RATE CONSTANTS AND ISOTOPE EFFECTS
2147
state. To calculate the electronic structure and proper- depends linearly on σ with parameter ρ = −3.1. The
ties of the particles that participate in catalyzed NHPI negative sign of ρ means that an electron is partly
oxidation, we used the semi-empirical PM3 method transferred from phenol to a radical in the transition
(
MOPAC program), which yields reasonably accurate state of the reaction, while the high absolute value of ρ
results for the experimentally determined properties of confirms the substantial polarity of the transition
molecular entities containing C, H, O, N atoms while state, which lowers the activation energy of the reac-
shortening the time needed for calculations [19, 20].
tion of H-atom abstraction. Similar dependences were
also obtained for substituted benzylic alcohols and
benzaldehydes [24].
The data on the distribution of electron density
presented in Table 3 show that the charge on the ter-
minal oxygen atom of a PINO radical (−0.365) is
In comparing the energies of transition states of the
much higher than that of a peroxyl radical (−0.193). types C···H···O and O···H···O, we must consider the
To compare the charge distribution in the TS of the possible role of triplet repulsion. In the latter case, the
reaction of hydrogen abstraction by PINO radicals, we energy of triplet repulsion is close to zero [1], reducing
selected two substrates with the same BDE of the reac- the activation energy of the reaction when attacking
tive bonds: p-xylene (a C–H bond) and phenol (an O-centered radicals on O–H bonds. In our opinion, it
O–H bond). From the data of Table 3, it follows that is better to speak here not of the energy of triplet repul-
the charges on the H and C atoms in p-xylene and on sion but of triplet attraction, since triplet oxygen is
the N and O atoms in phenol differ substantially.
To estimate qualitatively the energy of Coulomb
interaction in the TS –О···Н···С–, we must know the
much stabler than singlet oxygen, and we are consid-
ering the interaction between the О···О atoms.
Certain data on the TS of H atom abstraction reac-
distance between the atoms. The distance between the tions can be obtained by studying the kinetic isotope
O and C atoms in the TS is estimated to lie in the range effect (KIE) in these reactions. The reaction rate con-
of 2.6–3.1 Å [21, 22]. The distance between the O and stants of H atom abstraction by PINO radicals from
C atoms in the TS least advantageous for the manifes- molecules of acenaphthene, p-xylene, and their deu-
tation of Coulomb forces (the loosest TS) was used to tero analogs were determined from the dependence of
estimate the Coulomb energy upon the abstraction of the observed pseudo–first order rate constants of
a H atom from a C–H bond by a radical: 3.1 Å. If we PINO consumption on the substrate (RH, RD) con-
assume that the bond being broken is elongated by centration. The KIE was thus determined from the
2
0%, the distance between the C and H atoms in the ratio of the rate constants of the reactions between
TS is 1.3 Å, and the distance between the O atom of PINO and the molecules of substrates and their deu-
the radical and the H atom in the TS is thus 1.8 Å. The tero analogs. The obtained values of KIE for acenaph-
same values were used for distances О···О and О···Н, thene and p-xylene in acetonitrile at 25°С were 11.6
and for the transition state of phenol. As we can see, and 22.0, respectively.
the Coulomb energy for PINO is somewhat higher
The maximum KIE of hydrogen, calculated by
than that of a peroxyl radical, and its contribution is assuming the complete loss of zero-point vibrations in
especially greater in the reaction involving phenol. the transition state of the reaction, can be determined
Note that these values grow when the TS is tighter, and using the formula [25]
the bond being broken is more elongated.
hc(γ(C−H)−γ(C−D))
kH
2kT
On the other hand, a comparison of the energies of
the lowest unoccupied molecular orbitals (LUMO) for
the radicals (−1.66 eV for PINO and 0.03 eV for
=
e
,
kD
where h is the Planck constant; c is the speed of light,
cm/s; k is the Boltzmann constant; T is the tempera-
ture, K; and γ(С–Н) and γ(С–D) are the frequencies
of the stretching C–H and C–D vibrations in the alkyl
•
t-BuOO ) shows that PINO will accept an electron
•
more readily than t-BuOO ; i.e., the fraction of the
structures with charge transfer in the TS with the par-
ticipation of PINO is much larger, which helps to
lower the potential barrier of the reaction.
−1
moieties of alkylarene. These are 2884 and 2175 cm
for acenaphthene, so the KIE should be 5.5 for ace-
We may therefore conclude that the electron- naphthene at 25°С.
acceptor properties of the PINO radical and its elec-
tron density distribution (the charge on an atom with
an unpaired electron) helps to reduce the activation
energy of any reaction in which it participates.
One α-deuterium atom and two β-deuterium
atoms will also affect the reaction rate constant when
hydrogen is substituted for deuterium in the
‒
CH ‒CH − moiety of the acenaphthene molecule.
2 2
The polar factor is especially pronounced in the The KIE for β-deuterium in radical reactions does not
reactions between PINO and phenols. This explains exceed 1.1 for each deuterium atom [25]. Allowing for
their high reactivity in hydrogen abstraction reactions, all possible secondary KIEs, we obtain the value of 7.7
compared to substrates with the same C–H bond for the maximum KIE for the hydrogen of acenaph-
energy as phenols. The results from [23] testify to the thene. The KIE of hydrogen, observed in the reaction
role of the polar factor: the logarithm of the rate con- of PINO with acenaphthene, thus exceeds the maxi-
stant of the reaction of substituted phenols with PINO mum KIE, which was calculated assuming a total loss
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 90 No. 11 2016