Inorganic Chemistry: Toward the 21st Century - American Chemical

7 Electron Transfer Mechanisms R. J . K L I N G L E R , S. F U K U Z U M I , and J. K . K O C H I

Downloaded by AUBURN UNIV on November 17, 2016 | http://pubs.acs.org Publication Date: March 3, 1983 | doi: 10.1021/bk-1983-0211.ch007

Indiana University, Department of Chemistry, Bloomington, I N 47405

The finely tunable steric and polar properties inherent to alkyl ligands can be exploited in both the homogeneous and the heterogeneous electron transfers from several classes of organometals. Outer -sphere mechanisms pertain to electron transfer with iron(III) oxidants such as Fe(phen)3, since the oxidations of various organometals are singularly unaffected by steric effects and follow the free energy correlation established by Marcus Theory. Likewise the rates of heterogeneous electron transfer at a platinum electrode are shown to be directly related to the homogeneous chemical oxidation with Fe(phen)3 provided they are evaluated at the same potential, i.e., driving force. The free energy relationship for the outer-sphere rates of electron transfer, which can be measured by the electrochemical method over an extended region far from the equilibrium potential, shows the asymptotic behavior at both the endergonic and exergonic limits describable by the empirical Rehm-Weller equation. The contrasting inner-sphere mechanism for electron transfer applies to the oxidation of the same series of organometal donors RM by either hexachloroiridate(IV) or tetracyanoethylene (TCNE), in which steric effects play an important kinetic role. The observation of transient, charge-transfer absorption bands from metastable [RM TCNE] complexes can be used to evaluate the work term for ion-pair formation with the aid of the Mulliken formulation. A single, unified free energy relationship applicable to inner-sphere processes relates the activation free energy to the standard free energy change for electron transfer and the work term. The large variations in the apparent Brønsted slopes (from unity to even negative values) can be attributed to changes in the 3+

3+

0097-6156/83/0211-0117$10.75/0 © 1983 American Chemical Society Chisholm; Inorganic Chemistry: Toward the 21st Century ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

118

INORGANIC CHEMISTRY: TOWARD THE 21ST CENTURY


work term arising from steric effects in ion-pair formation. T r a d i t i o n a l l y , e l e c t r o n t r a n s f e r processes i n s o l u t i o n and at surfaces have been c l a s s i f i e d i n t o outer-sphere and innersphere mechanisms ( 1 ) . However, the experimental b a s i s f o r the q u a n t i t a t i v e d i s t i n c t i o n between these mechanisms i s not com p l e t e l y c l e a r , e s p e c i a l l y when e l e c t r o n t r a n s f e r i s not accom panied by e i t h e r atom o r l i g a n d t r a n s f e r ( i . e . , the bridged a c t i vated complex). We wish t o describe how the advantage o f using organometals and a l k y l r a d i c a l s as e l e c t r o n donors accrues from the wide s t r u c t u r a l v a r i a t i o n s i n t h e i r donor a b i l i t i e s and s t e r i c p r o p e r t i e s which can be achieved as a r e s u l t o f branching the a l k y l moiety at e i t h e r the a- or β-carbon centers. S t r u c t u r a l V a r i a t i o n s i n E l e c t r o n Donors We consider the four s t r u c t u r a l l y d i v e r s e c l a s s e s o f organo metals I-IV, i n which the c o n f i g u r a t i o n and c o o r d i n a t i o n about the metal centers vary s y s t e m a t i c a l l y from o c t a h e d r a l , square planar, t e t r a h e d r a l t o l i n e a r , r e s p e c t i v e l y .

Me xPMe Ph >t' 2

\>Me Ph 2

II

Et

Et Sn

Et-Hg-Me

I III

IV

These organometals are e s p e c i a l l y d e s i r a b l e f o r k i n e t i c s t u d i e s since they are a l l s u f f i c i e n t l y s u b s t i t u t i o n s t a b l e i n s o l u t i o n to allow meaningful measurements t o be made. Moreover, f o r these n e u t r a l organometal donors, the work term o f the reactants w i s considered to be unimportant. An a d d i t i o n a l b e n e f i t derived from the use o f organometal donors l i e s i n the t r a n s i e n t character o f many o f the o x i d i z e d organometal c a t i o n s . As a r e s u l t , the back 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 minimal, and the e l e c t r o n t r a n s f e r process i s o v e r a l l i r r e v e r s i b l e i n these systems. As r e l a t i v e l y v o l a t i l e and e l e c t r o n - r i c h compounds, the p h o t o e l e c t r o n s p e c t r a of the alkylmetals III and IV are r e a d i l y a c c e s s i b l e , and the v e r t i c a l i o n i z a t i o n p o t e n t i a l s Irj can be a c c u r a t e l y measured. For example, the photoelectron spectra i n Figure 1 i l l u s t r a t e s how the lowest energy band o f a homologous s e r i e s o f d i a l k y l m e r c u r i a l s undergoes l a r g e , systematic v a r i a t i o n s merely by branching at the α-carbon o f the a l k y l l i g a n d (2). In these alkylmetals o f the main group elements, i o n i z a t i o n occurs from the highest occupied molecular o r b i t a l (HOMO) which has σ-bonding character, i . e . , they are σ-donors. Consequently r

Chisholm; Inorganic Chemistry: Toward the 21st Century ACS Symposium Series; American Chemical Society: Washington, DC, 1983.


7.

KLiNGLER E T A L .

Electron

8 9 10 l (RHgMe), eV D

Transfer

Mechanisms

119

Figure 1. He (I) photoelectron spectra of the lowest energy bands of Me Hg, EtHgMe, i-PrHgMe, and t-BuHgMe.


2

120

INORGANIC CHEMISTRY: TOWARD THE 21 ST

CENTURY


a l k y l ligands exert a large dominating i n f l u e n c e on the i o n i z a t i o n p o t e n t i a l s and the s t e r i c p r o p e r t i e s o f a l k y l m e t a l s . Both trends are i l l u s t r a t e d i n Figure 2 f o r the α-branched l i g a n d s : methyl, e t h y l , i s o p r o p y l , and t e r t - b u t y l on the l e f t , as w e l l as the βbranched ligands: e t h y l , η-propyl, i s o b u t y l , and neopentyl on the r i g h t (3). Note that the s t e r i c and p o l a r e f f e c t s g e n e r a l l y i n crease together i n the α-branched a l k y l l i g a n d s , whereas v a r i a t i o n s i n the s t e r i c e f f e c t dominate i n the β-branched a l k y l ligands. A l k y l r a d i c a l s share many o f the d e s i r a b l e p r o p e r t i e s o f or ganometals described above, i n s o f a r as 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 are concerned. Thus the s t e r i c p r o p e r t i e s o f a l k y l r a d i c a l s with a- and (3-branches f o l l o w the trends i n Figure 2. Moreover, the d i r e c t p a r a l l e l i n t h e i r donor p r o p e r t i e s i s shown i n Figure 3 by ALKYL RADICALS: d-Β ranched ft-Branched

•CH,

.CH, Me

Me Me I I - C H *C-Me Me

·ΟΗ ΟΗ 3

3

·ΟΗ ΟΗ 2

Me

Me

2

Me I *CH CH 2

Me

Me I -C^Ç-Me Me

a comparison o f the i o n i z a t i o n p o t e n t i a l s o f the s e r i e s o f abranched a l k y l r a d i c a l s (R«) with the I o f the corresponding alkylmethylmercurials (RHgMe) and d i a l k y l d i m e t h y l t i n compounds (R SnMe )(4). The same p a r a l l e l behavior i s a l s o observed with the β-branched a l k y l s e r i e s , although the v a r i a t i o n s i n the absolute values o f I a r e not as large (see Figure 2, r i g h t ) . D

2

2

D

Outer-Sphere E l e c t r o n T r a n s f e r The minimal interpénétration o f the c o o r d i n a t i o n spheres o f the reactants i s inherent i n any mechanistic formulation o f the outer-sphere process f o r e l e c t r o n t r a n s f e r . As such, s t e r i c e f f e c t s provide a b a s i c experimental c r i t e r i o n t o e s t a b l i s h t h i s mechanism. Therefore we wish to employ the s e r i e s o f s t r u c t u r a l l y r e l a t e d donors possessing the f i n e l y graded s t e r i c and p o l a r prop e r t i e s described i n the foregoing s e c t i o n f o r the study o f both homogeneous and heterogeneous processes f o r e l e c t r o n t r a n s f e r . Homogeneous Processes with T r i s - p h e n a n t h r o l i n e Metal(III) Oxidants. The r a t e s o f e l e c t r o n t r a n s f e r f o r the o x i d a t i o n o f these organometal and a l k y l r a d i c a l donors (hereafter designated g e n e r i c a l l y as RM and R*, r e s p e c t i v e l y , f o r convenience) by a s e r i e s o f t r i s - p h e n a n t h r o l i n e complexes ML o f i r o n ( I I I ) , ruthenium(III), and osmium(III) w i l l be considered i n i t i a l l y , s i n c e they have been p r e v i o u s l y e s t a b l i s h e d by Sutin and others as outer-sphere oxidants (5). 3+

3


Electron

Transfer

Mechanisms


K L i N G L E R ET AL.

Figure 3.

Direct relationship between the ionization potentials of alkyl radicals (R*) with I of the alkylmetals: RHgMe (O) and R SnMe (Φ). D

2

2


122

INORGANIC CHEMISTRY: TOWARD THE 21 ST CENTURY

3 +

f

The i r o n ( I I I ) complexes F e L , where L = 2 , 2 - b i p y r i d i n e and various s u b s t i t u t e d 1,10-phenanthrolines, cleave a v a r i e t y o f o r ganometals i n a c e t o n i t r i l e according to the general r e a c t i o n mechanism i n Scheme I (6). The a c t i v a t i o n process f o r o x i d a t i v e c l e a -


3

RM + F e L

3 +

+

RM

3

+

RM

-^Ëi.

R

. +

+ FeL +

2 + 3

, etc.

M

(1) (2)

Scheme I vage i s represented by the e l e c t r o n t r a n s f e r step i n eq 1. The organometal c a t i o n RM i s a t r a n s i t o r y intermediate which subsequently undergoes a r a p i d fragmentation i n eq 2, rendering the electron transfer i r r e v e r s i b l e . The same i r o n ( I I I ) complexes a l s o o x i d i z e a l k y l r a d i c a l s , p a r t i c u l a r l y those with secondary and t e r t i a r y centers, t o the corresponding carbonium ions (7). +

R- + F e L

3 + 3

—*· R

+

+ FeL

2 + 3

(3)

Since these carbonium ions are r e a c t i v e , the subsequent followup steps with solvent are s u f f i c i e n t l y r a p i d to make e l e c t r o n t r a n s f e r i n eq 3 r a t e determining and e s s e n t i a l l y i r r e v e r s i b l e . For a p a r t i c u l a r i r o n ( I I I ) oxidant, the r a t e constant ( l o g kp ) f o r e l e c t r o n t r a n s f e r i s s t r o n g l y c o r r e l a t e d with the i o n i z a t i o n p o t e n t i a l Irj o f the v a r i o u s a l k y l m e t a l donors i n Figure 4 ( l e f t ) ( 6 ) . The same c o r r e l a t i o n extends to the o x i d a t i o n o f a l k y l r a d i c a l s , as shown i n Figure 4 ( r i g h t ) ( 7 ) . [The cause o f the bend (curvature) i n the c o r r e l a t i o n i s described i n a subsequent s e c t i o n . ] S i m i l a r l y , f o r a p a r t i c u l a r a l k y l m e t a l donor, the r a t e constant (log k p ) f o r e l e c t r o n t r a n s f e r i n eq 1 v a r i e s l i n e a r l y with the standard r e d u c t i o n p o t e n t i a l s E° o f the s e r i e s o f i r o n ( I I I ) complexes F e L , w i t h L = s u b s t i t u t e d phenanthroline ligands (6). In order to account f o r the foregoing k i n e t i c behavior, we r e l y on the Marcus theory f o r outer-sphere e l e c t r o n t r a n s f e r t o provide the q u a n t i t a t i v e b a s i s f o r e s t a b l i s h i n g the f r e e energy r e l a t i o n s h i p (- products

2

Scheme I I I f

The rigorous combination o f the k i n e t i c s i n Scheme I I I with F i c k s laws o f d i f f u s i o n a f f o r d s the r e l a t i o n s h i p among these r a t e con s t a n t s as: k = k i [ k 2 ' / ( k - i + k ')] (15)


e

2

which i s the same as that obtained from a s t r a i g h t f o r w a r d steady s t a t e treatment. [Note that the homogeneous r a t e constant k i n Scheme I I I has been converted to i t s heterogeneous equivalent k f o r use i n eq 15.] The e v a l u a t i o n o f the i n t r i n s i c r a t e constant k i proceeds from the rearrangement o f eq 15, followed by the com b i n a t i o n with the Nernst expression to y i e l d 2

!

2

ki

0

=

k ki'{k ' - k e x p [ ( - n ^ / R T ) ( E - E ) ] } " e

2

1

(16)

e

The complete k i n e t i c expression i n eq 16 r e l a t e s the experimental r a t e constant k w i t h the forward rate constant k i , as a d i r e c t f u n c t i o n o f the decomposition r a t e constant k and the standard r e d u c t i o n p o t e n t i a l Ε . Since an independent measurement o f k = 1.2 cm s " (or k = 10 s" ) i s a v a i l a b l e f o r Me Co(M) , i t can be used i n conjunction with E° = 0.53 V to convert k t o k i , shown i n Figure 11 (14). Our problem now i s to determine the f u n c t i o n a l form o f t h i s experimental f r e e energy curve f o r the i n t r i n s i c r a t e constant k i for electron transfer. In a d d i t i o n to the Marcus eq 4, two other r e l a t i o n s h i p s are c u r r e n t l y i n use t o r e l a t e the a c t i v a t i o n f r e e energy t o the f r e e energy change 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 (15,16). e

f

2

f

2

1

5

1

+

2

2

e

Marcus :

AG* = AG *[1 + J£^]

()

Rehm-Weller:

AG* = ψ

Marcus-Levine-Agmon:

AG* = AG + ^ ί ΐ η { 1 + exp [- ^* ^ ] }

2

4

0

+ [φ

2

2

1

+ (AGo*) ] / Δ

2

(17) n

2

(18)

The f u n c t i o n a l form o f the f r e e energy r e l a t i o n s h i p s among these three formulations i s t y p i c a l l y i l l u s t r a t e d i n Figure 12 (17). Each o f these f r e e energy r e l a t i o n s h i p s employs the i n t r i n s i c b a r r i e r AG * as the disposable parameter. [The i n t r i n s i c b a r r i e r represents the a c t i v a t i o n energy f o r e l e c t r o n t r a n s f e r when the d r i v i n g force i s zero, i . e . , AG* = AGo* at AG = 0 or the e q u i l i 0


KLINGLER ET AL.

Electron

Transfer

Mechanisms


7.

Figure 12. The shapes of the free energy relationships for electron transfer according to Marcus (Equation 4) (· · ·), Rehm-Weller (Equation 17) ( ), and Marcus-Levine-Agmon (Equation 18) ( ).


133

134

21ST

INORGANIC CHEMISTRY: TOWARD THE

CENTURY

0

brium p o t e n t i a l E .] Since the i n t r i n s i c b a r r i e r i s the s i n g l e parameter i n eqs 4, 17, and 18, the a p p l i c a b i l i t y of these r e l a t i o n s h i p s to the experimental f r e e energy curve i n Figure 11 i s best c a r r i e d out by t e s t i n g each f o r the consistency of AGo*, which was c a l c u l a t e d from the experimental value of AG* at each AG. The r e s u l t i s g r a p h i c a l l y i l l u s t r a t e d i n Figure 13. Several features i n Figure 13 are noteworthy. F i r s t , i n the e q u i l i b r i u m region o f E° = 0.53 V, a l l three r e l a t i o n s h i p s y i e l d a c o n s i s t e n t value of the i n t r i n s i c b a r r i e r as AGo* = 6.3 k c a l mol" . [Note that the s c a t t e r of points i n the exergonic region a r i s e s from the experimental d i f f i c u l t i e s i n the measurement of k .] Second, the a p p l i c a b i l i t y of the Marcus eq 4 i s l i m i t e d to the region of the f r e e energy change about the e q u i l i b r i u m p o t e n t i a l . S i g n i f i c a n t d e v i a t i o n s occur i n the endergonic r e g i o n , p a r t i c u l a r l y at potent i a l s l e s s than -0.4 V. T h i r d , the Rehm-Weller and the MarcusLevine-Agmon r e l a t i o n s h i p s are e q u a l l y a p p l i c a b l e over the e n t i r e span of the experimental f r e e energy change. Both r e l a t i o n s h i p s y i e l d values of AG * which deviate l e s s than 0.3 k c a l mol" only at the extrema. This t e s t thus represents a unique example o f the experimental v e r i f i c a t i o n o f these f r e e energy r e l a t i o n s h i p s over an unusually extended range o f the d r i v i n g f o r c e . Owing to i t s simpler f u n c t i o n a l form, a l l subsequent d i s c u s s i o n s of the f r e e energy r e l a t i o n s h i p f o r e l e c t r o n t r a n s f e r w i l l be based on the Rehm-Weller r e l a t i o n s h i p . The Rehm-Weller formulation of the f r e e energy r e l a t i o n s h i p i n eq 17 can be r e w r i t t e n as 1


e

1

0

AG* (AG*

- AG)

=

AG *

2

0

to emphasize i t s h y p e r b o l i c form (18). The asymptotes o f AG* = 0 and AG* = AG p r e d i c t the t r a n s f e r c o e f f i c i e n t s i n the exergonic and endergonic l i m i t s to be 0 and 1, r e s p e c t i v e l y . The magnitude of the i n t r i n s i c b a r r i e r AGo* determines how r a p i d l y the t r a n s f e r c o e f f i c i e n t s approach these l i m i t s , as shown i n Figure 14 -- the r i g h t s i d e showing the f u n c t i o n a l v a r i a t i o n i n the a c t i v a t i o n f r e e energy with the d r i v i n g f o r c e , and the l e f t s i d e the a c t u a l v a r i a t i o n of 3 (19). Over the l i m i t e d region o f AG i n which the Marcus eq 4 i s a p p l i c a b l e , the inverse r e l a t i o n s h i p between the i n t r i n s i c b a r r i e r and the t r a n s f e r c o e f f i c i e n t i s given by eq 14. Indeed, t h i s remarkable and u s e f u l p r e d i c t i o n i s borne out by the constancy o f B AG * f o r a v a r i e t y o f organometals i n Table I (11). It i s i n t e r e s t i n g to note that the i n t r i n s i c b a r r i e r f o r the octahed r a l Me2Co(M) i s s i g n i f i c a n t l y l e s s than those f o r e i t h e r the t e t r a h e d r a l t e t r a l k y l t i n and lead compounds or the square p l a n a r dimethylplatinum(II) complex. 2

0

Inner-Sphere E l e c t r o n T r a n s f e r The s e r i e s of organometal donors I-IV are a l s o r e a d i l y o x i dized by the one-equivalent oxidant h e x a c h l o r o i r i d a t e ( I V ) as w e l l as by the organic acceptor tetracyanoethylene (TCNE) (3). In both


7.

KLiNGLER E T A L .

Electron

Transfer

135

Mechanisms

6 «ν 7


6 5

1

3

.4

:

.5

ι

ι

.6

Γ"

.7

b. I

I

I

!

I

1

!

I

I

I

I

ί

I

I

I

Γ

8| 7

-ι

kcal mol

.3

.4

.5

.6

.7

c. θ

7 6 5 .3

.4

.5

Potential

.6

.7

E, v o l t s

l

Figure 13. Test for the consistency of AG evaluated from the intrinsic rate constant (log ki) using Marcus Equation 4 (a), Rehm-Weller Equation 17 (b), and Marcus-Levine-Agmon Equation 18 (c) at various potentials. 0



136


AG

AG

Figure 14. Dependence of the Rehm-Weller free energy relationship on the intrinsic barrier Δ ϋ Λ Key: left, activation free energy change; and right, transfer coefficient variation.

Table I. Effect of Organometal Structure on the Transfer Coefficient and the Intrinsic Barrier. Organometal

2

β

AG*

AG*

b

AG* 1.1

Me Co(DpnH)

7.46

0.73

2.1

(s-Bu) Sn

7.65

0.31

10.0

1.0

2

u

EUPb

7.68

0.28

10.0

0.8

Me Pt(PMe Ph)

7.69

0.27

13.0

0.9

7.70

0.20

22.0

0.9

2

2

EtHgMe

2

M e a s u r e d b y CV a t 100 mV s ' . When t h e e f f e c t o f r e v e r s i b i l i t y i s t a k e n i n t o a c c o u n t t h e v a l u e i s 6.3 k c a l m o l " for rate-limiting electron transfer. 1

b


1

7.

Electron

KLINGLER ET AL.

Transfer Mechanisms

137

cases, the r a t e - l i m i t i n g step i n v o l v e s e l e c t r o n t r a n s f e r , i . e . , 2

IrCl " 6

+ RM

TCNE + RM

3

+

—>

IrCl "

— •

TCNE" + RM

6

+ RM

(19)

+

(20)

which i s e s s e n t i a l l y the same stoichiometry described t r i s - p h e n a n t h r o l i n e m e t a l ( I I I ) oxidants i n eq 1.

f o r the

2

R e a c t i v i t y Patterns f o r I r C l " and TCNE as Oxidants. A l though the r e a c t i v i t y p a t t e r n f o r I r C l ~ and TCNE are s i m i l a r , they are q u i t e d i s t i n c t from the outer-sphere p a t t e r n e s t a b l i s h e d f o r F e L . The c o n t r a s t i s g r a p h i c a l l y i l l u s t r a t e d i n Figure 15, i n which the second-order r a t e constants (log k) f o r each o f the three oxidants are p l o t t e d against the i o n i z a t i o n p o t e n t i a l s o f the same s e r i e s o f a l k y l m e t a l donors (3). The uniquely l i n e a r c o r r e l a t i o n f o r Fe(phen) was discussed i n the foregoing s e c t i o n f o r outer-sphere o x i d a t i o n . The marked d e v i a t i o n s o f a l l the points f o r I r C ^ and TCNE from any analogous r e l a t i o n s h i p i s unmistakable. In p a r t i c u l a r , the most s t e r i c a l l y hindered organo metal t e t r a - n e o p e n t y l t i n (entered as entry 18 i n Figure 15) shows the most pronounced deviant behavior. Furthermore i n Figure 16, the experimental values o f AG* f o r I r C l " ( r i g h t ) and TCNE ( l e f t ) c o n s i s t e n t l y f a l l below the s o l i d l i n e s r e p r e s e n t i n g the expected outer-sphere rates which were c a l c u l a t e d from the Marcus eq 4 by t a k i n g i n t o account the d i f f e r e n c e s i n the r e o r g a n i z a t i o n energies o f I r C l " and TCNE (3). With the exception o f t-Bu SnMe (entry 17) a l l the experimental r a t e s are f a s t e r than the c a l c u l a t e d values. The magnitudes o f the d e v i a t i o n s vary from 12.5 k c a l m o l " f o r the l e a s t s t e r i c a l l y hindered Mei+Sn t o ~0 f o r the hindered t-Bu SnMe . Indeed the departure from the outer-sphere c o r r e l a t i o n i s the most pronounced with the l a s t hindered a l k y l m e t a l s (see Figure 2 f o r a q u a l i t a t i v e expectation o f s t e r i c e f f e c t s ) . Thus among the symme t r i c a l t e t r a a l k y l t i n compounds Ri*Sn, the l e a s t hindered methyl and n - a l k y l d e r i v a t i v e s a l l l i e f a r t h e s t from the outer-sphere c o r r e lation. Conversely those t e t r a a l k y l t i n compounds with a- and βbranched a l k y l ligands c o n s i s t e n t l y l i e c l o s e s t t o the l i n e s i n Figure 16. The same s t e r i c dichotomy p e r s i s t s i n the o x i d a t i o n o f a l k y l r a d i c a l s by t r i s - p h e n a n t h r o l i n e i r o n ( I I I ) , i n which two competing processes occur -- v i z . , the o x i d a t i o n t o a l k y l c a t i o n s , pre v i o u s l y i d e n t i f i e d as an outer-sphere process i n eq 3, 6

2

6

3+


3

3+

3

2 -

2

6

2

6

2

2

1

2


2


138

INORGANIC CHEMISTRY: TOWARD THE 2 1 S T CENTURY

Figure 15. Contrasting behavior of IrClt (Φ) and TCNE (O) relative to Fe(phen) * ((3) in the correlation of rates (log k) of oxidation with the ionization potentials of alkylmetals (identified by numbers in Reference 3). 3

s


7.

K L I N G L E R E T AL.

Electron

Transfer

Mechanisms


^ s

O

S3

C

«

1.1

*>^~

ι

•à s

-Ο

Ο

v. κ«

JO


140


and aromatic s u b s t i t u t i o n on the phenanthroline 21 (7).

21 ST CENTURY

l i g a n d as i n eq


(21)

For the s e r i e s of β-branched a l k y l r a d i c a l s , the second-order r a t e constant k^ i n eq 3 i s r e l a t i v e l y unaffected by s t e r i c e f f e c t s [compare Figure 2 ( r i g h t ) ] as expected f o r an outer-sphere process. In strong c o n t r a s t , the r a t e constant kL f o r l i g a n d s u b s t i t u t i o n i n eq 21 i s adversely a f f e c t e d by i n c r e a s i n g s t e r i c e f f e c t s , as shown i n Figure 17. The measureable e f f e c t s o f s t e r i c p e r t u r b a t i o n on the r a t e s o f o x i d a t i o n o f encumbered a l k y l m e t a l s by IrCl6 ~ and TCNE i n Figure 16, and on the r a t e s o f l i g a n d s u b s t i t u t i o n by a l k y l r a d i c a l s on F e L i n Figure 17, are to be c l e a r l y d i s t i n g u i s h e d from the corresponding outer-sphere processes i d e n t i f i e d i n Figure 4, i n which s t e r i c e f f e c t s exert l i t t l e or no i n f l u e n c e on the r a t e s . Such a trend f o r the former must r e f l e c t s t e r i c e f f e c t s which per turb the inner c o o r d i n a t i o n sphere o f the a l k y l m e t a l or a l k y l r a d i c a l donor i n the t r a n s i t i o n s t a t e f o r e l e c t r o n t r a n s f e r . In deed we wish to employ t h i s c o n c l u s i o n as an o p e r a t i o n a l d e f i n i t i o n f o r the inner-sphere mechanism o f e l e c t r o n t r a n s f e r (3). In the context of the Marcus formulation, the lowering o f the a c t i v a t i o n b a r r i e r i n an inner-sphere process could a r i s e from the r e d u c t i o n o f the work term w as a r e s u l t o f the strong i n t e r a c t i o n i n the i o n i c products, e.g., [ R S n I r C l " ] and [R^Sn* TCNE"]. The e l e c t r o s t a t i c p o t e n t i a l i n such an ion p a i r i s a t t r a c t i v e and may cause the t e t r a a l k y l t i n to achieve a quasi f i v e - c o o r d i n a t e c o n f i g u r a t i o n i n the precursor complex, reminiscent o f a v a r i e t y of t r i g o n a l bipyramidal s t r u c t u r e s already well-known f o r t i n ( I V ) derivatives, i.e., 2

3 +

3

p

+

4

3

6

SnCllrCI, I

The extent to which s t e r i c e f f e c t s adversely a f f e c t the attainment of such intimate i o n - p a i r s t r u c t u r e s would be r e f l e c t e d i n an i n crease i n the work term and concomitant diminution of the i n n e r sphere r a t e . T h i s q u a l i t a t i v e c o n c l u s i o n accords with the reac t i v i t y trend i n Figure 16. However, Marcus theory does not pro vide a q u a n t i t a t i v e b a s i s f o r e v a l u a t i n g the v a r i a t i o n i n the work term of such ion p a i r s . To o b t a i n the l a t t e r we now t u r n to the M u l l i k e n theory of charge t r a n s f e r i n which the energetics o f i o n p a i r formation evolve d i r e c t l y , and provide q u a n t i t a t i v e informa-



7.


Electron

Transfer

141

Mechanisms

Figure 17. Steric effects (E ) on the rates (log k ) for the outersphere oxidation (O) and the rates (log k ) for the ligand substitution (Q) of Fe(phen) by βbranched alkyl radicals. 8

R

3+

L

s


142

INORGANIC CHEMISTRY: TOWARD THE 21ST

CENTURY

t i o n on the s t e r i c e f f e c t s . Before doing so, however, l e t us f o r mulate the problem i n a more general context i n which we consider organometals as e l e c t r o n donors D and the oxidants I r C U " and TCNE as e l e c t r o n acceptors A. 2

Mechanistic Formulation o f E l e c t r o n T r a n s f e r . The Importance o f the Work Term. A c c o r d i n g l y , the e l e c t r o n t r a n s f e r mechanism can be considered i n the l i g h t o f the standard p o t e n t i a l s E° f o r each redox couple, i . e . , E Q f o r the o x i d a t i o n o f the donor (D -> D + e " ) and E^ed f ° r e d u c t i o n o f the acceptor (A + e" -* A"). Thus the general r e a c t i o n scheme f o r an i r r e v e r s i b l e process i s represented by ( 2 0 ) : X

+

r t


D + A

^4

n

e

[DA]

+

^

[D A-]

*****

Products

i n which e l e c t r o n t r a n s f e r i n the encounter complex [D A] i s r a t e limiting. T h i s scheme i s p a r t i c u l a r l y a p p l i c a b l e t o systems which l i e i n the endergonic r e g i o n o f the d r i v i n g f o r c e [ i . e . , where the standard f r e e energy change, AG » 0 ] . The observed second-order r a t e constant k b i s then given by: 0

0

s

k

obs

=

k

W

K

et DA

where K i s the formation constant o f the complex and k i s the i n t r a m o l e c u l a r r a t e constant f o r e l e c t r o n t r a n s f e r . The thermochemical c y c l e f o r an i r r e v e r s i b l e e l e c t r o n t r a n s f e r i n the h i g h l y endergonic r e g i o n i s s c h e m a t i c a l l y i l l u s t r a t e d below. D A

e t

.D • A

fDA]

D>A"

e

Scheme IV According to the thermochemical c y c l e i n Scheme IV, the a c t i v a t i o n f r e e energy f o r e l e c t r o n t r a n s f e r AG* i n the encounter complex i s given by (16): AG*

=

AG

0

+ w

p

- w

(23)

r

0

AG corresponds t o the standard f r e e energy change o f the redox process: D + A •> D + A", and the work terms w and w represent the energy r e q u i r e d t o b r i n g together the products and r e a c t a n t s , +

p

r


7.

Electron

KLINGLER ET AL.

Transfer

143

Mechanisms

r e s p e c t i v e l y , to w i t h i n the mean separation r ^ i n the i o n p a i r [D A"*]. The observed second-order r a t e constant i n eq 22 can be expressed i n terms o f the a c t i v a t i o n f r e e energy AG* i n eq 23 which leads to the f r e e energy r e l a t i o n s h i p f o r e l e c t r o n t r a n s f e r as : +

k

log o b s

=

-275RT

(AG

+

°

+

V

C

l

(

2

4

)

where Ci = log (κΤ/h). Since the f r e e energy change f o r e l e c t r o n t r a n s f e r AG i s obtained from the standard p o t e n t i a l s of the donor and acceptor [ i . e . , A G = 2 ( E £ - E ° ) ] , the f r e e energy r e l a t i o n s h i p i n eq 24 may be represented by an equivalent form i n eq 25, 0

0


x

log k

o b s

=

" 2. 3RT

^

E

e d

°

x

+

W

p)

+

c

o

n

s

t

a

n

t

25

( )

when one i s d e a l i n g with a s e r i e s 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 with a f i x e d acceptor. Thus eq 24 and 25 s t a t e that the observed r a t e constant ( l o g k ) f o r e l e c t r o n t r a n s f e r can be expressed as the sum of the standard f r e e energy change (AG ) and the work term o f the products (w ). Previous c o n s i d e r a t i o n s of e l e c t r o n t r a n s f e r have tended to focus only on the magnitude of AG , without e x p l i c i t l y t a k i n g i n t o account the energetics of i o n p a i r [D A"] formation, i . e . , the work term Wp. Such an o v e r s i m p l i c a t i o n i s perhaps understandable i f one considers the experimental d i f f i c u l t y of d i r e c t l y e v a l u a t i n g the work terms o f i o n p a i r s by the usual procedures. The problem i s s e v e r e l y compounded by the ex ceedingly short l i f e t i m e s of the t r a n s i e n t i o n p a i r s which must be i n v o l v e d i n i r r e v e r s i b l e e l e c t r o n t r a n s f e r . We now wish to d i s cuss how the observation o f charge t r a n s f e r s p e c t r a i n these sys tems can be used to evaluate such i o n - p a i r i n g energies. o b s

0

p

0

+

E v a l u a t i o n of the Work Term from Charge T r a n s f e r S p e c t r a l Data. The i n t e r m o l e c u l a r i n t e r a c t i o n l e a d i n g to the precursor complex i n Scheme IV i s reminiscent of the e l e c t r o n donor-acceptor or EDA complexes formed between e l e c t r o n donors and acceptors (21). The l a t t e r i s c h a r a c t e r i z e d by the presence of a new absorption band i n the e l e c t r o n i c spectrum. According to the M u l l i k e n charge t r a n s f e r (CT) theory f o r weak EDA complexes, the absorption maxi mum h v corresponds to the v e r t i c a l (Franck-Condon) t r a n s i t i o n from the n e u t r a l ground s t a t e to the p o l a r e x c i t e d s t a t e ( 2 2 ) . C T

[D A]

+

[D A-]*

(26)

The a s t e r i s k i d e n t i f i e s an e x c i t e d i o n p a i r with the same mean separation r as that i n the precursor or EDA complex. The therD

A



144

mochemical c y c l e f o r such a charge t r a n s f e r t r a n s i t i o n i s schemat i c a l l y i l l u s t r a t e d below.

.D • A D% A"

[0 4

to* A]


Scheme V

The v e r t i c a l i o n i z a t i o n p o t e n t i a l o f the e l e c t r o n donor i s represented by I , and the e l e c t r o n a f f i n i t y o f the acceptor by E . The charge t r a n s f e r Scheme V i s akin t o the a d i a b a t i c e l e c tron t r a n s f e r c y c l e i n Scheme IV. In t h i s case the work term Wp* required to b r i n g the products D and A" together t o the mean separation r ^ i n the CT e x c i t e d s t a t e i s given by: D

A

+

w*

=

p

hv

C T

- I

+ C

D

(27)

2

where C = E + w and considered t o be constant f o r a f i x e d acceptor (23). In the l i m i t o f simple i o n - p a i r i n t e r a c t i o n s , the work term i s l a r g e l y coulombic, i . e . , Wp*s - e / r . We r e l a t e the work term Wp* to that o f a reference donor wjî* since the s e r i e s o f organometals i n Figure 15 i n v o l v e s e i t h e r TCNE o r I r C U " as the common accpetor. This comparative procedure allows the acceptor component i n a given s e r i e s t o drop out by c a n c e l l a t i o n , and i t follows from eq 27 that: 2

A

r

2

D A

2

Aw * p

=

w* p

- w°* =

Ahv

C T

- AI

D

(28)

In eq 28, A h v r e f e r s t o the r e l a t i v e CT t r a n s i t i o n energy with a common acceptor, and A I i s the d i f f e r e n c e i n the i o n i z a t i o n pot e n t i a l s o f the donor and the chosen reference. Thus by s e l e c t i n g a reference donor, we can express a l l changes i n the i o n - p a i r i n g energies i n the CT e x c i t e d s t a t e ( i n c l u d i n g s t e r i c , d i s t o r t i o n a l , and other e f f e c t s i n the D/A p a i r ) by a s i n g l e , composite energy term Awp*. We now r e t u r n to the thermal e l e c t r o n t r a n s f e r r e a c t i o n i n eq 20, i n which the r a t e - l i m i t i n g a c t i v a t i o n process has been shown to proceed from the e l e c t r o n donor acceptor complex (23), i . e . , C T

D

[RM

TCNE]

— ^

+

[RM TCNE"]

(29)

The v a r i a t i o n i n the d r i v i n g f o r c e i n eq 29 derives from two f a c tors: (1) the d i f f e r e n c e s i n the o x i d a t i o n p o t e n t i a l s o f the


7.

KLINGLER E T AL.

Electron

Transfer

145

Mechanisms

alkylmetals and (2) the changes i n the work terms i n the ion p a i r s r e s u l t i n g from d i f f e r e n c e s i n the s t e r i c e f f e c t s ( i . e . , mean separations). The f i r s t i s obtained from the f r e e energy change f o r e l e c t r o n t r a n s f e r ( i . e . , RM -* RM + e) i n the outer-sphere process (see eq 6). The change i n the work term i s equated t o Aw *, determined from the CT i n t e r a c t i o n i n eq 28 (24). Thus the l i n e a r corr e l a t i o n i n Figure 18 ( l e f t ) between the d r i v i n g f o r c e and the a c t i v a t i o n f r e e energy represents a l i n e a r f r e e energy r e l a t i o n ship f o r e l e c t r o n t r a n s f e r expressed as: +

p

AG*

=

AG

0

+ Aw * + C

(30)

p

where the constant C represents the reference terms (3) . Furthermore, the same r e l a t i o n s h i p a p p l i e s t o I r C l ~ , as shown by the c o r r e l a t i o n i n Figure 18 ( r i g h t ) . [The a p p l i c a b i l i t y o f the values o f Aw * obtained from TCNE t o the inner-sphere o x i d a t i o n with I r C l " i s probably f o r t u i t o u s . An i n d i c a t i o n o f t h e i r s i m i l a r i t y i s , however, apparent from a comparison o f Figure 15 or 16.]


2

6

p

2

6

A p p l i c a t i o n s o f the Ion-Pair Formulation. Electron transf e r mechanisms are r e c e i v i n g increased a t t e n t i o n i n a wide v a r i e t y o f organic and organometallic r e a c t i o n s such as (1) the a d d i t i o n o f halogens t o alkenes, (2) the e l e c t r o p h i l i c aromatic s u b s t i t u t i o n , (3) the D i e l s - A l d e r r e a c t i o n , and (4) the halogenolysis o f alkylmetals (24). Such mechanisms have been r e f e r r e d t o as s i n g l e e l e c t r o n t r a n s f e r o r SET since they d e r i v e t h e i r d r i v i n g f o r c e from one component (A = B r , H g C l , (NC) C=C(CN) , I ) a c t i n g as an one-electron acceptor r e l a t i v e t o the other component (D = C H , CH =CH , C H , Me Hg) which i s then considered t o be the e l e c t r o n donor. In each case, a charge t r a n s f e r i n t e r a c t i o n can be i d e n t i f i e d i n the precursor complex (24), and t y p i c a l v a r i a t i o n s i n the r e l a t i v e work term Aw * are shown i n Figure 19 as a f u n c t i o n o f the i o n i z a t i o n p o t e n t i a l o f the donor (25). Several features i n Figure 19 are noteworthy. F i r s t , the magnitude and the v a r i a t i o n o f the work term depends s t r o n g l y on the e l e c t r o n donor as w e l l as the acceptor. Thus w * i s r a t h e r constant f o r TCNE when i t i n t e r a c t s with various s u o s t i t u t e d anthracene donors (Figure 19a), but i t decreases s i g n i f i c a n t l y as the i o n i z a t i o n p o t e n t i a l o f the organometal donors increases (Figure 19b). Furthermore, the v a r i a t i o n i n w * i s the l a r g e s t with organometals, when considered among other donors such as arenes and alkenes. With a p a r t i c u l a r s e r i e s o f donors, the v a r i a t i o n o f w * i s the l a r g e s t with the mercury(II) complexes Hg(0Ac) and H g C l , among other acceptors such as TCNE and B r . We a s s o c i a t e such v a r i a t i o n s i n the work term w *with changes i n the mean separation r ^ i n the EDA complexes. Q u a l i t a t i v e l y , such changes may be viewed as s t e r i c e f f e c t s which hinder the c l o s e approach o f the acceptor and the donor. For example, the constancy o f w * f o r the substituted-anthracene donors accords with the minor s t e r i c p e r t u r b a t i o n a s u b s t i t u e n t i s expected t o exert 2

2

2

2

2

6

2

2

6

8

6

2

p

p

p

p

2

2

2

p

O



146

INORGANIC CHEMISTRY: TOWARD THE 21ST CENTURY

Figure 18. Relationship between the activation free energy AG* including the work term Aw * and the driving force for electron transfer AG° to TCNE (left) and IrCl ~ (right) following Equation 30. p

2

6



Electron

Transfer

Mechanisms

b


a

IONIZATION Figure 19.

POTENTIAL, eV

Variation of the work term Δ\ν * evaluated for various charge-transfer complexes. ρ

American Chemical Society Library 1155 16th St., N.W. Chisholm; Inorganic Chemistry: Toward the 21st Century Washington, D.C. 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

148


21 ST CENTURY

on a large d i f f u s e π-donor such as a p o l y c y c l i c aromatic network. By c o n t r a s t , bulky s u b s t i t u e n t s on a l k y l m e t a l s can e f f e c t large changes i n Wp* owing t o the l o c a l i z e d nature o f the i n t e r a c t i o n i n these σ-donors. These work terms can be employed i n the f r e e energy r e l a t i o n s h i p i n the same manner as that described f o r eq 20 above. For example, i n Figure 20 (top), we f i n d a d i r e c t r e l a t i o n s h i p between the E Q o f anthracenes and a l k y l m e t a l s and t h e i r r e a c t i v i t y (log k ) toward TCNE. The experimental p l o t shows two l i n e a r , but separate c o r r e l a t i o n s (25,26). I t i s noteworthy that the two d i f f e r e n t c o r r e l a t i o n s i n Figure 20 (top) emerge as a s i n g l e c o r r e l a t i o n when the work term Aw * i s included. The r e s u l t i n r i g h t f i g u r e i s a l i n e a r f r e e energy r e l a t i o n s h i p , X

o b s


D

log k

o b s

= "275RX

E

t^ ox

+

A w

p*

]

+

constant

(31)

which a p p l i e s t o both anthracene c y c l o a d d i t i o n and a l k y l m e t a l i n sertion. Note the l i n e i s a r b i t r a r i l y drawn with a slope o f u n i t y to emphasize the f i t o f both sets o f data t o eq 31. Such an u n i f i c a t i o n i s remarkable s i n c e these processes c l e a r l y represent i n h e r e n t l y d i s s i m i l a r r e a c t i o n types. Thus the D i e l s - A l d e r r e a c t i o n i s u s u a l l y considered t o i n v o l v e a concerted [2π + 4π] c y c l o a d d i t i o n , whereas the a l k y l m e t a l i n s e r t i o n r e q u i r e s a m u l t i s t e p s c i s s i o n o f a σ carbon-metal bond. The a p p l i c a b i l i t y o f eq 31 t o such d i v e r s e processes as anthracene c y c l o a d d i t i o n and a l k y l m e t a l inser t i o n d e r i v e s from a correspondence o f the work term v a r i a t i o n , i . e . , AWp* = Awp. The r e l a t i o n s h i p between the rates o f e l e c t r o p h i l i c brominat i o n (log k ) and the standard p o t e n t i a l s (E£ ) o f the arene, alkene, and a l k y l m e t a l donors i s shown i n Figure 20 (middle). A l though a rough l i n e a r c o r r e l a t i o n e x i s t s f o r each s e r i e s , there i s no c l e a r c u t i n t e r r e l a t i o n s h i p among any o f them. However, i f the v a r i a t i o n o f the work term Aw * derived from the CT data i s i n c l u d e d , the three separate r e l a t i o n s h i p s become a s i n g l e corre lation. The r e s u l t i n the r i g h t f i g u r e i s the same l i n e a r f r e e energy r e l a t i o n s h i p expressed i n eq 31. Indeed the l i n e i n the f i g u r e i s a r b i t r a r i l y drawn with a slope o f u n i t y t o emphasize the c o r r e l a t i o n o f the data with eq 31. Figure 19 (bottom) shows that the cleavage o f a l k y l m e t a l s by mercuric c h l o r i d e follows an apparent negative Br^nsted slope α ( l e f t f i g u r e ) . However, when the work term Wp* i s included with EQ , the curved f r e e energy r e l a t i o n s h i p with negative slopes i s transformed i n t o the l i n e a r c o r r e l a t i o n shown on the r i g h t . 0 D S

x

p

X

S i g n i f i c a n c e o f the Br^nsted Slope i n E l e c t r o n T r a n s f e r . Linear f r e e energy r e l a t i o n s h i p s have been e x t e n s i v e l y s t u d i e d f o r e l e c t r o n t r a n s f e r and r e l a t e d r e a c t i o n s i n both i n o r g a n i c and organic systems. For h i g h l y endergonic r e a c t i o n s , the Br0nsted slope α i s c l o s e t o u n i t y . In many cases, however, the more o r


7.

KLINGLER ET A L .

Electron

Transfer

149

Mechanisms

Log k


(MV) •

T C N E + R„M

Θ

T C N E + Anthracenes L5

IJO

" "% 0 Θ

B r + Ri»M 2

-5

Ο B r + X=

Inorganic Chemistry: Toward the 21st Century - American Chemical

Recommend Documents