Experimental and Computed Absolute Redox Potentials of Polycyclic

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J. Phys. Chem. A 2010, 114, 12299–12304

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Experimental and Computed Absolute Redox Potentials of Polycyclic Aromatic Hydrocarbons are Highly Linearly Correlated Over a Wide Range of Structures and Potentials Anthony P. Davis and Albert J. Fry* Department of Chemistry, Wesleyan UniVersity, Middletown, Connecticut 06459, United States ReceiVed: July 1, 2010; ReVised Manuscript ReceiVed: September 17, 2010

A more rigorous theoretical treatment of methods previously used to correlate computed energy values with experimental redox potentials, combined with the availability of well-developed computational solvation methods, results in a shift away from computing ionization potentials/electron affinities in favor of computing absolute reduction potentials. Seventy-nine literature redox potentials measured under comparable conditions from 51 alternant and nonalternant polycyclic aromatic hydrocarbons are linearly correlated with their absolute reduction potentials computed by density functional theory (B3LYP/6-31+G(d)) with SMD/IEF-PCM solvation. The resulting correlation is very strong (R2 ) 0.9981, MAD ) 0.056 eV). When extrapolated to the x-intercept, the correlation results in an estimate of 5.17 ( 0.01 eV for the absolute potential of the ferrocene-ferrocenium redox couple in acetonitrile at 25 °C, indicating that this simple method can be used reliably for both calculating absolute redox potentials and for predicting relative redox potentials. When oxidation and reduction data are evaluated separately, the overall MAD value is improved by 50% to 0.028 eV, which improves relative potential predictions, but the computed values do not extrapolate to a reasonable estimate of the absolute potential of the ferrocene-ferrocenium ion reference. Introduction The need for knowing the oxidation or reduction potential of a given substance under a particular set of experimental conditions (solvent, temperature, reference electrode, etc.) arises frequently. For example, electrocatalytic applications involving mediated electron transfer require a relatively close match between the catalyst and substrate: the catalyst must have a lower potential than the substrate, but if the potential is too low, the electrocatalytic process will take place at a negligible rate.1,2 Redox potentials are also sometimes used to gauge a compound’s biological activity for estimating toxicity3,4 or drug efficacy.5,6 Similarly, a number of applications in material science require substrates of known oxidation potential, with recent examples found in the development of new semiconductors,7 photooxidants,8 and redox shuttle additives for lithiumion cells.9 The solution might be as simple as measuring the potential of the desired substance under the conditions of interest, but more often, the compound of interest is unknown or the conditions of interest are difficult to duplicate. This frequently happens during mechanistic investigations, where one is obliged to estimate whether a short-lived reactive intermediate would be oxidized or reduced under the reaction conditions.10-14 When contemplating the synthesis of a new electrocatalyst,2,15,16 or a new material,7-9 one would like some assurance that the product is likely to have the desired redox potential before beginning a lengthy synthesis. Since Maccoll17 first reported a linear relationship between redox potential and Hu¨ckel LUMO β in the late 1940s, experimentally observed redox potentials have been correlated with a variety of computed theoretical parameters, for example, Hu¨ckel MO β values, ionization energies, Hammett sigma, etc.18 * To whom correspondence should be addressed. E-mail: afry@ wesleyan.edu. Fax: +1 860 685-2211. Phone: +1 860 685-2622.

The objective of these LFER correlation studies has always been to accurately predict attributes (viz., redox potential) of a compound in cases where there is no practical way to measure or compute the desired attribute. Generally, data for a series of compounds similar to the unknown compound of interest are plotted and fitted by linear regression to create a calibration line, which can then be used to predict values for the related unknown compound(s). Our initial work in this area involved Hu¨ckel computations,19 but the availability of better hardware and software in recent years has permitted us to carry out more sophisticated computations, including the computation of solvation energies to good accuracy, which is critical for the realistic assessment of chemical and electrochemical properties of organic substances. Our two most recent works correlated experimental redox data with theoretical electron affinities (EA)20 and ionization potentials (IP),16 both of which were obtained by density functional theory (DFT) computations. It was in the course of this work that a review of the literature revealed the computational similarity of our LFER work with that of computational chemists aiming to directly compute accurate redox potentials of organic compounds. In hindsight, the intersection of our efforts to develop an universal correlation line with the complete theoretical prediction of redox potentials was inexorable; after all, direct computation is essentially the “perfect correlation” of experiment and theory. Pioneered in the late 1980s by Reynolds and co-workers,5 the complete theoretical prediction of redox potentials using quantum theory has depended on incorporating ab initio calculations into a Born-Haber thermodynamic cycle (Scheme 1) to overcome the problematic issue of accounting for the effects of solvation. Most computational work on redox potentials of organic compounds to the current date utilizes the same Born-Haber cycle;21-24 generally, the gas-phase free energies of formation are calculated separately from the change

10.1021/jp106088n  2010 American Chemical Society Published on Web 10/28/2010

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energy(EA,IP) ) energyOx - energyRed

SCHEME 1: Born-Haber Cycle for Calculating E° from Gas-Phase Free Energiesa

(1)

In the case of IP, “Ox” represents the substrate radical cation, and “Red” represents the neutral substrate. For EA, “Ox” is the neutral substrate, and “Red” is the substrate radical anion. Computed SCF energy values from optimized structures were entered into eq 1, and the resulting EA/IP values were converted to electron volts. For simplicity, the energy(EA,IP) variable from eq 1 can be redefined as an equivalent “calculated potential” (E°calc), where free energies are used in lieu of SCF energy values in eq 1 and the data are expressed in electron volts:

E°calc ) (1/F)(∆G°Ox - ∆G°Red)

(2)

a

The free energy of the gas-phase reaction at the top provides ionization energy/electron affinity. The free energy of the solutionphase reaction at the bottom provides the absolute redox potential.

in energies due to solvation, and these are combined as illustrated in Scheme 1 to estimate the solvated free energies of the reaction. Especially noteworthy, Fu et al.12 used this approach to compute standard redox potentials of 270 structurally unrelated organic molecules in acetonitrile, using relevant experimental adiabatic IP values and experimental pKa values to validate the computational results. In this way, they were able to compute accurate gas-phase energies using a larger basis set (B3LYP/6-311++G(2df,2p)) and then incorporate accurately computed solvation energies from a smaller basis set (B3LYP/ 6-31+G(d,p)), saving significant computational cost, which remains a limiting factor in predicting redox potentials directly by computation, rather than estimating redox potentials by LFER correlation. By comparison, the computed gas-phase electron affinities in our LFER correlation to the peak reduction potentials of chalcones20 were recently computed as shown in the gas-phase (top) portion of the Born-Haber cycle (Scheme 1). In that study, we recognized the idealized necessity of having a slope of unity in a plot of electron volts versus volts, and we speculated that our nonunity slope of 0.374 might be explained by solvation effects.18 So, our next study, correlating computed ionization potential to the peak oxidation potentials of a series of triarylamines,16 involved the same energy computations as before, but now including the Gaussian 03 default IEF-PCM solvation (for acetonitrile).25 This did have the effect of generating a slope closer to unity (m ) 0.789), but the slope was still far enough from unity that a question remained as to whether the default IEF-PCM model was adequate, suggesting a search for a better theoretical model for solvation. Recently, Truhlar and co-workers have developed a “density” solvation model (SMD)26 specifically designed to produce more accurate solvation energies; a vibrational frequency analysis (FREQ) on the structure optimized with PCM solvation directly outputs the ∆G°(solv) values required for the bottom portion of Scheme 1. We have found that computing E°Abs(298) in one step with PCM solvation, as opposed to computing gas-phase free energies and solvation energies separately, provides excellent correlation results with literature values for the redox potentials of polycyclic aromatic hydrocarbons (PAHs), from DFT/B3LYP/631+G(d) optimizations using SMD/IEF-PCM solvation and a subsequent vibrational analysis.

Single-electron oxidation and reduction of a substrate (Sub) can be represented as

oxidation: Sub f Sub•+ + e-

(3)

reduction: Sub + e- f Sub•-

(4)

When the oxidation expression (eq 3) is reversed to represent the reduction of the radical cation, the reduction potential for both eqs can be expressed as

∆G°rxn ) -FE°Red ) (∆G°Red) - (∆G°Ox + ∆G°e-)

(5)

E°Red ) E°calc + (∆G°e-)/F

(6)

In absolute terms, (∆G°e-)/F is the potential of a free electron in its resting state in a vacuum: the absolute zero energy value of an electron.27 At absolute zero temperature, the absolute electron potential (∆G°e-) is defined to be zero, and so E°calc from eq 2 actually represents the absolute single electrode potential at 0 K (E°Abs(0)). When using free energies computed at 298 K, (∆G°e-)/F amounts to a small thermal correction to determine E°Abs at ambient temperatures:

E°Abs(298) ) E°calc(298) - 0.03766 eV

(7)

The energy value used here for a free electron at 298 K (-0.03766 eV) was calculated from enthalpy and entropy values for a free electron at 298 K derived by Bartmess.28 Experimental redox data, on the other hand, are measured on a relative scale against a reference electrode, and singleelectron oxidation and reduction are represented as:

oxidation: Sub + REF+ h Sub•+ + REF

(8)

reduction: Sub + REF+ h Sub•- + REF

(9)

As before, eq 8 can be reversed and expressed as a reduction, and thus both eqs 8 and 9 yield the same result:

Experimental Methods

∆G°rxn ) FE°exp ) (∆G°Red + ∆G°REF+) - (∆G°Ox + ∆G°REF) (10)

Theoretical Approach. In our previous work,16,20 EA and IP were calculated in the same manner:

and

Absolute Redox Potentials of PAHs

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E°calc ) E°exp - E°REF

(11)

E°REF ) (1/F)(∆G°REF+ + ∆G°REF)

(12)

where:

Subtracting both sides of eq 11 by 0.03766 eV (from eq 7) corrects both E°calc and E°REF to the absolute scale at 298 K:

E°Abs(298) ) E°exp + E°REF(298)

(13)

Equation 13, which is easily recognized as the fundamental relationship between experimental and absolute potential,18 implies that a plot of single electrode potential (E°Abs(298)) versus the experimental (formal) redox potential (E°′exp (vs REF)) should have a slope of unity, and the y-intercept of the plot should be the absolute standard reduction potential of the reference electrode (at 298 K). Equations 7 and 13 can be combined and rearranged into a single working equation, written in terms of °′ : E°calc and Eexp

E◦′ exp ) (E° calc - 0.03766 eV) - E° REF(298)

(14)

Absolute Potential of Reference Electrodes. Unfortunately, the absolute potentials of reference electrodes are not directly measurable, but a considerable effort has been made to determine these values by theory and experiment.27 The IUPACrecommended absolute potential of the NHE (SHE29) in MeCN at 25 °C is 4.60 ((0.10) eV.27 More recent estimates30,31 alter this value only slightly, within the stated range of uncertainty. Using the IUPAC value, commonly used reference electrodes, such as SCE(aq) and Ag/Ag+, can be estimated from relative potentials, but experimental factors cause the observed potentials of these references to vary somewhat. For example, the liquid junction potential difference between MeCN and the SCE(aq) is variable and can be ca. 95 mV.32-36 For these reasons, use of an internal standard has come into common practice, and the commonly recommended internal standard for organic electrochemistry is the ferrocene/ferrocenium ion pair (Fc/Fc+).37 Pavlishchuk and Addison conducted a modern, critical review of reference electrode potentials, and they determined that the best conversion constant between the SHE and Fc/Fc+ in acetonitrile at 25 °C is +0.624 V ((0.010 depending on electrolyte concentration).38 Adding this to Trasatti’s value for the SHE27 would make the theoretical absolute potential of Fc/ Fc+ 5.22 ( 0.11 eV in acetonitrile at 25 °C. Collection of Literature Data. The chemical literature is replete with experimental data on the redox potentials of hydrocarbons; however, finding collections of data that were observed under comparable conditions is a challenge. Likewise, the choice of reference electrode varies between different studies, and regardless, experimental conditions, error, and uncertainty can alter the measured redox potential for the same compound versus the same reference among different reports. We chose to start with a simple model study by investigating reversible single-electron redox data for alternant39 PAHs, expecting these might correlate best between theory and experiment. We chose to adjust literature redox data to the ferrocene/ferrocenium ion pair (Fc/Fc+) as a reference.37 Parker40-42 developed a technique of observing CV behavior for oxidations and reductions in the presence of suspended alumina to obtain reversible voltammograms. He chose 10 alternant PAHs for his experiments

(reported as Ep ( 30 mV vs SCE(aq)). Later, both Saji and Aoyagui43 (see endnote (1) in the Supporting Information) and Kubota et al.44 used the same suspended-alumina technique to collect reversible redox data45 for several PAHs, including many of the compounds reported by Parker; agreement in redox potentials among the three papers was excellent ((40 mV), even though all of the reduction data in both of the more recent papers were measured in N,N-dimethylformamide (DMF), rather than acetonitrile, and all of Saji’s data were collected at -11 °C. The three data sets were combined, and where values varied slightly for the same compound, the values were averaged. The combined data were then uniformly adjusted by -0.448 V to shift from the SCE(aq) reference to Fc/Fc+ (based on our own measurement of anthracene reduction as -2.425 V vs Fc/Fc+, done in 0.1 M LiClO4/MeCN). Although we had initially intended to exclude nonalternant PAHs,19,39 the inclusion of the Saji and Aoyagui data set brought three nonalternant PAHs (fluoranthene, rubicene, and periflanthene) that fit our linear regression very well, so it was decided to include such compounds in this study. Koper et al.46 found a good linear correlation between Hu¨ckel LUMO energies and the measured reduction potentials of 17 cyclopenta-fused nonalternant PAHs (in MeCN vs Ag/Ag+). Using the Koper et al. value for anthracene reduction, their data were uniformly adjusted by -0.325 V to convert to the Fc/Fc+ reference, and the converted values were added into the combined data set, again averaging where appropriate (discrepancies were e20 mV). Redox data for a great many compounds are also available from the literature as E1/2 values from polarographic data. One major issue in using this data, apart from the variety of experimental conditions, is that much of the data is not expressly reported in terms of reversibility, as with CV data. If the compound is not reduced or oxidized reversibly on the voltammetric time scale, the measured potentials will deviate from the thermodynamic formal potential by an unknown and probably variable amount. We selected two oft-cited polarographic works to consider for our data set: Pysh and Yang47 (to represent PAH oxidation) and Streitwieser and Schwager48 (for PAH reduction). The Streitwieser and Schwager data (measured in DMF vs Hg pool) required an adjustment of -1.015 V to match their value for anthracene reduction to our benchmark for anthracene reduction vs Fc/Fc+. The Pysh and Yang data set (in MeCN vs SCE) did not contain a value for anthracene reduction, so instead, the data was adjusted by -0.228 V to align their value for benzo[a]pyrene oxidation with both Parker’s and Kubota’s agreed value for benzo[a]pyrene oxidation, adjusted to the Fc/ Fc+ reference: +0.712 V vs Fc/Fc+. With the addition of these two data sets, the model PAH data set used herein was finalized with 79 data points (42 reduction; 28 oxidation) from 51 PAHs (30 alternant; 21 nonalternant). Computational Method. Each compound was optimized separately as neutral species, radical cation, and radical anion in DFT calculations at the B3LYP/6-31G+(d) level with simultaneous computation of SMD/IEF-PCM26 solvation energies in acetonitrile, using Gaussian 09, Rev. A.02.49 A tight convergence criterion (with int)ultrafine) was specified, and each structure was verified to be a true minimum by the absence of imaginary frequencies in the vibrational analysis. Free energy values were taken from the Gaussian output files as the “sum of electronic and thermal free energies” in the vibrational analyses.50 Absolute standard potentials (E°Abs(298)) were computed by taking the difference between ∆G° for the oxidized and reduced forms for each redox pair (cation/neutral and neutral/anion), converting ∆∆G° to E°calc using a conversion

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Figure 1. Plot of Ep ( 30 mV (lit.) vs computed E°Abs(298). Ep ( 30 mV data from Parker.42 E°Abs(298) data from DFT computations at B3LYP/ 6-31+G(d) with SMD/IEF-PCM solvation in acetonitrile.

factor of 27.2114 eV/hartree and then subtracting 0.03677 eV (eqs 2 and 7). Results Graphical Analysis. Initially, a plot for eq 13 was constructed using only Parker’s data, with the idea that the results would be better when all of the data was measured consistently by one laboratory (Figure 1). The correlation is extremely strong °′ (R2 ) 0.9995) and results in eq 15 for predicting Eexp (vs Fc/ + Fc in MeCN) from computed E°Abs(298):

E◦′ exp ) 1.157E° Abs(298) - 5.09

(R2 ) 0.9995)

(15)

This results in a mean absolute deviation (MAD) of 0.036 V °′ in Eexp for Parker’s data. The slope in Figure 1 (0.8642) does not meet the requirement of being unity (from eq 13); however, the x-intercept, -5.09 V, approximates the theoretical E°REF(298) value of Fc/Fc+ (-5.22 ((0.11) eV). This is significant because the x-intercept is the extrapolation of the plot to the absolute zero value of E°Abs(298), which must be equal in magnitude to E°REF(298). The y-intercept should have the same value, but its accuracy will suffer from any nonunity slope. These results change very little when the rest of the PAH data collected (see data table and endnote (2) in the Supporting Information) is included in a similar plot (Figure 2). The correlation coefficient is only slightly smaller (R2 ) 0.9981), and the following results for the prediction of experimental values of redox potentials (vs Fc/Fc+) of substances not treated in these correlations:

E◦′ exp ) 1.164E° Abs(298) - 5.17

(R2 ) 0.9981)

(16)

For the complete data set, this yields a MAD value of 0.056 °′ V in Eexp , and the x-intercept is 5.17 ((0.01) eVswithin the margin of error of the theoretical value of E°REF(298) for Fc/Fc+ (5.22 ( 0.11 eV).

Figure 2. Plot of avg. E1/2 (lit.) vs computed E°Abs(298). Avg. E1/2 (lit.) includes all PAH data from Parker,42 Saji,37 Kubota,44 Koper,46 Pysh,47 and Streitwieser.48 E°Abs(298) data from DFT computations at B3LYP/631+G(d) with SMD/IEF-PCM solvation in acetonitrile.

Discussion DMF versus Acetonitrile in PCM Computations. Acetonitrile and N,N-dimethylformamide have been used somewhat interchangably as polar aprotic solvents for organic electrochemistry. They possess nearly the same dielectric constant (at 293.2 K, εr ) 36.64 for MeCN; εr ) 38.25 for DMF),51 which is the main parameter used to compute solvation by the PCM method. However, idealized solvent radii and electrostatic contributions also affect solvation energy, and both are parameters in the PCM proceduresas computational accuracy improves, these small differences could aggregate to a significant discrepancy. We computed E°Abs(298) for all of the PAHs observed in DMF by Saji and Aoyagui43 using SMD/IEF-PCM (B3LYP/ 6-31+G(d)) for both MeCN and DMF for comparison. For those 20 data points, MeCN results only averaged 4 mV negative of the corresponding DMF values. Oxidation versus Reduction. Although the correlation coefficient in Figure 2 is close to unity, by visual inspection the reduction and oxidation data each appear as if they might be better evaluated as separate data sets. When fitted by linear regression separately, the results are eqs 17 and 18:

oxidation:E◦′ exp ) 0.932E° Abs(298) - 3.94

(R2 ) 0.9847) (17)

reduction:E◦′ exp ) 1.056E° Abs(298) - 4.90

(R2 ) 0.9924) (18)

Interestingly, the two slope values from eqs 17 and 18 are both much closer to unity. The correlation coefficients actually decrease slightly when evaluated this way, despite the appearance of a tighter linear fit, due to the substantial decrease in the data range. This is acceptable, but the x- and y-intercepts are no longer reasonably close to the theoretical value of E°REF(298) for Fc/Fc+ in MeCN. Further, eqs 17 and 18 result in MAD

Absolute Redox Potentials of PAHs values for the PAHs of 0.032 and 0.023 mV, respectively, or a combined MAD of 0.028 mVsa 50% reduction from the MAD value provided by the regression in eq 16. This implies that for accuracy in predicting E1/2 values, it is better to consider oxidation separately from reduction using eqs 17 and 18. Such a result may indicate that the disjoint between oxidation and reduction lies with the computational method, that is, that DFT/ B3LYP/6-31+G(d) consistently underestimates E°Abs(298). Furthermore, it appears that oxidations are underestimated by a much greater extent than reductions. Compared to a theoretical line with a slope of unity and a y-intercept of 5.22 eV (Fc/ Fc+), the reduction data have an average deviation of 465 meV, and the oxidation data have an average deviation of 917 meV. Larger Basis Sets. In our original design for this project, we intended to follow a common procedure of optimizing the molecular geometry with the 6-31+G(d) basis set and then calculating the energies of the structures with a more expensive basis set, such as 6-311++G(3df,2pd),52 as did Fu et al. (with 6-311++G(2df,2p)).12 Computation of E°Abs(298) values with a larger basis set (6-311++G(3df,2pd)) was found to cause a 10to-20-fold increase in computational time, but only yields a 10% improvement in E° values. Modelli and co-workers4 have shown that B3LYP/6-31+G* accurately reproduced experimental adiabatic electron affinities over DZP++, showing that higher computational costs can come with diminishing returns. In a more recent paper, Modelli demonstrated that reliable correlation data for PAHs can sometimes be obtained very cheaply (AM1 and HF/6-31G).53 Conclusions It has been shown through careful application of theory that current computational methods, namely DFT using B3LYP/631+G(d) and SMD/IEF-PCM solvation, can be used to closely approximate the absolute single-electron redox potential of polycyclic aromatic hydrocarbons. Implied herein is a definitive °′ ) of these new method of predicting the formal potential (Eexp compounds versus the ferrocene/ferrocenium ion redox pair using eq 16 above and free energy values computed as described. The practical value of this is two-fold: (1) the formal potential of a known compound can be compared, under a broad range of experimental conditions, to the computed potential of an otherwise unavailable compound by voltammetric measurement versus ferrocene or versus another reference that has been calibrated against ferrocene; and (2) having shown in this proofof-concept study that extrapolations of the data agree with accepted values of the absolute single-electron potentials of the reference, the absolute redox potential (E°Abs(298)) of an unavailable compound can be accurately estimated using the same computations and eq 7 above. By itself, the absolute redox potential of a compound has practical uses far beyond the reach of electrochemistry alone. The correlation plot in Figure 2 far exceeded expectations in regards to both the correlation coefficient (R2 ) 0.998) and the absence of scatter along such a wide range of potentials (4.4 V). We are currently investigating the experimental applicability of this methodology to a diverse array of organic compounds with encouraging results, and future work will investigate the predictive power of this method on estimating redox properties. Acknowledgment. We thank Wesleyan University for computer time supported by the NSF under grant number CNS0619508. Supporting Information Available: The material is divided into two parts: part 1: data table, endnotes, and list of PAHs

J. Phys. Chem. A, Vol. 114, No. 46, 2010 12303 (with structural formulas), and part 2: Cartesian coordinates for optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Steckhan, E. Top. Curr. Chem. 1987, 142, 1–69. (2) Wu, X.; Davis, A. P.; Fry, A. J. Org. Lett. 2007, 9, 5633–5636. (3) Cremonesi, P.; Rogan, E.; Cavalieri, E. Chem. Res. Toxicol. 1992, 5, 346–355. (4) Modelli, A.; Mussoni, L.; Fabbri, D. J. Phys. Chem. A 2006, 110, 6482–6486. (5) Reynolds, C. A.; King, P. M.; Richards, W. G. Nature 1988, 334, 80–82. (6) Reynolds, C. A. J. Am. Chem. Soc. 1990, 112, 7545–7551. (7) Nayak, P. K.; Periasamy, N. Org. Electron. 2009, 10, 1396–1400. (8) Speelman, A. L.; Gillmore, J. G. J. Phys. Chem. A 2008, 112, 5684– 5690. (9) Wang, R. L.; Moshurchak, L. M.; Lamanna, W. M.; Bulinski, M.; Dahn, J. R. J. Electrochem. Soc. 2008, 155, A66–A73. (10) Wawzonek, S.; Blaha, E. W.; Behkey, R.; Runner, M. E. J. Electrochem. Soc. 1955, 102, 235–242. (11) Fry, A. J. The Electrochemistry of Nonbenzenoid Hydrocarbons. 2. Benzenoid Hydrocarbons. In Topics in Organic Electrochemistry; Fry Albert, J., Britton, W. E., Eds.; Plenum Press: New York, 1986; pp 4-7. (12) Fu, Y.; Liu, L.; Yu, H.-Z.; Wang, Y.-M.; Guo, Q.-X. J. Am. Chem. Soc. 2005, 127, 7227–7234. (13) Opitz, A.; Wei-Opitz, D.; Gebhardt, P.; Koch, R. J. Org. Chem. 2006, 71, 1074–1079. (14) Park, Y. S.; Little, R. D. J. Org. Chem. 2008, 73, 6807–6815. (15) Wu, X.; Dube, M. A.; Fry, A. J. Tetrahedron Lett. 2006, 47, 7667– 7669. (16) Wu, X.; Davis, A. P.; Lambert, P. C.; Steffen, L. K.; Toy, O.; Fry Albert, J. Tetrahedron 2009, 65, 2408–2414. (17) Maccoll, A. Nature 1949, 163, 178–179. (18) Evans, D. H. Chem. ReV. 2008, 108, 2113–2144. (19) Fry, A. J.; Fox, P. C. Tetrahedron 1986, 42, 5255–5266. (20) Hicks, L. D.; Fry, A. J.; Kurzweil, V. C. Electrochim. Acta 2004, 50, 1039–1047. (21) Roy, L. E.; Jakubikova, E.; Guthrie, M. G.; Batista, E. R. J. Phys. Chem. A 2009, 113, 6745–6750. (22) Namazian, M.; Coote, M. L. J. Phys. Chem. A 2007, 111, 7227– 7232. (23) Li, X.-L.; Fu, Y. THEOCHEM 2008, 856, 112–118. (24) Shi, J.; Zhao, Y.-L.; Wang, H.-J.; Rui, L.; Guo, Q.-X. THEOCHEM 2009, 902, 66–71. (25) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. ReV. 2005, 105, 2999– 3093. (26) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 2009, 113, 6378–6396. (27) Trasatti, S. Pure Appl. Chem. 1986, 58, 955–966. (28) Bartmess, J. E. J. Phys. Chem. 1994, 98, 6420–6424. (29) Ramette, R. W. J. Chem. Educ. 1987, 64, 885. (30) Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 2007, 111, 408–422. (31) Fawcett, W. R. Langmuir 2008, 24, 9868–9875. (32) Nelson, I. V.; Iwamoto, R. T. Anal. Chem. 1961, 33, 1795–1796. (33) Kolthoff, I. M.; Thomas, F. G. J. Phys. Chem. 1965, 69, 3049– 3058. (34) Diggle, J. W.; Parker, A. J. Aust. J. Chem. 1974, 27, 1617–1621. (35) Datta, J.; Bhattacharya, S.; Kundu, K. K. Aust. J. Chem. 1983, 36, 1779–1784. (36) Izutsu, K. Pure Appl. Chem. 1998, 70, 1873–1880. (37) Gagne, R. R.; Koval, C. A.; Lisensky, G. C. Inorg. Chem. 1980, 19, 2854–2855. (38) Pavlishchuk, V. V.; Addison, A. W. Inorg. Chim. Acta 2000, 298, 97–102. (39) Jones, R. A. Y. Physical and Mechanistic Organic Chemistry, 2nd ed.; Cambridge University Press: Cambridge, United Kingdom, 1984. (40) Hammerich, O.; Parker, V. D. Electrochim. Acta 1973, 18, 537– 541. (41) Jensen, B. S.; Parker, V. D. J. Am. Chem. Soc. 1975, 97, 5211– 5217. (42) Parker, V. D. J. Am. Chem. Soc. 1976, 98, 98–103. (43) Saji, T.; Aoyagui, S. J. Electroanal. Chem. 1983, 144, 143–152. (44) Kubota, T.; Kano, K.; Uno, B.; Konse, T. Bull. Chem. Soc. Jpn. 1987, 60, 3865–3877. (45) Fry, A. J. Synthetic Organic Electrochemistry, 2nd ed.; John Wiley & Sons, Inc.: New York, 1989. (46) Koper, C.; Sarobe, M.; Jenneskens, L. W. Phys. Chem. Chem. Phys. 2004, 6, 319–327. (47) Pysh, E. S.; Yang, N. C. J. Am. Chem. Soc. 1963, 85, 2124–2130.

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