J. Phys. Chem. B 2001, 105, 8995-9001
8995
Effect of Ion Pairing on the Mechanism and Rate of Electron Transfer. Electrochemical Aspects† Jean-Michel Save´ ant Contribution from the Laboratoire d’Electrochimie Mole´ culaire, Unite´ Mixte de Recherche UniVersite´ sCNRS No 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 as reflected by the location of the corresponding half-wave (or peak) potential. Upon increasing the extent of ion pairing (by increasing the binding constant and/ or the concentration of associating ion), the following changes are expected, taking a reductive formation of the ion pair as example. For moderate ion pairing and fast 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 prompts the 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. Upon increasing the extent of ion pairing, the height of the predissociation wave rapidly drops to zero. Direct electron 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 reductive cleavages is discussed based on appropriate quantum chemical computations.
Electrochemical experiments are usually carried out in a solvent containing an excess of a strong electrolyte, the supporting electrolyte, which achieves the charge transport from one electrode to the other. Besides this cardinal function, the ions of the supporting electrolyte interact with the negatively or positively charged species generated from electron transfer at the electrode. In water, with the alkali metal salts normally used with this solvent, these interactions are not strong enough to lead to the formation of ions pairs. The same is true in most cases with the tetraalkylammonium perchlorates, tetrafluoroborates, hexafluoro phosphates, etc. habitually used in conventional dipolar aprotic solvents (acetonitrile, N,N-dimethylformamide, dimethylsulfoxide, etc., with dielectric constants of the order of 30-40). Addition of small alkali metal salts (typically, lithium and sodium salts) to the latter solvents usually results in significant formation of ion-pairs1 manifesting themselves by palpable changes of the electrochemical characteristics of the system under examination. In such solvents, dealing with species formed upon single electron transfer to neutral molecules, the extent of ion pairing is usually moderate. Its influence on the course of the electrochemical reaction may thus be depicted in most cases as triggered by a change in the reaction thermodynamics.2-10 More dramatic consequences in terms of mechanisms and kinetics are anticipated for larger values of the association constant as those encountered in solvents of low dielectric constants, such as ethers or polyhalogenated hydrocarbons (dielectric constants of the order of 5-10). Species resulting from a second electron transfer are even more prone to ion pairing than first electron-transfer products. The ion pair is then expected to be so strong that the resulting bond may acquire a covalent rather than an ionic character. This is, for example, likely to be the case with carbanions resulting from †
Part of the special issue “Royce W. Murray Festschrift”.
the reduction of alkyl radicals. Previous studies have indicated the importance of follow-up protonation in the electron-transfer reactivity of alkyl radicals in solvents such as acetonitrile and dimethylformamide upon addition of an acid to the solution.11 Ion pairing is likely to play a similar role. In solvents of low dielectric constants, ion pairs involving carbanions are nothing else than organometallic compounds. In this respect, modern views on the importance of radicals and electron transfer in organometallic chemistry, as for example in the Grignard reaction,12 have created a need for more electron-transfer reactivity data concerning radical, ion radicals, and carbanions in the solvents habitually used in this field. Transposition of electrochemical data gathered in more polar solvents may prove misleading insofar as dramatic effects of ion pairing may thus be overlooked. Last, but not least, electrochemistry in semisolid media, particularly in poly(ethylene glycol) melts, has recently received quite a lot of attention under the leadership of Royce Murray and co-workers.13 As emphasized by the authors, ionpairing effects are certainly important in these media. It is thus a pleasure to contribute to this issue in Royce’s honor with the analysis of a problem that bears some relation with his recent work. In the discussion below, the effect of ion pairing on the thermodynamics will be first recalled. How ion pairing affects the kinetics of the electrochemical production of an ion or an ion radical will then be discussed as a function of the association constant and the concentration of the counterion, taking as an example the case of a reduction process. The kinetics of the reverse reaction will then be investigated as a function of the same parameters, with emphasis on the case where the extent of ion pairing is so large that the predissociation mechanism is overtaken by direct electron transfer to the ion pair. In such circumstances, the question arises of whether the oxidative cleavage of the ion pair follows a stepwise or a concerted
10.1021/jp011374x CCC: $20.00 © 2001 American Chemical Society Published on Web 08/11/2001
8996 J. Phys. Chem. B, Vol. 105, No. 37, 2001
Save´ant free energy of formation of the ion pair, ∆G0a , according to eq 2
RT ln Ka ) E0A/B - ∆G0a F
0 EA+Z/C ) E0A/B +
Figure 1. Variation of the standard potential with the concentration of associated ion, [Z], and the association constant, Ka.
SCHEME 1
(2)
Effect of the Ion Pairing Equilibrium on the Rate of Electron Transfer. The standard potential of the global system shifts positively as the extent of ion pairing as represented in Figure 1. However the actual half-wave or peak potentials may not follow this prediction because of the interference of electrontransfer kinetics. As seen below, the interference of electrontransfer kinetics depends on the extent of ion pairing even if this is so fast in both directions as to remain at equilibrium and thus as to simply modify the thermodynamics of the system. This is the question we address now. Electron transfer in the A/B couple is of the outersphere type. We thus assume that the Marcus-Hush model15 adequately depicts its kinetics. The kinetic law is therefore given by eq 3 (here and henceforth, the energies are in eV and the potentials in volts):
i F F (C ) - exp - ∆G* (C ) ) Zel exp - ∆G* F RT A/B A 0 RT B/A B 0 (3)
[ (
)
(
)
(
) ]
with mechanism. The results will be described in terms of half-wave or peak potentials and wave shapes in the framework of steady state or cyclic voltammetric investigations of the problem. Various scenarios have been investigated in a recent study of the effect of ion pairing on homogeneous electron transfer, with particular emphasis on intramolecular electron transfer and on the attending migration of the associated ion.14 The present study is a complementary contribution in the sense that it rather focuses on electrochemical reactions, on the effect of augmenting the extent of ion pairing by increasing the concentration of the associating ion, and on the direct electrochemistry of the ion pair. Some of the conclusions extend to homogeneous bimolecular reactions as well. Results and Discussion
(
)
where i is the current density, E is the electrode potential, (CA)0 and (CB)0 are the concentrations of A and B at the electrode * surface, ∆G* A/B and ∆GB/A are the activation free energies of the forward and reverse electron-transfer respectively, λ is the total reorganization energy (internal+ solvation), and Zel is the preexponential factor. In the absence of ion pairing, the following equations apply for steady-state voltammetric techniques:9
(CA)x)0
The symbolism we use is defined in Scheme 1. The reduction of A produces B, which combines with Z to form the ion pair C. Transposition to an oxidative process is immediate. Thermodynamics. If electron transfer and ion pairing are fast, the half-wave or peak potential directly reflects the thermodynamic of the system represented by its standard potential, E°. The variation of E° with the concentration of Z and with the equilibrium constant for the formation of the ion pair, 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 potential varies 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 E° with Ka[Z] is given by eq 1:
RT ln(1 + Ka[Z]) E0 ) E0A/B + F
E - E0A/B 2 λ * 1+ , ∆GBfA ) 4 λ E - E0A/B 2 λ * 1, ∆GAfB - ∆G*BfA ) E - E0A/B (4) 4 λ
* ) ∆GAfB
(1)
Another quantity of interest is the standard potential for the concerted reductive formation of the ion pair (and, conversely, 0 the oxidative cleavage of the ion pair), EA+Z/C . It is related to the standard potential of the A/B couple and to the standard
0
C
)1-
(CB)x)0 i i and ) il il C0
(5)
where C0 is the total concentration of the species to be reduced or to be oxidized and il is the plateau current density, given by eq 6:
il )
FC0D δ
(6)
where D is the diffusion coefficient and δ is the thickness of the diffusion layer.16 A combination of eqs 3-6 provides the following expression of the voltammogram:
[ (
)]
E - EA/B Fλ i ) Λ0 exp 1+ il 4RT λ 0
(
1-
{
2
×
F i 1 + exp (E - E0A/B) il RT
[
]}) (7)
after introduction of the dimensionless parameter Λ0 (eq 8) which measures the competition between mass transport and electron transfer if the latter would be barrierless:
Effect of Ion Pairing
J. Phys. Chem. B, Vol. 105, No. 37, 2001 8997
Zelδ D
Λ0 )
(8)
The half-wave potential is obtained for i/il ) 0.5, thus leading to eq 9:
[ (
)]
E1/2 - EA/B Fλ 1+ exp 4RT λ 0 Λ 0
2
+ exp
[RTF (E
1/2
]
- E0A/B) ) 1 (9)
Figure 2 represents the variation of the half-wave potential, E1/2, with the reorganization energy, for a typical value of Λ0, 131 287, corresponding to Zel ) 4 × 103 cm s-1, D ) 10-5 cm2 s-1, and δ ) 3.3 × 10-4 cm. The results are displayed for a temperature of 298 K. To obtain the diagram corresponding to another temperature, T, it suffices to multiply the values on the vertical axis by T/298. Upon increasing λ, the half-wave potential deviates more and more from the equilibrium value, equal to the standard potential of 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 anodic current in the potential range where the reduction occurs and vice versa. The system is “quasireversible” in the transition between the left-hand and right-hand limiting behaviors, which covers only a small range of λ values. In fact the quasilinear portion of each half-wave potential curve is not strictly linear as seen in eq 9, as a result of the quadratic character of the Marcus-Hush law.15 In the presence of ion pairing, the second part of eq 5 is replaced by eq 10, whereas the first remains the same:
(CB)x)0 + (CC)x)0 C0
)
i il
Figure 2. Variation of the half-wave potential with the reorganization energy in the absence of ion pairing for Λ0 ) 131 287 (see text). Upper curve, oxidation; lower curve, reduction.
(10)
Taking account of the fact that the ion pairing reaction is at equilibrium (eq 11):
(CB)x)0 )
(CB)x)0 + (CC)x)0
(11)
1 + Ka[Z]
it follows that
(CB)x)0 )
i 1 il 1 + Ka[Z]
(12)
and therefore, for the equation of the reduction current-potential curve
[
(
)]
Fλ E - E0 i ) Λ0 exp 1+ il 4RT λ
( [ 1-
2
× F (E - E0) RT 1 + Ka[Z]
exp
i 1+ il
[
]
])
(13)
and the expression of the half-wave potential
exp
[ (
)] [
E1/2 - E0 Fλ 1+ 4RT λ 0 Λ
2
exp
+
]
F (E - E0) RT 1/2 ) 1 (14) 1 + Ka[Z]
Figure 3. Effect of ion pairing equilibrium on the electron-transfer rate. Variation of the half-wave potential with the extent of ion pairing for the following various values of the reorganization energy and for Λ0 ) 131 287 (see text). Thick full line: electron transfer and ion pairing 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 25 °C; /(RT/F) ) 50). Diamonds: reorganization energy (1.541 eV at 25 °C; /(RT/F) ) 60). Crosses: reorganization energy (1.797 eV at 25 °C; /(RT/F) ) 70).
Figure 3 summarizes the variations of the reduction half-wave potential with the extent of ion pairing for increasing values of the reorganization energy (filled symbols). The corresponding variations of the oxidation half-wave potential (open symbols in Figure 3) were obtained from the symmetry of the anodic and cathodic half-wave potentials around the standard potential of the system:
Eanodic + Ecathodic 1/2 1/2 ) E0 2
(15)
8998 J. Phys. Chem. B, Vol. 105, No. 37, 2001
Save´ant
where E° is given by the diagram in Figure 1. Again, the results are displayed for a temperature of 298 K, and the diagram corresponding to another temperature, T, is obtained by multiplying the values on the vertical axis by T/298. Perusal of Figure 3 suggests the following remarks. When the reorganization energy is large, i.e., when the electron transfer is intrinsically slow, increasing the extent of ion pairing has no effect on the cathodic wave. On the contrary, there is a strong effect on the anodic half-wave potential, which derives from the positive displacement of the global standard potential resulting from the increase of the extent of ion pairing. In the linear asymptotic portion, corresponding to prevalence of ion pairs over free ions, the slope is equal to 118 mV per decade. An interesting effect of ion pairing appears when electron transfer is initially in a reversible or quasi-reversible regime, i.e., for small reorganization energies (in Figure 3, this is clearly seen for the three smallest reorganization energies). Then, increasing the extent of ion pairing renders the system irreversible and controlled by the forward electron-transfer step. Consistently, the separation between the cathodic and anodic half-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 from equilibrium and become accessible to kinetic characterization within the available range of diffusion rate. In particular, detection and characterization of nonlinear activation-driving force relationships17-19 is anticipated to be facilitated by the occurrence of ion pairing because the variation of the transfer coefficient with potential is the larger the smaller the reorganization energy (eq 16):
(
)
E - EA/B 1 R) 1+ 2 λ 0
(16)
(x
RT ln F
Zel
RpF VD RT
- 0.78
)
(17)
(- for the reduction and + for the oxidation). V is the scan rate, and Rp is the transfer coefficient at the peak. Taking Rp ) 0.5 and the same value of Λ0 chosen for the representation given in Figure 3, the values of the peak potentials at 0.1 V/s are the same as the values given for the half-wave potentials displayed in this figure. From Ion Pairing at Equilibrium to the Direct Electrochemistry of the Ion Pair. Interference of the Association and Dissociation Kinetics. We have assumed so far that the ion pairing equilibrium is established instantaneously in both directions. In practice, this condition might not be exactly
[ (
)]
E - E0A/B 2 i Fλ ) Λ0 exp 1+ × il 4RT λ F exp (E - E0A/B) tanh(xσ) i RT 1- 1+ 1 + Ka[Z] il 1 + Ka[Z] xσ
( {
[
[
]})
]
(
σ ) ka [Z] +
)
1 δ2 Ka D
(18)
(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:
exp
[ (
)]
E1/2 - EA/B Fλ 1+ 4RT λ
exp
The variations of the peak potentials in cyclic voltammetry are qualitatively the same as those of the half-wave potential in steady-state techniques shown in Figure 3. When, intrinsically, and/or because of the effect of ion pairing, the system has become irreversible, the quantitative variations of the peak potentials may be derived from Figure 3 as follows. The quadratic law expressed by the first part of eq 4 can be linearized within the rather restricted potential range in which the cathodic or the anodic cyclic voltammetric waves develop. Thus, at the peak, the forward activation free energy may be expressed as:20 *,p ) ∆GAfB
fulfilled even though the rate constants of formation and dissociation of ion pairs are likely to be high. We now examine this question for the reduction and oxidation processes successively, for cases where the ion-pairing agent, Z, is in large excess over the reactant, A. For the reduction process, adaptation of previous treatments of “EC” reaction schemes21,22 to the present conditions (involving particularly the introduction of a quadratic law depicting the electron-transfer kinetics) leads to the following the voltammogram eq 18, in which the kinetic parameter σ, measuring the competition between the follow-up reaction and diffusion, is defined by eq 19:
0
[
Λ0
2
+
][
]
tanh(xσ) F (E - E0A/B) 1 + Ka[Z] RT 1/2 xσ 1 + Ka[Z]
) 1 (20)
As summarized in Figure 3, when electron transfer is intrinsically slow, i.e., for reorganization energies above ca. 1.3 eV, the reaction is under the kinetic control of the forward electron transfer whatever the rate of the follow-up ion pairing step. The effect of the kinetics of ion pairing should be more apparent for smaller values of the reorganization energy, those corresponding to the S-shape behavior visible in Figure 3. As a demonstrating example, Figure 4 shows the variation of the half-wave potential with the extent of ion-pairing (measured by Ka[Z]) for reorganization energy equal to 0.770 eV, assuming that the ion pair formation is diffusion controlled (taking as a rate constant 1011 M-1 s-1),23 for concentrations of the associating ion that ranges from 10-3 to 1 M. The full line in Figure 4 recalls the variations expected when the ion pairing equilibrium is established. The actual variations computed for [Z] ) 1 M are not far from this limiting behavior, but the deviation rapidly augments as [Z] decreases. The horizontal asymptote reached for larger values of Ka[Z] thus represents a mixed kinetic control by the electron transfer and the ion-pairing step. What happens simultaneously with the oxidation process is the question we tackle now. For the reduction process, the height of the wave remained unchanged and the effect of the ion-pairing kinetics was on the location of the half-wave potential. The situation is different for the oxidation process where the most important effect is a decrease of the plateau current upon increasing the extent of ion pairing until the complete vanishing of the wave. Quantitatively, adaptation of the previous treatments
Effect of Ion Pairing
J. Phys. Chem. B, Vol. 105, No. 37, 2001 8999
Figure 4. Effect of ion pairing kinetics on the rate of the reduction process. Variation of the half-wave potential with the extent of ion pairing for a reorganization energy of 0.770 eV, for Λ0 ) 132 187, and for a diffusion-controlled rate of formation of the ion pair (see text). Dashed line: electron transfer and ion pairing at equilibrium. Thick full line: ion pairing at equilibrium. The various symbols correspond to different concentrations of the associating ion. Circles: 1 M. Squares: 0.1 M. Diamonds: 0.01 M. Triangles: 0.001 M.
Figure 5. Effect of ion pairing kinetics on the rate of the oxidation process. Variation of the plateau current with the extent of ion pairing for a diffusion-controlled rate of formation of the ion pair. The various symbols correspond to different concentrations of the associating ion. Circles: 1 M. Squares: 0.1 M. Diamonds: 0.01 M. Triangles: 0.001 M.
SCHEME 2
of “CE” mechanisms22,24 leads to the following expression of the plateau current:
i ) il
1 1 + Ka[Z]
tanh(xσ)
(21)
xσ
with the same definition of symbols as before. Examples of this rapid disappearance of the wave are shown in Figure 5 for a diffusion-controlled formation of the ion-pair (same value of the rate constant as before). Direct Electrochemistry of the Ion Pair. After the predissociation mechanism for the oxidation of the ion pair has been shut down as depicted in the preceding section, the only remaining possibility is direct removal of one electron from the ion pair combined with the expulsion of the associating ion. Then, the half-wave (and peak) potential becomes independent of the concentration of the associating ion. The situation is the oxidative counterpart of reductive cleavage, a well-documented reaction both at the experimental and theoretical levels.25 Electron transfer and ion expulsion may similarly occur concertedly or in two successive steps (Scheme 2). The factors that govern the occurrence of the concerted vs the stepwise mechanism have been analyzed in detail in the reductive 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 of ∆G0cleavage (eq 22): 0 0 ∆G0cleavage ) BDFERMfR•+M• - ERM •+/RM + EM+/M•
(22)
Small bond dissociation free energies (BDFE), difficult reduction of the leaving cation, and difficult removal of the exchanging
electron from a transitorily hosting orbital (such as a π orbital present in the R moiety) are thus favorable factors for the concerted pathway and vice versa for the stepwise pathway. In the concerted case, it is tempting to model the reaction dynamics according to the theory of dissociative electron transfer previously applied to several reductive cleavage reactions.25 In this model, the reactant potential energy profile is approximated by a homolytic dissociation Morse curve and the product curve is assumed to be equal to the repulsive part of the reactant curve.26 It may seem odd to represent the dissociation of an ion pair by a homolytic dissociation curve. A dissociation curve reflecting the Coulombic interaction between the two ions would seem a priori more likely. We have investigated this question, taking as example methyllithium in diethyl ether as the solvent. The potential energy profiles for its ionic and homolytic dissociations where obtained by means of density functional calculations (see the methodology section). They are represented in Figure 6. In the gas 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 difference in energy is considerably reduced in ether, heterolytic dissociation is still more difficult than homolytic dissociation in this solvent (3.44 instead of 2.44 eV). During the homolytic dissociation the multiplicity of the system passes from 1 to 3. This is the reason that we have computed the potential energy for both situations at large C-Li distances. Taking the effect
9000 J. Phys. Chem. B, Vol. 105, No. 37, 2001
Save´ant
Figure 6. Potential energy profiles for the dissociation of CH3Li (from density 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.
of the change in multiplicity into account, it is seen that the potential energy profile may be represented by a Morse curve (eq 23) with a good accuracy:
G ) G0 + BDERMfR•+M•{1 - exp[- β(x - x0)]}2
(23)
with BDERMfR•+M• ) 2.01 and 2.44 eV and β ) 1.34 and 1.26 Å-1 in the gas phase and in diethyl ether, respectively. These observations validate the application of the dissociative electron-transfer theory to the direct oxidation of ion pairs insofar as it follows a concerted mechanism. Going to structurally looser binding and/or to a more polar solvent may result in the heterolytic dissociation becoming easier than the homolytic dissociation calling for a modification of the conventional dissociative electron-transfer model. Two facts should however be taken into account in this connection. One is that, in the concerted case, the intrinsic barrier is large because it contains a bond-breaking contribution. It follows that the reaction needs to be exergonic in order to proceed at a palpable rate. The transition state has thus a reactant-like character corresponding to a relatively modest stretching of the breaking bond. At the transition state, the potential energy profile may thus correspond to homolytic dissociation even though an inflection toward a heterolytic dissociation profile may well take place at larger bond lengths. A second remark is that when ion pairing becomes weaker and weaker, the predissociation mechanism overrides the direct oxidation of the ion pair. It is therefore likely that the conventional Morse curve model of dissociative electron transfer will apply satisfactorily to most of the cases where ion pairing is so strong that direct electron transfer from the ion pair takes place and is concerted with bond cleavage. In the concerted case, the half-wave (and peak) potential is given by eq 14 and Figure 2, in which E0A/B is replaced by E0A/C and λ by BDERMfR•+M• + λ0, where λ0 is the solvent reorganization energy. Conclusions The main conclusions emerging from the preceding discussion may be summarized as follows in the case where the formation
of the ion pair is the result of a reductive process, noting that they can be transposed with no difficulty to the case of an oxidative process. The first effect of ion pairing is to stabilize the reduced form. When ion pairing follows a fast electron-transfer step 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 ensues (Figure 1, eq 1). Because it rapidly consumes the initial reduction product, thus hampering back electron transfer, increased ion pairing will moreover prompt the forward electron transfer to become rate determining. This has no palpable effect on the location of halfwave (or peak) potential in the case where electron transfer is intrinsically slow. The effect of ion pairing appears for relatively fast electron transfers (Figure 3, eq 14). It converts a reversible reduction process into an irreversible process governed by the forward electron transfer. In these circumstances, ion pairing thus reveals the kinetics of electron transfer. On the oxidation side, the reaction follows a predissociation mechanism as long as the extent of ion pairing is not too large (Figure 3). The energy cost of the predissociation step makes the oxidation wave shift toward positive potential. As the extent of ion pairing further increases, the kinetics of the predissociation step come into play leading progressively to the disappearance of the wave. The only remaining possibility is direct electron transfer from the ion pair. Its association with the expulsion of the associating ion may involve concerted breaking of the bond or a two-step mechanism where the bond breaks after removal of the electron. The situation is closely similar to the case of reductive cleavage, a well-documented reaction both theoretically and experimentally. The question just arises whether, in the concerted case, the previously developed theory of dissociative electron-transfer applies. Computation of the dissociation potential energy profile shows that this is indeed the case for CH3Li in diethyl ether as the solvent. This conclusion most probably extends to most systems involving strong ion pairing and concerted bond breaking. Methodology for Quantum Chemical Calculations Density functional (B3LYP/6-31G*)27 optimizations and energy calculations were performed with the Gaussian 98 package.28 Solvation free energies were calculated on the gasphase optimized conformations according to the SCRF (selfconsistent reaction field) method using the polarized continuum (overlapping spheres) model (PCM).29 References and Notes (1) Swarc, M. Ions and Ion pairs in Organic Reactions; WileyInterscience: New York, 1972, 1974; Vols. 1 and 2. (2) Peover, M. E.; Davies, J. D. J. Electroanal. Chem. 1963, 6, 46. (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.; TenderendeGuminska, 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)
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