Effect of the structure of nitroxyl radicals on the kinetics of their acid-catalyzed disproportionation

Article abstract of DOI:10.1002/poc.3247

Acid-catalyzed disproportionation of cyclic nitroxyl radicals R ₂NO^-￠ includes the half-reactions of their oxidation to oxoammonium cations R₂NO⁺ and reduction to hydroxylamines R₂NOH. For many nitroxyl radicals, this reaction is characterized by its-～100% reversibility. Quantitative characteristics of acid-base and redox properties of the whole redox triad may be obtained from research of kinetics and equilibrium of this reaction. Here, we have examined the kinetics for the disproportionation of twenty piperidine-, pyrroline-, pyrrolidine-, and imidazoline nitroxyl radicals in aqueous H₂SO ₄, and interpreted it in terms of the excess acidity function X. The rate-limiting step of this reaction is R₂NO^-￠ oxidation by its protonated counterpart R₂NOH^+-￠. Kinetic stability of R₂NO^-￠ in acidic media depends on the basicity of nitroxyl group. This basicity is influenced predominantly by protonation of another, more basic group in radical structure, and its proximity to nitroxyl group. The discovered estimates of pK values for radical cations R₂NOH^+-￠ (from-5.8 to-12.0) indicate a very low basicity of nitroxyl groups in all commonly used R₂NO ^-￠. For the first time, a linear correlation is obtained between the one-electron reduction potentials of oxoammonium cations and the basicity of nitroxyl groups of related radicals. Copyright

Full text of DOI:10.1002/poc.3247

Research Article
Received: 27 May 2013,
Revised: 9 September 2013,
Accepted: 4 October 2013,
Published online in Wiley Online Library: 6 November 2013
(wileyonlinelibrary.com) DOI: 10.1002/poc.3247
Effect of the structure of nitroxyl radicals
on the kinetics of their acid-catalyzed
disproportionation
Ivan V. Tikhonova*, Vasily D. Sen’b, Leonid I. Borodina, Evgeny M. Plissa,
Valery A. Golubevb and Alexander I. Rusakova
Acid-catalyzed disproportionation of cyclic nitroxyl radicals R2NO• includes the half-reactions of their oxidation to oxoammonium
cations R2NO+ and reduction to hydroxylamines R2NOH. For many nitroxyl radicals, this reaction is characterized by its ~100%
reversibility. Quantitative characteristics of acid–base and redox properties of the whole redox triad may be obtained from
research of kinetics and equilibrium of this reaction. Here, we have examined the kinetics for the disproportionation of twenty
piperidine-, pyrroline-, pyrrolidine-, and imidazoline nitroxyl radicals in aqueous H2SO4, and interpreted it in terms of the excess
acidity function X. The rate-limiting step of this reaction is R2NO• oxidation by its protonated counterpart R2NOH+•. Kinetic stabil-
ity of R2NO• in acidic media depends on the basicity of nitroxyl group. This basicity is influenced predominantly by protonation of
another, more basic group in radical structure, and its proximity to nitroxyl group. The discovered estimates of pK values for
radical cations R2NOH+• (from ꢀ5.8 to ꢀ12.0) indicate a very low basicity of nitroxyl groups in all commonly used R2NO•. For
the first time, a linear correlation is obtained between the one-electron reduction potentials of oxoammonium cations and the
basicity of nitroxyl groups of related radicals. Copyright © 2013 John Wiley & Sons, Ltd.
Keywords: acidity function; disproportionation; kinetics; nitroxyl radicals; reduction potentials
INTRODUCTION
EXPERIMENTAL
Nitroxyl radicals 1a,c,d,f,g,i,j,o–r were synthesized according to[17]; radi-
cals 1b,e,k,m,s were synthesized as described in[18–24], respectively. The
purity of compounds was checked by TLC and HPLC [Milikhrom chro-
matograph equipped with a 2ꢁ 64-mm column (Separon C18, 5 μm)
and a UV detector (λ 220 nm), eluent 40% aqueous MeCN]. All studied
The unique combination of paramagnetic and redox properties of
nitroxyl radicals is the basis of their numerous applications in chem-
istry as catalysts for oxidation,[1,2] active materials for organic batte-
ries,[3] redox mediators in dye-sensitized solar cells,[4] agents for
living polymerization,[5] in physics in research aiming to create
organic magnets,[6] in biology as spin probes,[7] contrast agents
for magnetic tomography,[8] antioxidants,[9–11] and modifiers of
chemotherapeutic properties of cancer drugs.[12] Deeper under-
standing of the relationship between structure and redox proper-
ties of nitroxyl radicals is of importance for their efficient use.
Disproportionation of nitroxyl radicals in acidic media involves
the oxidation half-reaction to oxoammonium cations and reduction
to hydroxylamines. As shown for 2,2,6,6-tetramethylpiperidin-1-
oxyl,[13] disproportionation study provides a great deal of informa-
tion concerning the acid–base and redox properties of the triad
oxoammonium cation 2 – nitroxyl radical 1 – hydroxylamine 3
(Scheme 1), and also allows the determination of stability of the par-
ticipating species.
The latter is of great importance for usage of nitroxyl radicals as ox-
idation catalysts, redox mediators in solar cells and batteries active
materials. On the other hand, new nitrones or nitroso compounds
can be synthesized due to the instability of some oxoammonium cat-
ions.[14,15] Imidazolidine nitroxyl radicals, which can be easily oxidized
by RO•2 radicals to unstable oxoammonium cations, may be used for
selective detection of RO•2 radicals in biological medium.[16]
* Correspondence to: Ivan V. Tikhonov, P.G. Demidov Yaroslavl State University,
Yaroslavl, Russia.
E-mail: ivan_t13@mail.ru
a I. V. Tikhonov, L. I. Borodin, E. M. Pliss, A. I. Rusakov
P.G. Demidov Yaroslavl State University, Yaroslavl, Russia
In the present study, we studied the kinetics of disproportion-
ation of the series of 20 nitroxyl radicals in a wide range of acid
concentration to determine the quantitative characteristics of
the reaction and to find possible correlations between the radicals
structure and their resistance to acid-catalyzed disproportionation.
b V. D. Sen', V. A. Golubev
Institute of Problems of Chemical Physics, Russian Academy of Sciences,
Chernogolovka, Moscow Region, Russia
J. Phys. Org. Chem. 2014, 27 114–120
Copyright © 2013 John Wiley & Sons, Ltd.

EFFECT OF THE STRUCTURE OF NITROXYL RADICALS
Reaction mixtures were prepared either by adding solid nitroxyl radi-
cals to aqueous H2SO4 or oleum (4.1 and 26.8%) at ~20 °C under intense
stirring or by mixing a small portion of a 0.1–0.01 M aqueous solution of 1
with an ice-cooled solution of H2SO4. The kinetics of disproportionation
was studied in a possibly broader range of acid concentration for each
radical. Processing of the experimental data was performed in the coor-
dinates of the second-order kinetic equation:[13]
Scheme 1. Redox-triad oxoammonium cation 2 – nitroxyl radical 1 –
hydroxylamine 3
1=½1ꢃ ¼ 1=½1ꢃ0 þ keft
nitroxyl radicals had a purity of at least 98%. IR reflection spectra of the
crystals were recorded on a Perkin Elmer Spectrum 100 spectrometer.
The dependence of the effective rate constants on the concentration of
H2SO4 was analyzed using the acidity function H0 and excess acidity
function X. H0 values were taken from[28] and X and log [H+] values were
taken from.[29] EPR spectra parameters for radical cations 1aH+, 1dH+,
1eH+ are listed in Table 1.
2,2,6,6-Tetramethyl-4-(3,3-dimethylureido)piperidin-1-oxyl 1 h
N,N-Dimethyl carbamoyl chloride (1.07 ml, 11.5 mmol) was added during
15 min to a stirred solution of 4-amino-2,2,6,6-tetramethylpiperidin-1-
oxyl (1.71 g, 10 mmol) and Et3N (1.46 ml, 10.5 mmol) in 10 ml of chloro-
form at 0 °C. Reaction mixture was kept at ~ 20 °C for 12 h, then diluted
with chloroform (20 ml) and washed with 0.5 N aqueous HCl and satu-
rated NaCl solution. Organic phase was dried with Na2SO4, evaporated
to ~ 5 ml, and the product was precipitated by adding of hexane
(20 ml); yield of 1 h is 2.18 g (90%), pink crystals, m.p. 177–178 °C
(benzene) (165–169 °C[25]). IR-spectrum, ν, cmꢀ1: 3390 (N–H), 2989,
2975, 2939 (C–H), 1640 (C = O), 1530 (CONH), 1363, 1221, 768.
RESULTS AND DISCUSSION
Kinetic study
Ranges of H2SO4 concentrations, in which R2NO• disproportion-
ate with measurable rate, highly depend on the structure of
nitroxyl radicals. At [H2SO4] ≥ 35%, the reaction rate for
piperidin-N-oxyls was too high to be measured by the used tech-
nique. Pyrrolin- and pyrrolidin-N-oxyls 1p–t were more stable.
They disproportionate with measurable rates at [H2SO4] = 15–
50%. The most stabile imidazolin-N-oxyl 1u decays with signifi-
cant rate at [H2SO4] ≥ 50%. In these ranges (see Table S1), EPR
spectra of nitroxyl radical solutions consist of three lines and
are related to unprotonated radicals. Consumption of nitroxyl
radicals obeys the second-order kinetics over a wide range of
2,2,6,6-Tetramethyl-4-phenyl-1,2,5,6-tetrahydropyridin-1-oxyl 1 m
Some modification of method described in[26] was used for synthesis of
1 m. H2SO4 (96%, 30 ml) was added during 30 min to a stirred suspension
of 4-hydroxy-2,2,6,6-tetramethyl-4-phenylpiperidine[27] (7.0 g, 30 mmol)
in water (30 ml). The mixture was heated for 1 h in a boiling water bath,
then cooled in ice, made alkaline with NaOH (70 g) solution in water
(200 ml), and extracted with ethyl acetate (50 mlꢁ 4). The organic phase
was dried (K2CO3) and evaporated to give 2,2,6,6-tetramethyl-4-phenyl-
1,2,5,6-tetrahydropyridine (6.5 g) as a yellowish oil. It was dissolved in
10% aqueous MeCN (150 ml), then Na2WO4 (0.3 g) and three 5-ml por-
tions of H2O2 (30%) were added at 6-h intervals with stirring. The mixture
was allowed to stand at ~ 20 °C for 2 days. The yellow precipitate was
filtered, washed with 0.1 N HCl and water until neutral washes are
obtained, and then air-dried; yield of 1 m: 6.3 g (91%), orange crystals,
m.p. 136–137 °C (MeOH) (134–135 °C[26]). IR-spectrum, ν, cmꢀ1: 3082,
3058, 3032 (phenyl C–H), 2983, 2938, 2878 (CH3, CH2), 1666, 1600, 1578,
1495 (Ph, C = C), 1449, 1353, 1288, 1254, 1185, 1143, 1034, 887, 755, 692.
The kinetics of disproportionation of nitroxyl radicals in H2SO4 solu-
tions was studied by EPR at 20 °C. EPR measurements were performed
with an Adani CMS 8400 spectrometer using glass ampoules of ~1 mm
internal diameter. Spectra of all studied radicals in aqueous solutions
and in sulfuric acid represent triplets of equal intensities. Intensity of cen-
tral line of the spectrum was used as an analytic signal. At [1] ≤ 2ꢂ10ꢀ3 M,
the intensity of EPR signal (I) was found to be a linear function of [1]. The
unique calibration plot was used for each radical. Typical calibration plot
is shown in Supplement (Fig. S1).
Table 1. EPR spectra parameters for nitroxyl radicals 1a,d,e
in aqueous solution and radical cations 1aH+, 1dH+, 1eH + in
26.8% oleum
Nitroxyl
radical
g-factor
( 0.0001)
aN, mT
( 0.01)
aH, mT
( 0.01)
1a
2.0057
2.0047
2.0061
2.0048
2.0059
2.0047
1.73
2.15
1.65
2.19
1.74
2.19
—
0.31
—
0.38
—
1aH+
1d
1dH+
1e
1eH+
0.36
Changes of the Q-factor of a resonator under the influence of H2SO4
were taken into account with the external standard, which is an ampoule
with a diameter of ~1 mm filled with solution of 1c in chlorobenzene.
External standard was attached to a working ampoule, and its EPR signal
intensity was determined for different H2SO4 concentrations while gain
value was constant. Radical concentration was determined from the cal-
ibration curve in the coordinates log [1] = aꢂlog I + b + log φ. The slope a is
close to 1 and b is the constant depending on the units of intensity I. In
this equation, φ is a reduction of Q-factor of the resonator, φ = I0st/Ist,
where I0st and Ist are the intensities of the EPR signal of the external stan-
dard when working ampoule was filled with either water or H2SO4 solu-
tion, respectively. The φ value depends on [H2SO4] and is in the range of
1 – 1.2. The concentration of [1] was determined by adding correction
(log φ) to the log [1] value obtained from calibration curve for 1 in water.
Figure 1. Kinetic curves of disproportionation of 1c (a) and their
anamorphoses 1/[1c] (b) at 20 °C. [H2SO4], %: 1 – 1.6; 2 – 8.0; 3 – 15.4; 4 – 22.4
J. Phys. Org. Chem. 2014, 27 114–120
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I. V. TIKHONOV ET AL.
[H2SO4] and [1] = (2–200) 10ꢀ5 M. As an example, the consump-
tion curves and their anamorphoses 1/[1] for nitroxyl radical 1c
are shown in Fig. 1. Effective rate constants kef as determined
from the equation 1/[1] = 1/[1]0 + keft, grow with increasing
[H2SO4] (see Table S1).
À
Á
0
log kef – log½Hþꢃ ¼ log 2k2 þ pK1Hþ þ m≠m*X þ log f1 (6)
À
Á
log kef þ log½Hþꢃ ¼ log 2k2 –pK1Hþ þ ðm≠ –2Þm*X þ log f1
0
(7)
In contrast to the unsubstituted radical 1a,[13] which shows a
spectrum of protonated radical 1aH+ at [H2SO4] ≥ 85%, solutions
of nitroxyl radicals 1b–t in 85 – 100% H2SO4 and low-
concentration oleum (4.1% oleum is studied) are EPR-silent.
From the whole series of studied radicals 1b–u, the spectra of
cation radicals 1H+ with time-decreasing intensity were obtained
for nitroxyl radicals 1d,e only at oleum concentration >20% (see
Table 1, Fig. S2 and S3).
The plots of log kef – log [H+] versus X are linear (Fig. 2a) for
radicals 1b–u in accordance with Eqn (6). Table 2 summarizes
the slopes of plots, which equals to m≠m*, and interceptions at
X= 0, which equals to log(2 k02)+pK1H+ + log f1. The parameter m*,
or solvation coefficient, accounts for the susceptibility of the
protonated base to be stabilized by solvation, especially by
H-bonding. For a set of related bases, the m* parameters usually
have similar values. The parameter m≠ characterizes a similar
property of the transition state.[29]
The bell-shaped dependence of log kef on excess acidity X was
established[13] for nitroxyl radical 1a (Fig. 2b). Experimental kef
values increase with [H2SO4] up to [H2SO4] ~ 30%, while the rad-
ical is predominantly in the unprotonated form, and decrease
when [H2SO4] ≥ 85%, while the equilibrium (1) is shifted toward
the protonated radical. At intermediate concentrations of
H2SO4, the reaction is virtually over in less than 1 min.
These data are consistent with the previously proposed
mechanism,[13] which includes reactions (1) – (3). The rate-
limiting step of the reaction is an electron transfer from free 1
to the protonated nitroxyl 1H+. The sum of these reactions is
the stoichiometric equation (4).
When the equilibrium (1) is shifted to the left, the kinetics and
mechanism of the disproportionation of nitroxyl radicals formally
resemble previously proposed A-2 mechanism (Eqn 8).[29,30] A-2
(a)
In a strongly acidic medium, equilibrium (4) is shifted to
the right and the rate of the reverse comproportionation
reaction between 2 and 3 is negligible [for 1a at aH+ ≥ 1 M
the effective rate constant of the reverse reaction k–ef
k
=
ꢀ2K3H+/(K3H+ + aH+) ≤ 6ꢁ 10ꢀ6 Mꢀ1 sꢀ1[13]]. Preliminary analysis
of the kinetic data by the use of Hammett’s acidity function
H0 has shown that for nitroxyl radicals 1b–s the slopes of the
log kef – H0 plot are in the range of 1.25–2.05. The excess acid-
ity function approach[29,30] seems to be the most convenient
instrument for the analysis of acid-catalyzed reactions, for
which Δlog kef/ΔH0 ≠ 1. According to the mechanism (1) – (3)
and in terms of the Cox and Yates approach,[30] the
disproportionation rate for 1 is determined by the Eqn (5)
(b)
2
–dð½1ꢃ þ ½1HþꢃÞ=dt ¼ kef½1ꢃΣ ¼ 2k20a1a1Hþ=f≠
0
¼ 2k2 ½1ꢃ½1Hþꢃðf1f1Hþ=f≠Þ
(5)
Here, kef is the measured rate constant; k02 is the medium independent
rate constant of reaction (2) (in dilute solution)[13,29]; [1], [1H+], and
[1]Σ are the concentrations of 1, 1H+, and their sum, respec-
tively; a and f are the activities and activity coefficients of the
reagents; f≠ is the activity coefficient of the transition state.
Given that [1]Σ = [1] + [1H+] and K1H+ = a1aH+/a1H+ = ([1][H+]/
[1H+])(f1fH+/f1H+), after necessary transformations (see[13]), we
come to equations describing the dependence of kef on the
excess acidity function X under the assumption that the equilib-
rium (1) is shifted toward unprotonated 1 (6) or protonated
radicals 1H+ (7).
Figure 2. Excess acidity analysis of the disproportionation of nitroxyl
radicals 1 in sulfuric acid at 20 °C. a) log kef ꢀ log [H+] versus X dependen-
cies for 11 selected R2NO•; the letters are identical with the nitroxyl
radicals numbering (see Experimental), b) (1) log kef ꢀ log [H+] versus
X and (2) log kef + log [H+] versus X for nitroxyl radical 1a[13]
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EFFECT OF THE STRUCTURE OF NITROXYL RADICALS
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I. V. TIKHONOV ET AL.
mechanism is characteristic for hydrolysis of some esters. It in-
cludes the fast equilibrium of formation of protonated molecule
and the rate-limiting step of its interaction with a nucleophile.
disproportionation is still too high and it does not allow the EPR
registration of radical cations 1H+. The spectrum of radical cation
for radical 1 m also is not detected though 1 m cannot be pro-
tonated at an alternative group. Being dissolved in 26.8% oleum,
it forms a red solution, which is not typical for other radicals and
indicates some side reactions.
The kef values for consumption of 1dH+ and 1eH+ in 26.8%
oleum at 20 °C were 9 and 6 Mꢀ1 sꢀ1. Unknown X values for oleum
did not allow to link the kinetic parameters of consumption of 1d,
e and their protonated forms 1dH+ and 1eH+, as it was done for
radical 1a in sulfuric acid.[13] Moreover, while the effective con-
stant kef of 1aH+ consumption in the range [H2SO4] = 85–99.3%
For such reactions, the m≠ value is close to 1, and conditions of
hydration of protonated molecule SH+ and transition state are
decreases, and in 99.3% H2SO4 is equal to 0.062 Mꢀ1 sꢀ1 [13]
, kef
similar.[30] Experimental m≠ value for 1a (1.25 0.05, Table 2[13]
)
grows in oleum. At 20°C in 4.1 and 26.8% oleum kef is equal to
0.17 and 1.2Mꢀ1 sꢀ1. The observed increase of 1aH+ consumption
rate in oleum may be due to the participation of SO3 as a Lewis
acid and the formation of 1a· · · SO3 complex, acting as an
oxidant. If such a complex is formed, its steady-state concentra-
tion is very low and is not detected in the EPR spectrum.
Examples of disproportionation of nitroxyl radicals under the
influence of Lewis acids are known in the literature.[39]
corresponds to the A-2 mechanism. The m* value is associated
with differences in the solvation of the protonated and
unprotonated forms of various bases.[29] As applied to R2NO•,
value m* > 1 means greater slope for K1H+ versus X dependence,
than in the case of primary nitroanilines (m* = 1). Authors[38]
believe that m* and m≠ values reflect the differences in the
solvation energy of protonated molecules and transition states
in reactions with their participation. Greater values of these
parameters correspond to a weaker stabilization of the particles
by hydrogen bonds. For R2NO•, this stabilization can be reduced
due to steric hindrances around nitroxyl group.
The results of this study allow estimating the acidity constants
of protonated radicals K1H+. It is reasonable to assume that the
reduction potentials of oxoammonium cations 2 to nitroxyl
radicals 1 (E2/1) and the reduction potentials of cation radicals
1H+ to hydroxylamines 3 (E1H+ /3) (see[13]) under the influence
of substituents vary roughly equally, and the difference between
them changes insignificantly. According to Marcus theory, in this
case, the rate constant of limiting step (2) is structure indepen-
dent and close to that of 1a k02 = 1.4ꢁ 105 Mꢀ1 sꢀ1 for all studied
radicals. Assuming log(2 k02) > > log f1 < < pK1H+, and intercepts
at X = 0 in Eqn (6) are equal to log(2 k02) + pK1H+ + log f1, we ob-
tain estimated values pK1H+ = intercept ꢀ log(2 k02) (Table 2).
The pK1H+ values vary from ꢀ6.2 for 1b to ꢀ12.0 for 1u, i.e. by
almost 6 units of pK. The closer the protonated substituent is
to the nitroxyl group, the greater reduction of the basicity of
nitroxyl group it causes: 1e < 1b,c,f–k,n,o < 1p–t < 1u. At equal
acid concentration, the disproportionation rate constants kef de-
crease in the same sequence (Table S1). Interestingly, the car-
bonyl group in 1o has about the same effect on pK1H+ as the
The spectra of protonated radicals 1H+ were not detected for
any of studied radicals 1b–u at acid concentration up to
[H2SO4] = 99.5%. The values of acidity function X for oleum are
unknown. That is why we were unable to determine the kinetic
parameters of 1H+ consumption for these radicals according to
Eqn (7) as well as to separate m≠ and m* values in m≠m* product.
However, minor changes in m≠m* values for all studied nitroxyl
radicals imply subtle differences in the values of the multipliers.
Therefore, for nitroxyl radicals 1b–u, values m≠ and m* are close
to those found for 1a.
Compared with the radical 1a (Fig. 2a), the maximum rates of
disproportionation of radicals 1b–u are shifted to [H2SO4] ~
100% because of a decrease in the basicity of the nitroxyl
groups. For all studied radicals, except 1d,e, the EPR spectra of
protonated radicals were not detected even in 4.1 and 26.8%
oleum. Radicals 1d,e in 26.8% oleum give EPR spectra of radical
cations 1dH+ (Fig. S2) and 1eH+ (Fig. S3); their parameters are
shown in the Table 1. Most of studied radicals, except 1a,d,m,
contain amide, ether, carboxyl, hydroxyl, carbonyl, and imino
groups, which are more basic[38] than the nitroxyl group in 1a.
We believe, that protonation of these groups reduces the basic-
ity of the nitroxyl group to such an extent that the equilibrium
(1) is not shifted enough to the right even at the highest studied
acidity of the medium (26.8% oleum). In this case, the rate of
protonated amino group in 1 k (pKa of amino group is 9.5[40]
and the trimethylammonium group in 1 l.
)
Stability of disproportionation products
If hydroxy- and oxoammonium salts, which are formed by dispro-
portionation, are stable, the initial radical can be regenerated by
simple neutralization of acid. This procedure may be used to assess
the stability of redox triad 1–2–3. For piperidin-, pyrrolin-, and
pyrrolidin-N-oxyls, potentially less stable part-
ners are oxoammonium cations. Piperidin-N-
oxyls, which contain amide, ester, or halogen
substituents at 4-position of the heterocycle,
and pyrrolin-N-oxyl 1p and pyrrolidin-N-oxyl
1 s form stable oxoammonium cations;
therefore, they are capable of being almost
quantitatively regenerated from the products
of their disproportionation after acid neutral-
ization to pH 7–8 (Table S2). In contrast to
them, oxoammonium cation 2o is strongly
destabilized by the carbonyl group and the
Scheme 2. Transformations of nitroxyl radical 1u in strong acids
regeneration of the radical 1o after
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EFFECT OF THE STRUCTURE OF NITROXYL RADICALS
pyrrolidin-, and imidazolin-N-oxyls in acidic media are kineti-
cally more stable due to lower basicity of their nitroxyl groups.
In strongly acidic medium, substituents such as amino,
hydroxyl, carboxyl, ether, ester, amide, and imine groups un-
dergo protonation before nitroxyl group of radical. This causes
the greater decrease in the basicity of the latter, the shorter is
C-atom chain separating substituent and nitroxyl group.
2. In the approximation of a constant value of medium-
independent rate constant k02, estimated pK1H+ values were
obtained for protonated radicals 1H+. These values are in
the range from ꢀ5.8 to ꢀ12.0 for the studied nitroxyl radicals.
3. The product of parameters m≠m* takes into account peculiar-
ities of solvation of the radical cations 1H+ and transition
state of the rate-limiting reaction. Also, it connects the effec-
tive rate constants kef with the excess acidity function X. For
the studied nitroxyl radicals, product m≠m* weakly depends
on their structure. This indicates a common mechanism and
small differences in the solvation energies of radical cations
1H•+, which differ greatly in the values of pK1H+. Dispropor-
tionation of nitroxyl radicals is the only known electron trans-
fer reaction in organic compounds, for which the kinetics is
well described in terms of the excess acidity function X.
4. A correlation E2/1 versus pK1H+ is found, allowing to predict
either one value if the other is known.
Figure 3. Plot of ꢀ96.5ꢁ E2/1 versus 5.7ꢁ pK1H+ for piperidin-N-oxyls (1)
and pyrrolin-/pyrrolidin-N-oxyls (2); the letters are identical with the
nitroxyl radicals numbering (see Experimental)
neutralization of its acid solution is negligible. The detailed mech-
anism of fragmentation of cation 2o is studied in.[15,41]
The basicity of the nitroxyl group in 1u is the lowest among
the studied nitroxyl radicals. This is the result of protonation of
the nitrone group (for nitrones pK ~ 7 is typical[42]) and its prox-
imity to the nitroxyl group. When treated in the cold with strong
acids, radical 1u forms stable crystalline salts 4u (Scheme 2).[43,44]
In solution, 1u disproportionates with substantial rate at
[H2SO4] ≥ 50% (Table S1). The reaction products, salts 2u and
3u, are unstable in acid solution. They fully hydrolyze to
acetonoxime, benzoic acid, and α-hydroxylamino ketone in
24 h at ~ 20 °C.[45]
Acknowledgements
The experimental part was carried out on equipment of the
Scientific and educational center ‘Physical organic chemistry’
and the Center for collective usage of scientific equipment
‘Diagnostics of micro and nanostructures’ of Yaroslavl State
University. The work was financially supported by the Ministry
of Education and Science of Russian Federation (State contract
No. 16.552.11.7006) and Russian Foundation for Basic Research
(Grant No. 13-03-00131).
E2/1 versus pK1H+ correlation
Reduction potentials E2/1 of one-electron couple 2/1 are known
for a number of the studied radicals (Table 2). These potentials
correlate linearly with the values of pK1H+ found in this work.
Piperidin-N-oxyls (line 1) and pyrrolin-/pyrrolidin-N-oxyls (line 2)
fit two different correlation dependencies (Fig. 3).
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Lines 1 and 2 correspond to Eqns (9) and (10) with coefficients
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the one-electron reduction of oxoammonium cations 2 and ion-
ization of radical cations 1H+ are derived as: ΔG2/1 =ꢀzFE =
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