11. Electrochemical Redox Potentials and Comproportionation/Disproportionation .sfn When people report Eox, Ered, or E½, the number quoted probably does not have the thermodynamic significance that a true formal potential (E°) is supposed to have. It was difficult to tell whether an electron transfer was reversible or not using polarography, and now people usually use cyclic voltammetry (CV, introduced by Shain in 1961), where it is easy to tell. Because some reserve E° for values determined under experimentally unobtainable “standard conditions”, formal potentials are sometimes called E°’ or Ef. E° may be thought of as the potential at which the rate of electron transfers to and from the electrode are the same. In practice E° values for couples for which both oxidation states are long-lived come from averaging the reduction and oxidation peak potentials in a cyclic voltammogram: E° = (Ep

ox+Epred)/2. When a reaction is electrochemically reversible (scan rate small compared to the

heterogeneous electron transfer rate at the electrode surface) Epox - Ep

red = 57 mV for a single electron transfer at 25 °C. Errors in determining E±’ remain small when (Ep

ox - Epred) is under about

100 mV; Epred + 30 mV < E± < Ep

ox –30 mV.1 The CV shown breaks the convention that potential scans should be to more negative potential and

reduction current should be plotted up (it instead uses the IUPAC convention). It is recommended to measure ∆E± from ferrocene0/+ or bis(biphenyl)-chromium0/+ (that is, to use an internal standard in CV experiments),2 and to report the E° vs ferrocene employed if another reference electrode is reported. Although by convention electrochemical reactions were written as if they were reductions, oxidized form first, E(A0,A+) means exactly the same as E(A+,A0). E° is the potential at which electrons transfer to and from the electrode at the same rate, and I have paid no attention to this convention. Although E± values in acetonitrile with tetrabutyl-ammonium perchlorate (TBAP) as supporting electrolyte appear to be the most frequently reported

ones for organic compounds, many other reference electrodes and supporting electrolytes are also used. Experimental E±’ values depend slightly on the supporting electrolyte employed (usually ignored because there is no way to account for this using thermodynamic cycles). All E± values determined will depend slightly on supporting electrolyte, details of the cell construction and liquid junction potential. Data taken on a single electrochemical apparatus under exactly the same conditions should be used if the formal potentials are to be compared accurately. A newer electrochemical technique is called a square wave voltammogram, which produces a peak at the position half-way between the cyclic voltammetry peaks, so they are easier to interpret, which is valuable when complex, overlapping waves are present:

OMe

OMeOMe

OMe

2 Superimposed cyclic and square wave voltammograms of the compound at the right.3

Potential (V)

Current (i)

Eo' =

Epox

Epred

(more positive)

Oxidation

0

0.057 V if completely

electrochemically reversible

iox

ired

iox = ired if

completely

reversible

∆Ep

(Epox

+Epred

)/2

chemically

2

In comparing E± values it is often necessary to convert values from one reference electrode to another Amatore and Kochi4 give as standard conversion factors used for converting experimental measurements to this number: (An Ag/Ag+ reference electrode potential actually depends upon the

E(NHE) = E(SCE) + 0.24 = E(AgCl/Cl) + 0.28 = E(Ag/AgClO4) + 0.66 = E(Ag/AgI) + 0.75

the details of its construction). Biochemists work in water and use exclusively NHE values, but they are not popular with people who work in non-aqueous solvents, because they cannot be directly measured. Bordwell5 reports Ep values measured relative to ferrocene (presumably in DMSO), which are converted to NHE values by subtracting 0.125 V [E±’(ferrocene, NHE) = +0.145 using the +0.24 conversion quoted above4 and 0.395 vs SCE for ferrocene]. When both Ep

ox and Epred are not observed because of rapid radical ion decomposition, the redox

wave is referred to as being chemically irreversible. It is difficult to tell whether a chemically irreversible wave is electrochemically reversible or not, but the former is often routinely (and implicitly) assumed. Even the position of the peak potential relative to E±’ is in principle not known. There is a 30 mV shift to lower Ep

ox for each power of 10 in the rate of the following reaction destroying a radical cation, but there also is a shift in the opposite direction if the rate constant for heterogeneous electron transfer, ks, is slow relative to the scan rate. Most work ignores consideration of ks. Ep

ox values will move if the scan rate is changed for a chemically irreversible redox wave, and they are sometimes very hard to reproduce, even in the same laboratory. However, if the only cause for irreversibility is rapid following reactions, and the reaction products do not foul the electrode surface, reproducible numbers that can be quite useful are observed. Amatore and Kochi4 showed that this is true for 18 alkyl substituted benzenes under conditions where their oxidations are irreversible, CF3CO2H containing (CF3CO)2O. A plot of Ep

ox(CH3CN) versus E±’(TFA) is a good straight line having a slope of 0.94, intercept 0.10 and average vertical deviation of the Ep

ox points from the linear regression of 49 mV. From theoretical work by Nadjo and Saveant,6 Ep(Ar) = E∞’(Ar) - 0.030log[kRT/(Fv)] + C where C depends on the exact nature of the follow-up decomposition steps, but is close to 60 mV.4 E±’ can be reasonably estimated from the peak potential if the reason for irreversibility is only rapid following reactions (hard to know!):6

(Ep - 0.18 V) < E∞’ < (Ep - 0.29 V)

[using following reaction k values of < 1012 s-1, heterogeneous ET rate constants ks in the range 10-3 to 10 cm s-1, α near 0.5, D near 10-5 cm2 s-1, and scan rate v in the range 0.050 to 100 V s-1.] Wayner, McPhee, and Griller7 have used pulsed photolytic radical generation combined with a phase-sensitive voltammetry experiment to measure E1/2 values to within an estimated 0.1 V of E±’ values for 19 R3C·,R3C

+ couples. They also use the assumption that only the entropy for hydrogen atom formation needs to be considered, and use a –8 kcal/mole T∆S±’ term in converting to bond dissociation energy. They explicitly point out the assumption that everyone uses that BDE is independent of phase. Very fast scan rates can be used with microelectrodes, but the current potential curves are quite different from cyclic voltammograms. The best source of redox potentials up to 1996 is the review of Connelley and Geiger, which reports exclusively values relative to ferrocene.8 Values relative to the saturated calomel electrode (SCE) are common in the organic literature. E° values from equilibration of photogenerated known E° radical cations with unknown ones that cannot be measured electrochemically are starting to become available,9a including C3 to C12 N-alky primary amines (E° = 1.49-1.52 vs SCE in MeCN).9b

3

Some E∞’ Values vs SCE Ferrocenes

(0/1) 10 Substituted Benzenes(0/1) 4,8

Cp2Fe +0.395 PhH 2.62 1,2Me2 2.16 1,2,4Me3 1.905(5) Cp’2Fe +0.281 PhMe 2.25 1,3Me2 2.11 1,2,4,5Me4 1.75,1.753(4) CpCp*Fe +0.124 PhEt 2.27 1,4Me2 2.01 Me5 1.71 Cp*

2Fe –0.109 PhiPr 2.32 1,3,5Me3 2.02 Me6 1.58 PhtBu 2.21

Hetero-substituted8

S

S

dithiirane

0/+

+1.20

S

N0/+

N-Me-thiazine

+0.70

S

S S

S

+0.33

NC

NC CN

CN

TCNE

+0.24

-/0

0/+

N

N0/+

Me2-phenazine

0.14

Me2N NMe2

TMPD

0/+

+0.12

N N+ +

Methyl Viologen

or paraquat

-0.45

+/2+

O O

benzoquinone

-0.54

-/0

-/0

O O

Cl

Cl Cl

Cl

Chloranil

O

Ph

Ph

Ph +

Ph3-pyrylium

-0.29+0.02 Fused-Ring Aromatics

(0/+) 11,12,13

biphenyl

-

1.91, 1.92

triphenylene

1.83

1.68,1.55

naphthalene

1.62,1.54

fluoranthene

1.61

phenanthrene

1.83

1.59,1.50

chrysene

1.64

1.45,1.35

benzanthr.anthracene 1234-dibenzan.

1.44

1.37,-

1.37

1.20,1.09

pyrene

1.36

1.22,1.16

acenaphth.

1.31,-

perylene

1.06

0.97,0.85

tetracene

0.87,0.77

Parker11

ref.12,13

- -

-

- - -Eo'

E1/2

Parker11

ref.12,13

Eo'

E1/2

ref. 9a Eo 1.953(6)

Alkyl Radical

(0/+) 7

HCH2

CHMe

CMe2

0.76

0.73

0.37

0.16

H

0.35

0.09

O

O

H 0.31

O

OO

H 0.31

O

O

H -0.08

iPrOMe

Me

MeOH

H

-0.10

-0.24

O

O-0.34

H

OH -0.35

EtOH

Me-0.45

NBz2

H

NH2

Me

-0.92

-0.85

N CMe

Me H

H

N CMe

Me Me

H

-1.03

-1.12Me3C

4

Redox potentials versus Ferrocene (mostly from ref. 8)

1.36

3

1.14

NBr

Br

0.92

Br

NBr

2+/+

0.87

Br

3+/2+

0.86

Fe

"Very strong" oxidants (Eo > +0.8 vs Fc)

NN S

S

3

1.00 0.87Ce+4/+3

1.30

Ce+4/+3

0.88Cl5C6)3N +/0

1.72

NCC6H5)3N +/0

1.08

3

N O N O

thianthrene"Phen3Ru"

1.34

(Science 2000, 289,101)

N

BrBr

BrBr

Br

Br

Ph

(MeCN) (MeCN) (MeCN)

Ru

(MeCN) (MeCN)

(CH2Cl2) (MeCN)(HClO4) (H2O)(CH2Cl2) (MeCN)

(CH2Cl2)

+/0+/0 +/0 +/0

+/0 +/0

"Magic green"

Note that Ce4+/3+, NO+/0 and Ag+/0 have E°’ values that are very sensitive to solvent. Ag+ can be rendered a more effective oxidant by coupling the ET with precipitation of AgX, which effectively removes it from the equilibrium. C60

0/-, which is insoluble in the solvents usually used for electrochemistry, is even more sensitive to solvent.

3

0.70

N+/0Br

0.55

3+/2+

0.66

33

0.49

+/0

0.27

SMo

S

S

SF3C

F3C

CF3

CF3

+/0

"Strong" oxidants (Eo +0.2-+0.8 vs Fc)

NN

Mo(tfd)3

Fe

Ac

Ac

0.40

Cu(O3SCF3)20/-

0.40

Fe

0.33

Ac

PtCl6 2-/-

Ni(tfd)3

0.31

Ag +/0

0.65

Ag +/0

0.41

N+/0Me

+/0

0.56

SNi

S

S

SF3C

F3C

CF3

CF3

Fe(bipy)3

N O

(MeCN)(MeCN) (MeCN)(CH2Cl2)

(MeCN)

Fe

(MeCN)

(MeCN) (MeCN) (H2O)

Cu(OTf)2

(CH2Cl2) (THF)(DMF)

OMe

OMe

0/+

0.71(MeCN)

Org.Syn. 2005,82,1"Magic Blue"

"Mild oxidants/ Weak reductants" (Eo -0.5-+0.2 vs Fc)

0.16 0.13

Fc

0.00(all)

Ph3C +/0

-0.11

trityl

Ag +/0

0.18

(acetone)

0.04

Ag +/0

-0.27

+0.18(MeCN) +0.07(MeCN)

0/-

-0.14(MeCN)

2I-TCNQ

-0.30(MeCN)

0/-

N+/0MeO OO

Cl Cl

NC CN

+/0

FeNC

NC

CN

CN

NC

NC CN

CN

3

0/-

TCNE

(MeCN) (MeCN)(MeCN)

Cl2 2Cl- I22Br-Br2

DDQ

(MeCN)

(these are not reversible single electron transfers!)

(MeCN)

An3N

5

Redox potentials versus Ferrocene (mostly from ref. 8)

+/0

Cp*2Fe

-0.59

tropylium

-0.65

C60 0/-

"Weak oxidants/ Mild reductants" (Eo -1.5 to -0.5 vs Fc)

-0.98

(PhMe-MeCN)

-1.15

+/0

-1.33-1.32 -1.70

+/0 +/0 +/0

FeCr CoCr Cr

(MeCN) (THF)(CH2Cl2) (CH2Cl2)(CH2Cl2)very sensitive(MeCN)

0/-

"Very strong reductants" (Eo < -2.4 vs Fc)

-2.47

(glyme)

-2.60

Li+/0

-2.64

Na +/0

-3.04

0/-

-2.95 -3.10

Li(Hg)

(H2O) (NH3) (THF) (DMF) (THF)

"Strong reductants" (Eo -2.4 to -1.5 vs Fc)

-1.91 -2.01

Co

Cp*2Co

Cr +/0+/0

-2.17

O

Ph Ph

-2.30

0/- 0/-

-2.26

Na +/0

-2.25

Fe

-2.36

Na(Hg)+/0

(non-aq.)

K +/0

-238-2.30

+/0

(THF) (DMF) (THF) (THF)(NH3)(NH3)(DMF)(MeCN)

benzophenone acenaphth.

6

Comproportionation and Disproportionation Here these terms refer to electron transfer equilibria (shown for oxidations):

M0 + M2+2M+ Kcomp =

[M+]2

[M0][M2+]Kdisp =

[M+]2

[M0][M2+]Kcomp

Kdisp Signs are a big headache here, and some people talk about comproportionation, while others talk about disproportionation, which are related by Kcomp = 1/Kdisp. For oxidations, Eo

2-Eo1 > 0

makes Kcomp positive, while for reductions, Eo2-E

o1 < 0 makes Kcomp positive. When Kcomp is

very positive, a solution of the radical ion is stable, and when Kcomp is very negative, electron transfer disproportionation makes the solution contain little radical ion, and instead consist mostly of neutral and diion. A compound with Kcomp < 1 is said to have a redox inversion. Electron repulsion usually makes the second electron harder to add or remove than the first, but there are exceptions. Although the Coulomb term for like charges approaching in a solvent is 332.1/rεS kcal/mol when r is in Å, it is difficult to see how this relates to ∆Eo for electron removal/addition because solvation differences are important, and the electron distribution in a molecule makes it hard to guess what r should be. Gas phase values would be much larger, 4.2 eV calculated for anthracene reduction, but some measured ∆Eo values for oxidation in acetonitrile are shown below:

N

NN

N

+0.85 V

NN

N

N

-0.12 V

NN

N

N

-0.045 V

NN

+0.18 V

N N

Eo2 - E

o1 = +1.19 V

A B C D E

The ∆Eo for removal of 1 and 2 electrons of 1.19 V (27.4 kcal/mol) for hydrazine A drops to 0.85 V (19.6 kcal/mol) for tetraaminoethylene B,14 where the nitrogens are farther apart. Using εS = 37.5 for acetonitrile produces an “effective r” of 0.45 Å. Changing solvent changes ∆Eo some, but not very much, and the dielectric constant inside a molecule is not as large as that of the solvent. Using εS = 2 (that of a saturated hydrocarbon) produces an “effective r” of 8.5 Å, clearly too large. The difference is only 0.18 V for the 5-bond-bridged diaminodiene C, but redox inversion occurs for D and a larger one for E.15 This is clearly mostly a steric effect. Although twist about the N-diene and =C–C= single bonds costs little energy in the neutral compound, and twist at the central bond is favorable in the dication to keep the charges apart, in order to delocalize charge to all four nitrogens in the radical cation most effectively, the single bonds must line up so the p-orbitals are not twisted. This costs energy because non-bonded interaction is increased, so Eo

1 is raised and Eo2 lowered by these steric effects. Evans discussed

redox inversions for systems that undergo significant geometry change quite successfully in terms of AM1 calculations and very simple models,16 and recently has reviewed the area in detail.17

How solvation energy influences ∆Eo has recently been discussed in some detail by Savéant and coworkers.18 For carotenoids and other molecules with lots of conjugated double bonds, the coulomb effect gets smaller as the number of double bonds increases. The molecules shown are calculated not to change conformation significantly upon redox; the π systems remaining all trans and planar. The

redox inversion that makes Kcomp < 1 (addition or removal of a second electron easier than the

2

15

5

ββββ-carotene

2

15

5

canthaxanthinO

-0.029

+0.197

-0.085

+0.060

Kcomp < 1

Oxidation Reduction

Eo2 - Eo

1

"redox inversion"

7

first) occurs for oxidation of the hydrocarbon and reduction of the diketone, but the alternate reduction and oxidations, respectively, show the “normal” pattern. This occurs because charge tends to build up on the ends of the pi systems in the carotene dication (tetraalkylalkenes are significantly easier to oxidize than di- and trialkyl ones) and the diketone dianion (enones are significantly easier to reduce than polyenes). In the monoions and “unfavorably charged” diions, the charge is calculated to be more smeared out, the end group atoms having charges more similar to the charges on the middle ones. Solvation occurs most effectively at positions of highest charge, so the solvent stabilization energy is significantly larger for the more charge-localized systems, and it is large enough to turn around the coulomb effect, which is rather small for these large systems. Interestingly, this effect (which occurs for other polyene-connected systems as well, and is no artifact) still could not be calculated properly.18 DFT calculations could only actually be carried out with the 6-31G* basis set for these rather large systems (larger basis sets would be desirable for ions). Even the more economical polarized continuum solvation energy calculations (“COSMO”, the modern versions of dielectric continuum theory) of Tomasi that are presently implemented in Gaussian that treat the molecule as a series of overlapping spheres of various complexity depending on how much time/money is spent, can only be partially implemented. They are in the right direction, but could only be carried out on the gas phase geometry/charge distribution, which gets the solvation effect to be too small to invert the oxidiation potentials. It is pointed out that the charge distribution should change to increase the amount of charge at the ends in solution, and hence the effect, but that it took too long to optimize structures in the presence of the continuum solvent. So even treating the solvent as a continuum was still too expensive to apply to the actual molecules of interest in 2001; computers and electronic structure code get better all the time, of course. 1 Nicholas, A.M. de P.; Arnold, D.R. Can. J. Chem. 1982, 60, 2165. 2 Commission on Electrochemistry "Recommendation on Reporting Electrode Potentials in Nonaqueous Solvents" Pure

Appl. Chem. 1984, 56, 460. 3 Shulka, R.; Lindeman, S. V.; Rathore, R. Org. Lett. 2007, 9, 4091-4. 4 (a) Howell, J.O.; Goncalves, J.M.; Amatore, C.; Klasnic, L.; Wightman, R.M.; Kochi, J.K. J. Am. Chem. Soc. 1984, 106, 3968. (b) Amatore, C.; Lefrou, C. J. Electroanal. Chem. 1992, 325, 239. 5 Bordwell, F.G.; Cheng, J.-P.; Harrelson, J.A., Jr. J. Am. Chem. Soc. 1988, 110, 1229. 6 Nadjo, L.; Saveant, J.-M. J. Electroanal. Chem. 1973, 48, 113. 7 Wayner, D.D.M.; McPhee, D.J.; Griller, D. J. Am. Chem. Soc. 1988, 110, 132. 8 Connelly, N. G.; Geiger, W. E. Chem. Rev. 1996, 96, 877-910. 9 (a) Guirado, G.; Fleming, C. N.; Lingenfelter, T. G.; Williams, M. L.; Zuilhof, H.; Dinnocenzo , J. P. J. Am. Chem.

Soc. 2004, 126, 14086. (b) Bourdelande, J. L.; Gallardo, I.; Guirado, G. J. Am. Chem. Soc. 2007, 129, 2817. 10 Nelsen, S. F.; Wang, Y.; Ramm, M. T.; Accola, M. A.; Pladziewicz, J. R. J. Phys. Chem., 1992, 96, 10654-8. 11 Parker, V. D. J. Am. Chem. Soc. 1976, 98, 98. 12 Abdel-Shabaz, A. A.; Wilkinson, F. J. Phys. Chem. A 2000, 104, 5747. 13 Rathore, R.; Kochi, J. K. Adv. Phys. Org. Chem. 2000, 35, 193-318. Quotes “E±” and IP/EA values for a much wider variety of compounds than those listed. The problem is most of these are polarographic redox potentials for irreversible waves that have an unknown relation to E±. Nevertheless, it is a useful source of especially IP and EA values. On p.4, Fused-Ring Aromatics, I compare ref. 12 and 13 from 2000 with ref. 11 numbers that I believe actually correspond to E±’. You should not assume that a newer quoted number is a better one; you must find where it came from. 14 Hunig, S. Liebigs Ann. Chem. 1975, 1039, 1060, 1090. 15 Fritsch, J. M.; Wingarten, H.; Wilson, J. D. J. Am. Chem. Soc. 1970, 92, 4038. 16 Evans, D. H.; Hu, K. JCS. Faraday Trans. 1996, 92, 3983-90. 17 Evans, D. H. Chem. Rev. 2008, 108, 2113-2144. 18 Hapiot, P.; Kispert, L. D.; Konovalov, V. V.; Savéant, J.-M. J. Am. Chem. Soc. 2001, 123, 6669.