Kinetics and thermodynamics of reversible disproportionation-comproportionation in redox triad oxoammonium cations - Nitroxyl radicals - Hydroxylamines

Article abstract of DOI:10.1002/poc.3392

Kinetics and equilibrium of the acid-catalyzed disproportionation of cyclic nitroxyl radicals R₂NO· to oxoammonium cations R₂NO⁺ and hydroxylamines R₂NOH is defined by redox and acid-base properties of these compounds. In a recent work (J. Phys. Org. Chem. 2014, 27, 114-120), we showed that the kinetic stability of R₂NO· in acidic media depends on the basicity of the nitroxyl group. Here, we examined the kinetics of the reverse comproportionation reaction of R₂NO+ and R₂NOH to R₂NO· and found that increasing in -I-effects of substituents greatly reduces the overall equilibrium constant of the reaction K₄. This occurs because of both the increase of acidity constants of hydroxyammonium cations K_3H+ and the difference between the reduction potentials of oxoammonium cations ER₂NO+/R₂NO· and nitroxyl radicals ER₂NO·/R₂NOH. pH dependences of reduction potentials of nitroxyl radicals to hydroxylamines E_1/3σ and bond dissociation energies D(O-H) for hydroxylamines R₂NOH inwater were determined. For a wide variety of piperidine- and pyrrolidine-1-oxyls values of pK_3H+ and ER₂NO+/R₂NO· correlate with each other, as well aswith the equilibriumconstants K₄ and the inductive substituent constants ωI. The correlations obtained allowprediction of the acid-base and redox characteristics of redox triads R₂NO·-R₂NO+-R₂NOH.

Full text of DOI:10.1002/poc.3392

Research Article
Received: 23 August 2014,
Revised: 12 October 2014,
Accepted: 16 October 2014,
Published online in Wiley Online Library: 5 December 2014
(wileyonlinelibrary.com) DOI: 10.1002/poc.3392
Kinetics and thermodynamics of reversible
disproportionation–comproportionation in
redox triad oxoammonium cations – nitroxyl
radicals – hydroxylamines
Vasily D. Sen’a*, Ivan V. Tikhonovb, Leonid I. Borodinb, Evgeny M. Plissb,
Valery A. Golubeva, Mikhail A. Syroeshkinc and Alexander I. Rusakovb
Kinetics and equilibrium of the acid-catalyzed disproportionation of cyclic nitroxyl radicals R2NO• to oxoammonium cations
R2NO+ and hydroxylamines R2NOH is defined by redox and acid–base properties of these compounds. In a recent work
(J. Phys. Org. Chem. 2014, 27, 114-120), we showed that the kinetic stability of R2NO• in acidic media depends on the basicity
of the nitroxyl group. Here, we examined the kinetics of the reverse comproportionation reaction of R2NO+ and R2NOH to R2NO•
and found that increasing in –I-effects of substituents greatly reduces the overall equilibrium constant of the reaction K4. This
occurs because of both the increase of acidity constants of hydroxyammonium cations K3H+ and the difference between the re-
duction potentials of oxoammonium cations ER2NO+/R2NO• and nitroxyl radicals ER2NO•/R2NOH. pH dependences of reduction poten-
tials of nitroxyl radicals to hydroxylamines E1/3Σ and bond dissociation energies D(O–H) for hydroxylamines R2NOH in water were
determined. For a wide variety of piperidine- and pyrrolidine-1-oxyls values of pK3H+ and ER2NO+/R2NO• correlate with each other,
as well as with the equilibrium constants K4 and the inductive substituent constants σI. The correlations obtained allow prediction
of the acid–base and redox characteristics of redox triads R2NO•–R2NO+–R2NOH. Copyright © 2014 John Wiley & Sons, Ltd.
Keywords: comproportionation; free-energy relationships; hydroxylamines; nitroxyl radicals; oxoammonium salts; reduction potentials
wherein the ratio of concentrations [2][3]Σ / [1]2 = 1 (refer to
Supporting). Direct determination of K4 from the concentrations
INTRODUCTION
of reagents near pHeq cannot be carried out with sufficient accu-
racy as a result of the low rate of achievement of the equilibrium.
Constant K4 may be determined with good accuracy from the data
on the kinetics of disproportionation of 1 in strongly acidic
solutions and comproportionation of 2 and 3 at pH≫ pHeq.[19]
In the previous work,[18] we studied the influence of the struc-
ture of 21 nitroxyl radicals on the kinetics of disproportionation
in aqueous H2SO4 and found a correlation between the basicity
of nitroxyl groups and reduction potentials of oxoammonium
cations E2/1. In the present study, we investigated the kinetics
of comproportionation of eight pairs of oxoammonium 2 and
hydroxyammonium salts 3H+ and for the first time revealed the
effect of substituents and heterocyclic ring structure on the equi-
librium constant K4. pH dependences of reduction potentials of
Nitroxyl radicals 1, oxoammonium cations 2 and hydroxylamines
3 form a stable organic redox triad with efficient one and two
electron transfer (Scheme 1).
Because of these properties, nitroxyl radicals provide, inter
alia, new opportunities in the synthesis of advanced materials,[1]
‘green’ catalysts’ design for the oxidation of organic com-
pounds,[2,3] active materials for organic batteries[4,5] and elec-
tronic devices.[6] Just like their inorganic congener – nitric
oxide[7] – nitroxyl radicals at submillimolar concentrations
exhibit antioxidant and cytoprotective properties,[8,9] but at
concentrations ≥10ꢀ3 M, they increase oxidative stress and exert
a cytotoxic effect on tumor cells.[10–12] Analogously to other
redox active agents,[13] nitroxyl radicals modulate the activity of
clinically used anticancer drugs and may improve their chemo-
therapeutic properties.[14–16]
For effective use of nitroxyl radicals in such applications, it is
important to know the redox and acid–base characteristics of a
wide variety of structures 1–2–3. A convenient way to accom-
plish this is to study in detail the acid catalyzed disproportion-
ation of nitroxyl radicals. For many radicals, this reaction is
~100% reversible[17,18] (Scheme 2).
It includes half reaction of reduction of nitroxyl radicals 1 → 3
and oxoammonium cations 2 → 1, as well as acid–base equilibria
of protonation of radicals 1 and hydroxylamines 3. The overall
equilibrium constant of disproportionation K4 is an integral charac-
teristic, which reflects changes of the values that characterize these
processes, and provides information on the structure–property re-
lations. For each nitroxyl radical, there is the equilibrium value pHeq
* Correspondence to: V.D. Sen’, Institute of Problems of Chemical Physics,
Russian Academy of Sciences, Chernogolovka, 142432, Russian Federation.
E-mail: senvd@icp.ac.ru
a V. D. Sen’, V. A. Golubev
Institute of Problems of Chemical Physics, Russian Academy of Sciences,
Chernogolovka, 142432, Russian Federation
b I. V. Tikhonov, L. I. Borodin, E. M. Pliss, A. I. Rusakov
P.G. Demidov Yaroslavl State University, Yaroslavl, 150000, Russian Federation
c M. A. Syroeshkin
N. D. Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences,
Moscow, 119991, Russian Federation
J. Phys. Org. Chem. 2015, 28 17–24
Copyright © 2014 John Wiley & Sons, Ltd.

V. D. SEN’ ET AL.
resonance (EPR) signal of radicals 1 at 20 °C. EPR measurements were
performed with Adani CMS 8400 spectrometer using glass ampoules of
~1 mm internal diameter. Spectra of all radicals 1 in aqueous solutions
represent triplets of equal intensities. Intensity of central line of the spec-
trum was used as an analytic signal. At [1] ꢁ2 ꢂ 10ꢀ3 M, the intensity of
EPR signal (I) was found to be a linear function of [1]. The unique calibra-
tion curve in coordinates of log [1] = a ꢂ log I + b was used for each
radical. At that, the slope a is close to 1 in all cases.
Scheme 1. Redox–triad oxoammonium cation 2 – nitroxyl radical 1 –
hydroxylamine 3
The chemicals used for buffer solutions preparation were reagent
grade. Buffer solutions were prepared by mixing of 0.1 M glycine or
0.1 M KCl with 0.1 M HCl. In case of 2 + 3H+ pairs with low pK3H+
values, the kinetics of comproportionation was studied in HCl or
HClO4 solutions. Reaction mixtures were prepared by mixing of
10ꢀ1–10ꢀ2 M solutions of 2 and 3H+ in suitable buffer system.
Comproportionation of 2 and 3H+ proceeds with reasonable rate at
pHeq ꢃ pH ꢃ pK3H+ and is first order with respect to both cations.
For each 2 + 3H+ pair, the reaction kinetics was studied for pH inter-
val wider than 0.5 pH units. Because the consumption of one mole
of 2 is accompanied by the formation of two moles of 1, the current
concentration of 2 is equal to [2] = [2]0 ꢀ 0.5[1]. At [3H+]0 ≫ [2], the
processing of the experimental data was performed in the coordinates
of the pseudo-first-order kinetic equation:
Scheme 2. Acidity-dependent reversible disproportionation–comproportionation
in redox triad 1–2–3
nitroxyl radicals E1/3Σ and bond dissociation energies D (O–H) for
hydroxylamines 3 in water were determined. The linear free-
energy relationships between the reduction potentials E2/1
,
È
À
ÁÉ
ln ½2ꢄ0= ½2ꢄ0–0:5½1ꢄ ¼ kef
t
dissociation constants of hydroxyammonium cations K3H+ and
the equilibrium constant K4 were found. For the radicals of piper-
idine and pyrrolidine series, values of pK3H+ and E2/1 show good
correlations with the inductive substituent constants σI.
where [2]0 is initial concentration of the oxoammonium salt and [1] is current
concentration of radical 1. Effective rate constants kef are given in Table S1.
Data on the kinetics of disproportionation of radicals[18] were supple-
mented by the results for 1f, i. The obtained k02 / K1H+ values are listed in
Table 1. Estimated pK1H+ ( 0.3) values were found to be ꢀ7.0 (1f) and ꢀ8.4 (1i).
The pK3H+ values (refer to Table 1) were determined by potentiometric
titration of 3H+ salts according to Albert and Sergeant.[23] Initial concentra-
tions of 3H+ salts were 0.010–0.015 M. Titration was performed with 0.2 N
NaOH carbonate-free solution in an argon atmosphere at 20 °C using Mettler
Toledo FE20 pH meter, which was calibrated with standard buffer solutions.
Voltamperometric studies were performed using an IPC-Pro computer-
controlled potentiostat (Econix). Curves were recorded using a three-
electrode circuit with a disk glassy carbon electrode (d = 1.70 mm) as a
working electrode, platinum wire as a counter electrode, and saturated
calomel electrode as a reference electrode. Oxidation of radicals 1 was
studied at scan rates of 0.05, 0.1, 0.2, 0.3 and 0.4 V sꢀ1 at [1] = 5 ꢂ 10ꢀ3 M
in 0.1 M LiClO4 aqueous solution at 25 °C in argon flow. Peak potentials
were approximated to zero current (Fig. S1). Difference between the po-
tentials of cathodic and anodic peaks in all cases did not exceed 70 mV,
which corresponds to a reversible process. Obtained midpoint potentials
E2/1 = (Epc + Epa) / 2 were corrected by +244 mV to assign to the normal
hydrogen electrode (Table 1).
EXPERIMENTAL
References on methods for the synthesis of nitroxyl radicals 1 are listed in
Supporting Information. Oxoammonium perchlorates 2b–i were synthe-
sized by oxidation of radicals 1 with Cl2 + NaClO4 solution using adapted
method.[20] Hydroxyammonium salts 3H+ were synthesized by reduction
of radicals 1 in MeOH/EtOH – HCl solution[21] either by hydrogenation
[22]
(H2/Pd/C) or reduction with Na2S2O4
of radicals 1 yielding hydroxyl-
amines 3, which then were transformed to 3H+ salts by reacting with
acids (refer to Supporting).
Letter designations of points in the figures correspond to the number-
ing of compounds.
RESULTS AND DISCUSSION
Kinetics
According to EPR and potentiometric titration, solutions of hydroxyl-
amines 3H+ are stable for more than 1 week under conditions of
comproportionation reaction (pH < 4). The studied oxoammonium
salts 2 (except for 2g[24]) in the same solutions do not undergo
any significant changes during more than 1 day. Stoichiometry
and kinetics of the comproportionation 2+3H+ was studied at
[3H+]0 ≫[2]0. Except for the pair 2g +3H+g, within the limits of
experimental error, the final concentrations of radicals 1 formed in
the reaction are equal to 2[2]0. This is consistent with previous data
for the reaction of 2a +3a.[19] In the case of reaction 2g +3H+g, the
final concentration of 1g is less than 2[2g]0 because of parallel
autoreduction of 2g and partial destruction of piperidine ring.[24]
The kinetics of comproportionation of 2 and 3H+ salts in buffer solu-
tions was studied by following the increase of electron paramagnetic
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Copyright © 2014 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2015, 28 17–24

OXOAMMONIUM CATIONS – NITROXYL RADICALS – HYDROXYLAMINES
Table 1. Kinetic and thermodynamic parameters of the disproportionation/comproportionation reactions for redox triads 1–2–3
1–2–3
k
ꢀ2, Mꢀ1 sꢀ1
pK3H+
( 0.03)
K4, Mꢀ2
E2/1, V versus
D(O–H),
kJ/mol ( 1.0)
0
102·k2 /K1H+
,
NHE ( 0.003)a
M
ꢀ2 sꢀ1[18]
a[19]
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
21 1[19]; 18[17]
7.4 0.5
8.9 1.2
3.0 0.2
3.9 0.3
1.3 0.1
0.83 0.13
0.26 0.11
0.062 0.007
4.4 0.4
4.4 0.4
—
51
1
6.90
6.31
5.82
5.83
5.48
5.17
4.18
5.27
4.50
6.20b
6.00
5.79
5.57
5.55
5.55
5.02
4.86b
3.83
5.85
5.67
5.22
4.25
4.71
33000 2000
1400 200
380 70
0.734
0.784
0.818
0.843
0.865
0.890
0.920
0.877
0.972
0.813 (pH ~3)
0.818
—
294.7
295.0
297.9
296.0
299.4
298.4
299.8
287.2
289.7
295.6e
296.6e
—
135 10
156 18
207 15
234 21
310 22
396 43
98
50
7
7
6.2 1.0
0.35 0.07
0.14 0.06
0.00103 0.00002
440c
3640 190
19100 500
—
—
—
—
—
—
—
—
—
—
—
—
—
—
340c; 480d
180d
—
—
—
—
67d
—
0.850
—
—
63c; 61d
61d
298.1e
—
14c; 5.4d
3.0c; 2.6d
0.17c; 0.02d
—
0.879
0.908 (pH ~3)
0.962
0.809
0.805
0.883
0.970
0.972
300.1e
300.1e
304.1e
—
1.1 0.1
0.89 0.14
0.55 0.08
—
s
t
u
v
w
—
—
—
—
—
—
—
—
—
—
—
aData of this work. Known literature values of E2/1 potentials are listed in Table S3.
bThe carboxyl group of 3H+j is titrated first, pK 4.34; pK value of amino group is 10.1 0.1 in case of 3H+q.
cFound from K4 versus E2/1 correlation (Eqn 18).
dFound from K4 versus K3H+ correlation (Eqn 17).
eValues of K4 were used from K4 versus E2/1 correlation (Eqn 18).
The rate constant for 2g +3H+g was determined by subtracting the
contribution of 2g autoreduction in studied buffer systems.
According to the previously proposed mechanism (1–3),[17,19]
the rate-limiting step of comproportionation is the oxidation of
base 3 by cation 2.
Given that [3] = [3H+]0K3H+ / (K3H+ + aH+) (refer to Supporting),
the comproportionation rate is determined by Eqn 5.
ꢀd½2ꢄ=dt ¼ 0:5 d½1ꢄ=dt ¼ k ½2ꢄ½3ꢄ
(5)
ꢀ2
¼ kꢀ2K3Hþ ½2ꢄ½3Hþ ꢄ =ðK3 þ aHþ Þ
Hþ
0
When [3H+]0 ≫ [2]0, the dependence of ln{[2]0 / ([2]0 ꢀ 0.5[1])} on
time is linear to a conversion of ≥90% (Fig. 1) and corresponds to
the reaction of first order in [2].
(1)
(2)
(3)
(4)
Equation for the effective rate constant kef = k K3H+[3H+]0 /
ꢀ2
(K3H+ + aH+) under the actual experimental conditions (aH+ ≫K3H+
)
simplifies to kef = k K3H+[3H+]0 / aH+. Accordingly, the effective
ꢀ2
rate constant kef is proportional to [3H+]0 (refer to Supporting,
Table S1, the data for the reaction 2d+ 3H+d) and inversely pro-
portional to aH+. The oxidation of 3H+ cation or hydroxylamine
3ꢀ anion, which is possible theoretically, does not make any
substantial contribution to the rate of the process in the studied
range of pH. Using stopped-flow technique, the rate constant of
cation 2a with anion 3aꢀ was found to be 3.3ꢂ 104 Mꢀ1 sꢀ1 and
2a + 3aꢀ comproportionation contributed to the rate of reaction
only at pH > 9.[25] Calculated at different pH values of kꢀ2 =kefaH+
/
(K3H+[3H+]0) are listed in Table S1. Mean values of kꢀ2 and its stan-
dard deviations are given in Table 1.
Complete set of constants characterizing mechanism (1)–(4)
was obtained only for radical 1a.[17] For other studied radicals,
acidity constants pK1H+ are calculated using the rate constant
0
k2 found for radical 1a.[18] The rate constants of the forward
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V. D. SEN’ ET AL.
Figure 1. Kinetic curves of the consumption of 2d (1), accumulation of
1d (2), and the dependence of ln{[2]0 / ([2]0 ꢀ 0.5[1])} (3) on time for
the comproportionation of 2d and 3H+d at 20 °C in glycine buffer
solution, pH 2.97, [2d]0 = 2.8 ꢂ 10ꢀ4, [3H+d]0 = 3 ꢂ 10ꢀ3 M
Figure 2. Comparison of voltammetric curves for the oxidation (1) and
reduction (2) of radical 1a (5 · 10ꢀ3 M) in aqueous 0.1 M LiClO4 at 20 °C
and scan rate 0.1 V sꢀ1
and reverse reactions of equilibrium (2) depend on the differ-
ence between the reduction potentials of cation radicals 1H+
to hydroxylamines 3 (E1H+/3) and reduction potentials of
oxoammonium cations E2/1. Weak dependence of constants
(7)
k
on the nature of substituents R for compounds a–g
ꢀ2
indicates small changes in the difference E1H+/3 ꢀ E2/1 for
Given that [3]Σ = [3H+] + [3] + [3ꢀ] = [1], the dependence of
E1/3Σ on aH+ can be written in the form:[17]
piperidine derivatives. Growth of k for pyrrolidine h and
ꢀ2
pyrroline i derivatives is likely because of a significant increase
in E2/1 caused by a high strain in the five-membered rings of
oxoammonium cations.
E1
¼ E0 =3––ðRT=FÞlnK3K3Hþ
(8)
1
=3Σ
À
Á
2
þðRT=FÞln K3K3Hþ þ aHþ
K
3Hþ þ aHþ
The equilibrium constants K4 were calculated from effective
rate constants of disproportionation k20 / K1H+, rate constants
k
and acidity constants of hydroxyammonium cations K3H+
:
Under standard conditions (aH+ = 1 M), the equilibrium constant
K4 is determined by the difference of pH-dependent potential
E1/3Σ and pH-independent potential E2/1: E1/3Σ ꢀ E2/1 = (RT / F)
ln K4. At pH 0, the last term in Eqn 8 is negligible; hence, it follows
that E1/3Σ = E01/3ꢀ ꢀ (RT/ F)ln K3K3H+ = E2/10 + (RT / F)ln K4. It is rea-
sonable to suggest that K3 values for hydroxylamines 3 are close
enough to known value K3 = 2 ꢂ 10ꢀ14 M for H2NOH,[30] so that
at pH < 12 is true K3K3H+ + aH+K3H+ + aH+2 ≈ aH+K3H+ + aH+2. As a
result, we obtain Eqn 9 for E1/3Σ versus pH dependence at
ꢀ2
K4 = k20 / (K1H+
kꢀ2K3H+). The values of K4 strongly depend on
the structure of nitroxyl radicals and in the studied series of
compounds 1a–i change by more than seven orders of magni-
tude (Table 1). The values of K4 for radicals 1k–r were found from
K4 versus E2/1 and K4 versus K3H+ correlations (refer to the
succeeding texts).
Reduction potentials E1/3Σ
pH < 12 based on the found values of E2/1, K4 and K3H+
.
Figure 2 shows the voltammetric curves of reversible oxidation (1)
and irreversible reduction (2) for radical 1a. The irreversibility of
electroreduction of radicals 1 on a timescale of this method (refer
to also[26,27]) follows from the absence of a peak on the reverse part
of the curve, a significant (~two times) decrease of the reduction
peak current, its broadened shape and large slope (Fig. S2).
Therefore, a reliable determination of pH-dependent reduc-
tion potentials of nitroxyl radicals to hydroxylamines E1/3Σ by
cyclic voltammetry is not feasible.[25,28,29] However, the depen-
dences of E1/3Σ on pH may be calculated using the values of E2/1, K4
and K3H+ obtained in this work (Table 1). The reduction of 1 to the
sum of 3H+, 3 and 3ꢀ includes half-reaction (6) and acid–base
equilibria (3) and (7).
À
Á
2
E1
¼ E2 þ 0:059 log K4 þ 0:059 log aHþ
K
3Hþ þ aHþ (9)
=3Σ
=1
These dependencies for radicals 1a–c, g–i are shown in Fig. 3.
The values of E1/3Σ for radicals 1a–i, k, n, p–r at selected pH are
given in Table S2. Taking into account the experimental errors of
used constants, the errors of E1/3Σ values does not exceed
10 mV.
The intersections of plots E1/3Σ versus pH and E2/1 lines
correspond to pHeq values at which the ratios of concentrations
([2][3]Σ) / [1]2 = 1. The values of K3H+ shift the inflections on the
E1/3Σ versus pH plots, so that of the two radicals (for example,
1a and 1c) one may be more potent oxidant at high and the
other at low pH. At pH 7, radicals 1h and 1g exhibited the lowest
(0.103 V) and the highest (0.234 V) values of E1/3Σ among the
studied radicals 1a–i. The pH-dependent potentials for two-
electron reduction of oxoammonium cations to hydroxylamines
(6)
may be calculated as E2/3Σ = E2/1 + E1/3Σ
.
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OXOAMMONIUM CATIONS – NITROXYL RADICALS – HYDROXYLAMINES
Figure 3. Plots of E1/3Σ versus pH and pH-independent potentials E2/1
for selected radicals 1. Lettering of lines corresponds to designation of
compounds (refer to Experimental)
Figure 4. Plot of pK3H+ versus σI for piperidine (1) and pyrrolidine
hydroxylamines (2)
Data concerning the salts 3H+m, n, p are not included in
Fig. 4 because we failed to find σI values for their substituents
R in the literature. Salt 3H+j does not obey Eqn 11 probably
because of the strong intramolecular interaction of the carboxylate
and hydroxyammonium groups.
Correlations for acid–base and redox properties in the
triad 1–2–3
For aliphatic compounds, the linear free-energy relationship is
most developed as linear dependencies of properties of the
compounds on inductive substituent constants σI. Inductive ef-
fect is defined as the difference of the measured parameters
for the substituted and unsubstituted molecules. Mathemati-
cally, it is expressed by Eqn 10 where the constant σI depends
on the variable substituent only, and the constant ρI depends
on the system under study.[31]
E2/1 versus σI
The values of reduction potentials E2/1 obtained in this study and
known from literature are listed in Tables 1 and S3. For the draw-
ing of correlation dependences E2/1 versus σI, the data from both
tables were used. Piperidine and pyrrolidine derivatives with
known constants of substituents σI give a good linear correlation
(Fig. 5, Eqns 13 and 14) with coefficients of determination
R2 = 0.98 (line 1) and 0.99 (line 2).
ΔE ꢀ ΔE° ¼ ρIσI
(10)
The E value may stand for the reaction energy, Gibbs energy or
the activation energy. A similar equation can also be formulated for
the other physical properties. Using the literature data and the
data obtained in this work, we analyzed the possible correlation
in the triad of 1–2–3 for such parameters as substituent constants
σI, acidity constants pK3H+, reduction potentials E2/1 and equilib-
rium constants K4. The free-energy differences of the one-electron
reduction of oxoammonium cations 2 and equilibriums (3)
and (4) are derived as: ΔG2/1 = ꢀzFE = ꢀ96500 (C molꢀ1) ꢂ E2/1
(V) = ꢀ96.5ꢂ E2/1 and ΔGK = ꢀRTꢂ ln K = ꢀ5.7 ꢂ log K (kJ/mol).
E2=1 ¼ ð0:262 0:010Þ ꢂ σI þ ð0:742 0:004Þ
E2=1 ¼ ð0:362 0:015Þ ꢂ σI þ ð0:767 0:005Þ
(13)
(14)
At σI = 0, Eqns 13 and 14 give the expected values of E2/1 for
redox couples 2a/1a and 2,2,5,5–tetramethyl-1-oxopyrrolidinium
pK3H+ versus σI
The data on pK3H+ obtained in this work are listed in Table 1, and
literature constants σI are given in Table S3. The values of pK3H+
correlate very well with inductive constants σI in the case of
hydroxylamines with neutral and positively charged substitu-
ents R (Fig. 4). Lines 1 for 1-hydroxypiperidines and 2 for 1-
hydroxypyrrolidines correspond to Eqns 11 and 12 with
determination coefficients R2 0.985 and 0.975. At σI = 0, Eqns
11 and 12 give the expected pK3H+ values for 3H+a and 1-hydroxy-
2,2,5,5-tetramethylpyrrolidine,[32] for which the experimental pK3H+
value is apparently unknown.
pK3Hþ ¼ ðꢀ3:22 0:13Þ ꢂ σI þ ð6:84 0:06Þ
pK3Hþ ¼ ð–3:30 0:30Þ ꢂ σI þ ð6:18 0:10Þ
(11)
(12)
Figure 5. Plot of E2/1 versus σI for the piperidine (1) and pyrrolidine (2)
derivatives
J. Phys. Org. Chem. 2015, 28 17–24
Copyright © 2014 John Wiley & Sons, Ltd.
wileyonlinelibrary.com/journal/poc

V. D. SEN’ ET AL.
cation/2,2,5,5-tetramethylpyrrolidine-1-oxyl. Satisfactory correla-
tion E2/1 versus σI for some pyrrolidine derivatives was first
reported in work.[27]
An increase in electronegativity of substituents R should lead
to decrease in both рК5 and stability of salts 2. Among the
oxoammonium salts studied here, 2g is the less stable. Even in
an acidic aqueous solution, it undergoes partial autoreduction
to radical 1g. Mechanism of the process involves the fragmenta-
tion of N-oxide 4g and the reduction of 2g to radical 1g by frag-
mentation products.[24] In alkaline medium, the rate of reaction
increases, and the composition of the products indicates that
the main primary process is an attack of OHꢀ on C–H bonds of
the piperidine ring of 2g.[35]
E2/1 versus pK3H+
Cross-correlation of E2/1 versus pK3H+ follows from the linear
dependences of these parameters on inductive constants of
substituents σI (Figs. 4 and 5). Data on E2/1 and pK3H+
obtained in this study (Table 1), as well as literature data
on E2/1 (Table S3), were used to build this relationship.
Compounds of the piperidine series with uncharged and single-
bonded substituents R showed good correlation (Fig. 6, line 1),
which corresponds to Eqn 15.
K4 versus pK3H+
Formula for determination of K4 = k20 / (K1H+
kꢀ2K3H+) suggests
that, at least for the nitroxyl radicals with the same heterocycle,
the relationship between log K4 and pK3H+ is linear. The data ob-
tained for the piperidine derivatives a–f give a good correlation
(Fig. 7) corresponding to Eqn 17.
À
Á
ΔGE2 ¼ ð1:49 0:05Þ ꢂ ΔGK 3H –ð129 2Þ R2 ¼ 0:985
(15)
=1
þ
The good quality of the same plot (Fig. 6, line 2) for the studied
series of pyrrolidine derivatives (Eqn 16) confirms the trend.
À
Á
À
Á
ΔGK ¼ ð–1:99 0:14Þ ꢂ ΔGK 3Hþ þ ð52:8 5Þ R2 ¼ 0:97
(17)
4
ΔGE2 ¼ ð1:97 0:11Þ ꢂ ΔGK 3H –ð143 3Þ R2 ¼ 0:97
(16)
=1
þ
Increasing in –I-effects of substituents in the series of a–f deriv-
atives reduces the overall equilibrium constant by Δ(log K4) ≈ ꢀ3.7.
This occurs because of increase in acidity constants of hydro-
xyammonium cations Δ(pK3H+) ≈ 1.7 and decrease of the ratio of
equilibrium constants characterizing the reactions (1) and (2):
Δ[log(K2 / K1H+)]≈ ꢀ2 (Table. 1). Any more detailed analysis of
K2 / K1H+ ratio would be speculative because the difference
Δ(pK1H+) = ꢀ7.0 ꢀ (ꢀ5.8)= ꢀ1.2 for the series of a–f derivatives is
The slopes of the dependences (15) and (16) are equal to 1.49
and 1.97 and reflect a greater influence of the substituents R on
the free energy of the reduction 2 → 1 as compared with their
influence on the dissociation equilibrium of hydroxyammonium
cations 3H+. The most basic hydroxylamine 3a corresponds to
redox couple 2a/1a with the lowest potential E2/1. Also, electro-
philic properties and stability of oxoammonium cations depend
on the inductive effects of substituents R. Relative to water as a
standard base, acidity constant pK5 for 2a is known to be 14.5
(Scheme 3).[33] N-oxide 4a (R = H) have a limited stability and is
a bit stronger protic acid with pK6 13.1. Salts 5ꢀМ+ were
obtained by treatment of 2a with excess of alkalies MOH.[34]
0 [18]
obtained assuming the same value of the rate constants k2 .
Equation 17 allows calculating the values of K4 for the
piperidineoxyls with known pK3H+ values (Table 1). Data point for
triad g was not included in the correlation. Carbonyl group causes
the geometry of the cycle (the twist conformation for 1g[36]) differ-
ent from the chair conformation characteristic of piperidine deriv-
atives with single-bonded substituents R. Probably, this is the
reason for the deviation of ꢀ5.7 ꢂ logK4 value for triad g in this
and other (refer to Fig. 8) studied dependencies. High-lying points
of triads h, i in Fig. 7 correspond to low values of K4 for the
pyrroline and pyrrolidine derivatives.
K4 versus E2/1
Values of E2/1 obtained in this study and known from literature
(Tables 1 and S3) were used to build this relationship. For a series
Figure 6. Plot of ꢀ96.5 ꢂ E2/1 versus 5.7 ꢂ pK3H+ for compounds of the
piperidine (1) and pyrrolidine (2) series. To avoid overlapping, symbols of
plot (2) are shifted upwards by 10 kJ/mol. Triangle symbols are for outliers
Figure 7. Plot of ꢀ5.7 ꢂ log K4 versus 5.7 ꢂ pK3H+ for redox triads a–i.
Scheme 3. Acidic properties of cations 2 and N-oxides 4
Triangle and circus symbols are for outliers
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Copyright © 2014 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2015, 28 17–24

OXOAMMONIUM CATIONS – NITROXYL RADICALS – HYDROXYLAMINES
E1 ¼ E2 þ 0:059·logðK4·K3H Þ ¼ E2 þ 0:059ðlogK4–pK3HþÞ
=3
=1
þ
=1
(23)
Calculated E1/3 values are shown in Table S2. Equation 24 is
obtained for calculation of bond dissociation energy D(O–H) in
hydroxylamines 3 taking into account the approximately equal
entropies for 1 and 3, as well as TΔS corrections for atom H•,
which at 25 °C is 34.3 kJ/mol.[37]
Â
Ã
DðO–HÞ ¼ 96:5 E2 þ 0:059ðlogK4–pK3HþÞ þ 237:4ðkJ=molÞ
=1
(24)
The values of D(O–H) calculated by Eqn 24 are presented in
Table 1. Error in determining E1/3 (Eqn 23) does not exceed
10 mV, thus corresponding to an error of 1 kJ/mol for the cal-
culated D(O–H). The obtained values of D(O–H) are by 0–4 kJ/mol
higher for 3a, e, k[38] and by 4–10 kJ/mol higher for 3a, c, g[39]
than values found from hydrogen atom exchange equilibria in
non-polar solvents. Higher values of D(O–H) are characteristic for
polar solvents and are because of hydrogen bonding between
the solute and solvent.[40]
Figure 8. Plot of ꢀ5.7 ꢂ log K4 versus ꢀ96.5 ꢂ E2/1 for redox triads a–i.
Triangle and circus symbols are for outliers
of compounds a–f, values of ΔGK4 correlate well with ΔGE2/1
(Fig. 8, Eqn 18).
À
Á
ΔGK ¼ ð–1:35 0:05Þ ꢂ ΔGE2=1–ð121 4Þ R2 ¼ 0:99
(18)
4
CONCLUSIONS
From the found correlations (Eqns 17 and 18), similar values of
K4 were obtained for piperidineoxyls 1k–r (Table 1). Together
with the data on potentials E2/1 and values of pK3H+, it allows
one to calculate by Eqn 9 the expected dependences of poten-
tials E1/3Σ versus pH for radicals 1k–r (refer to Table S2).
(1) Comproportionation rate constants kꢀ2 in the series of piperi-
dine derivatives a–g are weakly dependent on changes in re-
duction potentials of oxoammonium cations to nitroxyl
radicals E2/1. It is expected that the potentials of the second re-
dox half reaction of equilibrium (2), that is, the reduction of
radical cations 1H+ to hydroxylamines 3, should change in par-
allel to the potentials E2/1, so that the difference between them
(E1H+/3 ꢀ E2/1) and the equilibrium constant K2 for nitroxyl rad-
icals of the same heterocycle remain approximately constant.
(2) –I-Effects of substituents R increase the constants kꢀ2, K1H+ and
K3H+ thus reducing the overall equilibrium constant K4 = k2 /
Bond dissociation energies D(O–H) for hydroxylamines 3
In an analogous manner as it was performed for the hydroqui-
nones,[37] for the reduction of radicals 1 to hydroxylamines 3, a
thermodynamic cycle can be constructed comprising the reac-
tion (19)–(21). The sum of the free energies of these reactions
correspond to the bond energies D(O–H) (reaction 22).
(k ꢂ K1H+ ꢂ K3H+) in the studied series a–i by more than
ꢀ2
seven orders of magnitude.
(3) Pyrrolidine and pyrrolineoxyls are 0.1–0.15 V weaker oxidants
than piperidine derivatives that is in agreement with their
greater stability in biological samples. Values of pK3H+
determine the position of inflections on E1/3Σ–pH depen-
dences, so that of the two radicals one may be more potent ox-
idant at high and the other at low pH.
(19)
(4) Values of reduction potentials E2/1 and acidity constants pK3H+
correlate well with the inductive constants of substituents σI. In
addition, the free energies ꢀ96.5 ꢂ E2/1 and ꢀ5.7 ꢂ log K3H+
are linearly related with each other, as well as with the free en-
ergy of a disproportionation–comproportionation equilibrium –
5.7 ꢂ log K4. These linear free-energy relationships allow
predicting the redox and acid–base properties of triads 1–2–3.
(5) The found bond dissociation energies D(O–H) for hydroxylamines
in water are in the range 287–304 kJ/mol, which is 0–10 kJ/mol
higher than the known values for non-polar solvents. This
agrees with the expected increase in the values of D(O–H) in
water as a result of the formation of hydrogen bonds.
(20)
(21)
(22)
Acknowledgements
Potential E1/3 is related to potential E2/1 and equilibrium con-
stants K2 / K1H+ = K4 ꢂ K3H+ by equation E2/1 ꢀ E1/3 = ꢀ(RT / F)ln
(K2 / K1H+). Consequently, it can be calculated from the known
values of E2/1, K4 and pK3H+ (Eqn 23).
Authors are grateful to Russian Foundation for Basic Research
(Grant No. 13-03-00131) and Russian Scientific Foundation (Grant
No. 14-23-00018) for financial support.
J. Phys. Org. Chem. 2015, 28 17–24
Copyright © 2014 John Wiley & Sons, Ltd.
wileyonlinelibrary.com/journal/poc

V. D. SEN’ ET AL.
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SUPPORTING INFORMATION
Additional supporting information may be found in the online
version of this article at publisher’s web-site.
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