Medium Effects on the Reductive Cleavage of the Carbon−Halogen

J. Phys. Chem. B 2001, 105, 2003-2009

2003

Medium Effects on the Reductive Cleavage of the Carbon-Halogen Bond in Methyl and Methylene Halides Milan Fedurco,* Chantal Jorand Sartoretti, and Jan Augustynski Department of Chemistry, UniVersity of GeneVa, CH 1211 GeneVa 4, Switzerland ReceiVed: October 5, 2000; In Final Form: January 4, 2001

The thermodynamics and kinetics of dissociative electron transfer to a series of small aliphatic halocarbon molecules, including CH3Br, CH2Br2, CH3I, and CH2I2, are investigated. Such studies are of general interest because of the involvement of some of these compounds in the catalytic ozone depletion cycle, their toxicity, and their cancerogenic effects once present in the environment. Because of fairly large solubilities of these compounds in water, comparative kinetic experiments could be performed in N,N′-dimethylformamide (DMF) and in aqueous solutions. As expected, cathodic reduction of these molecules on glassy carbon in DMF takes place at quite negative potentials (ca. -2 to -3.2 V vs Fc/Fc+), and their kinetics follow predictions of the dissociative electron transfer (DET) model (Save´ant, J.-M. J. Am. Chem. Soc. 1987, 109, 6788). In contrast, similar experiments performed in aqueous solutions revealed many orders of magnitude faster kinetics of electron transfer to CH3I, CH2I2, and CH2Br2 molecules with the corresponding overpotentials about 1 V lower than those predicted on the basis of the DET model.

Introduction Activation of the carbon-halogen bond attracted considerable attention of electrochemists during the last three decades.1-4 Extensive experimental work on the reduction of aromatic and aliphatic halides on inert carbon electrodes led to the development of an analytic model for the dissociative electron transfer (DET) by J.-M. Save´ant.1b More recently, the investigations regarding carbon-halogen bond cleavage have been extended, in the case of platinum/aqueous solution interface, to the quantum chemical treatment, combined with molecular dynamics simulations.5 All of these studies agree that the dissociative reduction of simple alkyl halides takes place with practically no intervention of the corresponding R-X•- anion radicals. This is often called a concerted ET-bond-breaking process, in contrast to the electroreduction of highly polar perfluorinated hydrocarbons (i.e., CF3X) or aromatic halides undergoing stepwise ET reactions. The Save´ant dissociative electron transfer (DET) model has been demonstrated to work reasonably well for a number of reactants with quite different activation energy requirements where the bond (i.e., C-X, sCdNs, dNsX, -O-O-, -S-X, etc.) dissociation energy has been shown to vary from ca. 1.5-3 eV. Some deviations from its predictions have been reported in the case of the activation of tertiary aliphatic peroxides (several orders of magnitude in terms of heterogeneous rate constant) and were explained as being due to solvent cage and entropy effects and, eventually, nonadiabaticity of ET reactions.6 The present work describes another prominent exception where, apparently, the DET model is not applicable. We were prompted to undertake this study by the observation of an unexpectedly large (ca. 1 V) shift between the voltammetric peak potentials associated with the reduction of CH3I in DMF and in aqueous solution (cf. curve a in Figure 1 parts A and B). We have first conducted a series of measurements in DMF, under conditions similar to those used by Andrieux et al.2a in the case of n-butyl halide reduction. Then, * To whom correspondence should be addressed.

Figure 1. Experimental and simulated cyclic voltammograms (circles and solid line, respectively) for the reduction of 5.45 mM CH3I at a glassy carbon electrode in DMF/0.1 M TBAPF6 (A) and in aqueous solution containing 1 M NaClO4 (B).22,23 Curve c in B represents a cyclic voltammogram for 6 mM K3[Fe(CN)6]. Scan rate: 50 mV s-1.

similar experiments as those in DMF were carried out in aqueous solutions in order to assess the effect of the reaction medium on the kinetics of CH3X and CH2X2 reduction.

10.1021/jp003646m CCC: $20.00 © 2001 American Chemical Society Published on Web 02/17/2001

2004 J. Phys. Chem. B, Vol. 105, No. 10, 2001 Experimental Section All solutions were freshly made from analytical reagent-grade chemicals and high-purity water (Millipore Purification System). Alkyl and methylene halides were obtained from Aldrich, with exception of CH3Br (Merck), and were of the highest available purity. The measurements were performed at room temperature, 22 ( 1 °C, using a two-compartment cell in which a platinum counter electrode (large area Pt grid) was separated from a glassy carbon working electrode by a Nafion membrane. Some measurements were also done in a small cell with the total volume of 1-3 mL, where the cathodic and anodic compartments were separated by a fine ceramic frit. The cross section of a glassy carbon rod of 7 or 3 mm in diameter (Sigradur K, Germany and Metrohm, Switzerland, respectively) embedded in a Teflon cylinder served as the working electrode. Prior to use, the glassy carbon electrodes were polished mechanically to a mirror polish using alumina powders (0.3 and 0.05 µm, Buehler) on a polishing cloth (Mecaprex, WELL) and were rinsed several times with distilled water. The electrode potential was cycled in 1 M NaClO4 from 0 to 1.9 V and back and between 0 and -1.6 V, at 50 mV s-1 prior to each measurement. All of the potentials in the aqueous solutions were measured against a Ag/AgCl,Cl- reference electrode and are reported against NHE. Providing that the peak separation for the [Fe(CN)6]3-/4- redox reactions in 1 M NaClO4 solution was larger than 70 mV, electrodes were repolished until the required reversibility was restored. Prior to their immersion into the organic electrolyte, glassy carbon electrodes were dried in the oven (80 °C). N,N-dimethylformamide (DMF) (99,9+%, Aldrich), packed under nitrogen in Sure/Seal bottles was used as received. Tetrabutylammonium hexafluorophosphate (TBAPF6) was dried before use at 100 °C for 24 h. Cyclic voltammograms in DMF/0.1 M TBAPF6 electrolyte were recorded against a quasireference Ag/Ag+ electrode (0.01 M AgClO4/0.09 M TBAPF6 in acetonitrile) and are reported versus the ferrocene/ ferrocinium couple (Fc/Fc+). Results and Discussion I. Thermodynamics of Dissociative Halocarbon Reduction in Water and DMF. Because in a majority of cases the electrochemical reduction of aliphatic alkyl halides

R-X + e- f R• + Xcan be considered as a concerted ET-bond-breaking (and chemically irreversible) process,1,2 the equilibrium potential for a given RX/R• + X- couple (E°RX/R•+X-) cannot be determined directly through electrochemical measurements. The standard potential E° is then calculated from the Gibbs energies of formation of reactants and reaction products in water (∆fG°,H2O) according to eq 1:2b

FE°RX/R•+X-,H2O ) ∆fG°,H2O(RX) - ∆fG°,H2O(R•) - ∆fG°,H2O(X-) (1) The latter can be estimated from the gas-phase Gibbs energies of formation of individual species according to the equilibrium

RXH2O + R•g S RXg + R•H2O so that

FE°RX/R•+X-,H2O ) ∆fG°,g(RX) - ∆fG°,g(R•) - ∆fG°,H2O(X-) - ∆G4° (2)

Fedurco et al. where ∆G4° reflects the difference in energies of formation of radicals and neutral species in the gas phase and in water, respectively, (∆G4° ) 11.67 and 12.9 kJ mol-1 for CH3Br and CH3I, respectively).2b According to ref 4d, the ∆G4° term in eq 2 can be neglected in the case of alkyl halide reduction in DMF. This will be also the case in the present work. The strategy adopted in the present work is to use in the calculation of E°RX/R•+X- potentials only those experimental heats of formation which are in a good agreement with the results of recent quantum chemistry calculations, where the optimization of molecular geometries has been done using the high quality ab initio perturbative second- or fourth-order Møller-Plesset calculations (MP2-MP4). Enthalpies of formation for carbon-centered radicals such as •CH3, •CH2Br, •CH2I, and n-Bu•, generated in the course of electroreduction of halocarbon molecules, are available either from direct measurements or, in some cases, from the calculations. The condition put down here is that the calculated vibrational spectra for such species have to be in good agreement with their experimental IR or Raman spectra. Table 1 shows measured (experimental) and calculated heats of formation of selected halides together with Gibbs energies of formation and E° values for the one-electron reduction of halogenated molecules and radicals (except for E° for n-butyl halides taken from ref 2b). In particular, the results of our calculations suggest that the equilibrium potential for the oneelectron reduction of CH3I and CH3Br in aqueous solution are practically identical. Actually, the calculated reduction potentials for both molecules are very similar despite quite different Gibbs energies of formation of CH3I (∼ +16 kJ mol-1) and CH3Br (∼ -27 kJ mol-1) in the gas phase. This is mainly due to the large difference in the hydration energies of bromide and iodide anions ∆Gf,X-°,H2O ) -103.4 and -51.3 kJ mol-1, respectively, (cf. eq 2). The larger dissociation energy for CH3Br as compared to CH3I (Table 1), which might render the reduction potential for the former molecule more negative (cf. eq 3) is, in fact, compensated by the difference in redox potentials for the iodine and bromine atoms in water E°(X/X-)aq ) 1.34 and 1.95 V, respectively, vs NHE:4c

FE°CH3X/•CH3+X-,H2O ) -D0 - T(ShCH3X - Sh•CH3 - ShX•) + FE°(X/X-)aq (3) where Sh is the molar entropy of the species involved in the bondbreaking process. The dissociation energy D0 of the carbonhalogen bond can be readily obtained from the tabulated heats of formation, shown in Table 1, using eq 4:

D0 ) ∆fH°(R•) + ∆fH°(X) - ∆fH°(R-X)

(4)

It follows also from these calculations that methyl bromide is more difficult to reduce than n-butyl bromide (E°n-BuBr/n-Bu•+Br-,H2O ) -0.615 V, estimated previously by Andrieux et al.)2b despite practically identical D0 values of ca. 290 kJ mol-1 for both molecules (Table 1). The difference of ca. 0.1 V in E°RBr/R•+Br- potentials is mainly due to a relatively large Gibbs energy of formation of butyl radical in the gas phase, ca. 145 kJ mol-1.2b More specifically, the large and negative molar entropy of formation of the butyl radical causes a large deviation of ∆fG°,g (n-Bu•) from ∆fH°,g (n-Bu•) on the order of 84 kJ mol-1 (Table 1). Note that the values of enthalpy and Gibbs energy of formation for the •CH3 radical are practically identical. It should also be mentioned that our estimate of ∆fG°,g(n-Bu•), using more recent data7c

Reductive Cleavage of the Carbon-Halogen Bond

J. Phys. Chem. B, Vol. 105, No. 10, 2001 2005

TABLE 1: Computed and Experimentally Determined Thermodynamic Properties of Various Halides and Radicals in the Gas Phase (T ) 298.15 K) and Estimation of the Standard Potentials of the RX/R•+X- Couple in H2O and DMF CH3Br

CH3I

n-BuBr

n-BuI

∆fH° a

-36.9f -35.5g

14.7g

-107.4g -110.3i

S° b

246.4g 245.9f

254.1g

369.8h

∆fG° a

-27.45f -26.30g

15.7h 16.4l

-12.8m

31.3m

D0c

292.9g 296.7k

239.4k 238.1p

289.5m

247.0m 205.1g

E°RX/R•+X-H2O d

-0.733q

-0.730l,r -0.769q

-0.615m -0.801s

E°RX/R•+X-DMF e

-1.227V -1.239x

-1.208V -1.216y

-1.109m -1.295i,z

CH2Br2

-17.38g

4.48f

CH2I2

CH2Br•

CH2I•

:CH2(3B1)

n-Bu•

CH3•

80.9j

146.0g 146.9k

113.0g 118.0h

169.0g 174.2f

230.1g

395.2g

309.7g 309.1h

259.6f

211.0g

194.9g

329j

194.2g

95.8g 101.1h

160.1f

225.2o

372.9g

149.9m 165.0n

145.7g

296.7g 281.6f

223.9p

332.89f

271.9p

-0.698m

-0.558f,q

-0.809t (-0.359)*

-1.133q

-0.999u

-1.075m

-1.052x

-1.186t,u (-0.736)*

-1.627x

-1.376u,y

293.2g 2.89f

a kJ mol-1. b J mol-1 K-1. c Bond dissociation energy kJ mol-1. d Standard potential of the RX/R• + X- couple in water (V vs NHE) assuming E°Br/Br-H2O ) 1.95 V and E°I/I-H2O ) 1.34 V vs NHE (ref 4c). e Standard potential of the RX/R• + X- couple in DMF (V vs SCEaq) assuming E°Br/Br-DMF ) 1.48 V and E°I/I-DMF ) 0.99 V vs SCEaq (taken from ref 4c). f Thermodynamic properties obtained from ab initio MP4/6-31G**// MP2/6-31G* calculations by Paddison and Roux (ref 9) in conjunction with experimentally established enthalpies of formation (isodesmic reactions). The radicals •CH2Br and •CH3 were calculated at the RHF/6-31G* level and then refined at the MP2/6-31G* level. g Reference 7a. h Reference 7b. i Ab initio MP2/6-311+G** calculations; ∆ H°(n-BuBr) was determined from the isodesmic reaction (ref 8). j Reference 7c. k Reference 7d. l Calculated f from the experimental ∆fH° and S° values taken from ref 7a and eq 1. m Taken from ref 2b. n ∆fH°(n-BuBr) taken from ref 8 and eq 1. o Calculated using eq 3 assuming S°(CH2I•) ) 211.0 J mol-1K-1; other thermodynamic data taken from ref 7a. p Calculated from eq 4 and the experimental ∆fH° values taken from ref 7a. q Calculated from eq 1 and the gas-phase Gibbs energies of formation for the brominated hydrocarbons and radicals taken from ref 9a. r Calculated using eq 1 and our estimate of ∆fG°(CH3I) from the enthalpy of formation and entropy data in ref 7a. s E° estimated from eq 2 using ∆fH°(n-BuBr) ) -110.3 kJ mol-1 from ab initio MP2/6-311-G** calculations (ref 8) and ∆fG°(n-Bu•) ) 165 kJ mol-1. t E° estimated from the ∆fG°(CH2I2) ) 95.1 kJ mol-1 and other thermodynamic data from ref 7a. u E° estimated using ∆fG°(•CH2I) ) 225.2 kJ mol-1 and other thermodynamic data from ref 7a. V Calculated using eq 1 and the gas-phase Gibbs energy of formation from ref 7a. x Equation 1 and the gas-phase Gibbs energies of formation for the brominated hydrocarbons and radicals from ref 9. y Equation 1 and related thermodynamic data from ref 7b.z E° estimated using eq 1; ∆fH°(n-BuBr) was taken from ref 8; and other data were taken from ref 7a. *E° was increased by 0.45 V in order to get satisfactory agreement between ∆G0q,theor(1) and ∆G0q,exp (see the text).

∆fH°,g(n-Bu•) ) 80.9 kJ mol-1 and S°n-Bu• ) 329 J mol-1 K-1, gives from eq 5

∆fG°n-Bu• ) ∆fH°n-Bu• - 298.15[S°n-Bu• -

∑S°(elements)]

(5)

165 kJ mol-1 (instead of 145 kJ mol-1 determined in ref 2b). The theoretical enthalpy of formation for the n-BuBr molecule ∆fH°,g ) -110.3 kJ mol-1 (298.15 K)8 was obtained from the isodesmic reaction between the MP2/6-311+G**-optimized CH3Br and n-butane (comparable with the experimental value of -107 kJ mol-1 reported in ref 7a). These two modifications lead to the theoretical E°n-BuBr/n-Bu•+Br-,H2O ) -0.801 V vs NHE, somewhat more negative than the value previously reported by Andrieux et al.2b To make possible the analysis of the kinetic data for the reduction of methylene halides, it is useful to estimate theoretical standard potentials for the one-electron reduction of CH2Br2, CH2I2, and the •CH2Br and •CH2I radicals, formed during reductive cleavage of the parent methylene halide molecules. Paddison and Tschuikow-Roux9 have recently reported the results of perturbative fourth- and second-order Møller-Plesset calculations (ab initio MP4/6-31G** and MP2/6-31G*) for a series of brominated hydrocarbons including methylene and methyl bromides. According to these calculations (and to the experimental results cited therein), the dissociation energy for the C-Br bond in CH2Br2 should be in the range of 280-293 kJ mol-1, very close to the corresponding D0 for CH3Br. On the other hand, D0 values for CH3I and CH2I2 are significantly lower, namely, 239 and 224 kJ mol-1, respectively. The bond strength of 205 kJ mol-1 for the C-I bond in n-BuI, as suggested in ref 7a, is likely to be somewhat low considering the results of previous electrochemical measurements2b and, also, those reported in the present work.

Paddison and Tschuikow-Roux9 report also gas-phase thermodynamic data for the •CH2Br radical as a function of the temperature. Using their value of ∆fH° (•CH2Br) at room temperature (a very similar result has been reported in refs 10 and 11), one can estimate the driving force (∆E) in a vacuum for the C-Br bond scission in •CH2Br to give a bromine atom and carbene biradical, namely, triplet carbene CH2(3B1):

D0(•CH2Br) ) ∆fH° (CH2) + ∆fH° (Br) - ∆fH° (•CH2Br) D0(•CH2Br) ) 392.5 + 111.885 - 174.22 ) 330.165 kJ mol-1 ∆E ) D0(•CH2Br) - EA(Br) ∆E ) 3.422 - 3.365 ) 0.057 eV where EA(Br) is the electron affinity of the bromine atom.7a Thus, it seems that the C-Br bond cleavage in CH2Br2 is energetically slightly less demanding than in CH3Br. On the other hand, the C-Br bond scission in •CH2Br requires a much larger energy. In fact, the standard potential for the reduction of the •CH2Br radical in DMF is, apparently, the most negative of all halides studied in the present work (cf. Table 1). The evolution of the standard potential as a function of halide structure is easier to follow from Figure 2A (empty circles) where it can be compared with experimentally measured peak potentials recorded during electroreduction of 5.45 mM solutions of CH3X and CH2X2 on a glassy carbon electrode in DMF (filled circles). In all cases, the determined Ep values are markedly more negative than the corresponding E° values. In particular, methyl bromide and n-butyl bromide undergo reduction at potentials close to -3.2 V vs Fc/Fc+ couple (or -2.85 V vs SCEaq), i.e., with the overpotential of 1.5-1.7 V.

2006 J. Phys. Chem. B, Vol. 105, No. 10, 2001

Fedurco et al.

Figure 2. A. Calculated standard redox potentials for the dissociative one-electron reduction of various halocarbon molecules and radicals in water (open circles), the corresponding peak potentials (Ep) estimated using the DET model (filled circles), and the Ep values determined experimentally (filled triangles) at a glassy carbon electrode in 1 M NaClO4(aq). E° for CH2I2 was increased by 0.45 V in order to get satisfactory agreement between ∆G0q,theor and ∆G0q,exp (*) (the same applies to part B). The dotted line indicates the onset potential for the H2 evolution at a glassy carbon electrode in neutral perchlorate solution. B. Standard redox potentials (E°) for the one-electron reduction of halogen-containing molecules (c ) 5.45 mM) and radicals in N,N-dimethylformamide (open circles) and the corresponding peak potentials (filled circles) measured at a glassy carbon electrode. Scan rate: 50 mV s-1.

Note that all of the iodine-containing molecules listed in Figure 2A undergo reductive cleavage at more positive potentials than those of their brominated analogues. The observed large negative shifts in Ep potentials with respect to calculated E° reflect extremely sluggish kinetics of dissociative ET. The latter are determined by the interplay between the driving force of the electrochemical reaction on the one hand and the free energy of activation on the other. How these variables may affect kinetics of electrode reactions in DMF and in aqueous solutions will become evident from the discussion in the following section. II. Heterogeneous ET Kinetics Associated with the Reduction of CH3X and CH2X2. In accordance with the classical Marcus-Hush model of ET,12 the heterogeneous rate constant (kel) is expected to decrease exponentially with the increase in activation energy of the forward electrochemical reaction ∆Gelq

kel(E) ) κAel exp[(-(∆Gelq/RT)]

(6)

where κ is the transmission coefficient and Ael is the preexponential term often replaced by the heterogeneous collision frequency Zel (vide infra). The exponential part of the latter expression has been extended for the case where the ET to an aliphatic alkyl halide is accompanied by an immediate breaking of the carbon-halogen bond.1b In the gas phase, the reaction driving force is determined by the difference in the dissociation energy of the C-X bond and the electron affinity of the halide atom. In the case of halocarbon cleavage induced by collision

with Kr atoms13 or of a photoinduced ET,14,15 such processes are extremely fast and may even be terminated within a single rotational or vibrational period. For example, photochemical cleavage of the C-I bond in CH3I or CH2I2 occurs within 5014 or 150 fs, respectively. The heterogeneous bond-breaking process in a condensed phase is somewhat more complex because the rate of ET reaction reflects concomitant changes of polarizability and of the dipole moment of the carbon-halogen bond along the reaction coordinate, coupled to the outer-shell polarization modes of the solvent. In the process of bond breaking, the halide atom in CH3X becomes more electron deficient as the C-X bond lengthens. In this respect, both iodine and bromine are ideal leaving groups. The bond-breaking process in n-alkyl halides (i.e., n-butyl halide) has been suggested to be accompanied by relatively high adiabaticity of the ET reaction, i.e., κ ) 1 (eq 6).1,2 This is in contrast to the bond scission in symmetric di-tert-butylperoxides and other molecules where significant nonadiabaticity of ET reactions is observed.6 On the other hand, the effect of the solvent on the magnitude of the preexponential term Ael is not so straightforward. The solvent affects bond oscillations in the course of bond cleavage, and as shown recently by Cukier et al.,16 kinetics of dissociative ET will depend on the ratio between the solvent reorganization energy (λos) and the reorganization energy associated with the bond breaking (λz). Accordingly, the dynamics of an electron crossing the barrier might depend either on the relaxation time along the bond-breaking coordinate τz or on the solvent relaxation dynamics along the x coordinate (i.e., the solvent longitudinal relaxation time). The slower of the two processes should control the kinetics of outer-shell bond-breaking reactions.16b The replacement of water by DMF is expected to lead to approximately a 5-fold decrease in the heterogeneous rate constant, due exclusively to the larger solvent longitudinal relaxation time of DMF (τL ) 1.1 ps) as compared to that of water (τL ) 0.23-0.24 ps).17 However, it is important to realize that the λos values for the studied halide molecules (cf. Table 2) both in DMF and in aqueous solutions remain lower than those of λz by a factor of ca. 2-2.5. As shown recently by Voth et al.,5a the solvent relaxation dynamics may, eventually, affect the magnitude of the Ael term in eq 6; however, this is expected for temperatures significantly higher than the room temperature. According to Save´ant,2b,4 the heterogeneous rate constant at zero overpotential (η ) 0) is proportional to one-fourth of the sum of the bond dissociation energy and the outer-shell solvent reorganization energy, determining the height of the intrinsic barrier ∆G0q,theor

∆G0q,theor ) 1/4(D0 + λos)

(7)

The potential-dependent activation barrier for the forward ET ∆Gelq (cf. eq 6) can be obtained upon the substitution of eq 7 in eq 8, representing the unified Save´ant-Marcus expression for the dissociative ET

∆Gelq ) ∆G0q[1 + F(E - E°RX/R•+X- - Φr)/4∆G0q]2

(8)

where E is the electrode potential, η ) E - E°RX/R•+X- is the overpotential, and Φr is the potential at the outer Helmholtz plane. It is useful to define here the midpoint potential (Em), which is simply 1/2(Ep + Ep/2) (cf. Figure 1) and the corresponding driving force at Em

∆G° ) F(Em - E°RX/R•+X- - Φr)

(9)

Reductive Cleavage of the Carbon-Halogen Bond

J. Phys. Chem. B, Vol. 105, No. 10, 2001 2007

TABLE 2: Kinetic Data for the One-Electron Dissociative Reduction of Alkyl Halides and Methylene Halides in DMFa Calculated on the Basis of the DET Model n-BuI

n-BuBr

CH2I2

CH2Br2

CH3Br

-Em -E° Zc Ael Rexp ∆Gmq -∆G° rRXc a1c λ1/4c λ2/4c D0/4

2.361 1.075b 4.63 × 103 4.5 × 104 0.288 0.434 1.286 3.56 2.88 0.181 0.259 0.531d, (0.640b)

2.756b 1.109b 5.37 × 103 5.1 × 104 0.250 0.440 1.713 3.492 2.73 0.191 0.279 0.750b

1.529 1.186 3.84 × 103 4.0 × 104 0.315 0.431 0.343 (0.793)* 3.174 2.687 0.194 0.274 0.580d, 0.620f

2.182 1.208 5.27 × 103 4.5 × 104 0.31 0.433 0.974 2.914 2.557 0.204 0.288 0.617

CH3I

-2.188 1.052g 4.76 × 103 5.1 × 104 0.346 0.434 1.136 3.030 2.495 0.209 0.297 0.730g, (0.769d)

∆G0q,theor (1)

0.821e, (0.712d)

0.941b

0.774

0.824f, (0.821d)

∆G0q,theor (2)

0.899e, 0.790d

1.029b

0.854

0.908f, 0.905d

0.939g, 0.978d 0.99f 1.017g, 1.057d

2.760 1.227 6.45 × 103 5.1 × 104 0.30 0.484 1.533 2.792 2.375 0.219 0.310 0.766g 0.759d, (0.769f) 0.99g, 0.98d

∆G0q,exp R(theor)c R(pred)c

0.970, 0.900e 0.334 (0.35e) 0.321, (0.334e)

1.051e 0.31 0.32e

0.590, (0.777) 0.427, (0.372)

0.850 0.357 0.359

0.914 0.345 0.355g, (0.360d)

1.076g, 1.070d 1.069f 1.119d 0.329 0.313, 0.314d

a The concentration of all of the compounds was 5.45 mM. DMF + 0.1 M TBAPF at a glassy carbon electrode, V ) 0.05 V s-1 (25 °C). 6 Electrode potentials are given in volts, and all of the energies are given in eV. b Taken from refs 2b and 4d. c Heterogeneous collision frequency Z ) (RT/2πM)1/2; rRX ) (3M/4πNAF)1/3. Effective reactant radius (Å): a1 ) 0.5(rRX + rX-) with rBr- ) 1.96 and rI- ) 2.2 Å. Solvent reorganization energy calculated using eq 12 (Pekar factor γDMF ) 0.463) and assuming λ1 ) λos/1.6 (cf. ref 1b); λ2 ) 3.15/a2 where a2 ) rX-(2rRX - rX-)/RX; rBr) 1.96 and rI- ) 2.2 Å. R(exp) estimated using eq 17, R(theor) using eqs 15 and 16. and R(pred) using eqs 7 and 16. d Calculated using the experimental thermodynamic data taken from ref 7a. e Taken from ref 4d. fCalculated using the experimental thermodynamic data taken from ref 7d. g Thermodynamic data taken from ref 9a. *∆G° was increased by 0.45 eV in order to get satisfactory agreement between ∆G0q,theor(1) and the ∆G0q,exp.

Note that Φr will be set equal to zero in the present work for the reasons outlined in ref 21. The experimental activation energy at Em

∆Gqm ) RT ln[Zel(RT/RFVD)] + 0.145RT

(10)

depends on the scan rate V, the diffusion coeffcient D, and the heterogeneous collision frequency

Zel ) [RT/(2NAπM)]1/2

(11)

where NA is the Avogadro constant and M is the molecular weight (in grams). Finally, ∆G0q,theor (eq 7) can be estimated from the known D0 values for the studied compounds (cf. Table 1), and the theoretical λos can be obtained from eq 12:

λos ) (NAe2/8π0)(1/op - 1/s)(1/aeff)

(12)

where γ ) (1/op - 1/s) is the Pekar factor (γDMF ) 0.463 and γH2O ) 0.549).17 Note that the solvent reorganization energy is inversely proportional to the effective reactant radius aeff (eq 12). The effective reactant radius, in the case of linear alkyl halides, can be determined using eq 13:

aeff ) 1/2(rRX + rX-)

(13)

where rX- is the diameter of halide anions (X ) Cl-, Br-, and I-) taken as 1.81, 1.96, and 2.2 Å, respectively, and

rRX ) (3Mw/4πNAF)1/3

(14)

where Mw is the molecular mass of alkyl halide and F is the density. Finally, the intrinsic barrier ∆G0q,theor, calculated from eq 7, can be compared with the experimental ∆G0q,exp value4b ∆G0q,exp ) 1/4{[(∆G° - 2∆Gqm)2 - (∆G°)2]1/2 - ∆G° - 2∆Gqm} (15)

The calculated value of the transfer coefficient is then given by

R ) 0.5(1 + ∆G°/4∆G0q)

(16)

(see legend to Table 2 for the additional information concerning the estimation of theoretical and predicted transfer coefficients R(theor) and R(pred)), while its experimental value is obtained from the relation

R(exp) ) (RT/F)[1.85/(Ep/2 - Ep)]

(17)

(for other ways of estimating R(exp) see ref 4d). Experimentally obtained activation parameters for the reduction of selected halides in DMF are presented in Table 2. Apparently, there exists a fairly good agreement between the predictions of the Save´ant DET model and the cyclic voltammetric data for the reductive cleavage of aliphatic halides in DMF. This can be easily checked by comparing ∆G0q,theor with ∆G0q,exp which, in an ideal case, should be equal. The largest deviation of ∆G0q,exp from the theoretical value is found in the case of CH2I2 reduction. This is not completely unexpected because our E°CH2I2/CH2I•+I- estimate is quite an approximate one because of the uncertainty regarding the gas phase ∆fG°•CH2I value (chosen arbitrarily). Providing the DET model applies to the CH2I2 reduction in DMF, one can go backward and estimate the driving force and, subsequently, E°CH2I2/•CH2I+I- from the known dissociation energy of the C-I bond in this molecule and the theoretical estimate of λos (Table 2). Thus, the value of E°CH2I2/•CH2I+I- ) -0.736 V vs SCEaq would bring the experiment into good agreement with the theory and would correspond to an increase in the reaction driving force by 0.45 eV. In other cases, the experimental values of the intrinsic barrier (∆G0q,exp) in Table 2 are close to ∆G0q,theor(1) and ∆G0q,theor(2) obtained using eqs 7 and 12. In the case of n-BuI reduction, better agreement between the theory and experiment was obtained in

2008 J. Phys. Chem. B, Vol. 105, No. 10, 2001

Fedurco et al.

TABLE 3: Predictions of the DET Model for Selected Halocarbon Molecules in Watera ab λosc λosd D0e Ael f ∆G0(1)q theor ∆G0(2)q theor ∆Gmq ∆G0(1)q expected -∆G° -E° H2O -Emg -Epg

n-BuI

n-BuBr

CH2I2

CH3I

CH2Br2

CH3Br

2.88 1.373 0.856 2.56h 4.5 × 104 0.854 0.931 nswl

2.73 1.448 0.904 3.00h 5.1 × 104 0.976 1.065 nsw

0.733 nsw

0.615h nsw

2.687 1.472 0.920 2.32i 4.0 × 104 0.81 0.89 0.431 0.809 0.875 0.809 (0.359)* 1.684 (1.234) 1.763 (1.313)

2.557 1.548 0.968 2.48j 4.5 × 104 0.862 0.95 0.440 0.860 0.980 0.730 1.819 1.898

2.495 1.584 0.992 2.92k, (3.076i) 5.1 × 104 0.978k 1.06k 0.434 1.020 1.42 0.558k 1.978 2.057

2.375 1.664 1.040 3.036i 5.1 × 104 1.02i 1.11i 0.347 1.060 1.52 0.733i 2.253 2.332

a H2O + 1 M NaClO4 at a glassy carbon electrode at 0.05 V s-1 (25 °C). Electrode potentials are given in V; all of the energies, in eV. b Effective reactant radius (Å): a ) 0.5(rRX + rX-) in Å; rRX ) (3M/4πNAF)1/3; rBr- ) 1.96 and rI - ) 2.2 Å. c Calculated solvent reorganization energy using the eq 12. Pekar factor: γ(H2O) ) 0.549. d λos ) λos/1.6 (cf. ref 1b). e Bond dissociation energy (eV). f Calculated preexponential factor from eq 11 (cm s-1). g R(exp) was assumed equal to 0.3. h Reference 2b. i Calculated using the thermodynamic data from ref 7a. j Calculated using the thermodynamic data from ref 7d. k Calculated using the thermodynamic data from ref 9a. l nsw ) nonsoluble in water. *E° was increased by 0.45 V in order to get satisfactory agreement between ∆G0q,theor(1) and the ∆G0q,exp (see the text).

TABLE 4: Peak Potential Values for the Reduction of Selected Aliphatic Halocarbons in DMF and Watera n-BuI

n-BuBr

2.903

-Ep in DMF/0.1 M TBAPF6 (V vs Fc/Fc+) 3.13 2.064 2.717 2.605

CH2I2

CH3I

CH2Br2

nswb

-Ep in H2O/1 M NaClO4 (V vs NHE) nsw 0.611 0.932 1.047

CH3Br 3.3

a Reactant concentration: 5.45 mM. Scan rate: 0.05 V s-1. b nsw ) nonsoluble in water.

Figure 3. Tafel plot for the electroreduction of 5.45 mM CH3I in 1 M NaClO4(aq) on a glassy carbon electrode obtained from the convolution analysis of the voltammetric data shown in Figure 1B.

ref 4d (∆G0q,exp ) 0.90 eV); the result ∆G0q,exp ) 0.97 eV obtained in the present work seems to be somewhat high. Satisfactory agreement was also found between the experimental and predicted transfer coefficients listed in Table 2. The described kinetic behavior of methyl and methylene halide reduction in DMF, which basically follows predictions of the DET model, is in contrast with the results of the corresponding measurements performed in aqueous solutions. Figure 3 shows the dependence of the rate constant on the overpotential (Tafel plot) for the reduction of CH3I in 1 M NaClO4(aq) on a glassy carbon electrode obtained from the convolution analysis of the cyclic voltammogram shown in Figure 1B. Both the convolution analysis of the voltammogram as well as its numeric simulation21 are consistent with an irreversible one-electron process having the apparent rate constant at zero overpotential k°(app) ) 2 × 10-4 cm s-1 and R ) 0.48. This suggests an extremely fast kinetics of the CH3I reduction as compared to that of the glassy carbon/DMF system. Additional measurements have revealed that the CH3I reduction in aqueous solution on glassy carbon is a pH-independent process. Thus, the cathodic peak remained unchanged after adjustment of the solution pH from 7.0 to 2.0. This observation is consistent with the transfer of the first electron to CH3I as being the rate-determining step of the electrode reaction. In fact, we have found that CH3I, CH2I2, and CH2Br2 undergo electroreduction on glassy carbon from an aqueous 1 M NaClO4 solution selectively even though such processes are expected

to take place at very negative potentials exceeding -2 V (i.e., in the hydrogen-evolution region). The Ep potentials for the reduction of these molecules calculated on the basis of the Save´ant DET model are shown in Table 3, whereas the corresponding experimental peak potentials recorded on glassy carbon in aqueous solutions are presented in Table 4. Thus, the overpotentials for the reduction of CH3I, CH2I2, and CH2Br2 in aqueous solutions are lower respectively by ca. 0.97, 1.15, and 1.0 V than those predicted. Another observation is equally important. The values of the experimentally measured transfer coefficient Rexp for the latter three compounds have been found to range from 0.48 to 0.5. Such a value is assumed by the DET model providing the estimated Ep would be very close to the corresponding E°RX/R•+X- potential, which is actually not the case (cf. Table 3). If the observed effects were due to changes in the entropic term in eq 8, affecting the reaction driving force, Ep would follow the E°RX/R•+X- shift; however, Rexp should in such a case remain close to 0.3. This clearly shows that the factors which control reaction kinetics in aqueous solutions and in an aprotic solvent are different. Note that, in all cases, one is dealing with the one-electrontransfer reactions, and in addition, there is no effect of the solution pH on the peak potential. In principle, one can also exclude double-layer effects in a classical sense (i.e., Frumkin correction) as a reason for the rate enhancement of halocarbon reduction upon replacement of an organic solvent (DMF) by water. In fact, the potential of zero charge (pzc) for glassy carbon in a NaClO4 solution is close to -0.22 V vs SCE.18 Doublelayer effects are expected to be less important in acid solutions where a large fraction of the surface carboxylic groups on carbon should be in the undissociated form. Because, as already mentioned, the change in solution pH from 7 to 2 did not affect cathodic current associated with the halocarbon reduction, one

Reductive Cleavage of the Carbon-Halogen Bond can conclude that acceleration of the electrode reaction in aqueous solution is hardly attributable to the double-layer effects. It is also important to note in this connection that the kinetic data calculated on the basis of the DET model rely on the exactitude of the estimated values of standard redox potentials. Thus, any inaccuracy of the calculated E°(X/X-) values used in eq 3 would automatically affect the magnitude of the reaction driving force (cf. eq 9). This, in turn, would result in a shift of the estimated values of the peak potentials Ep. We have also checked for the relative ordering of LUMO orbitals in halocarbon molecules with respect to vacuum (or to NHE, in our case). It is interesting in this connection that HF/6-31G(d,f) calculations by F. Mizutani,19 and our own density functional calculations (DFT/TZVP)20 predict an increase in the LUMO energy in the order: CH2I2 < CH2Br2 < CH3I < CH2Cl2 < CH3Br < CH3Cl. In addition, the DFT calculations20 indicate that the LUMO orbitals for •CH2Br, •CH2I, and •CH3 radicals are lower in energy than those of CH2X2 and CH3X molecules. The LUMO orbital of •CH2Br is lower in energy than the LUMO of the carbene triplet CH2(3B1) as well as the lowest electron acceptor level in CH2Br2. This is consistent with the fact that the electron affinity of the •CH2Br radical in the gas phase is very positive (+0.82 eV) and exceeds that of the free triplet carbene (EA ) 0.65 eV).7a This would also suggest that these reaction intermediates undergo electroreduction at more positive potentials than the parent molecules. The observed behavior of CH3I, CH2I2, and CH2Br2 on a glassy carbon electrode in aqueous solution appears in agreement with the latter hypothesis. Concluding Remarks As shown by the above-described results, the change of the reaction medium (both the solvent and the supporting electrolyte) leads to a remarkable enhancement of the kinetics of halocarbon reduction. Neither the overvoltages observed in aqueous solutions, by ca. 1 V lower than the calculated values, nor the transfer coefficients (close to 0.5) can actually be accounted for within the framework of the DET model. Among the hypothetical reasons which could explain, at least in part, the latter discrepancies one can mention a possible formation in aqueous solution of aggregates of halocarbon molecules. In fact, the hydrophobic nature of halocarbons is expected to favor van der Waals interactions, leading to the formation of dimers and/or larger clusters. The accessibility of solvent (water) molecules to the C-X (X ) Br or I) bond in such clusters could be restricted in comparison with the isolated molecules. This could lower the λos contribution in eq 7, resulting in an enhancement of the kinetics of ET reactions. However, taking into account that the outer-shell solvation energy constitutes only some 25% of the total ∆G0q, the limited access of the solvent to the bond to be cleaved cannot account by itself for the observed ET kinetics in water. It should be also mentioned that the vibrations in molecular clusters should, in principle, differ from those in isolated monomers. This could in turn affect the magnitude of the inner-shell reorganization energy. Quantum chemistry combined with molecular dynamics studies are required to get a deeper insight into such a nonideal ET-induced halocarbon cleavage. Acknowledgment. We would like to acknowledge Dr. J. Mareda for his ab initio calculations for several alkyl halide molecules and for helpful discussions. This work was supported by the Swiss National Science Foundation.

J. Phys. Chem. B, Vol. 105, No. 10, 2001 2009 References and Notes (1) (a) Andrieux, C. P.; Save´ant, J.-M.; Su, K. B. J. Phys. Chem. 1986, 90, 3815. (b) Save´ant, J.-M. J. Am. Chem. Soc. 1987, 109, 6788. (c) Andrieux, C. P.; Gallardo, I.; Save´ant, J.-M. J. Am. Chem. Soc. 1989, 111, 1620. (d) Bertran, J.; Gallardo, I.; Moreno, M.; Save´ant, J.-M. J. Am. Chem. Soc. 1992, 114, 9576. (2) (a) Andrieux, C. P.; Ge´lis, L.; Medebielle, M.; Pinson, J.; Save´ant, J.-M. J. Am. Chem. Soc. 1990, 112, 3509. (b) Andrieux, C. P.; Gallardo, I.; Save´ant, J.-M.; Su, K. B. J. Am. Chem. Soc. 1986, 108, 638. (3) (a) Fleischmann, M.; Mensoli, G.; Pletcher, D. Electrochim. Acta 1973, 18, 231. (b) Hush, N. S. J. Electroanal. Chem. 1999, 460, 5. (4) (a) Andrieux, C. P.; Le Gorande, A.; Save´ant, J.-M. J. Am. Chem. Soc. 1992, 114, 6892. (b) Save´ant, J.-M. Acc. Chem. Res. 1993, 26, 455. (c) Save´ant, J.-M. Tetrahedron 1994, 50, 10117. (d) Save´ant, J.-M. J. Am. Chem. Soc. 1992, 114, 10595. (5) (a) Koper, M. T. M.; Voth, G. A. Chem. Phys. Lett. 1998, 282, 100. (b) Calhoun, A.; Koper, M. T. M.; Voth, G. A. Chem. Phys. Lett. 1999, 305, 94. (c) Koper, M. T. M.; Voth, G. A. J. Chem. Phys. 1998, 109, 1991. (d) Calhoun, A.; Koper, M. T. M.; Voth, G. A. J. Phys. Chem. B 1999, 103, 3442. (6) (a) Donkers, R. L.; Maran, F.; Wayner, D. D. M.; Workentin, M. S. J. Am. Chem. Soc. 1999, 121, 7239. (b) Andrieux, C. P.; Save´ant, J.-M.; Tardy, C. J. Am. Chem. Soc. 1998, 120, 4167. (7) (a) CRC Handbook of Chemistry and Physics; 76th ed.; Lide, D. R., Frederikse, H. P. R., Eds., CRC Press: Boca Raton, FL, 1995. (b) Stull, D. R., Westrum, E. F., Jr.; Sinke, G. C. The Chemical Thermodynamics of Organic Compounds; John Wiley & Sons: New York, 1969. (c) Seetula, J. A.; Slagle, I. R. J. Chem. Soc, Faraday Trans. 1997, 93, 1709. (d) McMillen, D. F.; Golden, D. M. Annu. ReV. Phys. Chem. 1982, 33, 493. (8) Butyl bromide structure was obtained from ab initio MP2/6311+G** calculation, and ∆fH° (n-BuBr) at 298.15 K was determined from the isodesmic reaction CH3Br + n-Bu S n-BuBr + CH4, with the experimental enthalpies of formation for n-Bu and CH4 taken from ref 7a (J. Mareda, University of Geneva, unpublished results). (9) (a) Paddison, S. J.; Tschuikow-Roux, E. J. Phys. Chem. A 1998, 102, 6191. (b) Paddison, S. J.; Tschuikow-Roux, E. Int. J. Thermophys. 1998, 19, 719. (10) Espinosa-Garcı´a, J.; Do´be´, S. J. Phys. Chem. A 1999, 103, 6387. (11) Li, Z.; Francisco, J. S. J. Chem. Phys. 1999, 110, 817. (12) (a) Marcus, R. A. J. Chem. Phys. 1956, 24, 966. (b) Marcus, R. A. J. Chem. Phys. 1956, 24, 979. (c) Marcus, R. A. J. Chem. Phys. 1965, 43, 679. (d) Hush, N. S. J. Chem. Phys. 1958, 28, 962. (e) Hush, N. S. Trans. Faraday Soc. 1961, 57, 557. (13) Parthasarathy, R.; Finch, C. D.; Wolfgang, J.; Nordlander, P.; Dunning, F. B. J. Chem. Phys. 1998, 109, 8829. (14) Marvet, U.; Zhang, Q.; Brown, E. J.; Dantus, M. J. Chem. Phys. 1998, 109, 4415. (15) Kwok, W. M.; Phillips, D. L. J. Chem. Phys. 1996, 104, 2529. (16) (a) Zhu, J.; Spirina, O. B.; Cukier, R. I. J. Chem. Phys. 1994, 100, 8109. (b) Spirina, O. B.; Cukier, R. I. J. Chem. Phys. 1996, 104, 538. (17) (a) van der Zwan, G.; Hynes, J. T. J. Phys. Chem. 1985, 89, 4181. (b) Fawcett, W. R.; Foss, C. A., Jr. Electrochim. Acta 1991, 306, 1767. (18) (a) Korobanov, A. A.; Vilinskaya, V. S.; Burshtein, R. Kh. Electrokhimiya 1978, 14, 104. (b) Kusu, F.; Yuasa, K.; Takamura, K. Anal. Sci. 1993, 9, 583. (19) http://goofy.ims.ac.jp/pgv/data/nsort.htm. (20) Density functional calculations were performed using DeFT, a program written by Dr. A. St-Amant (University of Ottawa, Canada): http:// www.ccl.net/cca/software/SOURCES/FORTRAN/DeFT/index.shtml. (21) (a) Imbeaux, J. C.; Save´ant, J.-M. J. Electroanal. Chem. 1973, 44, 169. (b) Antigona CV simulation software package was kindly provided to us by L. Mottier (University of Bologna, Italy). (22) Note that it is convenient to report potentials with respect to a reference redox couple in the same solution in order to avoid errors because of the liquid junction potentials. Ferrocene is not soluble in water; however, E° for the Fc/Fc+ couple in SDS micelles in water has been recently reported as 0.23-0.26 V vs SCE (Doherty, A. P.; Scott, K. J. Chem. Soc., Faraday Trans. 1996, 92, 4541). (23) The magnitude of this effect can be appreciated by comparing the shift of the cathodic peak potential Ep with respect to the standard redox potential of the [Fe(CN)6]3-/4- couple in aqueous solution against the ferrocene (Fc/Fc+) couple in DMF. We have chosen the latter two reference systems because their respective E° values are very close, equal to 0.356 and 0.400 V vs NHE, respectively.7a Although CH3I in DMF undergoes an irreversible one-electron reduction with Ep ) -2.72 V vs Fc/Fc+, the corresponding value of Ep in aqueous solution is much less negative, ca. -1.29 V vs [Fe(CN)6]3-/4- couple. The latter potential is only ∼0.2 V more negative than the theoretical estimate of E°CH3I/•CH3+I-H2O ) -0.73 V vs NHE.