effect of ion pairing on the mechanism and rate of electron transfer. electrochemical aspects

7/29/2019 Effect of Ion Pairing on the Mechanism and Rate of Electron Transfer. Electrochemical Aspects

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Effect of Ion Pairing on the Mechanism and Rate of Electron Transfer. Electrochemical

Aspects

Jean-Michel Saveant

Contribution from the Laboratoire dElectrochimie Moleculaire, Unite Mixte de Recherche UniVersitesCNRSNo 7591, UniVersite de Paris 7, Denis Diderot, 2 place Jussieu, 75251 Paris Cedex 05, France

ReceiVed: April 12, 2001; In Final Form: June 22, 2001

Ion pairing may have a strong influence on the kinetics and mechanisms of electrochemical reactions asreflected by the location of the corresponding half-wave (or peak) potential. Upon increasing the extent ofion pairing (by increasing the binding constant and/ or the concentration of associating ion), the followingchanges are expected, taking a reductive formation of the ion pair as example. For moderate ion pairing andfast electron transfer, a positive shift of the reversible half-wave (or peak) potential by 59.6 mV (at 25 C)per 10-fold increase of the associating ion concentration is predicted. Next, fast and strong ion pairing promptsthe forward electron transfer to become rate determining. On the oxidation side, a predissociation mechanism,involving a positive shift of the wave, prevails as long as the extent of ion pairing is not too large. Uponincreasing the extent of ion pairing, the height of the predissociation wave rapidly drops to zero. Directelectron transfer to the ion pair, associated with the expulsion of the associating ion, then takes place according

to a mechanism in which the breaking of the ion-pair bond is successive to or concerted with electron transfer.In the latter case, the applicability of the dissociative electron-transfer theory previously developed for reductivecleavages is discussed based on appropriate quantum chemical computations.

Electrochemical experiments are usually carried out in asolvent containing an excess of a strong electrolyte, thesupporting electrolyte, which achieves the charge transport fromone electrode to the other. Besides this cardinal function, theions of the supporting electrolyte interact with the negativelyor positively charged species generated from electron transferat the electrode. In water, with the alkali metal salts normallyused with this solvent, these interactions are not strong enoughto lead to the formation of ions pairs. The same is true in most

cases with the tetraalkylammonium perchlorates, tetrafluorobo-rates, hexafluoro phosphates, etc. habitually used in conventionaldipolar aprotic solvents (acetonitrile, N,N-dimethylformamide,dimethylsulfoxide, etc., with dielectric constants of the orderof 30-40). Addition of small alkali metal salts (typically, lithiumand sodium salts) to the latter solvents usually results insignificant formation of ion-pairs1 manifesting themselves bypalpable changes of the electrochemical characteristics of thesystem under examination. In such solvents, dealing with speciesformed upon single electron transfer to neutral molecules, theextent of ion pairing is usually moderate. Its influence on thecourse of the electrochemical reaction may thus be depicted inmost cases as triggered by a change in the reaction thermo-dynamics.2-10 More dramatic consequences in terms of mech-

anisms and kinetics are anticipated for larger values of theassociation constant as those encountered in solvents of lowdielectric constants, such as ethers or polyhalogenated hydro-carbons (dielectric constants of the order of 5-10). Speciesresulting from a second electron transfer are even more proneto ion pairing than first electron-transfer products. The ion pairis then expected to be so strong that the resulting bond mayacquire a covalent rather than an ionic character. This is, forexample, likely to be the case with carbanions resulting from

the reduction of alkyl radicals. Previous studies have indicatedthe importance of follow-up protonation in the electron-transferreactivity of alkyl radicals in solvents such as acetonitrile anddimethylformamide upon addition of an acid to the solution.11

Ion pairing is likely to play a similar role. In solvents of lowdielectric constants, ion pairs involving carbanions are nothingelse than organometallic compounds. In this respect, modernviews on the importance of radicals and electron transfer inorganometallic chemistry, as for example in the Grignard

reaction,12 have created a need for more electron-transferreactivity data concerning radical, ion radicals, and carbanionsin the solvents habitually used in this field. Transposition ofelectrochemical data gathered in more polar solvents may provemisleading insofar as dramatic effects of ion pairing may thusbe overlooked. Last, but not least, electrochemistry in semisolidmedia, particularly in poly(ethylene glycol) melts, has recentlyreceived quite a lot of attention under the leadership of RoyceMurray and co-workers.13 As emphasized by the authors, ion-pairing effects are certainly important in these media. It is thusa pleasure to contribute to this issue in Royces honor with theanalysis of a problem that bears some relation with his recentwork.

In the discussion below, the effect of ion pairing on thethermodynamics will be first recalled. How ion pairing affectsthe kinetics of the electrochemical production of an ion or anion radical will then be discussed as a function of the associationconstant and the concentration of the counterion, taking as anexample the case of a reduction process. The kinetics of thereverse reaction will then be investigated as a function of thesame parameters, with emphasis on the case where the extentof ion pairing is so large that the predissociation mechanism isovertaken by direct electron transfer to the ion pair. In suchcircumstances, the question arises of whether the oxidativecleavage of the ion pair follows a stepwise or a concerted Part of the special issue Royce W. Murray Festschrift.

8995J. Phys. Chem. B 2001, 105, 8995-9001

10.1021/jp011374x CCC: $20.00 2001 American Chemical SocietyPublished on Web 08/11/2001


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mechanism. The results will be described in terms of half-waveor peak potentials and wave shapes in the framework of steadystate or cyclic voltammetric investigations of the problem.

Various scenarios have been investigated in a recent studyof the effect of ion pairing on homogeneous electron transfer,with particular emphasis on intramolecular electron transfer andon the attending migration of the associated ion.14 The presentstudy is a complementary contribution in the sense that it ratherfocuses on electrochemical reactions, on the effect of augment-ing the extent of ion pairing by increasing the concentration ofthe associating ion, and on the direct electrochemistry of the

ion pair. Some of the conclusions extend to homogeneousbimolecular reactions as well.

Results and Discussion

The symbolism we use is defined in Scheme 1. The reductionof A produces B, which combines with Z to form the ion pairC. Transposition to an oxidative process is immediate.

Thermodynamics. If electron transfer and ion pairing arefast, the half-wave or peak potential directly reflects thethermodynamic of the system represented by its standardpotential, E. The variation of E with the concentration of Zand with the equilibrium constant for the formation of the ionpair, Ka is represented in Figure 1. It defines the zones of

thermodynamic stability of the three species involved, A, B,and C. When the concentration of ion pairing agent, [Z],overshoots the association constant, Ka, the standard potentialvaries linearly with the log of the product Ka[Z] with a slope(RT/F) ln(10) () 0.0596 at 25 C). The global variation of Ewith Ka[Z] is given by eq 1:

Another quantity of interest is the standard potential for theconcerted reductive formation of the ion pair (and, conversely,the oxidative cleavage of the ion pair), EA+Z/C

0 . It is related tothe standard potential of the A/B couple and to the standard

free energy of formation of the ion pair, Ga0, according to

eq 2

Effect of the Ion Pairing Equilibrium on the Rate of

Electron Transfer. The standard potential of the global systemshifts positively as the extent of ion pairing as represented inFigure 1. However the actual half-wave or peak potentials maynot follow this prediction because of the interference of electron-transfer kinetics. As seen below, the interference of electron-transfer kinetics depends on the extent of ion pairing even ifthis is so fast in both directions as to remain at equilibrium andthus as to simply modify the thermodynamics of the system.This is the question we address now. Electron transfer in theA/B couple is of the outersphere type. We thus assume that theMarcus-Hush model15 adequately depicts its kinetics. Thekinetic law is therefore given by eq 3 (here and henceforth, theenergies are in eV and the potentials in volts):

with

where i is the current density, Eis the electrode potential, (CA)0and (CB)0 are the concentrations of A and B at the electrodesurface, GA/B

* and GB/A* are the activation free energies of

the forward and reverse electron-transfer respectively, is thetotal reorganization energy (internal+ solvation), and Zel is the

preexponential factor.In the absence of ion pairing, the following equations applyfor steady-state voltammetric techniques:9

where C0 is the total concentration of the species to be reducedor to be oxidized and il is the plateau current density, given byeq 6:

where D is the diffusion coefficient and is the thickness ofthe diffusion layer.16

A combination of eqs 3-6 provides the following expressionof the voltammogram:

after introduction of the dimensionless parameter 0 (eq 8)which measures the competition between mass transport andelectron transfer if the latter would be barrierless:

Figure 1. Variation of the standard potential with the concentrationof associated ion, [Z], and the association constant, Ka.

SCHEME 1

E0) EA/B

0+

RT

Fln(1 + Ka[Z]) (1)

EA+Z/C0

) EA/B0

+RT

Fln Ka ) EA/B

0- Ga

0 (2)

i

F) Z

el[exp(- FRTGA/B* )(CA)0 - exp(-

F

RTGB/A

* )(CB)0](3)

GAfB*

)

4(1 +E- EA/B

0

)

2

, GBfA*

)

4(1 -E- EA/B

0

)

2

, GAfB*

- G*

BfA ) E- EA/B0 (4)

(CA)x)0

C0

) 1 -i

iland

(CB)x)0

C0

)i

il(5)

il )FC

0D

(6)

i

il)

0 exp[- F4RT(1 +E- EA/B

0

)

2

]

(1 - iil{1 + exp[ FRT(E- EA/B

0 )]}) (7)

8996 J. Phys. Chem. B, Vol. 105, No. 37, 2001 Saveant


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The half-wave potential is obtained for i/il ) 0.5, thus leadingto eq 9:

Figure 2 represents the variation of the half-wave potential,E1/2, with the reorganization energy, for a typical value of0,131 287, corresponding to Zel ) 4 103 cm s-1, D ) 10-5

cm2 s-1, and ) 3.3 10-4 cm. The results are displayed fora temperature of 298 K. To obtain the diagram correspondingto another temperature, T, it suffices to multiply the values onthe vertical axis by T/298.

Upon increasing , the half-wave potential deviates more andmore from the equilibrium value, equal to the standard potentialof the A/B couple, ultimately reaching a quasilinear behavior.The system may be considered as irreversible when the

quasilinear region is attained, meaning that there is no anodiccurrent in the potential range where the reduction occurs andvice versa. The system is quasireversible in the transitionbetween the left-hand and right-hand limiting behaviors, whichcovers only a small range of values. In fact the quasilinearportion of each half-wave potential curve is not strictly linearas seen in eq 9, as a result of the quadratic character of theMarcus-Hush law.15

In the presence of ion pairing, the second part of eq 5 isreplaced by eq 10, whereas the first remains the same:

Taking account of the fact that the ion pairing reaction is atequilibrium (eq 11):

it follows that

and therefore, for the equation of the reduction current-potentialcurve

and the expression of the half-wave potential

Figure 3 summarizes the variations of the reduction half-wavepotential with the extent of ion pairing for increasing values ofthe reorganization energy (filled symbols). The correspondingvariations of the oxidation half-wave potential (open symbolsin Figure 3) were obtained from the symmetry of the anodicand cathodic half-wave potentials around the standard potentialof the system:

0)

Zel

D(8)

exp[ F4RT(1 +E1/2 - EA/B

0

)

2

]

0+ exp[ F

RT

(E1/2 - EA/B0 )] ) 1

(9)

(CB)x)0 + (CC)x)0

C0

)i

il(10)

(CB)x)0 )(CB)x)0 + (CC)x)0

1 + Ka[Z](11)

(CB)x)0 )i

il

11 + Ka[Z]

(12)

i

il)

0 exp[- F4RT(1 +E- E

0

)2

]

(1 - iil[1 +exp[ FRT(E- E

0)]1 + Ka[Z]

]) (13)

exp[ F4RT(1 +E1/2 - E

0

)

2

]

0+

exp[ FRT(E1/2 - E0)]1 + Ka[Z]

) 1 (14)

Figure 2. Variation of the half-wave potential with the reorganizationenergy in the absence of ion pairing for 0 ) 131 287 (see text). Uppercurve, oxidation; lower curve, reduction.

Figure 3. Effect of ion pairing equilibrium on the electron-transferrate. Variation of the half-wave potential with the extent of ion pairingfor the following various values of the reorganization energy and for0 ) 131 287 (see text). Thick full line: electron transfer and ionpairing at equilibrium. Close symbols: reduction. Open symbols:oxidation. Circles: reorganization energy (0.514 eV at 25 C; /(RT/F)) 20). Squares: reorganization energy (0.770 eV at 25 C; /(RT/F) )30). Upward triangle: reorganization energy (1.027 eV at 25 C; /(RT/F) ) 40). Downward triangle: reorganization energy (1.284 eV at 25C; /(RT/F) ) 50). Diamonds: reorganization energy (1.541 eV at 25C; /(RT/F) ) 60). Crosses: reorganization energy (1.797 eV at 25C; /(RT/F) ) 70).

E1/2anodic

+ E1/2cathodic

2) E

0 (15)

Effect of Ion Pairing J. Phys. Chem. B, Vol. 105, No. 37, 2001 8997


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where E is given by the diagram in Figure 1. Again, the resultsare displayed for a temperature of 298 K, and the diagramcorresponding to another temperature, T, is obtained by mul-tiplying the values on the vertical axis by T/298.

Perusal of Figure 3 suggests the following remarks. Whenthe reorganization energy is large, i.e., when the electron transferis intrinsically slow, increasing the extent of ion pairing has noeffect on the cathodic wave. On the contrary, there is a strongeffect on the anodic half-wave potential, which derives from

the positive displacement of the global standard potentialresulting from the increase of the extent of ion pairing. In thelinear asymptotic portion, corresponding to prevalence of ionpairs over free ions, the slope is equal to 118 mV per decade.

An interesting effect of ion pairing appears when electrontransfer is initially in a reversible or quasi-reversible regime,i.e., for small reorganization energies (in Figure 3, this is clearlyseen for the three smallest reorganization energies). Then,increasing the extent of ion pairing renders the system irrevers-ible and controlled by the forward electron-transfer step.Consistently, the separation between the cathodic and anodichalf-wave potentials increases with the extent of ion pairing.The reason for this behavior is that the reverse electron transfer(B f A) is annihilated by the immediate and irreversible

transformation of the free ion B into the ion pair C.In such cases, ion pairing helps electron transfer depart fromequilibrium and become accessible to kinetic characterizationwithin the available range of diffusion rate. In particular,detection and characterization of nonlinear activation-drivingforce relationships17-19 is anticipated to be facilitated by theoccurrence of ion pairing because the variation of the transfercoefficient with potential is the larger the smaller the reorga-nization energy (eq 16):

The variations of the peak potentials in cyclic voltammetryare qualitatively the same as those of the half-wave potentialin steady-state techniques shown in Figure 3. When, intrinsically,and/or because of the effect of ion pairing, the system hasbecome irreversible, the quantitative variations of the peakpotentials may be derived from Figure 3 as follows.

The quadratic law expressed by the first part of eq 4 can belinearized within the rather restricted potential range in whichthe cathodic or the anodic cyclic voltammetric waves develop.Thus, at the peak, the forward activation free energy may beexpressed as:20

(- for the reduction and + for the oxidation). V is the scanrate, and Rp is the transfer coefficient at the peak. Taking Rp )0.5 and the same value of0 chosen for the representation givenin Figure 3, the values of the peak potentials at 0.1 V/s are thesame as the values given for the half-wave potentials displayedin this figure.

From Ion Pairing at Equilibrium to the Direct Electro-

chemistry of the Ion Pair. Interference of the Association

and Dissociation Kinetics. We have assumed so far that theion pairing equilibrium is established instantaneously in bothdirections. In practice, this condition might not be exactly

fulfilled even though the rate constants of formation anddissociation of ion pairs are likely to be high. We now examinethis question for the reduction and oxidation processes succes-sively, for cases where the ion-pairing agent, Z, is in large excessover the reactant, A.

For the reduction process, adaptation of previous treatmentsof EC reaction schemes21,22 to the present conditions (involv-ing particularly the introduction of a quadratic law depictingthe electron-transfer kinetics) leads to the following the volta-

mmogram eq 18, in which the kinetic parameter , measuringthe competition between the follow-up reaction and diffusion,is defined by eq 19:

where ka is the rate constant for the formation of the ion pair.The variation of the half-wave potential may thus be derived

from eq 20:

As summarized in Figure 3, when electron transfer isintrinsically slow, i.e., for reorganization energies above ca. 1.3eV, the reaction is under the kinetic control of the forwardelectron transfer whatever the rate of the follow-up ion pairingstep. The effect of the kinetics of ion pairing should be moreapparent for smaller values of the reorganization energy, thosecorresponding to the S-shape behavior visible in Figure 3. Asa demonstrating example, Figure 4 shows the variation of thehalf-wave potential with the extent of ion-pairing (measuredby Ka[Z]) for reorganization energy equal to 0.770 eV, assumingthat the ion pair formation is diffusion controlled (taking as arate constant 1011 M-1 s-1),23 for concentrations of the associat-ing ion that ranges from 10-3 to 1 M. The full line in Figure 4

recalls the variations expected when the ion pairing equilibriumis established. The actual variations computed for [Z] ) 1 Mare not far from this limiting behavior, but the deviation rapidlyaugments as [Z] decreases. The horizontal asymptote reachedfor larger values ofKa[Z] thus represents a mixed kinetic controlby the electron transfer and the ion-pairing step.

What happens simultaneously with the oxidation process isthe question we tackle now. For the reduction process, the heightof the wave remained unchanged and the effect of the ion-pairingkinetics was on the location of the half-wave potential. Thesituation is different for the oxidation process where the mostimportant effect is a decrease of the plateau current uponincreasing the extent of ion pairing until the complete vanishingof the wave. Quantitatively, adaptation of the previous treatments

R )12(1 +

E- EA/B0

) (16)

GAfB*,p

)RT

F

(ln

Zel

R

pFRT

VD

- 0.78

)(17)

i

il)

0 exp[- F4RT(1 +E- EA/B

0

)2

]

(1 - iil{1 +exp[ FRT(E- EA/B

0 )]1 + Ka[Z] [1 + Ka[Z]

tanh()

]}) (18)) ka([Z] + 1Ka)

2

D(19)

exp[ F4RT(1 +E1/2 - EA/B

0

)

2

]

0+

exp[ FRT(E1/2 - EA/B0 )][1 + Ka[Z] tanh()

]1 + Ka[Z]

) 1 (20)



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of CE mechanisms22,24 leads to the following expression ofthe plateau current:

with the same definition of symbols as before. Examples ofthis rapid disappearance of the wave are shown in Figure 5 fora diffusion-controlled formation of the ion-pair (same value ofthe rate constant as before).

Direct Electrochemistry of the Ion Pair. After the predis-sociation mechanism for the oxidation of the ion pair has beenshut down as depicted in the preceding section, the onlyremaining possibility is direct removal of one electron from theion pair combined with the expulsion of the associating ion.Then, the half-wave (and peak) potential becomes independentof the concentration of the associating ion.

The situation is the oxidative counterpart of reductive

cleavage, a well-documented reaction both at the experimentaland theoretical levels.25 Electron transfer and ion expulsion maysimilarly occur concertedly or in two successive steps (Scheme2). The factors that govern the occurrence of the concerted vsthe stepwise mechanism have been analyzed in detail in thereductive case and may be transposed to the present situation.As far as the molecular structure of the ion pair is concerned,the concerted pathway is favored by small values ofGcleavage

0

(eq 22):

Small bond dissociation free energies (BDFE), difficult reductionof the leaving cation, and difficult removal of the exchanging

electron from a transitorily hosting orbital (such as a orbitalpresent in the R moiety) are thus favorable factors for theconcerted pathway and vice versa for the stepwise pathway.

In the concerted case, it is tempting to model the reactiondynamics according to the theory of dissociative electron transferpreviously applied to several reductive cleavage reactions.25 Inthis model, the reactant potential energy profile is approximatedby a homolytic dissociation Morse curve and the product curveis assumed to be equal to the repulsive part of the reactantcurve.26 It may seem odd to represent the dissociation of anion pair by a homolytic dissociation curve. A dissociation curvereflecting the Coulombic interaction between the two ions wouldseem a priori more likely.

We have investigated this question, taking as examplemethyllithium in diethyl ether as the solvent. The potentialenergy profiles for its ionic and homolytic dissociations whereobtained by means of density functional calculations (see themethodology section). They are represented in Figure 6. In thegas phase, heterolytic dissociation of CH3Li, into CH3- and Li+,is much more difficult than homolytic dissociation, into CH3

and Li (8.88 eV instead of 2.01 eV). Although the differencein energy is considerably reduced in ether, heterolytic dissocia-tion is still more difficult than homolytic dissociation in thissolvent (3.44 instead of 2.44 eV). During the homolyticdissociation the multiplicity of the system passes from 1 to 3.This is the reason that we have computed the potential energyfor both situations at large C-Li distances. Taking the effect

Figure 4. Effect of ion pairing kinetics on the rate of the reductionprocess. Variation of the half-wave potential with the extent of ionpairing for a reorganization energy of 0.770 eV, for 0 ) 132 187,and for a diffusion-controlled rate of formation of the ion pair (seetext). Dashed line: electron transfer and ion pairing at equilibrium.Thick full line: ion pairing at equilibrium. The various symbolscorrespond to different concentrations of the associating ion. Circles:1 M. Squares: 0.1 M. Diamonds: 0.01 M. Triangles: 0.001 M.

i

il)

1

1 + Ka[Z]tanh()

(21)

Gcleavage0

) BDFERMfR+M - ERM0

+/RM + EM+/M0 (22)

Figure 5. Effect of ion pairing kinetics on the rate of the oxidationprocess. Variation of the plateau current with the extent of ion pairingfor a diffusion-controlled rate of formation of the ion pair. The varioussymbols correspond to different concentrations of the associatingion. Circles: 1 M. Squares: 0.1 M. Diamonds: 0.01 M. Triangles:0.001 M.

SCHEME 2



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of the change in multiplicity into account, it is seen that thepotential energy profile may be represented by a Morse curve(eq 23) with a good accuracy:

with BDERMfR+M ) 2.01 and 2.44 eV and ) 1.34 and 1.26-1 in the gas phase and in diethyl ether, respectively.

These observations validate the application of the dissociativeelectron-transfer theory to the direct oxidation of ion pairsinsofar as it follows a concerted mechanism. Going to structur-ally looser binding and/or to a more polar solvent may result inthe heterolytic dissociation becoming easier than the homolyticdissociation calling for a modification of the conventionaldissociative electron-transfer model. Two facts should howeverbe taken into account in this connection. One is that, in theconcerted case, the intrinsic barrier is large because it containsa bond-breaking contribution. It follows that the reaction needsto be exergonic in order to proceed at a palpable rate. Thetransition state has thus a reactant-like character correspondingto a relatively modest stretching of the breaking bond. At thetransition state, the potential energy profile may thus correspondto homolytic dissociation even though an inflection toward aheterolytic dissociation profile may well take place at largerbond lengths. A second remark is that when ion pairing becomesweaker and weaker, the predissociation mechanism overridesthe direct oxidation of the ion pair. It is therefore likely thatthe conventional Morse curve model of dissociative electrontransfer will apply satisfactorily to most of the cases where ionpairing is so strong that direct electron transfer from the ionpair takes place and is concerted with bond cleavage.

In the concerted case, the half-wave (and peak) potential isgiven by eq 14 and Figure 2, in which EA/B

0 is replaced by EA/C0

and by BDERMfR+M + 0, where 0 is the solvent reorga-nization energy.

Conclusions

The main conclusions emerging from the preceding discussionmay be summarized as follows in the case where the formation

of the ion pair is the result of a reductive process, noting thatthey can be transposed with no difficulty to the case of anoxidative process.

The first effect of ion pairing is to stabilize the reduced form.When ion pairing follows a fast electron-transfer step a positiveshift of the reversible half-wave (or peak) potential by 59.6 mV(at 25 C) per 10-fold increase of the associating ion concentra-tion ensues (Figure 1, eq 1).

Because it rapidly consumes the initial reduction product, thus

hampering back electron transfer, increased ion pairing willmoreover prompt the forward electron transfer to become ratedetermining. This has no palpable effect on the location of half-wave (or peak) potential in the case where electron transfer isintrinsically slow. The effect of ion pairing appears for relativelyfast electron transfers (Figure 3, eq 14). It converts a reversiblereduction process into an irreversible process governed by theforward electron transfer. In these circumstances, ion pairingthus reveals the kinetics of electron transfer.

On the oxidation side, the reaction follows a predissociationmechanism as long as the extent of ion pairing is not too large(Figure 3). The energy cost of the predissociation step makesthe oxidation wave shift toward positive potential. As the extentof ion pairing further increases, the kinetics of the predissocia-

tion step come into play leading progressively to the disappear-ance of the wave. The only remaining possibility is directelectron transfer from the ion pair. Its association with theexpulsion of the associating ion may involve concerted breakingof the bond or a two-step mechanism where the bond breaksafter removal of the electron. The situation is closely similar tothe case of reductive cleavage, a well-documented reaction boththeoretically and experimentally. The question just ariseswhether, in the concerted case, the previously developed theoryof dissociative electron-transfer applies. Computation of thedissociation potential energy profile shows that this is indeedthe case for CH3Li in diethyl ether as the solvent. Thisconclusion most probably extends to most systems involvingstrong ion pairing and concerted bond breaking.

Methodology for Quantum Chemical Calculations

Density functional (B3LYP/6-31G*)27 optimizations andenergy calculations were performed with the Gaussian 98package.28 Solvation free energies were calculated on the gas-phase optimized conformations according to the SCRF (self-consistent reaction field) method using the polarized continuum(overlapping spheres) model (PCM).29

References and Notes

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(3) Fujinaga, T.; Izutsu, K.; Nomura, T. J. Electroanal. Chem. 1971,29, 333.(4) (a) Kalinovski, M. K. Chem. Phys. Lett. 1970, 7, 55. (b) Kalinovski,

M. K. Chem. Phys. Lett. 1971, 8, 378. (c) Lasia, A.; Kalinovski, M. K. J.Electroanal. Chem. 1972, 36, 511. (d) Kalinovski, M. K.; Tenderende-Guminska, J. Electroanal. Chem. 1974, 55, 227. (e) Kapturkiewicz. J. Phys.Chem. 1978, 82, 1141.

(5) Holleck, L.; Levine, S. J. Electroanal. Chem. 1973, 43, 175.(6) Krygovski, T. M.; Lipsztajn, Y.; Galus, Z. J. Electroanal. Chem.

1973, 42, 261.(7) (a) Ryan, M. D.; Evans, D. H. J. Electrochem. Soc. 1974, 121,

881. (b) Ryan, M. D.; Evans, D. H. J. Electroanal. Chem. 1976, 67, 333.(c) Evans, D. H. J. Phys. Chem. B 1998, 102, 9928. (d) Evans, D. H.;Lehmann, M. W. Acta Chem. Scand. 1999, 53, 765.

(8) Hazelrigg, M. J.; Bard, A. J. J. Electrochem. Soc. 1975, 122, 211.(9) (a) Chauhan, B. G.; Fawcett, W. R.; Lasia, A. J. Phys. Chem. 1977,

81, 1476. (b) Fawcett, W. R.; Lasia, A. J. Phys. Chem. 1978, 82, 1114. (c)

Figure 6. Potential energy profiles for the dissociation of CH3Li (fromdensity functional calculations, see the methodology section). b:homolytic fragments, CH3 + Li; (: ionic fragments, CH3- + Li+. O:singlet curve; : triplet curve. Full line: best fit Morse curve for the

homolytic dissociation.

G ) G0+ BDERMfR+M{1 - exp[-(x - x0)]}

2 (23)



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Fawcett, W. R.; Lasia, A. Can. J. Chem. 1981, 59, 3256. (d) Andreu, R.;Calvente, J. J.; Fawcett, W. R.; Molero, M. J. Phys. Chem. B 1997, 101,2884.

(10) (a) Andrieux, C. P.; Saveant , J.-M. Saveant, J. Electroanal. Chem.1974, 57, 27. (b) Andrieux, C. P.; Robert, M.; Saveant, J.-M. J. Am. Chem.Soc. 1995, 117, 9340.

(11) Hapiot, P.; Konovalov, V.; Saveant, J.-M. J. Am. Chem. Soc. 1995,117, 1428.

(12) Garst, J. F.; Ungvary, F. Mechanism of Grignard Reagent Forma-tion. In Grignard Reagents: New DeVelopments; Richey, H. G., Ed.;Wiley: Chichester, U.K., 2000; pp 185-275.

(13) (a) Dickinson, E.; Williams, M. R.; Hendrickson, M. R.; Masui,

H.; Murray, R. W. J. Am. Chem. Soc. 1999, 121, 613. (b) Williams, M. R.;Masui, H.; Murray, R. W. J. Phys. Chem. B 2000, 104, 10699.(14) Marcus, R. A. J. Phys. Chem. B 1998, 102, 10071.(15) (a) Marcus, R. A. J. Chem. Phys. 1956, 24, 966. (b) Marcus, R. A.

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effect of ion pairing on the mechanism and rate of electron transfer. electrochemical aspects

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