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ORIGINAL PAPER
The use of calculated reorganization energies in experimentalelectrochemical kinetics
Mihai Buda
Received: 29 April 2013 /Revised: 20 June 2013 /Accepted: 21 June 2013# Springer-Verlag Berlin Heidelberg 2013
Abstract Calculated reorganization energies in solution usingthe polarizable continuum model implemented in Gaussian 03are compared to experimental values of the heterogeneous rateconstants for the reduction of a wide variety of neutral mole-cules in dimethylformamide. The calculated reorganizationenergies are fully consistent with the experimental data; thecomputational procedure may in fact be quite useful for esti-mating the reorganization energies for outer-sphere electro-chemical reactions. From the comparison between the calcu-lated reorganization energy values and the experimental valuesfor the heterogeneous rate constants, the adiabaticity of theredox couples' is discussed.
Keywords Reorganization energy . Computational chemistry .
Electrochemical kinetics . Theoretical electrochemistry
Introduction
During the past few years, a renewed interest for comparingexperimental electrochemical kinetic data with theoreticalpredictions from modern approaches to the heterogeneouselectron transfer has arisen [1–6]. To this end, a procedure forcalculating reorganization energies suitable for electrochem-ical reactions, implemented in the commercial Gaussianpackage, was tested, and the results are checked againstexperimental data. The present paper aims to assess the pro-cedure's effectiveness by checking whether calculated reor-ganization energies are consistent with heterogeneous rateconstants data for the electroreduction of a wide variety of
compounds in dimethylformamide (DMF). The method in-volves the computation of equilibrium and nonequilibriumGibbs free energies in solution using the polarizable contin-uum model (PCM) during a vertical transition; its implemen-tation in Gaussian 03 is discussed in detail in Cossi andBarone [7, 8] and Tomasi et al. [9]. One main drawback ofthis method is that the calculated reorganization energy is, infact, a value corresponding to a very large (infinite) distancebetween the molecule and the electrode, as the influence ofthe latter is completely neglected. Nevertheless, the calculat-ed values do seem to be consistent with experimental data forheterogeneous rate constants.
Calculation details and choice of experimental data
All calculations were performed using Gaussian 03 [10].Density functional theory was chosen as a good compromisebetween speed and accuracy, with B3LYP functional usedfor all calculations for molecules not containing metals (ex-cept o-nitrobenzoic acid and metronidazole, which form anintramolecular hydrogen bond, and for which, M052X waspreferred, as it gives better results for hydrogen bondinginteractions); B3P86 was used for the metal complexes.Molecule optimizations were performed in a vacuum (it isassumed that the geometry in the solvent is virtually identicalto the one in vacuum), and only for o-nitrobenzoic acid andmetronidazole, the optimizationswere ran in dimethylformamide(as the hydrogen bonding depends on the solvent's polarity).Since for polar solvents, the continuum dielectric solvationmodels C-PCM and IEF-PCM implemented in Gaussian 03 givevery similar results, the slightly faster C-PCMwas used to for allcalculations. As basis sets, 6-31+G(d,p) level (for organicmolecules) or else 6-311G(d,p) or cc-pVDZ and SDD pseudo-potentials and basis sets (for metal complexes) as defined inGaussian 03 E.01 were deemed accurate enough for the purposeof this paper. All optimized structures (most of them ran using an
M. Buda (*)Department of Applied Physical Chemistry, Electrochemistry andInorganic Chemistry, Faculty of Applied Chemistry and MaterialsScience, “Politehnica” University of Bucharest, Calea Grivitei 132,010737 Bucharest, Romaniae-mail: [email protected]
J Solid State ElectrochemDOI 10.1007/s10008-013-2163-7
ultrafine grid and very tight optimization criteria) were checkedto be minima, with no imaginary frequencies.1
The molecular cavity was always custom built, with ex-plicit hydrogens and no added spheres for smoothing thecavity; the van der Waals radii were taken from Böes et al.[11] and Batsanov [12]. The parameter values used for de-scribing dimethylformamide are as follows: EPS=36.71,RSOLV=2.647, DENSITY=0.007777, VMOL=128.7, andEPSINF=2.039; the scaling factor for solute cavities waschosen as 1.39 [11]. It was found that for molecules withpolar groups (such as nitro compounds), a cavity with tes-serae areas of either 0.15 or 0.175 Å2 may give better results,while for nonpolar molecules and highly symmetrical ones(such as tetracene), a tesserae area of 0.25–0.275 Å2 mayperform better. The calculated values change slightly whenthe tesserae area changes, but the changes are not significant(∼2–3 % in the final value for λ).
The nonequilibrium solvation energy was calculatedusing the “NONEQ” keyword, as implemented in Gaussian03, according to which in a vertical transition, the solvatedsystem is considered to respond only to the optical dielectricconstant; the procedure is detailed in Cossi and Barone [7,8]; see also Tomasi et al. [9] (a very similar procedure hasbeen implemented in GAMESS [13]). Once the optimizedgeometries were obtained, four single-point calculationswere performed in order to obtain the equilibrium andnonequilibrium solvation free energies (corresponding to avertical transition) in solution, as detailed below for anthra-cene (Ant) reduction:
Step 1 Read the (optimized) geometry of Ant, calculate theequilibrium free energy for Ant in DMF, and writethe slow solvation charges needed in the next stepfor calculating the nonequilibrium free energy ofAnt− (noneq = write), G0(Ant).
Step 2 Read the (optimized) geometry of Ant and the slowsolvation charges computed in the previous step andcalculate the nonequilibrium free energy in DMF forAnt− (using the solvent's optical dielectric constant)in the presence of the fixed slow charges from theprevious step (noneq = read), G*(Ant−) (first verti-cal transition; the free energy for Ant− is calculatedat the geometry of Ant).
Step 3 Read the (optimized) geometry of Ant−, calculatethe equilibrium free energy for it in DMF, and writethe slow solvation charges needed in the next stepfor calculating the nonequilibrium free energy ofAnt (noneq = write), G0(Ant−).
Step 4 Read the (optimized) geometry of Ant− and the slowsolvation charges computed in the previous step and
calculate the nonequilibrium free energy in DMF forAnt (using the solvent's optical dielectric constant)in the presence of the fixed slow charges from theprevious step (noneq = read), G*(Ant) (second ver-tical transition; the energy for Ant is calculated at thegeometry of Ant−).
Two values for the reorganization energy are thus obtained:
Antþ e–→Ant– λ→ ¼ G� Ant–ð Þ–G0 Ant–ð ÞAnt–→Antþ e– λ← ¼ G� Antð Þ–G0 Antð Þwith λ being calculated as a simple arithmetic mean betweenλ→ and λ←.
No frequency contributions were considered for the freeenergy in solution, as it was argued that all the vibrational,rotational, and translational molecular contributions in solu-tion are already included in the solvation model [14]; thus,the free energy in solution calculated using the PCM modelis considered to be a “true” Gibbs free energy.
The reorganization energies calculated in this mannerneglect the image–charge interactions and therefore corre-spond to Hush's expression for the solvent reorganizationenergy (Eq. 1, [15]) rather than the classical Marcus one(Eq. 2, [16], see also [17]):
λ0 ¼ e2
4πε0
1
εop−1
εs
� �� 1
2að1Þ
λ0 ¼ e2
4πε0
1
εop−1
εs
� �� 1
2
1
a−1
R
� �ð2Þ
where εop and εs are the optical and static dielectric con-stants, respectively; a is the radius of the reactant molecule(assumed to be spherical); and R is twice the distance be-tween the reactant molecule and the electrode. For unchargedinterfaces, image–charge interactions may become important[18], but Hale showed that for charged interfaces, the image–charge interactions may be neglected [17]. While the relativeimportance of image–charge interactions is still a matter ofdebate, for the purpose of the present paper, they areneglected; the calculated values for the reorganization ener-gy are compared quite well to other calculated values, e.g.,aromatic hydrocarbons [17] and tert-nitrobutane [19].
The experimental data were chosen to correspond to “out-er-sphere” (http://goldbook.iupac.org/O04351.html) electro-chemical reactions and match as closely as possible to theexperimental conditions from the study of Dietz and Peover[20] and Kojima and Bard [21], namely, DMF as solvent,tetrabutylammonium supporting electrolyte and mercuryelectrode. Since the heterogeneous rate constants for thereduction of neutral molecules in organic solvents are strong-ly influenced by the size of the cation of the supportingelectrolyte [22–25], the choice of tetrabutylammonium as
1 Any calculation details, includingGaussian output files, may be obtainedupon request from the author.
J Solid State Electrochem
the supporting electrolyte for experimental data was madebased on the availability of the experimental data, and also,its lesser tendency to form ion pairs with organic anions com-pared to, e.g., tetraethylammonium [26].Whenever experimen-tal data for more than one concentration of supporting electro-lyte were available, the value measured at the highest concen-tration was retained. The nature of the anion in the supportingelectrolyte was deemed less important; as all reductions takeplace at potentials significantly more negative than the potentialof zero charge (pzc) of Hg, it is the cation which is mostlyresponsible for the structure of the double layer. Indeed, thecapacitance–voltage curves for tetrabutylammonium perchlo-rate and iodide are very similar in the region negative of the pzc[27], while the same curves for different tetraalkylammoniumions show rather large differences in the same region [22, 28].The possible influence of the double layer was checked usingboth uncorrected and double-layer corrected heterogeneousrate constants; the double-layer data for correcting the apparentrate constants were taken from the literature [20–22, 29, 30].The apparent values (i.e., not corrected for double layer) of theheterogeneous rate constants given in Dietz and Peover [20]and Peover and Powell [31] were scaled down from 30 °C tothe more common temperature of 22 °C using the calculatedreorganization energy (λ) and assuming that ΔH#≈λ/4. Sincethe formal charge of the reacting species does seem to have aninfluence (albeit a rather unclear one, [29, 32]) on the(corrected) heterogeneous rate constant, only reductions fromneutral species were considered. Thus, all the electrochemicalreactions discussed can be described as A0+e−→A−. Datainvolving reduction of sulfur-containing organics (such as sul-fides, disulfides, thiocarbonates), which are susceptible to in-teract strongly with mercury electrodes [33] were generallyavoided, with only a couple of exceptions: the reduction of4,6-dimethyl-1-phenyl-2-thiopyrimidine fits well in group I
[34], while the reduction of 4,5-bis(ethylthio)-1,3-dithiole-3-thione [35] falls in group II; in both cases, experimental datashow no evidence of adsorption during their reduction.
Diffusion coefficients not available from the original ref-erence were estimated using the general procedure describedin Wilke and Chang [36]. Whenever cyclic voltammetry(CV) was used to calculate the apparent heterogeneous rateconstant, the relationships from the study of either Neudeckand Dittrich [37] or Lavagnini et al. [38] were used; forexample, the data for the heterogeneous rate constant forthe reduction of 4,4-dimethyl-2-cyclohexen-1-one wererecalculated using the original data from Fig. 2 in the litera-ture [39] and using theΔEp–Ψ relationship from the study ofNeudeck and Dittrich [37]. Care was taken to avoid as muchas possible uncompensated ohmic drop issues, and data werecarefully selected. For example, the reduction of 2-nitroanisolehas a peak separation of about 100 mV at 10 V/s, while 3-nitroanisole and 4-nitroanisole show in the same conditionspeak separations of about 65 and 58 mV, respectively [40],strongly suggesting that the wider separation for 2-nitroanisoleis indeed due to slower electrochemical kinetics. In other cases(e.g., [41, 42]), the use of relatively fast scan rates (>10 V/s)was considered as a reliable procedure per se.2 In still othercases, it was estimated that the heterogeneous rate constants areslow enough so that the influence of uncompensated ohmicdrop may be considered small [43]. Whenever the electrontransfer step was followed by a chemical reaction, data forwhich the peak current ratio was lower than ∼0.6 were notconsidered. Nevertheless, even with all these precautions, the
2 CV with fast scan rate without ohmic drop compensation usually yieldsvery distorted curves.
Fig. 1 Theln ks �
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ πkBT=λð Þp� �
–λdependence for molecules ingroups I (numbers) and II(letters). The numbers and letterscorrespond to the lines inTables 1 and 2. The linesrepresent the theoretical linehaving F/4RT (∼9.7) slope
J Solid State Electrochem
Table 1 Group I of molecules
No. Redox couple λ→(eV)
λ←(eV)
λ(eV)
ks (cm/s) −φs
(mV)Ref.
1 1,4-bis(9-Fluorenyl)-ethene 0.804 0.769 0.786 6 125 Hoytink [71]
2 Tetracene 0.796 0.779 0.788 2.7 102 Dietz and Peover [20]
3 118 Hoytink [71]
3 Perylene 0.783 0.813 0.798 5 70 Kojima and Bard [21]
3 117 Hoytink [71]
4 9,9′-Bifluorenyl 0.807 0.845 0.826 6 127 Hoytink [71]
5 Anthracene 0.873 0.875 0.874 4 123 Hoytink [71]
1.6 111 Andrieux et al. [72]
5 76 Kojima and Bard [21]
2.4 121 Fawcett and Jaworski [73]
6 Dibenzofuran 0.912 0.881 0.897 2.9 89 Kojima and Bard [21]
7 trans-Stilbene 0.899 0.906 0.902 1.45 113 Dietz and Peover [20]
8 Dibenzothiophene 0.914 0.912 0.913 1.6 88 Kojima and Bard [21]
9 2,4,6-Trimethyl-trans-stilbene 1.000 0.897 0.948 0.92 116 Dietz and Peover [20]
10 1-Hydroxy-4-methoxyiminoanthraquinone
0.900 1.026 0.963 0.96 96 Amatore et al. [74]
11 Naphthalene 0.983 0.951 0.967 0.78 145 Dietz and Peover [20]
12 2,4,6,2′,4′,6′-Hexamethyl-trans-stilbene
1.048 0.890 0.969 0.48 112 Dietz and Peover [20]
13 Fluorenone 0.997 0.966 0.981 0.79 100 Ahlberg et al. [75]
14 2-Methyl-naphthalene 0.999 0.974 0.986 0.65 146 Dietz and Peover [20]
15 1,3-Dicyanobenzene 1.005 1.003 1.004 0.26 116 Gennaro et al. [76]
16 1,2-Dicyanobenzene 1.012 1.023 1.017 1.4 71 Kojima and Bard [21]
2 71 Garreau et al. [60]
0.32 112 Baránski and Fawcett [77]
17 1,4-Dicyanobenzene 1.001 1.032 1.017 0.68 67 Kojima and Bard [21]
0.82 67 Garreau et al. [60]
0.22 117 Baránski and Fawcett [77]
0.23 114 Gennaro et al. [78]
0.39 113 Fawcett and Jaworski [73]
0.18 111 Harman and Baranski [79]
18 4,4′-bis(Trimethylsilyl)biphenyl 1.067 0.966 1.017 0.34 128 Smith and Bauer [80] and Allred and Bush [81]
19 Dinitromesitylene 1.068 0.989 1.028 0.95 95 Ahlberg and Parker [22]
20 p-Tolunitrile 1.037 1.035 1.036 0.59 86 Kojima and Bard [21]
21 cis-Stilbene 1.109 0.982 1.046 0.91 107 Dietz and Peover [20]
22 m-Tolunitrile 1.057 1.046 1.052 0.63 85 Kojima and Bard [21]
23 o-Tolunitrile 1.058 1.048 1.053 0.63 84 Kojima and Bard [21]
24 Tetraphenylethene 1.096 1.027 1.062 0.2 115 Grzeszczuk and Smith [82]
25 α-Methyl-trans-stilbene 1.138 0.993 1.065 0.33 141 Dietz and Peover [20]
26 CpCo(1,3-COT) 1.015 1.13 1.073 0.28 98 Grzeszczuk and Smith [83]
27 Benzonitrile 1.082 1.067 1.075 0.61 83 Kojima and Bard [21]
0.30 140 Baránski and Fawcett [77]
0.29 118 Aalstad and Parker [84]
0.35 118 Aalstad and Parker [85]
0.45 118 Ahlberg and Parker [22]
28 4-Cyanopyridine 1.113 1.109 1.111 0.42 73 Kojima and Bard [21]
29 4,6-Dimethyl-1-phenyl-2-thiopyrimidine
1.121 1.16 1.14 0.28 119 Battistuzzi et al. [34]
30 Benzyl benzoate 1.077 1.218 1.148 0.24 129 Vincent and Peters [86]
J Solid State Electrochem
electrochemical rate constants obtained from CV data shouldbe regarded with caution, as the (residual) uncompensatedohmic drop and/or follow-up reaction will always have someinfluence on the rate constant values.
The only case for which classical d.c. polarography wasused to estimate the heterogeneous rate constant was for thereduction of diphenylcarbodiimide; the data from refs. [44,45] (but also its relative similarity to diphenyldiazomethane)suggest that it is kinetically controlled; the heterogeneousrate constant was extracted from the experimental data givenin Duty and Garrosian [44] and Garrosian et al. [45] follow-ing the procedure detailed in Mirkin and Bard [46].
Results and discussion
The calculated reorganization energies are checked againstexperimental data for heterogeneous rate constants; bothuncorrected and double-layer corrected rate constants werecompared [47]:
k0 ¼ ksexpF
RTz−αð Þφs
� �¼ ksexp −
F
2RTφs
� �
where k0 is the double-layer corrected rate constant; z=0 inall situations, as only uncharged species were considered,
and α was assumed to be 0.5; φs is the potential at thereaction site, assumed to be equal to the potential of the outerHelmholtz layer [47]. Since the use of double-layer correctedrate constants results in unrealistic values for the electroniccoupling element (see below), most of the discussion isactually confined only to uncorrected heterogeneous rateconstants, ks.
If one assumes that the major factor controlling the electrontransfer for an outer-sphere reaction is the reorganizationenergy, then one would expect from the classical Marcustheory a quasi-linear dependence in a ln(k)–λ plot. In fact,within the framework of the modern theories of heterogeneouselectron transfer reactions, a slightly more complex relation-ship is actually more suitable:
ks �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ πkBT
λ
� �s
¼ πνnβ
ln 1þ 4π2ρM H012
� �2hνn
ffiffiffiffiffiffiffiffiffi4πλkBT
r2664
3775exp −
λ4kBT
� �
where ks (in centimeter per second) is the (uncorrected) hetero-geneous rate constant, λ is the reorganization energy (inelectronvolt), kB is the Boltzmann constant (8.617×10−5 eV/K),
Table 1 (continued)
No. Redox couple λ→(eV)
λ←(eV)
λ(eV)
ks (cm/s) −φs
(mV)Ref.
31 p-Naphthalenedisulfonyl fluoride 1.245 1.164 1.204 0.3 61 Sanecki et al. [87]
32 2-Nitrosofuran 1.246 1.167 1.207 0.29 82 Stradins et al. [42]
33 Nitromesitylene 1.282 1.157 1.219 0.29 64 Garreau et al. [60]
34 4,4-Dimethyl-2-cyclohexen-1-one 1.24 1.206 1.223 0.054 130 Bastida et al. [39]
35 Heptalene 1.355 1.115 1.235 0.2 67 Oth et al. [41]
36 Aminonitrodurene 1.287 1.218 1.253 0.092 126 Peover and Powell [31]
37 1,3,5-Cyclooctatriene 1.369 1.173 1.271 0.083 132 Huebert and Smith [88] and Allendoerfer andRieger [89]
38 Fe(COT)(CO)3 1.302 1.251 1.276 0.24 106 Tulyathan and Geiger [90]
39 Nitrodurene 1.34 1.222 1.281 0.15 66 Garreau et al. [60]
40 Cobaltocene 1.287 1.275 1.281 0.06 118 Gennett and Weaver [29]
41 2-Nitroanisole 1.302 1.334 1.318 0.068 105 Núñez-Vergara et al. [40]
42 Camphorquinone 1.37 1.359 1.364 0.081 108 Ouziel and Yarnitzky [91]
43 p-Benzenedisulfonyl fluoride 1.432 1.302 1.367 0.07 65 Sanecki et al. [87]
44 Metronidazole 1.43 1.344 1.387 0.0209 101 Gála et al. [92]
45 CpFe-dibenzothiophene 1.768 1.235 1.503 0.004 85 Abd-El-Aziz et al. [93]
46 Benzocyclooctatetraene 1.721 1.319 1.520 0.0051 104 Jensen et al. [94]
47 Diphenyl oxalate 1.594 1.599 1.597 0.0045 124 Islam et al. [43]
48 Cyclooctatetraene 1.879 1.508 1.693 0.002 116 Huebert and Smith [88]
49 Diazodiphenylmethane 1.672 1.873 1.773 4.57×10−4 98 Bethell and Parker [95]
50 Diphenylcarbodiimide 1.722 2.265 1.993 1.67×10−4 124 Duty and Garrosian [44] and Garrossian et al. [45]
Cp cyclopentadienyl, COT cyclooctatetraene
J Solid State Electrochem
ρM is the density of states of liquid mercury (states perelectronvolt per atom), H12
0 is the electronic coupling elementat the reference distance (in electronvolt), h is Planck's constant(4.136×10−15 eV/s), β (per centimeter) is the distance depen-dence of the electronic coupling element, and νn (per second) isthe nuclear vibration frequency [48]. Thus, instead of theln(ks)–λ plot, it is more appropriate to use instead a
ln ks �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ πkBT=λð Þp� �
–λ plot:
ks �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ πkBT
λ
� �s¼ Z0exp −
π4kBT
� �
with Z0 ¼ πνnβ ln 1þ 4π2ρM H0
12ð Þ2hνn
ffiffiffiffiffi4πλkBT
p" #
:Note that Z0 depends
slightly on λ, but the dependence is rather weak and may beneglected; in the following, λ=1.25 eV was assumed for esti-mating the value of Z0.
It can be seen from Fig. 1 that the calculated reorganiza-tion energies are quite consistent with the experimental datafor a wide range of electrochemical reductions in DMF,ranging from very fast to very slow. The molecules were
divided into two major groups: reductions with comparative-ly small heterogeneous rate constants (group I) and reduc-tions with comparatively large heterogeneous rate constants(group II)—the substances in the latter category all contain atleast one, unhindered, polar group containing an oxygen atom,with only one exception, 4,5-bis(ethylthio)-1,3-dithiole-3-thione (which contains sulfur atoms instead). A fewmolecules,such as p-naphthalenedisulfonyl fluoride, p-benzenedisulfonylfluoride, camphorquinone, or Fe(COT)(CO)3 lie almost in themiddle between the two groups, but to simplify the discussion,they were placed within group I.
In group I of molecules (Fig. 1 and Table 1) long and flat,nonpolar molecules, such as tetracene and trans-stilbene, liewell below the theoretical line, possibly reflecting orienta-tion effects [49]. Sterically hindered molecules such ashexamethyl-trans-stilbene, 4,4′-bis(trimethylsilyl)biphenyl,and tetraphenylethene also tend to fall significantly belowthe line, probably because of a larger minimum separationdistance (r0 in [48]), reflected in a smaller value forH0
12. It isinteresting to note though that if the oxygen-containinggroup is also sterically very hindered, as is the case fornitromesitylene, dinitromesitylene, nitrodurene, and amino-nitrodurene (but not tetramethyl-p-benzoquinone and 2,6-di-tert-butyl-p-benzoquinone), then the molecules fall closer to
Table 2 Group II of molecules
Redox couple λ→ (eV) λ← (eV) λ (eV) ks (cm/s) −φs (mV) Ref.
a 2-Chloro-3-methyl-1,4-naphthoquinone 1.050 1.026 1.038 3.9 56 Garreau et al. [61] and Bethell and Parker [96]
b p-Diacetyl-benzene 1.072 1.051 1.061 2.3 66 Schmickler [60]
c m-Dinitrobenzene 1.075 1.008 1.042 2.7 46 Dietz and Peover [21]
d p-Naphthoquinone 1.106 1.089 1.097 2.1 35 Dietz and Peover [21]
e 2,6-di-tert-Butyl-p-benzoquinone 1.088 1.105 1.097 1.4 92 Glezer et al. [97]
f Tetramethyl-p-benzoquinone 1.121 1.114 1.117 1.2 97 Glezer et al. [97]
g p-Dinitrobenzene 1.18 1.098 1.139 0.93 36 Dietz and Peover [21]
h 4,5-bis(Ethylthio)-1,3-dithiole-3-thione 0.982 1.321 1.151 1.9 118 Battistuzzi et al. [35]
i m-Nitrobenzonitrile 1.246 1.151 1.198 1.8 49 Dietz and Peover [21]
j p-Benzoquinone 1.203 1.205 1.204 1.3 80 Glezer et al. [97]
k p-Nitrotoluene 1.264 1.144 1.204 1.97 116 Belèn et al. [31]
l p-Nitroaniline 1.234 1.192 1.213 0.88 122 Belèn et al. [31]
m o-Nitrotoluene 1.292 1.154 1.223 1.2 120 Belèn et al. [31]
n o-tert-Butyl nitrobenzene 1.379 1.226 1.303 0.32 120 Belèn et al. [31]
o Nitrobenzene 1.295 1.184 1.239 2.2 56 Dietz and Peover [21]
p o-Nitrobenzoic acid 1.671 1.501 1.586 0.013 92 Retzlav and Baumgärtel [98]
q CpCr(CO)2(NO) 1.508 1.689 1.599 0.026 119 Brillas et al. [99]
r Diethyl oxalate 1.72 1.618 1.669 0.0043 133 Stradins et al. [43]
s Dimethyl oxalate 1.727 1.623 1.675 0.0092 132 Stradins et al. [43]
t 2-Nitro-2,4,4-trimethylpentane 1.543 1.846 1.695 0.008 128 Belèn et al. [31]
u tert-Nitrobutane 1.667 1.960 1.813 0.0056 128 Belèn et al. [31]
v Di-isopropyl oxalate 2.058 1.619 1.838 0.0046 134 Stradins et al. [43]
Cp cyclopentadienyl
J Solid State Electrochem
the first group. It is thus conceivable that the electroniccoupling, H0
12, between mercury and a molecule containinga polar oxygen-containing group is, probably, significantlylarger than that for other molecules, making the reductions ingroup II comparatively much faster. One notable exception isthe reduction of fluorenone, which falls significantly belowthe line within group I.
It is also worth noting the rather large difference in theheterogeneous rate constants for the reduction of dimethyland diethyl oxalate (both in group II), for which no simpleexplanation seems evident—the difference may actually becaused by ohmic drop issues.
The question of the “degree of adiabaticity” of electro-chemical reactions has received a special interest recently [5,
6, 50]; it would be interesting to use the combination ofcalculated reorganization energies together with experimen-tal data for heterogeneous rate constants to assess whetherthe reductions discussed here are likely to be adiabatic or not;in order to achieve this, one should try to estimate the valuefor Z0 (in centimeter per second) as a function of the elec-tronic coupling, H0
12, by assigning reasonable values for theother parameters.
The nuclear vibration frequency, νn, can be taken roughlyas 1012 s−1 [5]; the value of the density of states for liquidmercury is a rather complicated matter [51–55], with typical(calculated) values of, e.g., 0.227 [52, 53] and 0.398states/eV/atom [56]; the latter values were chosen for calcu-lating estimated Z0; β may be estimated from experimental
Fig. 2 The value of Z0 as afunction of the electroniccoupling element H0
12; the twocircles represent the values forgroups I (empty circle) and II(filled circle)
Fig. 3 Theln ks �
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ πkBT=λð Þp� �
–λdependence for molecules ingroup II (letters) together withthe reduction of O2 (upper, filledcircle) and benzyl phenyl sulfide(lower, filled circle). The letterscorrespond to the lines inTable 2. The lines represent thetheoretical line having F/4RT(∼9.7) slope
J Solid State Electrochem
data of heterogeneous rate constants in DMF obtained usingdifferent tetraalkylammonium ions of different sizes as thesupporting electrolyte. Assuming that the position of thetetraalkylammonium ion in the inner Helmholtz layer is sim-ilar to the one suggested in the literature [23], then the changein distance by increasing the size in the tetraalkylammoniumchain by one carbon atom is roughly equal to the size of oneCH2 unit, taken as ∼1.25 Å [57, 58]. With this value andassuming an exponential decay with a distance for the hetero-geneous rate constant, the data for the reduction (in DMF)yield β=0.56 Å−1 for the reduction of benzonitrile, 0.26 Å−1
for the reduction of nitromesitylene [22], and 0.16 Å−1 for thereduction of p-nitrotoluene [24];3 although the three values arequite scattered, an average of the first two values, β=0.41 Å−1
was taken as a rough estimate (similar values can be found inpropylene carbonate; the reduction of nitromesitylene in thissolvent yields β=0.36 Å−1 [23], but with a rather poor fit).This value is significantly smaller than the value usuallyobtained for saturated alkyl chains in self-assembled mono-layers (∼1 Å−1; [48]), but it is probably more appropriate as itis obtained using data taken in DMF.
Even though the parameter values used for calculating Z0should be regarded as estimates only, the analysis of the datasuggests that the molecules from the first group are reducednonadiabatically (H0
12≈0.042 eV), while the ones in the sec-ond group are probably adiabatic or at least close to adiabatic[H0
12≈0.16 eV; note that this value is close to the upper limitfor an outer-sphere reaction, as defined by IUPAC (GoldBook, http://goldbook.iupac.org/O04351.html; Fig. 2)]. Ifone chooses to compare the double-layer corrected heteroge-neous rate constants, then for the first group, H0
12≈0.17 eVwould be obtained, but for the second group, a very large,rather unrealistic, value ofH0
12≈7.8 eV. This very large value(much larger than typical values of λ) would likely involvespecifically adsorbed reactants [59], while in some cases (e.g.,for p-diacetyl-benzene, which shows a very large double-layereffect [60] or 2-chloro-3-methyl-1,4-naphthoquinone, forwhich related compounds do seem to adsorb onto mercury[61]), this may eventually be imagined; for the other cases, theexperimental data show no evidence of it. Moreover, hetero-geneous rate constants for redox couples for which there isevidence for strong interaction with mercury electrodes (andthus presumably a significant contribution of an inner-spheremechanism), such as the reduction of O2 ([62–64]) and organ-ic sulfides ([65–67]) are (comparatively) more than an order ofmagnitude larger than those for group II molecules (Table 2).For example for O2 reduction in DMF (λ=1.926 eV), thecyclic voltammetry data in Dietz et al. [68] and Magno et al.[69] yield a value ks=0.017 cm/s (this value should be
regarded rather as a low-value estimate, ohmic compensationissues in the original references being unclear), while for thereduction of benzyl phenyl sulfide (λ=2.294 eV), ks=8.87×10−4 cm/s ([70]; see Fig. 3).
Conclusions
A quantum computational procedure, implemented in thecommercial quantum chemistry package Gaussian 03, usedfor estimating reorganization energies in solution, is checkedagainst experimental data of heterogeneous rate constants forthe electrochemical reductions involving neutral substancesof a wide variety of redox reactions in dimethylformamideon mercury electrodes. The calculated values for the reorga-nization energies are fully consistent with the experimentaldata, showing that the procedure can be used for estimatingreliable values for the reorganization energies for outer-sphere electrochemical reactions. The calculated and exper-imental values are used to divide the analyzed molecules intotwo groups: group I, for which the heterogeneous electrontransfer is likely nonadiabatic, and group II (having oxygen-containing, unhindered polar groups), for which the hetero-geneous electron transfer is adiabatic or close to adiabatic.
References
1. Costentin C, Robert M, Savéant J-M (2010) Reorganization ener-gies and pre-exponential factors in the one-electron electrochemicaland homogeneous oxidation of phenols coupled with an intramo-lecular amine-driven proton transfer. Phys Chem Chem Phys12:13061–13069
2. Costentin C, Robert M, Savéant J-M (2007) Adiabatic and non-adiabatic concerted proton-electron transfers. Temperature effectsin the oxidation of intramolecularly hydrogen-bonded phenols. JAm Chem Soc 129(32):9953–9963
3. Suwatchara D, Rees NV, Henstridge MC, Laborda E, Compton RG(2012) Experimental comparison of the Butler–Volmer and Mar-cus–Hush–Chidsey formalisms of electrode kinetics: the reductionof cyclooctatetraene at mercury hemispherical electrodes via cyclicand square wave voltammetries. J Electroanal Chem 665:38–44
4. Suwatchara D, Rees NV, Henstridge MC, Laborda E, Compton RG(2012) Molecular insights into electron transfer processes via var-iable temperature cyclic voltammetry. Application of the asymmet-ric Marcus–Hush model. J Electroanal Chem 685:53–62
5. Laborda E, Batchelor-McAuley C, Suwatchara D, Henstridge MC,Compton RG (2013) On the adiabaticity of electrode processes:effect of the supporting electrolyte cation on the kinetics ofelectroreduction of 3-nitrophenolate. J Electroanal Chem 694:30–36
6. Batchelor-McAuley C, Laborda E, Henstridge MC, Nissim R,Compton RG (2013) Reply to comments contained in “Are thereactions of quinones on graphite adiabatic?,” by N.B. Luque, W.Schmickler [Electrochim. Acta xx (2012) yyy]. Electrochim Acta88:895–898
7. Cossi M, Barone V (2000) Separation between fast and slowpolarizations in continuum solvation models. J Phys Chem A104(46):10614–10622
3 The data for tetramethyl and tetraethylammonium ions were not includ-ed, to minimize the influences from specific adsorption and ion pairing.
J Solid State Electrochem
8. Cossi M, Barone V (2000) Solvent effect on vertical electronictransitions by the polarizable continuum model. J Chem Phys112(5):2427–2435
9. Tomasi J, Mennucci B, Cammi R (2005) Quantum mechanicalcontinuum solvation models. Chem Rev 105(8):2999–3094
10. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA,Cheeseman JR, Montgomery JA TV Jr, Kudin KN, Burant JC,Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, CossiM, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M,Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, NakajimaT, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, HratchianHP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R,Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C,Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P,Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, StrainMC, Farkas O, Malick DK, Rabuck AD, Raghavachari K,Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, CioslowskiJ, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I,Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY,Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W,Wong MW, Gonzalez C, Pople JA (2004) Gaussian 03 revisionE01. Gaussian, Inc., Wallingford
11. Böes ES, Livotto PR, Stassen H (2006) Solvation of monovalentanions in acetonitrile and N,N-dimethylformamide: parameteriza-tion of the IEF-PCM model. Chem Phys 331(1):142–158
12. Batsanov SS (2001) Van der Waals radii of elements. Inorg Mater37(9):871–885
13. Shiratori K, Nobusada K (2008) Development of a finite-temperature density functional approach to electrochemical reac-tions. J Phys Chem A 112(42):10681–10688
14. Klamt A (2007) Communication to the Computational ChemistryList. www.ccl.net/cgi-bin/ccl/message-new?2007+11+20+009
15. Hush NS (1968) Homogeneous and heterogeneous optical andthermal electron transfer. Electrochim Acta 13(5):1005–1023
16. Marcus RA (1965) On the theory of electron-transfer reactions. VI.Unified treatment for homogeneous and electrode reactions. JChem Phys 43(2):679–701
17. Hale JM (1971) The rates of reactions involving only electrontransfer, at metal electrodes. In: Hush NS (ed) Reactions of mole-cules at electrodes. Wiley, New York, pp 229–257
18. Medvedev IG (2000) Non-local effects in the kinetics of heteroge-neous charge transfer reactions. J Electroanal Chem 481(2):215–221
19. Costentin C, Louault C, Robert M, Roge V, Saveant J-M (2012)Reorganization energy and pre-exponential factor from temperature-dependent experiments in electron transfer reactions. A typical ex-ample: the reduction of tert-nitrobutane. Phys Chem Chem Phys14:1581–1584
20. Dietz R, Peover ME (1968) Stereochemical effects in the electro-chemistry of some hindered stilbenes in dimethylformamide. Dis-cuss Faraday Soc 45:154–166
21. Kojima H, Bard AJ (1975) Determination of rate constants for theelectroreduction of aromatic compounds and their correlation with ho-mogeneous electron transfer rates. J Am Chem Soc 97(22):6317–6324
22. Ahlberg E, Parker VD (1983) The effect of tetraalkylammoniumions on the heterogeneous charge-transfer kinetics for the reductionof benzonitrile and dinitromesitylene in Dmf. Acta Chem Scand B37(8):723–730
23. Fawcett WR, Fedurco M, Opallo M (1992) The inhibiting effects oftetraalkylammonium cations on simple heterogeneous electron transferreactions in polar aprotic solvents. J Phys Chem 96(24):9959–9964
24. Kakutani T, Kinoshita H, Senda M (1974) Determination of kineticparameters of electroreduction of nitrobenzenes at mercury elec-trode in dimethylformamide by radio frequency polarographicmethod. Rev Polarogr 20(1–3):15–26
25. Petersen RA, Evans DH (1987) Heterogeneous electron transferkinetics for a variety of organic electrode reactions at the mercury-
acetonitrile interface using either tetraethylammonium perchlorateor tetraheptylammonium perchlorate electrolyte. J ElectroanalChem 222(1–2):129–150
26. Avaca LA, Bewick A (1973) Ion-pairing effects in the electroreductionof aromatic compounds. J Electroanal Chem 41(3):405–410
27. Yeager E, Conway BE, Kuwana T, Strojek JW, Von Benken W,Hush NS, Winograd N, Srinivasan VS, Peover ME, Grabowski ZR,Balasiewicz MS, Albery, Zuman P, Nieboer H, Czochralska B,Jordan J, Hoytink GJ, Parsons R, Bard AJ (1968) General discus-sion. Discuss Faraday Soc 45:175–186
28. Fawcett WR, Ikeda BM, Sellan JB (1979) Double layer structure atthe mercury/dimethylformamide interface. Can J Chem 57(17):2268–2277
29. Gennett T, Weaver MJ (1985) Double-layer effects on electrochem-ical kinetics in nonaqueous media. Dependence upon reactantcharge for some metallocene redox couples. J Electroanal Chem186(1–2):179–190
30. Belèn Meneses A, Antonello S, Arévalo MC, Maran F (2006)Double-layer correction for electron-transfer kinetics at glassy carbonand mercury electrodes in N,N-dimethylformamide. Electroanal18(4):363–370
31. Peover ME, Powell JS (1969) Dependence of electrode kinetics onmolecular structure nitro-compounds in dimethylformamide. JElectroanal Chem 20(3):427–433
32. Kakutani T,White CK, Rieke RD (1975) Effects of formal charge on theheterogeneous electron transfer rate at a mercury–dimethylformamideinterface for a series of organic salts. J AmChemSoc 97(25):7226–7230
33. Hammerich O, Parker VD (1981) Reactions of organic sulfurcompounds at electrodes. Sulfur rep 1(6):317–390
34. Battistuzzi R, Borsari M, Dallari D, Gavioli G, Tavagnacco C, CostaG (1994) Electrochemistry of 4,6-dimethyl-2-thiopyrimidine and4,6-dimethyl-1-phenyl-2-thiopyrimidine in dimethylformamide. JElectroanal Chem 368(1–2):227–234
35. FalsigM,LundH (1980) Electrochemical synthesis of tetrathioethylenes.Acta Chem Scand B 34:591–595
36. Wilke CR, Chang P (1955) Correlation of diffusion coefficients indilute solutions. AlChE J 1(2):264–270
37. Neudeck A, Dittrich J (1989) Zur Bestimmung von Geschwindig-keitskonstanten heterogener Elektronentransferreaktionen aus zyklischenVoltammogrammen. Z Chem 29(1):35–36
38. Lavagnini I, Antiochia R, Magno F (2004) An extended method forthe practical evaluation of the standard rate constant from cyclicvoltammetric data. Electroanal 16(6):505–506
39. Bastida RM, Brillas E, Costa JM (1987) Electrohydrodimerizationof 4,4-dimethyl-2-cyclohexen-1-one in dimethylformamide on amercury electrode. J Electroanal Chem 227(1–2):67–75
40. Núñez-Vergara LJ, Bollo S, Atria AM, Carbajo J, Gunckel S,Squella JA (2002) Free radical formation and characterization ofnitroanisole isomer reduction in different media. J Electrochem Soc149(10):E374–E382
41. Oth JFM, Müllen K, Königshofen H, Wassen J, Vogel E (1974) Thedianion of heptalene. Helv Chim Acta 57(8):2387–2398
42. Stradins J, Gavars R, Baumane L (1983) Intermediate products ofelectrochemical reduction of nitrofurans in aprotic media. ElectrochimActa 28(4):495–500
43. Islam N-u, Sopher DW, Utley JHP (1987) Electro-organic reactions.Part 27. The mechanism of cathodic cleavage of activated esters.Oxalates, squarates, and oxamates. Tetrahedron 43(5):959–970
44. Duty RC, Garrosian M (1983) Polarographic and potentiostaticreduction of carbodiimides in nonaqueous solvents. J ElectrochemSoc 130(9):1848–1851
45. Garrossian M, Khosravi M, Khayatian GR (1996) Polarographicand potentiostatic reduction of carbodiimides: a mechanistic study.J Sci Ind Res Iran 7(3):150–155
46. Mirkin MV, Bard AJ (1992) Simple analysis of quasi-reversiblesteady-state voltammograms. Anal Chem 64(19):2293–2302
J Solid State Electrochem
47. Savéant J-M (2006) Elements of molecular and biomolecular elec-trochemistry. Wiley Interscience, New York
48. Feldberg SW, Sutin N (2006) Distance dependence of heteroge-neous electron transfer through the nonadiabatic and adiabatic re-gimes. Chem Phys 324(1):216–225
49. Nazmutdinov RR, Rusanova MY, VanderPorten D, Tsirlina GA,Fawcett WR (2009) Toward the reactivity prediction: outersphereelectroreduction of transition-metal ammine complexes. J PhysChem C 113(7):2881–2890
50. Luque NB, Schmickler W (2013) Are the reactions of quinones ongraphite adiabatic? Electrochim Acta 88:892–894
51. Mattheiss LF, Warren WW Jr (1977) Band model for the electronicstructure of expanded liquid mercury. Phys Rev B 16(2):624–638
52. Chan T, Ballentine LE (1972) Electronic structure of liquid metalsfrom nonlocal energy-dependent model potentials. Can J Phys50(8):813–820
53. Chan T, Ballentine LE (1971) The density of states and opticalconductivity of liquid mercury. Phys Lett A 35(5):385–386
54. Grimvall G (1975) The heat capacity of liquid metals. Phys Scr11(6):381
55. Bose SK (1999) Electronic structure of liquid mercury. J PhysCondens Matter 11(24):4597
56. JohnW,KellerW (1979) Density of states of expanded liquidmercuryan effective medium approach. Phys Status Solidi B 94(2):603–609
57. Laridjani M, Leboucher P (2009) The structural dilemma of bulkpolyethylene: an intermediary structure. PLoS ONE 4(7):e6228
58. Smalley JF, Finklea HO, Chidsey CED, Linford MR, Creager SE,Ferraris JP, Chalfant K, Zawodzinsk T, Feldberg SW, Newton MD(2003) Heterogeneous electron-transfer kinetics for ruthenium andferrocene redox moieties through alkanethiol monolayers on gold. JAm Chem Soc 125(7):2004–2013
59. Schmickler W (1986) A theory of adiabatic electron-transfer re-actions. J Electroanal Chem 204(1–2):31–43
60. Garreau D, Saveant JM, Tessier D (1979) Potential dependence ofthe electrochemical transfer coefficient. An impedance study of thereduction of aromatic compounds. J Phys Chem 83(23):3003–3007
61. Pospíšil L, Glezer V (1983) Electrochemistry of intramolecularcharge-transfer complexes derived from 1,4-naphthoquinone: partI. Rate constants and adsorption on mercury in dimethylformamide.J Electroanal Chem 153(1–2):263–274
62. Peover ME, White BS (1966) Electrolytic reduction of oxygen inaprotic solvents: the superoxide ion. ElectrochimActa 11(8):1061–1067
63. Sudan Saha M, Che Y, Okajima T, Kiguchi T, Nakamura Y, TokudaK, Ohsaka T (2001) Current oscillation behavior of the O2/O2
− redoxcouple at a HMDE in non-aqueous aprotic media. J ElectroanalChem 496(1–2):61–68
64. Morrison MM, Roberts JL, Sawyer DT (1979) Oxidation-reductionchemistry of hydrogen peroxide in aprotic and aqueous solutions.Inorg Chem 18(7):1971–1973
65. Persson B, Nygård B (1974) Polarographic behaviour of diphenyldisulphide and some related compounds in aprotic solvents. JElectroanal Chem 56(3):373–383
66. Moiroux J, Deycard S, FleuryMB (1983) Electrochemical behaviorof 1,2-dithiole-3-thiones. J Electroanal Chem 146(2):313–331
67. Pragst F (1981) Electrogenerated chemiluminescence in mechanis-tic investigations of electroorganic reactions: part III. Reduction ofsome disulfides at the dropping mercury electrode. J ElectroanalChem 119(2):315–330
68. Dietz R, Forno AEJ, Larcombe BE, Peover ME (1970) Nucleophilicreactions of electrogenerated superoxide ion. J ChemSocB 0:816–820
69. Magno F, Seeber R, Valcher S (1977) A study of the reactionkinetics of electrogenerated superoxide ion with benzylbromide. JElectroanal Chem 83(1):131–138
70. Severin MG, Arevalo MC, Farnia G, Vianello E (1987) Homoge-neous and heterogeneous electron transfer to benzylphenylsulfide. JPhys Chem 91(2):466–472
71. Hoytink GJ (1969) Heterogeneous electron transfer to aromatichydrocarbon molecules. Surf Sci 18(1):1–10
72. Andrieux CP, Delgado G, Savéant JM, Su KB (1993) Improvementand estimation of precision in cyclic voltammetry: thermodynamicand kinetic determinations in chemically reversible systems. JElectroanal Chem 348(1–2):107–121
73. Fawcett WR, Jaworski JS (1983) Effect of solvent on the kinetics ofelectroreduction of organic molecules in nonaqueous media. J PhysChem 87(15):2972–2976
74. Amatore C, Anne A, Florent JC, Moiroux J (1986) Mechanism ofthe electrochemical reduction of hydroxyiminoanthraquinones inDMF. J Electroanal Chem 207(1–2):151–160
75. Ahlberg E, Svensmark B, Parker VD (1980) Precise electrodepotential measurements by cyclic voltammetry and the applicationto the measurement of heterogeneous charge transfer rates. ActaChem Scand B 34:53–57
76. Gennaro A, Romanin AM, Severin MG, Vianello E (1984) Radical–radical coupling in the electrochemical reduction of isophthalonitrile.J Electroanal Chem 169(1–2):279–285
77. Baránski A, FawcettWR (1979)Medium effects in the electroreductionof cyanobenzenes. J Electroanal Chem 100(1–2):185–196
78. Gennaro A, Maran F, Maye A, Vianello E (1985) C-CN bond cleav-age in the electrochemical reduction pattern of benzenedicarbonitriles.J Electroanal Chem 185(2):353–363
79. Harman AR, Baranski AS (1988) Convolutive voltammetry withmicroelectrodes. Can J Chem 66(5):1036–1046
80. Smith DE, Bauer HH (1971) Recent developments in alternatingcurrent polarography. C R C Crit Rev Anal Chem 2(2):247–343
81. Allred AL, Bush LW (1968) Electron spin resonance studies ofsilicon- and germanium-substituted anion radicals. J Am Chem Soc90(13):3352–3360
82. Grzeszczuk M, Smith DE (1984) Electrochemical investigations oftetraphenylethylene in dimethylformamide using Fourier transformfaradaic admittance measurements (FT-FAM). J Electroanal Chem162(1–2):189–206
83. Grzeszczuk M, Smith DE, Geiger WE (1983) Structural consequencesof electron transfer reactions. 8. Elucidation of isomerizationmechanismof the radical anion of (η4-cyclooctatetraene)cyclopentadienylcobaltwith FFT-faradaic admittance measurements. J Am Chem Soc105(7):1772–1776
84. Aalstad B, Parker VD (1982) Normalized potential sweepvoltammetry: part III. Elimination of the effect of uncompensatedresistance and the application to heterogeneous kinetics of rapidcharge-transfer processes. J Electroanal Chem 133(1):33–44
85. Ahlberg E, Parker VD (1981) Quantitative cyclic voltammetry: partI. Acquisition of precise electrode potential data during measure-ments in resistive media. J Electroanal Chem 121:57–71
86. Vincent ML, Peters DG (1992) Electrolytic cleavage of acyclic andcyclic aromatic esters: case studies of the reductions of benzylbenzoate and phthalide. J Electroanal Chem 327(1–2):121–135
87. Sanecki P, Skitał P,Kaczmarski K (2006) Numericalmodeling of ECE-ECE and parallel EE-EE mechanisms in cyclic voltammetry. Reduc-tion of 1,4-benzenedisulfonyl difluoride and 1,4-naphthalenedisulfonyldifluoride. Electroanal 18(10):981–991
88. Huebert BJ, Smith DE (1971) Stereochemical effects in organicelectrochemical kinetics: part 1. D.C. and A.C. polarographic studyof cyclooctatetraene. J Electroanal Chem 31(2):333–348
89. Allendoerfer RD, Rieger PH (1965) Electrolytic reduction ofcyclooctatetraene. J Am Chem Soc 87(11):2336–2344
90. Tulyathan B, Geiger WE Jr (1980) Structural consequences ofelectron-transfer reactions: part IV. Kinetics of the reduction ofcyclooctatetraene iron tricarbonyl. J Electroanal Chem 109(1–3):325–331
91. Ouziel E, Yarnitzky C (1977) Electrochemical reduction ofcamphorquinone in DMF in the presence of a proton donor. JElectroanal Chem 78(2):257–270
J Solid State Electrochem
92. GálaM, Sokolová R, KolivoškaV,Morovská A, TuroňováAM,HívešJ (2011) Metronidazole radical anion formation studied by means ofelectrochemical impedance spectroscopy. Collect Czechoslov ChemCommun 76(12):1607–1617
93. Abd-El-Aziz AS, Baranski AS, Piórko A, Sutherland RG (1988) Elec-trochemical studies of η5-cyclopentadienyliron hexafluorophosphates ofη6-substituted arenes and η6-heterocycles. InorgChimActa 147(1):77–85
94. Jensen BS, Ronlán A, Parker VD (1975) Reactions of aromaticanion radicals and dianions. Part III. Electrolyte and solvent effectson the kinetics of electron transfers to cyclooctatetraenes. ActaChem Scand B 29:394–396
95. Bethell D, Parker VD (1982) Intermediates in the decomposition ofaliphatic diazo-compounds. Part 17. Formation and reaction ofdiazodiphenylmethane anion radical in solution. J Chem Soc PerkinTrans 2(7):841–849
96. Glezer V, Stradins J, Friemanis J, Baider L (1983) The mechanismof electrochemical reduction of intramolecular charge-transfercomplexes derived from 1,4-naphthoquinone. Electrochim Acta28(1):87–95
97. Retzlav KJ, Baumgärtel H (1987) The influence of a faradaicprocess on the double-layer capacity. J Electroanal Chem 229(1–2):181–190
98. Brillas E, Farnia G, Severin MG, Vianello E (1988) Role of thecarboxy proton in heterogeneous electron transfer to o-nitrobenzoicacid. J Chem Soc Perkin Trans 2(7):1173–1178
99. Geiger WE, Rieger PH, Tulyathan B, Rausch MD (1984) Structuralconsequences of electron-transfer reactions. 10. Evidence for bend-ing of a nitrosyl group during one-electron reduction ofcyclopentadienyl metal nitrosyl compounds. J Am Chem Soc106(23):7000–7006
J Solid State Electrochem
