A computational study of the fluctional behaviour of group 14 substituted ortho -semiquinone radicals

Article abstract of DOI:10.1139/V10-082

The dynamics of the 1,4-migration of some O-substituted 3,5-di-tert-butyl-ortho-semiquinone radicals have been calculated by density-functional theory (DFT). There is very good agreement in the rate constant and Arrhenius parameters between these calculations and experimental values for migration of H, D, and the Me₃Si group. For the Me ₃Sn group, the calculations indicate an incredibly fast migration (k^293K = 2.0 × 10¹² s^-1), a result that is consistent with experimental data (k^293K > 10⁹ s^-1). Other O-substituents examined by DFT and compared with experimental data were H₃C and Me₂ClSn.

Full text of DOI:10.1139/V10-082

235
A computational study of the fluctional behaviour
of group 14 substituted ortho-semiquinone
radicals
K.U. Ingold and Gino A. DiLabio
Abstract: The dynamics of the 1,4-migration of some O-substituted 3,5-di-tert-butyl-ortho-semiquinone radicals have been
calculated by density-functional theory (DFT). There is very good agreement in the rate constant and Arrhenius parameters
between these calculations and experimental values for migration of H, D, and the Me3Si group. For the Me3Sn group, the
calculations indicate an incredibly fast migration (k293K = 2.0 ꢀ 1012 s–1), a result that is consistent with experimental data
(k293K > 109 s–1). Other O-substituents examined by DFT and compared with experimental data were H3C and Me2ClSn.
Key words: semiquinone radicals, group migration, group-coupled electron transfer, kinetics, density functional theory.
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Resume : Faisant appel a la theorie de la fonctionnelle de la densite (TFD), on a calcule la dynamique de la migration-1,4
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de quelques radicaux 3,5-di-tert-butyl-ortho-semiquinones O-substituees. Il existe un tres bon accord entre les constantes
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de vitesse et les parametres d’Arrhenius calculees et les valeurs experimentales pour la migration de H, D et du groupe
293K
Me3Si. Pour le groupe Me3Sn, les calculs predisent une vitesse de migration incroyablement rapide (k
s ), une valeur qui est en accord avec les donnees experimentales (k
= 2,0 ꢀ 1012
´
–1
293K
9
–1
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> 10 s ). Les autres O-substituants examines
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par la TFD et compares avec des donnees experimentales sont le H3C et Me2ClSn.
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Mots-cles : radicaux semiquinones, migration de groupe, transfert d’electron couple a un groupe, cinetique, theorie de la
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fonctionnelle de la densite.
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[Traduit par la Redaction]
that R3SnOOꢁ radicals had a similar structure, with the mag-
netically equivalent oxygen atoms arising from a fast (on the
EPR time scale, i.e., > ~107 s–1) 1,2-shift of the R3Sn group,
reaction 1. Density-functional theory (DFT) calculations
supported this hypothesis, giving inequivalent oxygen atoms
(outer/inner 17O hfs ratio = 1.47 (Sn)), with k1 = 5 ꢀ 108 s–1
at the experimental temperature of ~200 K.1
An anomaly in the electron paramagnetic resonance (EPR)
spectra of tri-organo group 14 peroxyl radicals, R3XOOꢁ, re-
cently drew our attention.1 Briefly, the g-values for this fam-
ily of radicals are rather similar (increasing from 2.015 for
X = C, through 2.024 for X = Sn, to 2.034 for X = Pb),
which implies that they all have rather similar structures.
However, their 17O hyperfine splittings (hfs) appeared incon-
sistent with similar structures. For X = C, Si, and Ge, the
two oxygen atoms are magnetically inequivalent, with the
outer 17O hfs being larger than the inner 17O hfs (outer/inner
17O hfs ratios 1.33 (C), 1.74 (Si), 1.67 (Ge)), which implies
an R3X–O–Oꢁ structure for these peroxyls. However, for X =
Sn the two oxygen atoms had been reported2 to be magneti-
cally equivalent.3 This led to the suggestion that trialkyltin
peroxyl radicals have ‘‘a penta-coordinate, trigonal bipyra-
midal structure . . . in which the vacant Sn 5d orbitals are
used to form a dative bond with the lone pair of electrons
on the terminal oxygen’’ of the peroxy function, structure
A.2 Since this appeared unlikely in view of the similarities
in the g-values of the group 14 peroxyls, we hypothesized
½1ꢂ
Since the computed rate constant for reaction 1 could not
be checked against experimental data, we searched for anal-
ogous reactions for which such data were available and set-
tled on the 1,4-shift of some trisubstituted group 14 moieties
between the two oxygen atoms in 3,6-di-tert-butyl-ortho-
semiquinone radicals, reaction 2.4
Received 2 May 2010. Accepted 11 June 2010. Published on the NRC Research Press Web site at canjchem.nrc.ca on 27 January 2011.
This article is part of a Special Issue dedicated to Professor J. C. Scaiano.
K.U. Ingold. National Research Council, 100 Sussex Drive, Ottawa, ON K1A 0R6, Canada.
G.A. DiLabio.1 National Institute for Nanotechnology, National Research Council, 11421 Saskatchewan Drive, Edmonton, AB T6G
2M9, Canada.
1Corresponding author (e-mail: Gino.DiLabio@nrc.ca).
Can. J. Chem. 89: 235–240 (2011)
doi:10.1139/V10-082
Published by NRC Research Press

236
Can. J. Chem. Vol. 89, 2011
1,4-shift for G = H3C was too slow to measure.6 It was con-
cluded that the coordinative unsaturation of tin and silicon
facilitates their coordination with a lone pair on the phe-
noxyl oxygen atom,10,11 which lowers the barrier for group
transfer.6 It was suggested that Me2SnCl migrates more
slowly than Me3Sn because the outer electrons of the chlor-
ine interact with the tin d orbitals, reducing the coordinative
unsaturation of the tin atom.6 It is the dynamics of reaction
2 with G = Me2SnCl and G = Me3Si that we hoped to match
by DFT computations to further support our hypothesis1 that
an R3SnOOꢁ radical has 2 magnetically equivalent oxygen
atoms2 because of a rapid 1,2-shift of the R3Sn group.
Since line-broadening effects have also been employed to
determine the values of k2 and the Arrhenius parameters for
G = H12 and G = D12 (see Table 1), our calculations were
extended to cover these two ortho-semiquinones.18–21 Before
we describe our computational results, it is important to rec-
ognize that there are ‘‘oddities’’ in the reported Arrhenius
parameters listed in Table 1 that probably arise from the
quite limited temperature range available in EPR line-
broadening kinetic measurements. That is, chemical
thermodynamics22 teaches us to ‘‘expect’’ an Arrhenius pre-
exponential factor (A) for reaction 2 with G = H and G = D
of ~1013–14 s–1. The same value, or possibly a slightly lower
value (~1012.5–13.5 s–1), should be expected for G = Me2SnCl
and G = Me3Si, implying that the experimental values for
the former group5–7 may have been slightly overestimated.
The experimental pre-exponential factors for G = H and
G = D are more than one log unit lower than ‘‘expected’’.
This suggests that quantum mechanical tunneling may be
significant for both H and D transfers at the temperatures in-
vestigated, an idea that is supported by the slightly higher
value of log A2 for G = D than for G = H (see Table 1).
It is also important to keep in mind that theory is not yet
capable of predicting Arrhenius parameters with high fidel-
ity to experimental values. Although significant improve-
ments in theoretical methods continue unabated, the
exponential sensitivity of kinetic parameters to computed
energies makes this a particularly challenging task for com-
putational chemistry. For anything but the smallest systems,
a better than order-of-magnitude accuracy from theory can-
not (yet) be expected.
½2ꢂ
In these radicals, the two tert-butyl substituents serve
three practical functions: (1) they simplify the EPR spectra
to splittings only by the two aromatic hydrogen atoms (and
G), (2) they ensure that the group, G, points towards the Oꢁ
moiety (rather than away), and (3) they increase the persis-
tence of the radicals, making the signals more intense and
easier to measure than would be the case for the unsubsti-
tuted radicals. These two substituents probably cause some
acceleration in the rates of reaction 2 relative to those of
similar reactions in ortho-semiquinones that lack these bulky
groups.
For G = Me3Sn, reaction 2 has been reported to be so
rapid that its rate constant could not be measured by EPR
line-broadening effects even at 183 K, the lowest tempera-
ture employed5 (a lower limit of 109 s–1 for this rate constant
was later estimated at 293 K6). The possibility that the ab-
sence of line broadening effects with G = Me3Sn was due
to the formation of a symmetric bridged structure, D, was
considered improbable for two very good reasons6: (1) D
would have considerable spin density on the tin and cause
very significant hfs by the 117Sn and 119Sn isotopes, but
these hfs were small (12.8 and 13.3 G, respectively)6; and
(2) for G = Me3Sn, the two ring protons give a 3.6 G triplet,
indicating that they are magnetically equivalent. The 3.6 G
hfs for this triplet was essentially identical to the hfs of the
two ring protons in radicals with G = Me2SnCl5 and G =
Me3Si6 at temperatures where these groups were migrating
rapidly (on the EPR time scale) between the two oxygen
atoms, namely 3.6 G5 (3.7 G)7 and ~3.9 G6, respectively.
For these last two G, the two aromatic hydrogen atoms be-
come magnetically inequivalent at low temperatures, trans-
forming into doublets of doublets: 5.2 and 2.6 G5 (5.0 and
2.5 G)7 for G = Me2SnCl, and 8.4 and 0.62 G6 for G =
Me3Si. For the tin-centered G, the earlier observations and
conclusions have been confirmed by Davies and Hawari,7
who greatly expanded the number of such tin-containing
semiquinone radicals and who also examined the migration
dynamics for G = Me2PbCl.8,9
We begin with the intramolecular H and D transfer proc-
esses. (Analogous intramolecular transfers in diamagnetic
systems have been studied by microwave and infrared spec-
troscopy.23) Our calculated values for log(A/s–1) for B?C
with G = H and G = D are about 12.6 and are therefore in
reasonable accordance with our ‘‘thermochemical expecta-
tions’’, being roughly one log unit larger than the reported
values. Computed rate constants, with tunneling corrections
obtained using an Eckart approach,24 are in excellent agree-
ment with experimental values. The computed kinetic iso-
tope effect (kH/kD) of 10 with tunneling (4.3 without
tunneling) is in very good agreement with the experimental
value of 10.7.
In addition to quantum mechanical tunneling, the mecha-
nism for the hydrogen and deuterium exchange must also in-
volve intramolecular proton-coupled electron transfer
(PCET).25 Figure 1a shows a side view of B (G = H) show-
ing relevant orbitals. The minimum energy structure of B
has an intramolecular hydrogen bond between the OH group
Values of k2 and the Arrhenius parameters for reaction 2
have been estimated from EPR line-broadening effects and
reported for G = Me2SnCl5,7 and Me3Si6 (see Table 1). The
Published by NRC Research Press

Ingold and DiLabio
237
Table 1. Experimental and calculated13–17 rate constants for reaction 2 at 293 K and
Arrhenius parameters (Ea in kcal/mol).
Experimental
Calculated
G
k2 (s–1)
3.2ꢀ109
0.3ꢀ109
<104
2.5ꢀ106
2.5ꢀ106
2.2ꢀ106
>109
log(A/s–1) Ea
k2 (s–1)
log(A/s–1) Ea
Ha,b
11.5
11.8
2.9
4.5
2.0ꢀ109c
0.2ꢀ109f
1.0ꢀ10–16
5.9ꢀ105
6.9ꢀ107
6.9ꢀ107
2.0ꢀ1012
12.7
12.6
13.1
12.4
12.8
12.8
12.8
2.0d
Da,e
H3Ch,i
Me3Sih,j
Me2SnClh,k
Me2SnCll
Me3Snh,m
2.5g
39.6
9.0
5.3
5.3
13.2
14.4
14.1
9.3
10.7
10.4
0.7
aExperimental data in heptane, ref. 17.
b273–393 K.
cWithout tunneling: 2.3 Â 108 s–1.
dWithout tunneling: 5.8 kcal/mol.
e293–393 K.
fWithout tunneling: 5.3 Â 107 s–1.
gWithout tunneling: 6.6 kcal/mol.
hExperimental data in toluene, ref. 6.
i263–473 K.
j273–333 K.
k163–223 K.
lExperimental data in xylene, ref. 7. 208–404 K. This reference also includes the following kinetic
data: G; k2/106 s–1; log(A/s–1); Ea (kcal/mol): Bu2SnCl, 0.47, 13.6, 10.6; Ph2SnCl, 0.49, 14.4, 11.7;
(MeCO2)3Sn, 25, 14.1, 8.9; Me2PbCl, 4.6, 11.7, 6.7.
m183–403 K.
Fig. 1. (a) Simplified illustration of the orbitals of the minimum energy structure of B (di-tert-butyl groups omitted). The lone-pair orbitals
are shaded gray and singly occupied orbitals are white. The intramolecular hydrogen bond is indicated by the red dashed line, which also
indicates the path transited by the proton during the exchange reaction. (b) Top-down and (c) tilted views of the hydrogen exchange transi-
tion state (TS) of an unsubstituted semiquinone with its singly occupied molecular orbital (SOMO). The SOMO is p-type and delocalized
across the OꢃꢃꢃHꢃꢃꢃO centres as well as through the ring. The colours of the orbital represent its relative phases. (d) Side view of a ball-and-
stick model of the hydrogen exchange TS of semiquinone. The black arrow indicates the direction of transfer of a proton, the path for which
lies in the plane of the ring. The blue arrow shows one possible route of the transferring electron, along a path that is parallel to the path of
the proton but out of the plane of the ring. The green, curved arrow shows a second route for the electron, along a path through the ring
orbitals and also out of the plane of the ring.
and the lone pair of electrons on the (formal) Oꢁ centre. This
hydrogen bond lies in the plane of the ring. Hydrogen ex-
change cannot occur easily via a hydrogen atom transfer
(i.e., a proton with its electron) because the lone pair on the
‘‘receiving’’ oxygen atom cannot accept an extra electron.
Instead, exchange occurs through a transition state involving
a proton transfer from the OH group to the Oꢁ across the
hydrogen bond. Concurrent with proton transfer, an electron
Published by NRC Research Press

238
Can. J. Chem. Vol. 89, 2011
˚
˚
Fig. 2. Transition state structures for reaction 2 with (a) G = CH3, R(H3C–O) = 2.09 A, (b) G = Me3Si, R(Me3Si–O) = 1.98 A, and (c) G =
Me2SnCl, R(Me2ClSn–O) = 2.24 A.
˚
˚
Fig. 3. (a) The minimum energy and (b) transition state (R(Me3Sn–O) = 2.27 A) structures for B with G = Me3Sn.
is transferred via the p-type bond involving the OꢃꢃꢃHꢃꢃꢃO
atoms, which is perpendicular to the ring. This is clearly
seen in the singly occupied molecular orbital (SOMO) of
the hydrogen exchange transition state (TS) illustrated in
Figs. 1b and 1c. The conjugative delocalization of the O or-
bitals into the ring provides a second ‘‘route’’ for the elec-
tron to take in the PCET process and this is also
demonstrated by the SOMO shown in Figs. 1b and 1c. The
path taken by the proton and possible paths used for trans-
ferring the accompanying electron are illustrated in Fig. 1d.
Theory has previously implicated multiple paths for transfer-
ring the electron in PCET processes that involve the follow-
ing bimolecular identity reactions: oxime + iminoxyl,26
toluene + benzyl, and phenol + phenoxyl.27
tion of the reaction coordinate reveals that the TS can be
reached by rotation of the SiMe3 group about the Si–O
bond. The resultant steric repulsion between the methyl
groups on G and the neighbouring tert-butyl substituent is
then sufficiently high that the Me3Si–O bond is lengthened
to the TS value.
For G = Me2SnCl, the predictions made by theory are in
somewhat poorer agreement with experimental data. How-
ever, the calculated log(A/s–1) is in line with thermochemical
expectations, vide supra. Calculations predict a rather small
activation energy of 5.3 kcal/mol, which contributes to the
large rate constant. The minimum energy structure of B
with G = Me2SnCl has the chlorine atom pointed toward
the adjacent tert-butyl group. To reach the TS (Fig. 2c), the
Me2(Cl)Sn group must rotate by about 908 while the
In principle, processes similar to PCET as described for
G = H and D in reaction 2 should also occur for other G,
provided that the central atom in G is able to undergo facile
valence shell expansion. If this is the case, we may general-
ize the PCET mechanism to ‘‘GCET’’, or group-coupled
electron transfer. It is clear that for G = CH3, GCET is not
able to occur. This is simply because pentavalent carbon is
energetically highly disfavoured (i.e., there is no energeti-
cally low-lying empty orbital on CH3). The calculations in-
dicate that the O–CH3 bond would need to lengthen by
˚
Me2(Cl)Sn–O bond must lengthen by about 0.09 A.
The case of G = Me3Sn is particularly interesting. The
calculations indicate that B (G = Me3Sn) has an asymmetric
energy minimum wherein there is no Me–Sn bond exactly
perpendicular to the plane of the aromatic ring (Fig. 3a).
This minimum energy structure produces all positive vibra-
tion frequencies, verifying that it is indeed a minimum on
the potential energy surface. Similarly, the TS structure,
shown in Fig. 3b, was verified as such with the calculations
giving one imaginary frequency associated with group trans-
fer (reaction 2). The magnitude of the imaginary frequency
is only 37.8 cm–1, indicating that reaching the TS requires
very little energy. In fact, the Me3Sn–O bond length in the
minimum energy structure only needs to be lengthened by
˚
0.65 A to reach the TS structure. Therefore, the barrier to
group transfer is very high and results in a very low rate
constant. A picture of the TS associated with reaction 2 for
G = CH3 is shown in Fig. 2a.
Additional calculations indicate that the barrier associated
with hydrogen atom transfer from G = CH3 to the (formal)
Oꢁ is much more likely than group transfer. The activation
barrier for this endothermic process is predicted by theory
to be about 25.5 kcal/mol.
˚
about 0.03 A to reach its TS length. Vibrational analyses
and potential energy surface scans show that the TS can be
reached from the minimum energy structure by a slight rota-
tion of the Me3Sn group about the Sn–O bond, as is evident
upon examination of Fig. 3. Inclusion of thermal corrections
(293 K) to the electronic energies results in a predicted Ea of
0.70 kcal/mol. This calculated Ea value is too small to be re-
liable but it does imply that transfer of the G = Me3Sn
group is extremely facile, in accordance with the experimen-
tal observations.28,29 Moreover, theory indicates that the
The calculated kinetic parameters with G = Me3Si are in
very gratifying agreement with experimental values. To
reach the TS (see Fig. 2b), the O–SiMe3 bond must lengthen
˚
by approximately 0.25 A. This results in a much lower bar-
rier height and larger rate constant for transfer with G =
Me3Si than for transfer with G = CH3. A detailed examina-
Published by NRC Research Press

Ingold and DiLabio
239
ney, C.; Harrison, P. G. J. Chem. Soc. Perkin Trans. 2,
1982, 631. doi:10.1039/P2980000625.
minimum energy structure should be represented by B and
not by D, which is also in accordance with the conclusions
reached by Prokof’ev et al.6 on the basis of EPR spectral
evidence, vide supra.
The present calculations are in sufficiently good agree-
ment with experimental data that it is fairly safe to conclude
that we have been employing appropriate methodology to
study these kinds of dynamic processes and they therefore
provide additional support for our earlier conclusion1 that
the R3Sn group in R3SnOOꢁ radicals undergoes such a fast
1,2-shift that the two oxygen atoms are magnetically equiv-
alent on the EPR time scale.
(10) In this connection, it has recently been demonstrated that
oxygen-centered radical attack on alkyl and aryl borane sub-
strates does not occur by a traditional SH2 process.11 Instead,
it involves a nucleophilic attack of an oxygen lone pair on
the empty boron p orbital. The unpaired electron on the oxy-
gen is not directly involved, but the boron–ligand bond
aligned with the SOMO cleaves and the ligand leaves
promptly. The mechanism was described as a nucleophilic
homolytic substitution at boron.
(11) Carra, C.; Scaiano, J. C. Eur. J. Org. Chem. 2008, 2008 (26),
4454. doi:10.1002/ejoc.200800187.
(12) Prokof’ev, A. I.; Bubnov, N. N.; Solodnikov, S. P.; Kabach-
nik, M. I. Tetrahedron Lett. 1973, 14 (27), 2479. doi:10.
1016/S0040-4039(01)96183-0.
Acknowledgements
We thank Prof. A. G. Davies for sharing his extensive
knowledge and for his continued advice and encouragement
and Dr. Bun Chan (University of Sydney) for helpful discus-
sions. We also thank P. Boulanger (University of Alberta)
for computational resources.
(13) Calculations were performed using B314LYP15/6-311+G(d,p)
as implemented in ref. 16. For radicals containing Sn, we
used the averaged relativistic effective potentials of LaJohn
et al.17 with the accompanying basis set, which was used un-
contracted.
(14) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. doi:10.1063/1.
464913.
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(18) It has been reported that ‘‘solvents capable of forming hydro-
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bonds are capable of forming bifurcated intra/intermolecular
H bonds,19 which reduces the rates of H-atom abstraction20
just as intermolecular H bonding reduces the rates of ab-
straction from simple phenols.21 Fortunately, the experiments
in question4a were done in heptane, which is neither an H-
bond donor nor acceptor, so the kinetic measurements should
be directly comparable with the computed dynamics.
(19) Litwinienko, G.; DiLabio, G. A.; Mulder, P.; Korth, H.-G.;
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