Hydrogen hyperfine splitting constants for phenoxyl radicals by DFT methods: Regression analysis unravels hydrogen bonding effects

Article abstract of DOI:10.1039/c003302b

DFT calculations using the B3LYP functional, medium-sized basis sets and empirical scaling of the results provide quantitative estimates of the hydrogen isotropic hyperfine splitting constants (hscs) in 2,6-di-alkyl phenoxyl radicals (1-11). Literature hs

Full text of DOI:10.1039/c003302b

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Organic &
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Chemistry
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Volume 8 | Number 14 | 21 July 2010 | Pages 3085–3344
ISSN 1477-0520
FULL PAPER
Riccardo Amorati et al.
FULL PAPER
Hydrogen hyperfine splitting
constants for phenoxyl radicals by
DFT methods: regression analysis
unravels hydrogen bonding effects
Stefan Bräse et al.
Enantioselective total synthesis of
plakotenin, a cytotoxic metabolite
from Plakortis sp

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PAPER
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Hydrogen hyperfine splitting constants for phenoxyl radicals by DFT
methods: regression analysis unravels hydrogen bonding effects†
Riccardo Amorati,*a Gian Franco Pedullia and Maurizio Guerrab
Received 19th February 2010, Accepted 20th April 2010
First published as an Advance Article on the web 17th May 2010
DOI: 10.1039/c003302b
DFT calculations using the B3LYP functional, medium-sized basis sets and empirical scaling of the
results provide quantitative estimates of the hydrogen isotropic hyperfine splitting constants (hscs) in
2,6-di-alkyl phenoxyl radicals (1–11). Literature hscs for phenoxyl (12), 4-methylphenoxyl (13) and
4-methoxyphenoxyl (14) radicals, on the other hand, are poorly predicted by using this method. This
different behaviour is explained considering that experimental hscs of 12–14 are influenced by H-bonds
formed between phenoxyls and their parent phenols, usually present in large amounts in solution as
radical precursors. This was confirmed experimentally by measuring the EPR spectra of 12–14 in the
presence of increasing amounts of their parent phenols, and by calculating the hscs in the case of the
formation of 1 : 1 and 1 : 2 complexes between these radicals and phenol. Relevance of these results to
the choice of reference hscs as benchmarks for theoretical calculations and to kinetic and
thermochemical determinations on unhindered phenoxyl radicals is discussed.
Introduction
Phenoxyl radicals represent one of the most important families of
biologically relevant radicals. Their formation is fundamental in
enzyme catalysis,1 in photosynthetic events,2 in the biosynthesis of
lignanes3 and in the action of phenolic antioxidants4 (Scheme 1).
Most information about phenoxyl radicals is provided by electron
paramagnetic resonance (EPR) spectroscopy, which allows to
detect and characterize structural and dynamic properties of
radicals in a wide range of environments.5 Isotropic hyperfine
splitting constants (hscs),‡ measured in the case of fast rotational
motion of radicals, give valuable insight into electronic properties
and presence of intra and inter-molecular hydrogen bonding
interactions. For instance, the addition of hexafluoropropanol
(HFP), a strong H-bond donor, has dramatic effects on isotropic
hscs of several phenoxyl radicals, including a-tocopheroxyl,6 while
H-bond accepting solvents, such as dimethylsulfoxide and acetoni-
trile, cause noticeable changes on hscs in neutral semiquinones.7
The abundance of data that can be extracted from experimental
hscs is nowadays interpreted with the help of theoretical calcula-
tions. Among the various approaches, methods relying on density
functional theory represent a convenient compromise between
accuracy and computational cost.5 The ability of DFT methods
to reproduce hydrogen hscs in the phenoxyl radical in vacuum or
Scheme 1 Relevant examples of phenoxyl radicals involved in biological
processes. A: biosynthesis of the lignan (+)-pinoresinol;3 B: antioxidant ac-
aDepartment of Organic Chemistry “A. Mangini”, University of Bologna, Via
S. Giacomo 11, 40126, Bologna, Italy. E-mail: riccardo.amorati@unibo.it;
Fax: (+39) 051-209-5684
tion of a-tocopherol;4a C: tyrosyl radical in the active site of prostaglandin
H synthase (PGHS-1).1c
bISOF, Consiglio Nazionale delle Ricerche, Via P. Gobetti 101, 40129,
Bologna, Italy
in aqueous environment has been already investigated in the past.
Eriksson noticed that hybrid DFT calculations provide reasonably
good estimates of hydrogen hscs in p radicals, such as phenoxyl and
benzyl.8 The hyperfine splitting constants for the phenoxyl radical
were also calculated by Barone and co-workers using the B3LYP
functional and the basis sets EPR-II and EPR-III.9 By using the
PCM model, the hscs for the ortho, meta and para hydrogens
were computed to change from 7.3, 2.8, 9.4 G in the gas phase
† Electronic supplementary information (ESI) available: Experimental hscs
from literature for 1–14; experimental hsc and EPR spectra at every parent
phenol concentration for 12–14; plots of experimental versus calculated
hsc for each computational level. See DOI: 10.1039/c003302b
‡ Theoretical calculations provide hyperfine coupling constants, which can
be positive or negative at a given atom. Hyperfine splitting constants,
measurable from EPR spectra, are the absolute values of the corresponding
coupling constants.
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to 6.6, 2.4, 9.8 G in water9 (experimental values in H2O: 6.6,
1.9, 10.2 G).10 Similar results were also obtained by Chipman,
who investigated the effect of water by employing the B3LYP
functional and a purposely tailored basis set ([631|41]), and by
explicitly considering H2O molecules.11
Results and discussion
Considering the difficulty of calculating “exact” hscs from a single
calculation,5 in the present work we used empirical relationships
between calculated and experimental constants to obtain reliable
hscs at a low computational cost. This approach is based on the fact
that, even at low levels of theory, the linearity of the experimental
vs. calculated hscs for a wide range of radicals is excellent.23
To compare calculated hscs with homogeneous experimental
data, only hscs measured in benzene were chosen from the litera-
ture. Typically, these data were obtained by stationary photolysis
of the parent phenols, in the presence of small amounts of tert-
butyl peroxide.13,24,25 The experimental values used to validate the
computational approach are reported in ESI.† Very small hscs,
that are those given by the hydrogens of the tert-butyl groups and
of the para substituents of 6 and 8 (Scheme 2), were not included
in the regression analysis.
Validation of theoretical methods for the description of a
molecular property critically depends, however, on the availability
of good-quality experimental values. While all hscs for phenoxyl
radicals reported in literature are coincident when measured in
water,10 those measured in apolar solvents are not. The hscs for
the phenoxyl radical generated in CCl4 using photolysis and a
flow system are 7.02, 2.05 and 10.13 G for ortho, meta and para
hydrogens,12 while the hscs obtained by stationary photolysis in
benzene13,14 are, on the basis of the considerations made above,
unexpectedly similar to those measured in water: 6.57, 1.84 and
10.07 G for ortho, meta and para hydrogens, respectively.13
In this work, we show that relatively inexpensive DFT methods
predict, in some cases almost quantitatively, hydrogen hscs of
phenoxyl radicals, and provide an explanation for the less clear
aspects of the chemistry of these radicals.
Experimental section
Materials
Solvents, phenol, 4-methylphenol and 4-methoxyphenol were
of the highest grade commercially available and were used as
received. Di-tert-butylperoxide was percolated through activated
basic alumina and stored at 5 ◦C.
Scheme 2
EPR experiments
Deoxygenated benzene solutions containing the investigated phe-
nol (5 ¥ 10-4 – 2 M) and di-tert-butylperoxide (5% v/v) were
sealed under nitrogen in a suprasil quartz EPR tube. The sample
was inserted in the cavity of an EPR spectrometer and photolyzed
with the unfiltered light from a 500 W high-pressure mercury lamp.
Hyperfine splitting constants were determined by numerical fitting
of experimental spectra13 and the error is within 0.02 G.
1. Regression analysis of hscs of hindered phenols
Good straight lines are obtained when the experimental hscs of
radicals 1–11 are plotted versus the calculated ones (see Fig. 1
and ESI†). Their slope, intercept and correlation coefficients are
reported in Table 1. Both B3LYP and PBE0 functionals provide,
after scaling, hscs in good agreement with experiments, B3LYP
being somewhat superior when all hscs are considered. These
results also confirm that good correlations between experimental
and calculated hscs are achieved already with small basis sets,23
such as 6-31G(d), with the exception of radical 4 which requires
the 6-311+(2df,p) basis set to be properly simulated (see ESI†).
Computational details
DFT calculations were carried out using the Gaussian03 system of
programs.15 Geometries were optimized at the B3LYP/6-31G(d)
level. This level has been demonstrated to yield sufficiently accu-
rate structures for phenoxyl radicals.9 Enthalpies at 298 K were
computed at the stationary points from frequency calculations
using a scaling factor of 0.9806 to account for anharmonicity.16
The nature of the ground states was verified by frequency
calculations (zero imaginary frequency). Hscs were obtained from
the absolute values of coupling constants calculated by using the
functionals B3LYP17 and PBE0518 (in Gaussian03: PBE1PBE).
Different basis sets were used: 6-31G(d),19 6-31+G(d,p),20 6-
311+G(2df,p) which has been previously suggested for reliable
hsc calculations,21 and the EPR-III basis set.22 The tight SCF
convergence criteria was used in single point calculations. The
influence of vibrational averaging on coupling constants was not
investigated, as it was previously found to have negligible effect in
this kind of radicals.9
Fig. 1 Experimental versus calculated hyperfine splitting constants for
1–11 (᭹)13,24,25 and for 12–14 (᭺: literature values;6,13 ꢀ; from this work,
at low parent phenol concentration). Panel a: all hscs. Panel b, hscs for
meta hydrogens.
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Table 1 Experimental versus calculated hyperfine splitting constants: data analysisa for phenoxyl radicals 1–11 (in gauss)
B3LYP
PBE0
6-31G(d)
6-31+G(d,p)
6-311+G(2df,p)
EPR–IIIb
6-311+G(2df,p)
EPR–IIIb
All H
Slope
Intercept
r2
1.152
-1.123
0.988
1.140
-0.964
0.993
1.160
-0.728
0.993
1.070
-0.680
0.994
1.179
-1.551
0.979
1.127
-1.788
0.985
meta H
Slope
Intercept
r2
0.863
-0.512
0.990
0.850
-0.348
0.993
0.943
-0.306
0.993
0.894
-0.379
0.998
0.778
-0.587
0.993
0.742
-0.671
0.998
a Hscexp = slope ¥ hsccalc + intercept. b Excluding radicals from compounds 4 and 5 since the basis sets for S and Cl atoms are lacking in EPR-III.
2. Experimental determination and simulation of hscs of
unhindered phenols
A peculiar behaviour is observed when plotting in the same graph
experimental vs. calculated hscs of ortho unhindered radicals 12–14
and those of 1–11 (Fig. 1). Phenoxyls 12–14 are more or less on the
same line of the hindered ones, if considering all hscs (Fig. 1a), but
when restricting the analysis only to the meta hydrogens, they are
visibly outside the main regression line (Fig. 1b, empty circles). The
hscs for 12–14 are still outside the regression line also employing
the PBE0 functional or different basis sets (see ESI†). This suggests
that the problem may not be in the method used to calculate hscs,
but in experimental data. As it has been previously reported that
hscs are strongly influenced by formation of H-bonds with HFP,6
we hypothesized that parent phenols present in the samples as
precursors of phenoxyl radicals might behave as H-bond donors.
These interactions are absent in the case of 1–11 as the ability to
donate H-bond is drastically reduced by steric repulsion.26,27,
§
To check this hypothesis, we measured the EPR spectra of
radicals 12–14 by stationary photolysis at various concentrations
of their respective parent phenols (Fig. 2). Experimental data,
summarized in Fig. 2, show remarkable changes of hscs with
the concentration of the parent phenols. The measured overall
hscs are expected to be due to the hsc of each species present in
solution (see Scheme 3 for the most important ones), weighted for
their molar fractions, as H-bonding equilibria are fast in the time
scale of EPR.6 Hscs measured at the smallest concentration of the
parent phenols provide an estimate of the “true” hscs in benzene
(Table 2) and are in better agreement with calculated ones than
those reported in literature (Fig. 1b, triangles).
Fig. 2 Proton hyperfine splittings measured in the EPR spectra of radicals
12 (᭺), 13 (᭹) and 14 (ꢀ) obtained by photolyzing increasing amounts
3
3
=
=
of phenol (R H), 4-methylphenol (R CH3) and 4-methoxyphenol
3
t
t
=
(R OCH3) in benzene containing 10% of BuOO Bu.
Scheme 3 Complexes formed by radicals 12 and 13 and their parent
phenols.
To have further insight into H-bonding effect on the hscs of
unhindered phenoxyls, we investigated radicals 12–14 by DFT
calculations in the presence of their parent phenols. The geometries
of the H-bond complexes, shown in Scheme 3 for 12 and
13, were optimized at the B3LYP/6-31G(d) level. Phenol was
§ The H-bond donating ability, expressed by the a2H parameter, of phenol,
4-methylphenol, 4-methoxyphenol, 2,6-tBu-4-MeC6H2OH and HFP are
0.60, 0.57, 0.57, ª0.18, 0.77 respectively (ref.26,27,28).
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Table 2 Comparison between the hsc values (in gauss) for radicals 12–14 calculated in the absence and in the presence of H-bond interactions with one
or two phenol molecules and the experimental hscs measured at the lowest and at the largest parent phenol concentration
Hsc 2,6 (2H)
Hsc 3,5 (2H)
Hsc 4
Radical
Calc’a
Exp
Calc’a
Exp
Calc’a
Exp
12
6.78
6.58
6.35
6.86b
6.63c
6.48b
6.24c
5.91b
2.11
1.95
1.81
2.01b
1.87c
1.79b
1.48c
0.99b
9.18
9.25
9.39
9.92 (H)b
10.01c
PhOH ◊ ◊ ◊ 12
2PhOH ◊ ◊ ◊ 12
13
6.43
6.14
5.84
1.85
1.64
1.42
11.64
12.18
12.68
11.63 (CH3)b
12.17c
PhOH ◊ ◊ ◊ 13
2PhOH ◊ ◊ ◊ 13
14
5.79
5.32
6.07
4.85
5.63
5.21
1.15
0.79
1.38
0.46
1.06
0.75
0.91
1.53
0.97
1.74
1.17
1.35
1.68 (OCH3)b
1.93c
PhOH ◊ ◊ ◊ 14a
PhOH ◊ ◊ ◊ 14b
2PhOH ◊ ◊ ◊ 14a
2PhOH ◊ ◊ ◊ 14b
3PhOH ◊ ◊ ◊ 14
5.29c
0.46c
a Hscs were calculated at the B3LYP/6-311+G(2df,p)//B3LYP/6-31G(d) level and then corrected using the following equations taken from Table 1: ortho
and para positions: hsccalc’ = 1.16 ¥ hsccalc -0.728; meta position: hsccalc’ = 0.943 ¥ hsccalc -0.306. b Measured in the present work at small concentration of
the parent phenol. c Measured in the present work at large concentration of the parent phenol.
chosen as H-bond donor in all cases to simplify calculations,
considering that phenol, 4-methylphenol and 4-methoxyphenol
have approximately the same H-bond donating ability.§,26,27 In the
case of 14, where the situation is complicated by the presence of
two H-bond acceptors, i.e. the -O∑ and the –OCH3 groups, the
structures reported in Scheme 4 were examined.
Table 2, it can be inferred that calculations correctly reproduce
the hsc variation observed experimentally, that is, on increasing
the number of H-bond donors (that is, the concentration of the
parent phenol), hscs for the ortho and meta hydrogens decrease,
while the para hsc increases.
Quantitative considerations can be made by restricting the
analysis only to the meta constants. Table 2 shows that the
experimental hscs measured in radicals 12 and 13 at the largest
concentrations of the parent phenol (1.8 and 2.0 M respectively)
are between the values calculated for the phenoxyl radicals forming
one or two H-bond interactions. Therefore, it may be concluded
that phenoxyl radicals 12 and 13 are complexed by, on average,
between one and two parent phenol molecules.
In the case of 14, complexation of the two possible H-bond
accepting sites (i.e. ArO∑ and OCH3 moieties) has very different
effects on hscs. H-bond donation to phenoxyl oxygen lowers
meta hydrogens hsc, whereas interaction with the oxygen atom
of the methoxy group has about equal but opposite effect on
this constant. The very low value of the meta-H hsc determined
experimentally at the largest concentration of the parent phenol
(1.4 M) is compatible only with the structure 2PhOH ◊ ◊ ◊ 14a
(Scheme 4). On the other hand, we can exclude any structure with
the OCH3 group acting as H-bond donor. This result is in good
agreement with the expected order of formation of the various
complexes, which can be derived from the values of the enthalpy
estimated for H-bond formation, reported in Scheme 4.
It may be also noted that 14 is complexed to a larger extent than
radicals 12 and 13, implying that the H-bonds between radical 14
and 4-methoxyphenols are stronger than those formed between
radicals 12 and 13 and their parent phenols. This observation
was confirmed by calculating the DHf values for the relevant H-
bonding equilibria, reported in Table 3.
Scheme 4 Possible complexes between radical 14 and phenol, and
calculated enthalpy for H-bond formation DHf (kcal mol-1). The species
preferentially formed are evidenced.
Hscs were calculated at the B3LYP/6-311+G(2df,p)//B3LYP/
6-31G(d) level and, to be compared to experimental results,
were corrected using the correlation equations for this level of
theory (see footnote a of Table 2). From the results reported in
Conclusions
In this work we have demonstrated that relatively cheap DFT
calculations using the popular B3LYP functional and small
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Table 3 Calculated
(B3LYP/6-311+G(2df,p)//B3LYP/6-31G(d))
strength of the H-bonds between phenoxyl radicals 12–14 and phenol
increased persistency, that reflects the decrease of the rate of self-
decay, of phenoxyl radicals at large HFP concentrations6 seems
to confirm this hypothesis. Further clarification of these points is
moleculesa
∑
∑
∑
DHf (PhOH ◊ ◊ ◊ OAr)b
DHf (2PhOH ◊ ◊ ◊ OAr)c
of great interest given the presence of ArOH ◊ ◊ ◊ OAr H-bonded
Radical
structures in natural systems, such as that shown in Scheme 1.
Finally, it can be also concluded that experimental hscs in
apolar solvents should be taken with caution as a reference for
theoretical calculations, in particular for radicals which are good
H-bond acceptors or donors, unless very low concentrations of
the precursors have been used in the EPR determinations.
12
13
14
-5.8
-6.2
-6.9d
-4.4
-4.8
-5.3e
a kcal mol-1, b PhOH + ∑OAr = PhOH ◊ ◊ ◊ OAr, c PhOH + PhOH ◊ ◊ ◊ OAr =
∑
∑
∑
2PhOH ◊ ◊ ◊ OAr, d PhOH ◊ ◊ ◊ 14a, e 2PhOH ◊ ◊ ◊ 14a.
and medium-sized basis sets provide, after scaling the results,
quantitative estimates of the proton hyperfine splitting constants
in phenoxyl radicals. The agreement between experimental and
calculated hscs is particularly good in the case of the meta H-atoms,
reasonably because the absence of substituents in this position
makes the regression approach more effective. For the other
hydrogens, the procedure described herein leads to hscs that are
0.5 G with respect to experimental values, thus representing a good
starting point for spectra interpretation in EPR spectroscopy. This
procedure has been successfully applied to clarify the association
state of three unhindered phenoxyl radicals.
Our results show that the majority of the hscs reported in the
literature for unhindered phenoxyl radicals in apolar solvents13,14
actually refer to the radicals forming extensive H-bonds with
parent phenols molecules. Unfortunately, as unhindered phenols
are very good H-bond donors, this can be avoided only by using
very diluted solutions, such as those employed in the present work
and in the experiments of Graf et al.12 Moreover, little differences
in parent phenol concentrations may lead to significant changes in
hscs, thus explaining why in apolar solvents there is such variability
of hsc values. In water, where each H-bond accepting or donating
site of the investigated phenoxyls is solvated by H2O molecules,
hscs are not dependent on the parent phenol concentration and
are therefore much more reproducible.10
This observation also opens several questions about the reli-
ability of kinetic and thermodynamic measures carried out on
unhindered phenoxyl radicals in apolar solvents. In the case of
the determination of the bond dissociation enthalpy (BDE) of
the phenolic O–H via the EPR equilibration technique,13 or via
the photoacustic calorimetric method (PAC),28 usually performed
with parent phenols in the 0.05–0.5 M concentration range, error
compensations can be envisaged as the cause for the relatively good
agreement between measured and computed results. The BDE-
lowering effect given by H-bonding with the phenoxyl radicals6
are counterbalanced by the BDE-increasing effect of H-bonds
formed by the ArOH group in the parent phenol.27
Acknowledgements
Financial support from MIUR (Research projects “Radicals and
Radical Ions: Basic Aspects and Role in Chemistry, Biology, and
Material and Environmental Sciences”, contract 2006033539) is
gratefully acknowledged.
Notes and references
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H
H
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the reagent radical more than the product phenol, so that the
driving force for H-atom abstraction is reduced. Formation of
two H-bond interactions, as happens when generating phenoxyl
radicals in the presence of very concentrated solutions of the
parent phenol,30 may lead to further reactivity decrease. The
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