N-H bond dissociation energies in N,N′-diphenyl-1,4-phenylenediamine and its aminyl radical

Article abstract of DOI:10.1007/s11172-005-0004-2

The N-H bond dissociation energy (D_NH) in the 4-anilinodiphenylaminyl radical formed from N,N′-diphenyl-1,4- phenylenediamine was experimentally determined and calculated by the quantum-chemical method. The experimental D_NH value was found from the enthalpy of the reaction of N,N′-diphenyl-1,4-benzoquinonediimine with 4-hydroxydiphenylamine taking into account the bond dissociation energies in 4-hydroxydiphenylamine and its aminyl and phenoxyl radicals, which were determined by the intersecting parabolas method from the kinetic data. The quantum-chemical calculations of D_NH used several semiempirical methods by the MOPAC program and the ab initio and DFT methods by the GAUSSIAN 94/98 program. The D_NH values, which were closest to the experimental values, were obtained by the B3LYP/6-31+G*method. The results of quantum-chemical calculations of the N-H and O-H bond dissociation energies in 4-hydroxydiphenylamine and its radicals are presented.

Full text of DOI:10.1007/s11172-005-0004-2

Russian Chemical Bulletin, International Edition, Vol. 53, No. 8, pp. 1609—1614, August, 2004
1609
N—H bond dissociation energies in N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine
and its aminyl radical
ꢀ
V. T. Varlamov and B. E. Krisyuk
Institute of Problems of Chemical Physics, Russian Academy of Sciences,
1 prosp. Akad. Semenova, 142432 Chernogolovka, Moscow Region, Russian Federation.
Fax: +7 (096) 524 9676. Eꢀmail: varlamov@icp.ac.ru, bkris@mail.ru
The N—H bond dissociation energy (DNH) in the 4ꢀanilinodiphenylaminyl radical formed
from N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine was experimentally determined and calculated by
the quantumꢀchemical method. The experimental DNH value was found from the enthalpy of
the reaction of N,N´ꢀdiphenylꢀ1,4ꢀbenzoquinonediimine with 4ꢀhydroxydiphenylamine takꢀ
ing into account the bond dissociation energies in 4ꢀhydroxydiphenylamine and its aminyl and
phenoxyl radicals, which were determined by the intersecting parabolas method from the
kinetic data. The quantumꢀchemical calculations of DNH used several semiempirical methods
by the MOPAC program and the ab initio and DFT methods by the GAUSSIAN 94/98
program. The DNH values, which were closest to the experimental values, were obtained by the
B3LYP/6ꢀ31+G* method. The results of quantumꢀchemical calculations of the N—H and
O—H bond dissociation energies in 4ꢀhydroxydiphenylamine and its radicals are presented.
Key words: N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine, 4ꢀanilinodiphenylaminyl radical,
N,N´ꢀdiphenylꢀ1,4ꢀbenzoquinonediimine, 4ꢀhydroxydiphenylamine, Nꢀphenylꢀ1,4ꢀbenzoꢀ
quinonemonoimine, bond dissociation energies, quantumꢀchemical calculations.
Quinoneimines 1 and 4 were synthesized by the oxidation of
3 and 2, respectively, with PbO2. A solution of compound 3 or 2
in benzene or diethyl ether was slowly passed through a glass
column packed with a mixture of PbO2 with glass wool.4
Quinoneimines were purified by preparative liquid chromatoꢀ
graphy on SiO2 (ether—hexane mixture as eluent) followed by
recrystallization from MeOH. The solvent was chlorobenzene
purified by a known procedure.4
Experiments were carried out under argon in a temperatureꢀ
controlled bubbleꢀtype quartz cellꢀreactor (volume 8.5 mL, optiꢀ
cal path length (l) 2.0 cm), which was set up in the cell compartꢀ
ment of a Specord UVꢀVIS spectrophotometer. In the course of
experiments, the absorbance of solutions (D) was continuously
detected at λ = 450 nm (near maxima of the absorption bands of
quinoneimines 1 and 4). The molar absorption coefficients of the
quinoneimines in a wide temperature interval were determined
taking into account the thermal expansion of chlorobenzene of
1•10–3 deg–1. The following equation was used for calculations
The N—H bond dissociation energy (DNH) in radicals
formed from 1,4ꢀphenylenediamine derivatives by H atom
abstraction characterizes simultaneously the reactivities
of two substances. On the one hand, the DNH values deꢀ
termine, to a considerable extent, the activity of these
radicals as reducing agents, i.e., donors of the H atom,
and on the other hand, they characterize the activity of
oxidation product of these radicals, namely, quinoneꢀ
imine, in reactions of H atom abstraction from valenceꢀ
saturated molecules or radicals.
Handbooks1,2 contain a few data on bond dissociation
energies in radicals: the DOH values are available only for
five 4ꢀhydroxyphenoxyl semiquinone radicals substituted
at the ring. The DNH and DOH values in the radicals formed
from 4ꢀhydroxydiphenylamine have been estimated only
recently.3 In this work, we determined DNH in the
4ꢀanilinodiphenylaminyl radical, which forms as an inꢀ
termediate in the reactions with participation of the antiꢀ
oxidant N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine.
ε = Dexp[1 + 0.001(T – 298)]/(l•c298),
where c298 is the concentration of the quinoneimine at 298 K.
The results obtained are presented below, errors of the ε values
being ≤1.5%.
Experimental
T/K
ε•10–3/L mol–1 cm–1
For experimental determination of DNH, we used the enꢀ
thalpy (∆H ) of the reaction of N,N´ꢀdiphenylꢀ1,4ꢀbenzoꢀ
quinonediimine (1) with 4ꢀhydroxydiphenylamine (2), affordꢀ
ing N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine (3) and Nꢀphenylꢀ
1,4ꢀbenzoquinonemonoimine (4). The ∆H value was found from
the temperature dependence of the equilibrium constant (K) of
this reaction.
1
4
298.2
321.5
341.6
364.2
381.0
6.975
6.839
6.719
6.624
6.548
2.995
2.950
2.920
2.875
2.840
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1549—1554, August, 2004.
1066ꢀ5285/04/5308ꢀ1609 © 2004 Springer Science+Business Media, Inc.

1610
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 8, August, 2004
Varlamov and Krisyuk
Quantumꢀchemical calculations of bond dissociation enerꢀ
gies in molecules and radicals were performed on RM600 (Instiꢀ
tute of Problems of Chemical Physics, Russian Academy of
Sciences, Chernogolovka) and POWER CHALLENDGER L
supercomputers (N. D. Zelinsky Institute of Organic Chemisꢀ
try, Russian Academy of Sciences, Moscow).
Table 1. Equilibrium constants (K) of the reversible reaction
between quinonediimine 1 and 4ꢀhydroxydiphenylamine (2)
T/K
Initial concentration of reactant/mol L–1
K*
[1]0•105 [2]0•104 [3]0•103 [4]0•105
341.6
—
—
—
5.63
5.63
2.82
5.63
33.59
33.59
—
5.40
—
3.25
10.72
10.72
7.88
8.44
7.28
8.44
5.04
6.70
7.56
7.59
4.05
8.40
2.70
8.10
7.88
15.19
7.84
7.52
—
175.2
132.4
145.0
132.6
194.2
162.1
97.8
105.0
112.4
114.3
100.2
107.8
Results and Discussion
—
The reversible reaction of quinonediimine 1 with
4ꢀhydroxydiphenylamine (2) is described by Scheme 1.
8.33
8.33
—
—
—
—
7.89
7.90
—
381.0
7.56
7.59
15.26
14.56
—
Scheme 1
—
* Average value: K = 156.9 10.1 (341.6 K) and 106.3 2.7
(381.0 K).
The results obtained are presented in Table 1. Using these
data, we have
K = const•exp[–∆H/(RT )] =
= 100.59 0.27exp[(10470 1880)/(RT )],
i.e., the enthalpy of the reaction is ∆H = –10.5 1.9
The temperature dependence of the equilibrium conꢀ
stant K was used to calculate the enthalpy of the reaction
(∆H ) by the equation
kJ mol–1
.
On the one hand, the heat effect of the reaction (Q) is
equal to the difference between the heats of hydrogenaꢀ
tion of quinoneimines 1 and 4 and, on the other hand, it
is equal to the difference between the sum of the N—H
bond dissociation energies in molecule 3 and radical 3N• *
and the sum of the bond dissociation energies in molꢀ
ecule 2 and in its 2O• and 2N• radicals**
d(lnK )/d(1/T ) = –∆H/R.
The K values were determined at temperatures of 381.0
and 341.6 K, when the equilibrium state is achieved within
a time shorter than 1 h. We failed to determine K with a
sufficient accuracy at lower temperatures. Although
quinoneimines 1 and 4 have close absorption spectra in
the visible region, their molar absorption coefficients at
λ = 450 nm differ considerably (see above), which makes
it possible to find separately concentrations of comꢀ
pounds 1 and 4. The equilibrium concentrations of the
components and the equilibrium constant of the reaction
were calculated using the value of limiting in time absorꢀ
bance (D∞)
Q = –∆H = [DNH(3) + DNH(3N•)] –
– [DOH(2) + DNH(2O•)] =
= [DNH(3) + DNH(3N•)] – [DNH(2) + DOH(2N•)].
The latter were found3 by processing the experimental
kinetic data using the intersecting parabolas method
(D/kJ mol–1): DOH(2) = 339.3, DNH(2O•) = 273.6,
DNH(2) = 353.4, and DOH(2N•) = 259.5. Then
DNH(3) + DNH(3N•) = 623.4 1.9 kJ mol–1
.
.
To estimate the N—H bond dissociation energy in the
N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine molecule (3), let
us use the correlation5
When the equilibrium state is achieved from the side of
the forward reaction (1 + 2), then
+
DNH(3) = (363.6 0.24) + (11.93 0.42)σ
(r = 0.995),
which has been used3 for the estimation of the N—H
bond dissociation energy in the 4ꢀhydroxydiphenylamine
,
* A radical formed by the abstraction of one H atom from the
NH group in molecule 3.
and if it is achieved from the reverse reaction (3 + 4), then
** Radicals formed by the abstraction of one H atom from the
OH or NH group in molecule 2.
.

N—H bond dissociation energies
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 8, August, 2004
1611
molecule (2) (σ+ is the Braun constant of the substituent
in the paraꢀposition of the benzene ring of diphenylꢀ
a
amine). Accepting for the —NHPh substituent σ+
=
N
–1.25 0.05,6 we obtain DNH(3) = 348.7 1.4 kJ mol–1
.
The value found agrees well with DNH(3) = 346.9
kJ mol–1, which has been obtained7 from the data on
the rate constants of the reactions of peroxide radicals with
aromatic amines processed in the framework of the paraꢀ
O
bolic model. In this case, DNH(3N•) = 274.7 3.3 kJ mol–1
.
Comparing this value with the above data for
4ꢀhydroxydiphenylamine radicals, we can see that the
value of DNH found for the Ph—NH—C6H4—N•—Ph
(3N•) radical virtually coincides with the N—H bond
dissociation energy in the Ph—NH—C6H4—O• (2O•)
phenoxyl radical formed from 4ꢀhydroxydiphenylꢀ
amine (2). This is an unexpected result because the exꢀ
perimental observations indicate that the dehydrogenatꢀ
ing activity of quinonediimine 1 is higher than that of
quinonemonoimine 4. According to the published data,8
the reaction of 1 with hydroquinone ceases within
1—2 min at room temperature and reactant concentraꢀ
tions of ~1•10–4 mol L–1. Our observations show that the
reaction involving 4 instead of 1 occurs much more slowly
under the same conditions. This indicates that the N atom
in quinonemonoimine 4, which mainly attacks the OH
groups of hydroquinone,3 has a lower (compared to that
of the N atom in molecule 1) activity in the reaction of
H atom abstraction, i.e., DNH(3N•) > DNH(2O•).
b
N
O
Fig. 1. Structures of 4ꢀhydroxydiphenylamine (2) (a) and
Nꢀphenylꢀ1,4ꢀbenzoquinonemonoimine (4) (b) (calculated by
B3LYP/6ꢀ31+G*).
To obtain an independent estimate of DNH(3N•), we
used quantumꢀchemical calculations. The bond dissociaꢀ
tion energies in the molecules and radicals were found as
heat effects of the reactions presented below.
N—H bond dissociation energies, because the B3LYP
calculation, according to the published data,9 using preꢀ
cisely these basis sets provides the most exact estimates
of DNH. The O—H bond dissociation energies were calꢀ
culated similarly. Note that no method was proposed so
far to obtain the most exact DOH values for O—H bonds.
The structures of compounds 2 and 4 obtained by
quantumꢀchemical calculations are shown in Fig. 1. The
structures of the aminyl (2N•) and phenoxyl (2O•) radiꢀ
cals formed from 2 are the same in appearance and, hence,
they are not presented. The total energies, some bond
lengths, and bond angles are presented in Tables 2 and 3.
The structure of a transꢀisomer was chosen for molecule 3,
and other structures were obtained from structure 3 by
geometry optimization (Fig. 2). As calculations showed,
Molecule → Radical + H atom
Radical → Molecule + H atom
The geometries of the molecules and radicals were primaꢀ
rily optimized by the semiempirical PM3 method. Then
the energies of the corresponding states were ab initio
calculated by the HF and DFT (B3LYP) methods using
the GAUSSIAN 94/98 program with the complete geomꢀ
etry optimization and ignoring symmetry. The 6ꢀ31G*
and 6ꢀ31+G* basis sets were used in calculations of the
Table 2. Total energies (Etot), bond lengths (d), and bond angles (ω) in 4ꢀhydroxydiphenylamine (2), two its radicals, and
benzoquinonemonoimine 4 (calculated by DFT/B3LYP/6ꢀ31+G*)
Comꢀ
pound
–Etot
/Hartree
d/Å
ω/deg
C—N
N—H
O—H
C—O
C—N—C
C—N—H
C—O—H
ꢀ
1.398, 1.409
2
593.8906604
593.252405
593.2634718
592.6567194
1.011
—
1.015
—
0.970
0.970
—
1.375
1.366
1.262
1.232
128.5
123.2
129.7
123.9
115.4
—
115.1
—
109.8
110.1
—
2N•
2O•
4
1.375, 1.360
ꢀ
ꢀ
1.410, 1.374
ꢀ
1.398, 1.299
—
—
ꢀ
Corresponds to the bond with the ring without an OH group.

1612
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 8, August, 2004
Varlamov and Krisyuk
Table 3. Total energies (Etot), bond lengths (d), and bond angles (ω) in the molecules of benzoꢀ
quinonediimine 1 and compound 3 and in radical 3N• (calculated by DFT/B3LYP/6ꢀ31+G*)
Comꢀ
pound
–Etot
/Hartree
d/Å
ω/deg
C—N
N—H
C—N—C
C—N—H
1
3
3N•
804.4504235
805.0825298
803.8394773
1.399a, 1.301b
1.398a, 1.406b
1.406a, 1.389b,
—
1.011
1.012
123.6
128.9
129.6, 123.1c
—
115.4, 115.5
115.1
1.380,a,c 1.352b,c
a Bonds with the external benzene ring.
b Bonds with the internal benzene ring.
c For the radical fragment.
a
b
c
N
N
N
N
N
N
Fig. 2. Structures of N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine (3) (a), 4ꢀanilinodiphenylaminyl radical (3N•) (b), and N,N´ꢀdiphenylꢀ
1,4ꢀbenzoquinonediimine (1) (c) (calculated by B3LYP/6ꢀ31+G*).

N—H bond dissociation energies
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 8, August, 2004
1613
the N atom in all compounds is sp2ꢀhybridized and plaꢀ
nar. In molecule 2, the planes of benzene rings form an
angle of 48°, the ring without an OH group is turned
by 20° relatively to the CNC plane, the second ring is
turned by 28°, and the О—Н bond lies in the plane of the
benzene ring linked with this bond. In the aminyl (2N•)
and phenoxyl (2O•) radicals, the benzene ring planes are
folded by 46 and 42°, the ring with the OH group is turned
by 21 and 12° relatively to the CNC group, and the secꢀ
ond ring is turned by 25 and 30°, respectively. In quinoneꢀ
monoimine 4, the ring planes are folded by 50° with reꢀ
spect to each other, the ring without an O atom is turned
by 41°, and the second ring is turned by 9°.
In molecule 3 (see Fig. 2), the planes of the ultimate
rings are parallel to each other, and the central ring is
turned by 49°. This geometry changes slightly in the radiꢀ
cal: the planes of the ultimate rings are not parallel by 3—4°
only. In molecule 1, the peripheral rings are parallel again,
and the central ring is folded by 53° .
Corrections to the zeroꢀpoint energy (see Table 4)
decreases the calculated bond dissociation energies for
both N—H and O—H bonds in molecule 2. In this case,
an agreement with experimental values worsens. This is
likely caused by the use of an incomplete set of basis
functions in calculations of bond dissociation energies.
For example, the N—H bond dissociation energy calcuꢀ
lated using the 6ꢀ31G basis set is ~14 kJ mol–1 lower than
that calculated in the 6ꢀ311+G** basis set.9 When calcuꢀ
lations at the B3LYP/6ꢀ31+G* level ignoring zeroꢀpoint
modes are used, an even number of errors is made (an
insufficiently complete basis set and ignoring zeroꢀpoint
modes), and they are mutually compensated. The addiꢀ
tion of diffusion functions changes noticeably the calcuꢀ
lated N—H and O—H bond dissociation energies in molꢀ
ecule 2, while this effect is not observed in the radicals
(2N• and 2O•) and in molecule 3, and rather exact reꢀ
sults are already obtained in the 6ꢀ31G* basis set (see
Table 4).
The results of calculation of the bond dissociation enꢀ
ergies are presented in Table 4. It is seen that semiempirical
methods, except PM3, are inappropriate for this task. The
nonempirical methods used for DNH calculation give alꢀ
most the same results for the 3N• radical. At the same
time, the result of calculation of DNH in molecule 3 using
the HF method is underestimated compared to that of the
more preferential B3LYP method. The same conclusions
can be made for the results obtained for molecule 2 and its
radicals. In this case, the HF method also gives reasonable
results for the radicals but strongly underestimates the
bond dissociation energies in the molecule. Therefore,
the HF calculations should be treated as intermediate or
preliminary for the B3LYP method. It should also be taken
into account that the PM3 calculation of bond dissociaꢀ
tion energies in molecules demonstrates a good agreeꢀ
ment with nonempirical calculations.
As can be seen from the data in Table 4, the experiꢀ
mental data agree, as a whole, with the results of quantumꢀ
chemical calculations, especially at the B3LYP/6ꢀ31+G*
level. The calculated N—H bond dissociated energy in
the N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine (3) molecule
almost coincides with DNH estimated by the relationship
for diphenylamines. The sums of bond dissociation enerꢀ
gies calculated by the quantumꢀchemical methods and
found by the intersecting parabolas method3 also coincide
DNH(molecule) + DOH(radical) =
= DOH(molecule) + DNH(radical)
for 4ꢀhydroxydiphenylamine molecule (2). At the same
time, the quantumꢀchemical calculations for radical 3N•
give the DNH value, which is ~15 kJ mol–1 higher than
that obtained experimentally from the enthalpy of the
Table 4. Quantumꢀchemical calculations of the bond dissociation energies (D/kJ mol–1) for the 4ꢀhydroxydiphenylamine (2)
and N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine (3) molecules and their radicals
Method/basis set
Ph—NH—C6H4—OH (2)
DOH(2)
DNH(2O•) DOH(2N•)
Ph—NH—C6H4—NH—Ph (3)
a
b
DNH(2)
Σ
DNH(3)
DNH(3N•)
Σ
AM1
MNDO
PM3
HF/6ꢀ31G*
B3LYP/6ꢀ31G*
B3LYP/6ꢀ31G* c
B3LYP/6ꢀ31+G*
B3LYP/6ꢀ31+G* c
Experiment
—
—
—
—
—
—
—
—
—
—
372.1
330.5
356.7
336.1
345.9
—
258.4
229.5
265.3
290.1
290.2
—
630.5
560.0
613.3
626.2
636.1
—
363.2
321.8
349.8
316.4
351.2
318.2
353.43
347.6
309.5
326.1
295.2
326.1
295.7
339.33
249.0
275.6
284.5
254.1
286.7
256.5
273.63
233.3
263.3
260.8
232.8
261.5
234.0
259.53
596.5
585.1
610.6
549.2
612.8
552.3
612.9
346.1
—
290.6
—
636.7
—
348.7 1.4 274.7 3.3 623.4 4.7
a DNH(2) + DOH(2N•) = DOH(2) + DNH(2O•).
b DNH(3) + DNH(3N•).
c Taking into account the correction for zeroꢀpoint modes.

1614
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 8, August, 2004
Varlamov and Krisyuk
reaction between compounds 1 and 2. As mentioned
above, this result agrees better with the data on the higher
reactivity of quinonediimine 1 compared to that of 4 in
dehydrogenation reactions.
the bond dissociation energies in 2 and its radicals, which
were obtained from the kinetic data and the parabolic
model of the transition state, were used in the calculaꢀ
tions) and calculated by the ab initio quantumꢀchemical
methods at the B3LYP/6ꢀ31+G* level (DNH(3N•) =
290.6 kJ mol–1). Since the experimental DNH(3N•) value
can be assumed as underestimated due to solvation efꢀ
fects, the whole range from 274.7 3.3 to 290.6 kJ mol–1
should be taken as an estimate of DNH(3N•) so far.
The calculated DNH(3N•) value is higher than the
experimental one due to, in our opinion, a consequence
of ignoring solvation effects in determination of enthalpy
of the 1 + 2 reaction rather than of the approximated
character of quantumꢀchemical calculations. In fact, the
enthalpy of the reaction includes (in addition to the difꢀ
ference in the dissociation energies of the cleaved and
formed bonds) the difference between the heats of solvaꢀ
tion of the starting substances and reaction products by the
solvent (chlorobenzene). Phenols, including 4ꢀhydroxyꢀ
diphenylamine (2), form relatively strong hydrogenꢀlinked
complexes with benzene rings of aromatic compounds: in
This work was financially supported by the Division of
Chemistry and Materials Science of the Russian Acadꢀ
emy of Sciences (Program "Theoretical and Experimental
Investigation of the Nature of Chemical Bonding and
Mechanisms of the Most Important Chemical Reactions
and Processes").
some cases, ∆Hsolv reaches ~10 kJ mol–1 10
The solvation
.
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thalpy of the 1 + 2 reaction, should be considered as the
lower estimate of the N—H bond dissociation energy in
the radical, being, most likely, higher than the indicated
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value by several kJ mol–1
.
We estimated the solvation energy for the compounds
considered by chlorobenzene in the framework of the
GAUSSIAN program using the polarized continuum
model.13—15 The results obtained are presented below (calꢀ
culation by the B3LYP/6ꢀ31+G*/PCM method) and conꢀ
firm that solvation should necessarily be taken into acꢀ
count.
Solvation energy/kJ mol–1
2
1
2N•
2O•
3
3N•
4
2.19
17.32
23.00
21.62
5.94
5.80 9.91
13. S. Miertus, E. Scrocco, and J. Tomasi, Chem. Phys., 1981,
55, 117.
14. S. Miertus and J. Tomasi, Chem. Phys., 1982, 65, 239.
15. M. Cossi, V. Barone, R. Cammi, and J. Tomasi, Chem. Phys.
Lett., 1996, 255, 327.
Thus, the N—H bond dissociation energy in the
4ꢀanilinodiphenylaminyl radical was estimated. Two
values were obtained: experimental (DNH(3N•) =
274.7 3.3 kJ mol–1) found from the enthalpy of the reꢀ
versible reaction of N,N´ꢀdiphenylꢀ1,4ꢀbenzoquinoneꢀ
diimine (1) with 4ꢀhydroxydiphenylamine (2) (data on
Received January 15, 2004