i n donor and acceptor o r b i t a l symmetry; e t c . However, simple e l e c t r o n - t r a n s f e r reac t i o n s tend t o be dominated by Franck-Condon f a c t o r s over most o f the normally a c c e s s i b l e temperature range. Even f o r outer3+ 2+ 3+ 2+ sphere r e a c t i o n s o f the Co(NH )^ ' and Co(OH )^ ' couples, 3

2

r e a c t i o n s i n which each o f the c o b a l t couples i n v o l v e s a (*A4 8 T^g) change i n s p i n m u l t i p l i c i t y , Franck-Condon f a c t o r s A

account f o r ~80% o f the observed a c t i v a t i o n b a r r i e r s ( 5 0 ) . Despite t h i s dominance o f Franck-Condon f a c t o r s , e l e c t r o n i c terms appear t o make c o n t r i b u t i o n s o f s e v e r a l orders o f magni tude t o the observed r a t e s o f many simple 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 (50-54). The preceding essays have noted, e x p l i c i t l y or i m p l i c i t l y , the i n c r e a s i n g importance o f e l e c t r o n i c f a c t o r s when donor and acceptor are h e l d a t r e l a t i v e l y l a r g e separa t i o n s . I t i s c l e a r l y important t o o b t a i n a b e t t e r understanding of the nature o f the long range e l e c t r o n i c c o u p l i n g between donor and acceptor, b u t the d e t a i l s o f e l e c t r o n i c i n t e r a c t i o n s i n 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 u s u a l l y masked by FranckCondon e f f e c t s ; and p u r e l y t h e o r e t i c a l estimates o f V f o r reac3+ 2+ t i o n s as simple as the Co(NH ), self-exchange (55) may be a few orders o f magnitude too s m a l l (50). I n seeking a c l a s s o f r e a c t i o n s more s e n s i t i v e t o t h e nature o f the e l e c t r o n i c matrix element, we have been examining e l e c t r o n i c energy t r a n s f e r ( o r e x c i t e d s t a t e quenching) r e a c t i o n s o f t r a n s i t i o n metal complexes (56, 57, 58). Among these, the most promising r e a c t i o n s appear 9

0

ο

to i n v o l v e quenching o f ( E ) C r ( I I I ) e x c i t e d s t a t e s w i t h t r a n s i t i o n metal complexes. E l e c t r o n i c Energy T r a n s f e r : C o ( I I I ) Quenching o f * C r ( I I I ) 2 3+1 Most o f our work has centered on t h e ( E ) C r ( P P ) ^ / ( A^)Co(III) reactions:

228

MECHANISTIC ASPECTS O F

2

1

q

( E ) C r ( I I I ) + ( A ) C o ( I I I ) -> 1

INORGANIC REACTIONS

4

( A ) C r ( I I I ) + (*X)Co(III)

(19)

2

[where PP represents p o l y p y r i d y l , i . e . , b i p y r i d y l , phenanthrol i n e , e t c . ] . A s p i n c o n s e r v a t i v e quenching process could y i e l d 3 5 e i t h e r a t r i p l e t or q u i n t e t (e.g., *X = Tor T ) e x c i t e d s t a t e of c o b a l t ( I I I ) . The quenching r a t e constants do not f o l l o w the expected e l e c t r o n t r a n s f e r p a t t e r n s and no o x i d i z e d or reduced s p e c i e s have been detected. Furthermore, does not appear t o be s e n s i t i v e t o the donor-acceptor energy gap and the i n t r i n s i c r e o r g a n i z a t i o n a l f a c t o r s are s m a l l ( 5 6 ) , i n d i c a t i n g t h a t FranckCondon f a c t o r s do not d i c t a t e the observed r e a c t i o n p a t t e r n s . This i s e q u i v a l e n t t o t a k i n g the d e n s i t y of s t a t e s f u n c t i o n ρ ~ 2 1 and may be a consequence of the v e r y narrow band Ε e m i s s i o n , the v e r y broad band C o ( I I I ) a b s o r p t i o n s , and l a r g e number of low energy C o ( I I I ) s t a t e s . Thus, k^ v a r i e s from 4 χ 10** M" s" t o 9

i g

Z g

1

0.7

χ 10** M ^

1

through a s e r i e s of C o L ^

+

quenchers (L =

1

NH^,

H^O, en/2, s e p u l c h r a t e / 6 , PP/2), w i t h the v a r i a t i o n being sys tematic i n s i z e , k where K an 25C,

q

= K V exp(-2aR)

(20)

Q

i s the i o n p a i r a s s o c i a t i o n constant as i n eq 15, V i s

intrinsic 1M

q

ionic

frequency

f a c t o r and α = 5 ±1 nm * ( r e a c t i o n s a t 2

3 +

s t r e n g t h ) . For the ( E ) C r ( I I I ) / C o ( M j , reac12-1 t i o n , ν - 3 χ 10 s . Since the quenching r e a c t i o n 20 i n v o l v e s a f o r b i d d e n t r a n s i t i o n i n the donor and the acceptor, a long-range, d i p o l e - a l l o w e d quenching mechanism i s f o r b i d d e n ; t h u s , the e f f e c t i v e d i s t a n c e f o r F o r s t e r quenching (59) i s < ~0.1 nm. Short range f a c t o r s which would c o n t r i b u t e t o the e l e c t r o n i c m a t r i x element i n c l u d e the e l e c t r o n exchange i n t e r a c t i o n (60) and any other component of a v e r y weak donor-acceptor quasi-bonding i n t e r a c t i o n (53). I n an exchange-allowed quenching mechanism, the Franck-Condon component i s u s u a l l y formulated as the donoracceptor s p e c t r a l overlap i n t e g r a l (60). That t h i s does not seem t o c o n t r i b u t e s i g n i f i c a n t l y t o the r e a c t i o n s 19 we have i n v e s t i g a t e d i s y e t another demonstration t h a t Franck-Condon f a c t o r s do not make s i g n i f i c a n t c o n t r i b u t i o n s t o these reac tions . The r e c i p r o c a l of or can be viewed as a mean o r b i t a l l o c u s f o r the p a r t i c u l a r donor and acceptor. Thus, one might p r e d i c t -1 3 + 3 + α ~ 12-14 nm f o r low s p i n Co or Cr , and values of α =

BUHKS E T A L .

9.


Rates

229

10-11 nm * have been estimated f o r a v a r i e t y o f 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 ( 8 , 5 3 ) . Our experimental value o f α = 5 ±1 nm" appears t o be a p p r e c i a b l y s m a l l e r than these estimates. How ever, our estimate o f α i s based on the c o l l i s i o n s o f spheres o f van d e r Waals r a d i i , and Newton (53) has p o i n t e d out t h a t t h e s t r o n g d i s t a n c e dependence o f V may r e q u i r e some interpéné t r a t i o n o f coordinated l i g a n d s . A l l o w i n g f o r such interpéné t r a t i o n would probably i n c r e a s e the numerical value o f a. On the other hand, t h e values o f α determined from experimental measurements o f k are somewhat b u f f e r e d a g a i n s t t h i s element o f q a r b i t r a r i n e s s i n choice o f R by the s t r o n g , b u t opposing, depen dence o f Κ on R ( n o t i n g t h a t or i s based on v a r i a t i o n s i n k /K ) . -1 Taken a t face v a l u e , α ~ 5 nm i m p l i e s some "expansion" o f the e f f e c t i v e d - o r b i t a l r a d i u s o f donor and/or acceptor. Nephel a u x e t i c (61) e f f e c t s have been p r e v i o u s l y proposed t o be impor t a n t i n energy t r a n s f e r r e a c t i o n s o f C r ( I I I ) complexes (62, 63) and some i n c r e a s e i n the e f f e c t i v e r a d i u s o f the d-7l e l e c t r o n s of C r ( I I I ) might be p l a u s i b l e . (Assuming α t o be a simple average o f R(Cr) and R(Co), the i m p l i c a t i o n i s a quadrupling o f 3+ the Cr gaseous i o n r a d i u s ) . However, the i n f o r m a t i o n now a v a i l a b l e does not a l l o w us t o separate the c o n t r i b u t i o n s o f donor and acceptor. A c t u a l l y , t h e s e p a r a t i o n o f donor and acceptor c o n t r i b u t i o n s t o the e l e c t r o n i c m a t r i x element i s n o t l i k e l y t o be simple. One might d e f i n e the resonance exchange r e a c t i o n s , 0

q

0

1

2

4

( E)Cr(III) + ( A )Cr(III)

t

4

2

^ ( A )Cr(III) + ( ^ C r d l l ) ' 2

and

k 1

(*X)Co(III) + ( Α )0ο(ΠΙ)· * 1

1

( A )Co(III) + C ^ C o C l H )

1

1

However, there i s no reason t o expect f o r the Franck-Condon i n dependent terms t h a t V

= (V^ V ) . F o r example,

V

for V

[ n ]j [(Ε* + Ε*) RT Γ in S' 3

h

(53) (where Ε* and Ε* a r e the c o o r d i n a t i o n sphere and s o l v e n t — m S r e o r g a n i z a t i o n a l e n e r g i e s ) , we would estimate /( ') ~ 2 χ 2

v

v

a

10

1 2

1

s ' ^ k J mol" )'

2

forCo(NH )

the v i b r o n i c a l l y allowed

3

3 + 6

while v

d

0

- 9 χ 10

1 3

s"

1

for

(64) resonance t r a n s f e r o f energy be-


230 2

4

tween E and A 5.5 nm

1

and

~ 5x10^ M ^s

1.34 nm 2

7

1

i f

= 3.4 nm \

F o r the quenching 1 2

ν /V q o V 7V o o

1

C r ( I I I ) ( t h i s leads t o k j - 1 0 M~ s'

2

1

- 3.5 x 1 0 s " ( k J v

1

reaction,

1

if a

d

assuming

we would

2

m o l ' ) ' , and ν = (v v , ) ' ' q a d

= =

estimate %

v

only i f J

-0.25.

, In general, Ψ ( U M A ^ ) ^ and cr^R t ^ l ^ ^ d l · " quently, the o f t e n proposed f a c t o r i n g o f "non-adiabatic" com ponents o f 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 (51, 65) cannot be gener ally valid. +

a

R

a

C o n s e

a

The P o s s i b i l i t y o f An Enhancement o f the P r o b a b i l i t y o f Long Range E l e c t r o n Transfer I t i s important t o determine whether some s p e c i f i c donoracceptor i n t e r a c t i o n s can r e s u l t i n a reasonably l a r g e numerical v a l u e o f V even f o r l a r g e donor-acceptor s e p a r a t i o n s . A tenta2+ t i v e answer seems t o be provided i n s t u d i e s o f the Co(NH )^X quenching o f ( E ) C r ( P P ) (57, 5 8 ) . Thus, k - 3-5 χ 1 0 -1 -1 ^+ M s f o r X = F, CN and f o r C o ( N H ) , b u t the quenching r a t e 3

2

3 +

6

q

3

constant increases w i t h t h e heavier k

7

q

8

6

h a l i d e s and pseudo-halides:

8

= 6 χ 1 0 , 1 χ 1 0 , 1.6 χ 1 0 , and 2 χ ΙΟ

B r , N , and NCS, r e s p e c t i v e l y . q

larger

f o r c i s - than

8

Furthermore, k

f o r trans-Co(N^jX^

1

M~V

for X = C l ,

i s about 5 times complexes.

These

enhanced r e a c t i v i t i e s p a r a l l e l the o x i d i z a b i l i t y o f X and are c o n s i s t e n t w i t h a donor-acceptor charge t r a n s f e r c o n t r i b u t i o n t o the i n t e r a c t i o n Hamiltonian. This M u l l i k e n - t y p e o f i n t e r a c t i o n (66) would f o r m a l l y c o r r e c t the ground s t a t e wave f u n c t i o n by i n t r o d u c i n g a s m a l l c o n t r i b u t i o n from a charge t r a n s f e r e x c i t e d 2+ s t a t e (here the e x c i t e d s t a t e would be the i o n p a i r , {Cr(PP)~ , 3+ Co(NH«)-(*X) } ) . Viewed i n t h i s manner, the enhanced quenching 2+ r a t e s o f the Co(NH )^X complexes are a t t r i b u t e d t o a charget r a n s f e r component i n the quasi-bonding donor-acceptor i n t e r a c t i o n . E x p e r i m e n t a l l y , t h i s leads t o a d d i t i o n a l components on the order o f 1-4 k J m o l " i n V . ο I n 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 , the most f r e q u e n t l y en countered, and most d i r e c t , analog o f t h i s k i n d o f charge t r a n s f e r i n t e r a c t i o n would i n v o l v e a C-T e x c i t e d s t a t e w i t h an e l e c t r o n t r a n s f e r r e d from the reducing agent t o a l i g a n d coordinated 3

1

9.

BUHKS ET AL.


Rates

231

to the o x i d a n t . T h i s c o u l d be an important f a c t o r i n r e a c t i o n s of i r o n or ruthenium complexes i n v o l v i n g p o l y p y r i d y l , p o r p h y r i n , etc. Summary Our s t u d i e s o f e l e c t r o n i c energy t r a n s f e r r e a c t i o n s are c o n s i s t e n t w i t h a s t r o n g decrease i n the e l e c t r o n i c i n t e r a c t i o n m a t r i x element i n accordance w i t h eq 2 . However, these s t u d i e s a l s o i n d i c a t e t h a t a t l e a s t two p o t e n t i a l l y d i s t i n g u i s h a b l e e f f e c t s can r e s u l t i n constants l a r g e r than one might n a i v e l y p r e d i c t u s i n g eq 2: 1. Nephelauxetic or other coordinated l i g a n d e f f e c t s which d e l o c a l i z e e l e c t r o n d e n s i t y may l e a d to a n u m e r i c a l l y s m a l l e r v a l u e o f α than found f o r the free i o n s . 2. S p e c i f i c donor-acceptor charge t r a n s f e r i n t e r a c t i o n s can l e a d to a r e l a t i v e l y l a r g e numerical value of the e l e c t r o n i c m a t r i x element, p o s s i b l y a t t r i b u t a b l e t o an i n c r e a s e i n V , and, t h u s , t o l a r g e r r a t e constants than those p r e d i c t e d by d i s t a n c e v a r i ations alone. Acknowledgements The e f f o r t s o f s e v e r a l co-workers are noted i n the c i t a tions. T h i s work was p a r t l y supported by the N a t i o n a l Science Foundation.

Literature Cited 1. Hopfield, J. J. Proc. Natl. Acad. Sci. USA 1974, 71, 3640. 2. Jortner, J. J. Chem. Phys. 1976, 64, 4860. 3. Kuznetsov, A. M.; Søndergard, N. C.; Ulstrup, J. Chem. Phys. 1978, 29, 383. 4. Sarai, A. Chem. Phys. Lett. 1979, 63, 360. 5 Christov, S. G. J. Electroanal. Chem. 1979, 100, 513. 6. Buhks, E.; Jortner, J. FEBS Lett. 1980, 109, 117. 7. Buhks, E.; Jortner, J. J. Phys. Chem. 1980, 84, 3370. 8. Buhks, E.; Bixon, M.; Jortner, J. Chem. Phys. 1981, 55, 41. 9. Jortner, J. J. Am. Chem. Soc. 1980, 102, 6676. 10. DeVault, D.; Chance, B. Biophys. J. 1966, 6, 825. 11. Dutton, P. L.; Kihara, T.; McCray, J. Α.; Thornber, J.P. Biochim. Biophys. Acta 1976, 226, 81. 12. Hales, B. J. Biophys. J. 1976, 16, 471. 13. Peters, K.; Avouris, Ph.; Rentzepis, P. M. Biophys. J. 1978, 23, 207. 14. Parson, W. W.; Schenk, C. C.; Blankenship, R. E.; Holten, D.; Windsor, M. W.; Shank, C. V., in "Frontiers of Biologi-

232

15. 16. 17.

18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.


cal Energetics," Vol. 1; Academic Press: New York, Ν. Y., 1978; p. 37. Parson, W. W. Ann. Rev. Microbiol. 1974, 28, 41. Hoff, A. J. Phys. Reports 1975, 54, 75. Dutton, P. L.; Leigh, J. S.; Prince, R. C.; Tiede, D. M. "Tunneling in Biological Systems"; Chance, B.; DeVault, D. C.; Frauenfelder, H.; Marcus, R. Α.; Schrieffer, J. R.; Sutin, N., Eds.; Academic Press: New York, 1979; p 319. Liberatore, F. Α.; Truby, M. F.; Klippenstein, G. L. Arch. Biochem. Biophys. 1974, 160, 228. Addison, A. W.; Bruce, R. E. Arch. Biochem. Biophys. 1977, 183, 328. Manwell, C. Comp. Biochem. Physiol. 1977, 58B, 331. Sieker, L. C.; Bolles, L.; Stenkamp, R. E.; Jensen, L. H.; Appleby, C. A. J. Mol. Biol. 1981, 148, 493. Klippenstein, G. L.; Van Riper, D. Α.; Oosterom, E. A. J. Biol. Chem. 1972, 247, 5959. Hendrickson, W. A. Naval Res. Rev. 1978, 31, 1 Hendrickson, W. Α.; Smith, J. L., private communication. Stenkamp, R. E.; Jensen, L. H. Adv. Inorg. Biochem. 1979, 1, 219. Stenkamp, R. E.; Sieker, L. C.; Jensen, L. H.; SandersLoehr, J. Nature 1981, 291, 263. Harrington, P. C.; DeWaal, D. J. Α.; Wilkins, R. G. Arch. Biochem. Biophys. 1978, 191, 444. Babcock, L. M.; Bradic, Z.;Harrington, P. C.; Wilkins, R. G.; Yoneda, G. S. J. Am. Chem. Soc. 1980, 102, 2849. Bradic, Z.; Harrington, P. C.; Wilkins, R. G.; Yoneda, G. Biochemistry 1980, 19, 4149. Muhoberac, Β. B.; Wharton, D. C.; Babcock, L. M.; Harring ton, P. C.; Wilkins, R. G. Biochim. Biophys. Acta. 1980, 626, 337. Harrington, P. C.; Wilkins, R. G. J. Am. Chem.Soc. 1981, 103, 1550. Harrington, P. C.; Muhoberac, Β. B.; Wharton, D. C.; Wilkins, R. G. Biochemistry 1981, 20, 6134. Ward, Κ. B.; Hendrickson, W. Α.; Klippenstein, G. L. Nature, 1975, 257, 818; and unpublished results. Stenkamp, R. E.; Sieker, L. C.; Jensen, L. H.; Loehr, J. S. J. Mol. Biol 1976, 100, 23. "Tunneling in Biological Systems", Chance, B.; DeVault, D. C.; Frauenfelder, H.; Marcus, R. Α.; Schrieffer, J. R.; Sutin, N., Eds.; Academic Press: New York, 1979; p 595. Moore, G. R.; Williams, R. J. P. Coord. Chem. Rev. 1976, 18, 125. Adman, Ε. T. Biochim. Biophys. Acta 1979, 549, 107. Wherland, S.; Gray, Η. B. "Biological Aspects of In organic Chemistry"; Addison, A.; Cullin, W.; Dolphin, D.; James, Β., Eds.; Wiley: New York, 1977; p 289.

9.

BUHKS E T A L .


Rates

233

39. Sutin, N. Adv. Chem. Ser. 1977, No. 162, 156. 40. Lappin, Α.; Segal, M.; Weatherborn, D.; Sykes, A. J. Am. Chem. Soc. 1979, 101, 2297. 41. Wherland, S.; Pecht, I. Biochemistry 1978, 17, 2585. 42. Mauk, A. G.; Scott, R. Α.; Gray, H. B. J. Am. Chem. Soc. 1980, 102, 4360. 43. Isied, S.; Worosila, G., Abstracts, New York ACS Meeting, September 1981. 44. Isied, S., Ph.D. Dissertation: Stanford Univ., 1973. 45. Isied, S.; Taube, H. J. Am. Chem. Soc. 1973, 95, 8198. 46. Fisher, H.; Tom, G.; Taube, H. J. Am. Chem. Soc. 1976, 98, 5512. 47. Rieder, K.; Taube, H. J. Am. Chem. Soc. 1977, 99, 7391. 48. Isied, S.; Vassilian, Α.; Lyon, J. J. Am. Chem. Soc., sub mitted for publication. 49. Isied, S.; Kuehn, C. J. Am. Chem. Soc. 1978, 100, 6752. 50. Endicott, J. F.; Durham, B.; Kumar, K. Inorg. Chem. 1982, 21, in press. 51. Chou, M.; Creutz, C.; Sutin, N. J. Am. Chem. Soc. 1977, 101, 847. 52. Brunschwig, B. S.; Logan, J . ; Newton, M. D.; Sutin, N. J. Am. Chem. Soc. 1980, 102, 5798. 53. Newton, M. D. Int. J. Quantum Chem., Quantum Chem. Symp. 1980, No. 14, 364. 54. Endicott, J. F.; Durham, B.; Glick, M. D.; Anderson, T. J . ; Kuszaj, J. M.; Schmonsees, W. G.; Balakrishnan, K. P. J. Am. Chem. Soc. 1981, 103, 1431. 55. Buhks, E.; Bixon, M.; Jortner, J . ; Navon, G. Inorg. Chem. 1979, 18, 2014. 56. Endicott, J. F.; Heeg, M. J . ; Goswick, D. C.; Pyke, S. C. J. Phys. Chem. 1981, 85, 1777. 57. Endicott, J. F.; Gaswick, D. C.; Heeg, M. J . ; Pyke, S. C. J. Am. Chem. Soc., submitted for publication. 58. Endicott, J. F.; Heeg, M. J . ; Gaswick, D. C.; Brubaker, G. R.; Pyke, S. C., work in progress. 59. Förster, Th. Ann. Physik 1948, 2, 55. 60. Dexter, D. L. J. Chem. Phys. 1953, 21, 836. 61. Jørgensen, C. K.; "Orbitals in Atoms and Molecules"; Academic Press: New York, 1962. 62. Balzani, V.; Boletta, F.; Scandola, F. J. Am. Chem. Soc. 1980, 102, 2152. 63. Balzani, V.; Indelli, M. T.; Maestri, M.; Sandrini, D.; Scandola, F. J. Phys. Chem. 1980, 84, 852. 64. Sutin, N. "Inorganic Biochemistry"; Eichhorn, G. L., Ed.; Elsevier: New York, 1973;p611. 65. Wilson, R. B.; Solomon, Ε. I. Inorg. Chem. 1978, 17, 1729. 66. Mulliken, R. S.; Person, W. B. "Molecular Complexes"; Wiley-Interscience: New York, 1969. RECEIVED April 21, 1982.

Four Aspects of the Distance Dependence of Electron-Transfer Rates

Recommend Documents