Kinetic solvent effects on hydrogen-atom abstractions: Reliable, quantitative predictions via a single empirical equation

Article abstract of DOI:10.1021/ja002301e

The rate of hydrogen-atom abstraction from XH by a radical, Y^·, can be solvent-dependent. In many cases, the kinetic solvent effect (KSE) is directly related to hydrogen-bonding interactions between XH and the solvent. The relative hydrogen-bond acceptor (HBA) properties of solvents are given by β₂/^H constants of Abraham et al. (Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Morris, J. J.; Taylor, P. J. J. Chem. Soc. Perkin Trans. 2 1990, 521-529). Room-temperature rate constants for hydrogen-atom abstraction, k_XH/Y^·/^S, have been determined in a number of solvents, S, where XH refers to several substituted phenols, tert-butyl hydroperoxide or aniline and Y^· is a tert-alkoxyl radical. In all cases, plots of log(k_XH/Y^·/^S/M^-1 s^-1) versus β₂/^H gave excellent linear correlations, the slopes of which, M_XH, were found to be proportional to the hydrogen-bond-donating (HBD)ability of XH, as scaled with α₂/^H parameters of Abraham et al. (Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Duce, P. P.; Morris, J. L.; Taylor, P. J. J. Chem. Soc., Perkin Trans. 2 1989, 699-711), with M_XH = - 8.3α₂/^H. This leads to a general empirical equation which quantifies KSEs at room temperature: log k_XH/Y^·/^S = log k_XH/Y^·O - 8.3α₂/^Hβ₂/^H, where k_XH/Y^·/^O refers to the rate constant in a non-HBA solvent for which β₂/^H = 0, generally a saturated hydrocarbon. Since M_XH depends only on XH, rate constants for hydrogen-atom abstraction from XH by any Y^· can be accurately predicted in any of the several hundred solvents for which β₂/^H is known on the basis of one single measured rate constant, provided α₂/^H for XH is known or measured. HBA solvents can have profound effects on some of the reactions and thermodynamic properties of hydroxylic substrates including: (i) reaction product profiles (ii) antioxidant activities, (iii) Hammett-type correlations, and (iv) O-H bond dissociation enthalpies. Finally, literature data (Nielsen, M. F.; Hammerich, O. Acta Chem. Scand, 1992, 46, 883-896) on KSEs for two proton-transfer reactions are shown to be correlated by the same equation which correlates KSEs for hydrogen-atom transfers.

Full text of DOI:10.1021/ja002301e

J. Am. Chem. Soc. 2001, 123, 469-477
469
Kinetic Solvent Effects on Hydrogen-Atom Abstractions: Reliable,
Quantitative Predictions via a Single Empirical Equation1
Darren W. Snelgrove,2a,b Janusz Lusztyk,2a J. T. Banks,2a,c Peter Mulder,2a,d and
K. U. Ingold*,2a,b
Contribution from the Steacie Institute for Molecular Sciences, National Research Council of Canada,
100 Sussex DriVe, Ottawa, Ontario, Canada K1A 0R6, Department of Chemistry, Carleton UniVersity,
1125 Colonel By DriVe, Ottawa, Ontario, Canada K1S 5B6, and Leiden Institute of Chemistry, Leiden
UniVersity, P.O. Box 9502, 2300 RA Leiden, The Netherlands
ReceiVed June 26, 2000. ReVised Manuscript ReceiVed NoVember 1, 2000
Abstract: The rate of hydrogen-atom abstraction from XH by a radical, Y•, can be solvent-dependent. In
many cases, the kinetic solvent effect (KSE) is directly related to hydrogen-bonding interactions between XH
and the solvent. The relative hydrogen-bond acceptor (HBA) properties of solvents are given by âH2 constants
of Abraham et al. (Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Morris, J. J.; Taylor, P. J. J. Chem. Soc.
Perkin Trans. 2 1990, 521-529). Room-temperature rate constants for hydrogen-atom abstraction, kXS H/Y
,
•
have been determined in a number of solvents, S, where XH refers to several substituted phenols, tert-butyl
hydroperoxide or aniline and Y• is a tert-alkoxyl radical. In all cases, plots of log(kXS H/Y•/M-1 s-1) versus â2H
gave excellent linear correlations, the slopes of which, MXH, were found to be proportional to the hydrogen-
bond-donating (HBD) ability of XH, as scaled with RH2 parameters of Abraham et al. (Abraham, M. H.;
Grellier, P. L.; Prior, D. V.; Duce, P. P.; Morris, J. J.; Taylor, P. J. J. Chem. Soc., Perkin Trans. 2 1989,
699-711), with MXH ) - 8.3RH. This leads to a general empirical equation which quantifies KSEs at room
2
temperature: log kSXH/Y• ) log kO • - 8.3RHâH, where kO • refers to the rate constant in a non-HBA solvent
XH/Y
2
2
XH/Y
for which âH2 ) 0, generally a saturated hydrocarbon. Since MXH depends only on XH, rate constants for
hydrogen-atom abstraction from XH by any Y• can be accurately predicted in any of the several hundred
solvents for which âH2 is known on the basis of one single measured rate constant, provided RH2 for XH is
known or measured. HBA solvents can have profound effects on some of the reactions and thermodynamic
properties of hydroxylic substrates including: (i) reaction product profiles (ii) antioxidant activities, (iii)
Hammett-type correlations, and (iv) O-H bond dissociation enthalpies. Finally, literature data (Nielsen, M.
F.; Hammerich, O. Acta Chem. Scand, 1992, 46, 883-896) on KSEs for two proton-transfer reactions are
shown to be correlated by the same equation which correlates KSEs for hydrogen-atom transfers.
There are immense compilations of rate constants for
elementary reactions of organic free radicals in homogeneous
solution3 and perhaps as much as half of these data refers to
hydrogen-atom abstraction reactions:
for Y• ) CumO• and XH ) tert-butyl hydroperoxide or phenol.7
The absence of a KSE on the cyclohexane reaction4 necessarily
implied that these KSEs were not due to solvent effects on the
CumO• radical.8 The observed KSEs for the Me3COOH/CumO•
and PhOH/CumO• reactions were accounted for in a roughly
quantitative manner by making three assumptions:7,10
Y• + XH
9
k8 YH + X•
(i)
Each substrate molecule, XH, can act as a hydrogen-bond
donor (HBD) to only a single hydrogen-bond acceptor (HBA)
solvent molecule, S, at any one time.
Although this huge body of information is neatly tabulated by
attacking radical, Y•, there is no all-encompassing (or even partly
encompassing) rationalization of the data. Thus, it is not obvious
why H-atom abstractions from some substrates are subject to
kinetic solvent effects (KSEs) while abstractions from other
substrates are not.
Our interest in this area was sparked when we demonstrated
that there was no KSE for Y• ) cumyloxyl (CumO•, PhCMe2O•)
and XH ) cyclohexane4,5 and that there were dramatic KSEs
(5) We have also demonstrated6 that there is no KSE for H-atom
abstraction from 1,4-cyclohexadiene by cumyloxyl radicals. Furthermore,
there can be no KSE for H-atom abstraction from a carbon atom by HO•
radicals, see: Kanabus-Kaminska, J. M.; Gilbert, B. C.; Griller, D. J. Am.
Chem. Soc. 1989, 111, 3311-3314.
(6) Wayner, D. D. M.; Lusztyk, E.; Page´, D.; Ingold, K. U.; Mulder, P.;
Laarhoven, L. J. J.; Aldrich, H. S. J. Am. Chem. Soc. 1995, 117, 8737-
8744.
(1) Issued as NRCC No. 43866.
(2) (a) SIMS. (b) Carleton. (c) NRCC Research Associate, 1994-1996.
(d) Visiting Scientist from Leiden University.
(7) Avila, D. V.; Ingold, K. U.; Lusztyk, J.; Green, W. H.; Procopio, D.
R. J. Am. Chem. Soc. 1995, 117, 2929-2930.
(8) Occasional suggestions9 that solvents influence the reactiVity of tert-
alkoxyl radicals in H-atom abstractions are obviously incorrect.
(9) See e.g., Kim, S. S.; Kim, S. Y.; Ryou, S. S.; Lee, C. S.; Yoo, K. H.
J. Org. Chem. 1993, 58, 192-196. Dokolas, P.; Loffler, S. M.; Solomon,
D. H. Aust. J. Chem. 1998, 51, 1, 1119-1120.
(3) See, e.g.: Radical Reaction Rates in Solution; Fischer, H., Ed.;
Landolt-Bo¨rnstein, New Series; Springer-Verlag: Berlin; 1984; Vol. 13,
subvolumes 13a-e (∼2000 pages); 1994; Vol. 18, subvolumes 18a-e2
(∼3000 pages).
(4) Avila, D. V.; Brown, C. E.; Ingold, K. U.; Lusztyk, J. J. Am. Chem.
Soc. 1993, 115, 466-470.
(10) Assumptions adumbrated earlier by Nielsen11 for phenols acting as
proton donors to an aromatic anion radical, vide infra.
10.1021/ja002301e CCC: $20.00 © 2001 American Chemical Society
Published on Web 12/28/2000

470 J. Am. Chem. Soc., Vol. 123, No. 3, 2001
SnelgroVe et al.
Scheme 1
The magnitude of the equilibrium constant, KSXH/S•, for the
formation of an XH-S hydrogen-bonded complex is essentially
independent of surrounding medium.
For steric reasons, the H-atom in the XH-S complex cannot
be directly abstracted by Y•. The solvent molecule in the XH-S
complex must first be replaced by Y•. A simple predissociation
model is illustrated in Scheme 1. The experimentally measured
rate constant for the XH/Y• reaction in solvent, S, that is,
kSXH/Y•, is given by:7
Figure 1. Plots of log(kSXH/RO•/M-1 s-1) vs the â2H value for the
solvent, S, for XH ) R-tocopherol (9), phenol (×), and tert-butyl
hydroperoxide (O).
kOXH/Y
1 + KSXH/Y [S]
•
reliable scales of relative HBA activities of common organic
solvents would appear to be the 1983 â-constants of Taft and
co-workers21 and their subsequent expansion and refinement by
Abraham and co-workers.22 We have chosen to use âH2 values
of Abraham et al.,23 which represent a general, thermodynami-
cally related scale of solute hydrogen-bond basicities in CCl4
and range in magnitude from 0.00 for a non-HBA solvent such
as an alkane24 to 1.00 for hexamethylphosphorustriamide
(HMPA), the strongest organic base. We chose the âH2 scale on
the pragmatic grounds that it is the most extensive of all â scales
with values tabulated for at least 400 organic compounds.27
Values of log(ksXH/RO•/M-1 s-1), where RO• ) tert-alkoxyl, in
various sterically nondemanding17 HBA solvents have been
plotted in Figure 1 for Me3COOH7 (10 solvents, r2 ) 0.97),
phenol7,12,17(11 solvents, r2 ) 0.98), and R-tocopherol12,14 (11
solvents, r2 ) 0.87, the lowest linear coefficient of determination
obtained with any substrate, vide infra). Obviously these KSE
kSXH/Y
)
(ii)
•
where kOXH/Y is the rate constant for reaction of Y• with non-
•
H-bonded XH.
It was recognized7 that the magnitude of the KSE (e.g.,
CCl4
XH/Y XH/Y
3
k
•/kMe COH) would generally be independent of Y•, because
•
the KSE is determined by the strength of the interaction between
XH and the HBA solvent. This was confirmed12 by demonstrat-
ing that the magnitude of the KSE for H-atom abstraction from
phenol by CumO• was essentially identical13 to that for H-atom
abstraction by 2,2-diphenyl-1-picrylhydrazyl radicals, DPPH•,
S1
S1
that is, kPhOH/CumO•/kS
) kPhOH/DPPH•/kPShOH/DPPH•, al-
2
2
•
PhOH/CumO
though in any particular solvent, the former reaction is faster
than the latter by the enormous factor of 1010, that is,
kSP1hOH/CumO ) 1010kSPh1 OH/DPPH•. The KSEs for H-atom abstrac-
•
tion from R-tocopherol (TocH, vitamin E) have also been shown
to be essentially identical13,19 for Y• ) Me3CO• and DPPH•,12
peroxyl radicals14 and a primary alkyl radical.18
In any analysis of solvent effects on chemical reactions, it is
customary to seek a linear relationship between some empirical
solvent parameter and the logarithm of the rate constant for
reaction, i.e., a linear free energy relationship.20 The most
(20) Reichardt, C. SolVents and SolVent Effects in Organic Chemistry;
Verlag Chemie: Weinheim, Germany, 1990.
(21) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. J.
Org. Chem. 1983, 48, 2877-2887 and references therein. See also: Marcus,
Y.; Kamlet, M. J.; Taft, R. W. J. Phys. Chem. 1988, 92, 3613-3622.
(22) For a brief summary of, and references to, the various â-scales, see
ref 17. For more detailed reviews of these scales, see: Abraham, M. H.
Port. Electrochim. Acta 1992, 10, 121-134. Abraham, M. H. Chem. Soc.
ReV. 1993, 73-83. Abraham, M. H. NATO Advanced Study Institute Series
C426; Plenum: New York, 1994, pp 63-78.
(11) Nielsen, M. F. Acta Chem. Scand. 1992, 46, 533-548. (b) Nielsen,
M. F.; Hammerich, O. Acta Chem. Scand, 1992, 46, 883-896.
(12) Valgimigli, L.; Banks, J. T.; Ingold, K. U.; Lusztyk, J. J. Am. Chem.
Soc. 1995, 117, 9966-9971.
(13) Rate constants for some, but not all, H-atom abstractions are about
3-5 times faster in tert-butyl alcohol (but not in methanol or ethanol) than
would be expected from tert-butyl alcohol’s HBA ability. Specifically, this
rate “acceleration” (actually, a less than expected rate reduction) has been
found in O-H bond-breaking by DPPH•12 and ROO•14 and in C-H bond-
breaking by DPPH•,15 but not for C-H bond-breaking by RO•4 or ROO•,16
or O-H bond breaking by RO•12, 17, or PhCMe2CH2•.18 The reason(s) for
the occasional anomalous behavior of tert-butyl alcohol are not currently
understood.
(23) (a) Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Morris, J. J.; Taylor,
P. J. J. Chem. Soc., Perkin Trans. 2 1990, 521-529. (b) See also: Abraham,
M. H.; Grellier, P. L.; Prior, D. V.; Taft, R. W.; Morris, J. J.; Taylor, P. J.;
Laurence, C.; Berthelot, M.; Doherty, R. M.; Kamlet, M. J.; Abboud, J.-L.
M.; Sraidi, K.; Guihe´neuf, G. J. Am. Chem. Soc. 1988, 110, 8534-8536.
Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Morris, J. J.; Taylor, P. J.
Tetrahedron Lett. 1989, 30, 2571-2574. Laurence, C.; Berthelot, M.;
Helbert, M.; Sraidi, K. J. Phys. Chem. 1989, 93, 3799-3802. Abraham,
M. H.; Lieb, W. R.; Franks, N. P. J. Pharm. Sci. 1991, 80, 719-724.
(24) In most of Abraham’s âH2 compilations, âH(CCl4) is given as 0.00,
since CCl4 is the solvent in which the strengths of2the interactions between
HBA’s and HBD’s are normally evaluated using infrared spectroscopy.
However, it is known from infrared studies on phenols that CCl4 is an HBA
(14) Valgimigli, L.; Banks, J. T.; Lusztyk, J.; Ingold, K. U. J. Org. Chem.
1999, 64, 3381-3383.
solvent relative to alkanes.25 We have found that â2H (CCl4) ) 0.05 gives
a much better fit for all our kinetic data than 0.00 and use 0.05 in this
paper. It should also be noted that when cyclohexane was used as the
(15) Valgimigli, L.; Ingold, K. U.; Lusztyk, J. J. Org. Chem. 1996, 61,
7947-7950.
(16) Lucarini, M.; Pedulli, G. F.; Valgimigli, L. J. Org. Chem. 1998,
63, 4497-4499.
reference, Abraham et al. reported âH2 (CCl4) ) 0.04.26
(25) Ingold, K. U.; Taylor, D. R. Can. J. Chem. 1961, 39, 481-487.
(26) Abraham, M. H.; Buist, G. J.; Grellier, P. L.; McGill, R. A.; Prior,
D. V.; Oliver, S.; Turner, E.; Morris, J. J.; Taylor, P. J.; Nicolet, P.; Maria,
P.-C.; Gal, J.-F.; Abboud, J.-L. M.; Doherty, R. M.; Kamlet, M. J.; Schuely,
W. J.; Taft, R. W. J. Phys. Org. Chem. 1989, 2, 540-552.
(17) MacFaul, P. A.; Ingold, K. U.; Lusztyk, J. J. Org. Chem. 1996, 61,
1316-1321.
(18) Franchi, P.; Lucarini, M.; Pedulli, G. F.; Valgimigli, L.; Lunelli, B.
J. Am. Chem. Soc. 1999, 121, 507-514.
(19) The rate of the TocH/Me3CO• reaction reaches the diffusion-
controlled limit in n-octane, n-hexadecane and CCl4.12
(27) Abraham, M. H.; Andonian-Haftvan, J.; Whiting, G. S.; Leo, A.;
Taft, R. W. J. Chem. Soc., Perkin Trans. 2 1994, 1777-1791.

Kinetic SolVent Effects on H-Atom Abstractions
J. Am. Chem. Soc., Vol. 123, No. 3, 2001 471
Table 1. Rate Constants (10-7 kXS H/RO•/M-1 s-1) for H-Atom Abstraction from Seven Phenols by tert-Alkoxyl Radicals in Various Solvents at
23 ( 2 °Ca
substituents
solvent
TocHc
(1)
2,4,6 Me3
(2)
Me3C
(4)
noned
(5)
4Cl
(6)
4CF3
(7)
3,5Cl2
(8)
â2H
b
I
II
alkanee
CCI4
PhCI
0.00
0.05h
0.09
0.14
0.26
0.38
0.40
0.42
0.44
0.45
0.45
0.49
990
420
360
310
200
-
210
160
-
-
190
130
87
23
4.6
-
6.0
4.1
-
-
1.9
110f
86
48
230
85g
71
17
94
87
29
16
3.5
0.59
-
110
-
40
6.9
1.9
-
-
0.79
III
IV
V
VI
VII
VIII
IX
X
PhH
-
28
13
PhOMe
HCO2Me
MeCO2Me
MeCO2H
MeCN
MeCO2Et
Val-lacti
Me3COH
49
12
-
5.6
1.0
0.95
1.8
0.58
0.75
-
2.1
0.39
-
0.54
0.21
-
-
0.10
30
77
94
29
17
-
-
8.3
-
-
-
-
-
-
XI
XII
-
-
-
18
0.36
-
a RO•) Me3CO• for phenols 1 and 4; ) CumO• for phenols 2, 5, 6, 7 and 8. Estimated errors in k ) (20%. Solvents are identified by Roman
numbers and substrates by Arabic numbers in all Tables and Figures. b Values are from ref 23a except for CCl4. c R-Tocopherol. Data are from refs
i
12 and 14. d Data are from refs 7, 12, and 17. e n-Pentane unless otherwise noted. f In n-octane. g In n-hexane. h See ref 24. γ-Valerolactone.
Scheme 2
data can be correlated by the equation:
log(kSXH/Y•/M-1 s-1) ) log(kXOH/Y•/M-1 s-1) + MXHâ2H
(iii)
where MXH represents the magnitude of the KSE for the
particular XH and for any Y •, and is the slope of the log kSXH/Y
•
versus âH2 line in Figure 1.
The magnitude of MXH must depend on the ability of XH to
form a hydrogen bond to a solvent molecule. This raises the
exciting possibility that, if MXH could be predicted from some
easily measured physical property of XH, then a single kinetic
measurement on an XH/Y• reaction in any solVent would allow
reliable rate constants to be calculated in any of the 400+ other
solvents for which âH2 values are known (and for any mixture
of these solvents). This goal has been achieved by rate constant
measurements for H-atom abstractions by tert-alkoxyl radicals
from a series of phenols. A simple, empirical equation describes
the observed KSEs (MXH values) and this equation has been
confirmed by extending our analyses to substrates which are
not HBAs (cyclohexane) or are only weak HBAs, for example,
tert-butyl hydroperoxide, 2-methoxyphenol (with its intramo-
lecular H-bond) and aniline.
first-order reactions of Me3CO• (i.e., to all reactions of Me3-
CO• other than its H-atom abstraction from XH).30 In each
solvent, at least five (often more) concentrations of XH were
employed, and kSXH/Me CO• was calculated via least-squares from
3
the plot of kSexptl versus [XH]. All of these plots gave excellent
straight lines (r2 g 0.98).
Extinction coefficients for some phenoxyl radicals were too
weak to yield reliable kinetic data. In most such cases, LFP
with dicumyl peroxide was employed and cumyloxyl radical
decay at ∼485 nm31 was monitored using five or more phenol
concentrations. Again the plots of kexptl versus [XH] gave
excellent straight lines (r2 g 0.98).
Results
The LFP measured bimolecular rate constants for H-atom
abstraction by Me3CO• or CumO• from the phenols in various
solvents at room temperature are given in Table 1. These phenols
exhibit a wide range of acidities (pKa’s) and hence were
expected to exhibit a wide range of HBD activities.
We chose Y• ) Me3CO• or CumO• because some data were
already available (vide supra) and because of the simplicity and
reliability of kinetic studies with these radicals using laser flash
photolysis (LFP). These radicals were generated at room
temperature by 308 nm LFP of either 0.22 M di-tert-butyl
peroxide or 0.13 M dicumyl peroxide, concentrations which give
an optical density (OD) of 0.3 at 308 nm in the 7 mm laser
cell. Phenoxyl radicals usually have absorption bands in the
370-505 nm range.28,29 The phenol was used in large excess
relative to the tert-butoxyl radicals so that the signal at the
phenoxyl radical’s band maximum builds-up with pseudo-first-
order kinetics:
The LFP technique could not be used with 4-methoxyphenol
because this compound absorbs at the 308 nm laser wavelength.
Rate constants were therefore obtained by competition kinetics/
product analyses32 using CumO• radicals generated by thermal
decomposition of dicumyl hyponitrite. Reactions were carried
out at 25 °C in the dark in argon-purged, sealed Pyrex reaction
vessels. Products were analyzed after 10 days which was
sufficient time for >99% of the hyponitrite to decompose.34
The products of principle interest are those derived from CumO•
radicals which escape the solvent cage and react either by
H-atom abstraction to form cumyl alcohol or by â-scission to
give acetophenone (see Scheme 2). To treat the H-atom
abstraction as a pseudo-first-order process, the hyponitrite:4-
methoxyphenol concentration ratio was 1:(g40) in all experi-
keSxptl ) kSO + kXS H/Me CO•[XH]
(iv)
3
where kSO corresponds to the combined first-order and pseudo-
(28) (a) Land, E. J.; Porter, G.; Strachan, E. Trans. Faraday Soc. 1961,
57, 1885-1893. (b) Land, E. J.; Porter, G. Trans. Faraday Soc. 1963, 59,
2016-2026. (c) Das, P. K.; Encinas, M. V.; Steenken, S.; Scaiano, J. C. J.
Am. Chem. Soc. 1981, 103, 4162-4166.
(29) For 2-methoxyphenoxyl, λmax ) 650-660 nm, see: Shukla, D.;
Schepp, N. P.; Mathivanan, N.; Johnston, L. J.; Can. J. Chem. 1997, 75,
1820-1829.
(30) Radical/radical reactions are unimportant under the conditions
employed.
(31) Avila, D. V.; Lusztyk, J.; Ingold, K. U.;. J. Am. Chem. Soc. 1992,
114, 6576-6577. Avila, D. V.; Ingold, K. U.; Di Nardo, A. A.; Zerbetto,
F.; Zgierski, M. Z.; Lusztyk, J. J. Am. Chem. Soc. 1995, 117, 2711-2718.

472 J. Am. Chem. Soc., Vol. 123, No. 3, 2001
SnelgroVe et al.
Table 2. Kinetic Data Derived from Cumyl Alcohol/Acetophenone
Product Ratios for the 4-Methoxyphenol (3)/ CumO• Reaction in
Five Solvents at 25 °C
studied decreased very substantially as the HBA abilities of the
solvent increased (see Tables 1 and 2). Plots of log(kXS H/RO
/
•
M-1 s-1) versus âH2 gave excellent straight lines (r2 g 0.98) for
all phenols except R-tocopherol (for which some k’s approach
the diffusion-controlled limit)19 and 4-methoxyphenol (for which
k’s were determined indirectly)32 see Supporting Information
and Table 3. The slopes of these lines, MXH, give the magnitude
of the KSE for XH, see eq iii. Values of MXH and of the
intercept, log(kXOH/Y•/M-1 s-1), are collected in Table 4. It
should be realized that an MXH value of -1.0 means that the
rate constant for H-atom abstraction will decrease by a factor
of 10 on changing the solvent from an alkane to HMPA, that
is, for R-tocopherol this change in solvents would reduce the
rate constant by a factor of 1000 and for 3,5-dichlorophenol by
1,000,000. These KSEs are not small!35
kS3/CumO•/kS
10-5 kSâ
(s-1
10-7 kS3/CumO
•
â
solvent
(M-1
)
)
(M-1 s-1
)
III
IV
V
VIII
IX
PhCl
PhH
PhOMe
MeCO2H
MeCN
7850
9710
5134
121
4.60a
3.11a
2.95b
16.3a
5.25a
361
302
153
19.6
11.1
211
a Rate constants from ref 4 have been multiplied by 0.83 to correct
for the 5 °C temperature difference. b This work, see text.
Table 3. Rate Constants (M-1 s-1) for H-Atom Abstraction from
Nine Phenols by DPPH• Radicals in n-Heptane at 23 ( 2 °C
O
•b
phenol
TocHc
2,4,6-Me3C6H2OH
4-MeOC6H4OH
4-Me3CC6H4OH
C6H5OH
Σσ+ a
kArOH/DPPH
There is only a poor correlation between MXH and pKa (see
Figure 2), the two 2,6-dimethyl-substituted phenols (1 and 2)
having significantly smaller MXH values than might have been
expected from their pKa’s, probably for steric reasons. Any steric
problems were overcome by using RH2 parameters of Abraham
et al.,38 which provide a direct measure of the relative ability
of a solute to act as a HBD. Values of RH2 range from 0.00
(e.g., alkanes) to nearly 1.0 for strong acids, for example, R2H
(CF3CO2H) ) 0.951 and have been tabulated for hundreds of
substrates,27,38 but not for R-tocopherol. We therefore redeter-
mined RH2 for five phenols and obtained values in good
agreement with the literature,27,38 following which we deter-
mined RH2 for R-tocopherol (Table 4). The MXH values are
plotted against RH2 for the eight phenols (filled circles in Figure
3). There is no KSE for H-atom abstraction from alkanes4 since
the R2H values for alkanes are 0.00.27,38 This boundary condi-
tion is included in the data series (shown by a filled square).
An excellent least-squares fitting is obtained:
1
2
3
4
5
-1.40d
-0.72d
-0.78
-0.26
0.00
7400e
42
240f
3.1
0.16e,g
1.1
6
7
8
12
4-ClC6H4OH
0.11
4-CF3C6H4OH
3,5-Cl2C6H3OH
3-ClC6H4OH
0.61
0.80
0.40
0.044
0.037
0.15
a From ref 37 assuming, when necessary, that multiple substituents
have additive electronic effects. b These rate constants were measured
using one concentration of DPPH and five or more concentrations of
the phenols in n-heptane. The phenol, its maximum concentration (M)
and in parentheses, 105 [DPPH] (M) were as follows: [2] e 8.5 ×
10-4 (3.4); [3] e 9.2 × 10-4 (1.2); [4] e 2.0 × 10-2 (2.2); [6] e 7.0
× 10-2 (2.5); [7] e 0.2 (2.6); [8] e 0.14 (46); [12] e 0.18 (1.8). c R-
Tocopherol. d Calculated using σ0+(Me) ) 0.66 σ+p (Me), see ref 55b.
e In n-octane, data from ref 12. f Measured value. The value calculated
from a kinetic measurement in DMSO was 174 M-1 s-1, see ref 57.
g Because this rate constant makes phenol an outlier in Figure S1
(Supporting Information), it was remeasured in the present work, and
a value of 0.22 M-1 s-1 was obtained (see Table S7).
MXH ) - 8.31RH2 + 0.005 (r2 ) 0.99)
which, for practical purposes, can be written as:
MXH ) -8.3RH2
(v)
ments which assured that no more than 5% of the phenol could
react with the CumO• radicals. At least six (often more) different
phenol concentrations were used. Plots of the GC/FID-
determined ratios of cumyl alcohol/acetophenone versus 4-meth-
oxyphenol concentration gave excellent straight lines (r2 g 0.97,
see Supporting Information). The slopes of these lines cor-
respond to the ratio of the rate constants for H-atom abstraction
(vi)
Equation vi is also applicable to H-atom abstractions by tert-
alkoxyl radicals from tert-butyl hydroperoxide,7 aniline,17 and
2-methoxyphenol33 with its intramolecular hydrogen bond which
reduces but does not eliminate intermolecular hydrogen bond-
from the phenol to â-scission, that is, slope ) kMS eOC H OH/CumO
/
•
6
4
kSâ (M-1). The results of these experiments are summarized in
Table 2. Mass balances were excellent in all solvents (see
Experimental Section and Supporting Information). Values of
kSâ at 30 °C were available for four of the five solvents4 and
were corrected to 25 °C by multiplying by 0.83. For anisole,
kPâhOMe was not available. It was measured at 30 °C by
(32) KSE’s for the Me3CO•/4-MeOC6H4OH reaction were also investi-
gated by 337 nm LFP of 30:70 (v/v) Me3COOCMe3/solvent mixtures.33
The bimolecular rate constants were then recalculated for the pure solvents
and, when plotted against âH, gave a slope (MXH) ) -4.21 (r2 ) 0.98)33 in
2
excellent agreement with the product derived slope of -4.32, vide infra.
(33) de Heer, M. I.; Mulder, P.; Korth, H.-G.; Ingold, K. U.; Lusztyk, J.
J. Am. Chem. Soc. 2000, 122, 2355-2360.
competition kinetics using cyclohexane (five concentrations) as
PhOMe
C6H12/CumO
the H-atom donor. The rate constant ratio: k
•/kPhOMe
â
was found to be 3.34 M-1 and, since kCPhHOMe
) 1.2 × 106
(34) The Arrhenius parameters for decomposition of this hyponitrite
are: log(A/s-1) ) 14.97 and Ea ) 27.3 kcal mol-1, (see: Mendenhall, G.
D.; Chen, H.-T. E. J. Phys. Chem. 1985, 89, 2849-2851) from which the
half-life at room temperature is 16 h.
•
12/CumO
PhOMe6
M-1 s-1 at 30 °C in all solvents,4 kâ
) 3.6 × 105s-1 at 30
°C and 3.0 × 105s-1 at 25 °C.
(35) Large KSEs have also been observed in solvent mixtures.28c,32,33
For example, a plot of Das et al.’s28c log(k/M-1 s-1) for the PhOH/Me3-
CO• reaction in 1:1 (v/v) mixtures of di-tert-butyl peroxide with benzene,
Rate constants, kOArOH/DPPH•, for H-atom abstraction by the
2,2-diphenyl-1-picrylhydrazyl radical, DPPH•, from a number
of phenols in a non-hydrogen-bonding solvent (n-heptane) were
also determined and are given in Table 3.
methanol, tert-butyl alcohol and pyridine against âH2 for these last four
compounds gives a good straight line with a slope of -3.9.
(36) Bordwell, F. G.; Cheng, J.-P. J. Am. Chem. Soc. 1991, 113, 1736-
1743.
Discussion
(37) Hansch, C.; Leo, A. Substituent Constants for Correlation Analysis
in Chemistry and Biology; Wiley-Interscience: New York, 1979. See also:
Hansch, C.; Leo, A.; Taft, R. W. Chem. ReV. 1991, 91, 165-195.
(38) Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Duce, P. P.; Morris,
J. J.; Taylor, P. J. J. Chem. Soc., Perkin Trans. 2 1989, 699-711.
Deriving an Empirical Equation to Describe H-Atom
Abstraction KSEs Quantitatively. Rate constants for H-atom
abstraction by tert-alkoxyl radicals from the eight phenols

Kinetic SolVent Effects on H-Atom Abstractions
J. Am. Chem. Soc., Vol. 123, No. 3, 2001 473
Table 4. Slopes, MXH, and Intercepts, log(kOXH/t-RO•/M-1 s-1), for Plots of log(kXS H/t-RO•/M-1 s-1) versus â2H for Various Substrates and Some
Relevant Substrate Parameters
R2H
pKaa
Σσ+ b
litc
this work
intercept
slope MXH
r2
1
2
3
4
5
6
7
8
9
TocHd
20.0e
19.4e
19.1
19.05
18.0
16.75
15.2
13.56
-
-1.40f
-0.72f
-0.78
-0.26
0.00
0.11
0.61
0.80h
-
-
0.370
-
0.550
0.571
0.590
-
9.91
9.37
10.1
9.53
9.12
9.34
8.94
9.07
8.57
8.76
8.09
-3.06
-3.22
0.87
0.98
0.95
0.98
0.98
0.99
0.98
0.98
0.97
0.97
0.98
2,4,6-Me3C6H2OH
4-MeOC6H4OH
4-Me3CC6H4OH
C6H5OH
4-ClC6H4OH
4-CF3C6H4OH
3,5-Cl2C6H3OH
Me3COOH
0.374
0.573
0.558
0.596
0.670
0.724
0.774
g
-4.32
-4.48
-5.15
-5.54
-5.88
-5.99
-3.52
-2.22
-2.00
0.680
0.728
0.442
-
-
0.264
0.261
10
11
C6H5NH2
2-MeOC6H4OH
-
-
-
-
-
a From ref 36. b From ref 37. c From ref 38.. d R-Tocopherol. e Values estimated by additivity principles; substituents (pKa): 2,6-Me2 (18.5);
3,5-Me2 (18.4); 4-MeO (19.1); 4-Me (18.9), and none (18.0). f Calculated using σ0+(Me) ) 0.66 σ+p (Me), see ref 55b. g See also footnote 32. h 2 ×
σ+meta(Cl).
The combination of eqs iii and vi yields a general, empirical
equation which reliably describes and predicts KSEs for H-atom
donors at ambient temperatures:
log(kXS H/Y•/M-1 s-1) ) log(kXOH/Y•/ M-1 s-1) - 8.3R2Hâ2H (vii)
Interestingly, a very similar equation can, be derived without
using any experimental kinetic data by combining the three
assumptions associated with Scheme 1 and Abraham’s thermo-
dynamic parameters for hydrogen bonding (see Supporting
Information), viz.,
log( kXS H/Y•/M-1 s-1) ) log(kXOH/Y•/ M-1 s-1) - 7.8 R2Hâ2H
(viii)
The strengths and weaknesses of eq vii are adumbrated below:
Strengths. (i) This is a general equation for hydrogen-atom
abstractions (and proton transfers, vide infra) in solution at room
temperature for C-H, O-H, and N-H hydrogen-atom donors.
Figure 2. Values of MXH plotted against pKa for phenols 1-8. The
data are from Table 4, and the phenols are identified by number.
(ii) Many R2H and âH2 values are available22,23,26,27,38 or can
be readily determined.
(iii) A single measured rate constant for the XH/Y• reaction
in any solvent permits the calculation of the rate constant in
any other solvent (or solvent mixture).
Weaknesses. These can only manifest themselves with XH
having small RH2 values (<0.2). For such substrates, the
(39) de Heer, M. I.; Korth, H.-G.; Mulder, P. J. Org. Chem. 1999, 64,
6969-6975.
(40) Tronche, C.; Martinez, F. N.; Horner, J. H.; Newcomb, M.; Senn,
M.; Giese, B. Tetrahedron Lett. 1996, 37, 5845-5848.
(41) Salikhov, A.; Fischer, H. Appl. Magn. Reson. 1993, 5, 445-455.
(42) For an overview of this work, see: Minisci, F.; Fontana, F. Chim.
Ind. 1998, 80, 1309-1316.
(43) Bravo, A.; Bjorsvik, H.-R.; Fontana, F.; Ligouri, L.; Minisci, F. J.
Org. Chem. 1997, 62, 3849-3857.
(44) Minisci, F.; Fontana, F.; Araneo, S.; Recupero, F.; Banfi, S.; Quici,
S. J. Am. Chem. Soc. 1995, 117, 226-232.
(45) Bravo, A.; Bjorsvik, H.-R.; Fontana, F.; Minisci, F.; Serri, A. J.
Org. Chem. 1996, 61, 9409-9416.
(46) We also have exploited this phenomenon by demonstrating that
4-HOC6H4CHdCH2 can be converted in a free-radical chain reaction to a
high molecular weight polymer in good HBA solvents such as HMPA.
Figure 3. Values of MXH plotted against RH2 (using values measured
(47) Howard, J. A.; Ingold, K. U. Can. J. Chem. 1964, 42, 1044-1056.
in this work) for phenols 1-8 (b), cyclohexane (9), tert-butyl
(48) Later, direct measurements of kSPhOH/Me COO at -32 °C by ESR in
•
hydroperoxide, aniline, and 2-methoxy-phenol (O, numbers 9, 10, and
11 solvents yielded rate constants which range3d from 5 × 102 M-1 s-1 in
11, respectively). The data are from Table 4.
49
hexane to ∼6 M-1 s-1 in an alcohol, an ether and two ketones. These
data correlate only roughly with âH2 (slope
) -4.2). Values of
kSPhCHO/Me COO were about 0.4 M-1 s-1 in all 11 solvents, as would be
ing33,49 (kinetic data are given in Table S6). These three
substrates have been included in Table 4 and their MXH values
plotted against RH2 as open circles in Figure 3.
•
expected3for a C-H bond-breaking reaction.
(49) Tavadyan, L. A.; Mardoyan, V. A.; Nalbandyan, A. B. SoV. J. Chem.
Phys. 1990, 5, 2537-2556.

474 J. Am. Chem. Soc., Vol. 123, No. 3, 2001
SnelgroVe et al.
H-bonding contribution to an observed KSE will be small which
allows other types of solvent effects to be observed. An
interesting example is the reaction:40
radicals. Alcohols are actually more reactive toward peracid
oxidation than alkanes, but this only becomes apparent if the
reactions are carried out in a poor HBA solvent.45
(ii) Phenolic Antioxidant Activity. Phenols are chain-
breaking antioxidants which retard the autoxidation of organic
materials. They trap the chain-carrying peroxyl radicals in
competition with the chain-propagating attack on the organic,
that is,
kS
•
H2CdCH(CH2)3C˙ (CH3)2 + GSH GSH/R 8
H2CdCH(CH2)3CH(CH3)2 + GS•
where GSH represents glutathione diethylester. In solvents of
increasing âH2 (CH2Cl2 to CH3CN) kS
slightly increases,
ksRH/ROO
ROO• + RH
•8 ROOH + R• or ROOR˙ H
•
GSH/R
whereas no change should have been expected since the
substrate is an alkylthiol for which RH2 ) 0.00.27,38 Another
type of solvent effect manifests itself, an increase in the
stabilization of a highly polarized transition state as the polarity
of the solvent is increased.
ksArOH/ROO
ROO• + ArOH
•8 ROOH + ArO•
The magnitude of kAs rOH/ROO decreases in HBA solvents, as
•
was first recognized in 1964 on the basis of solvent-induced
Similarly, the rate constants for tert-butyl radical addition to
acrylonitrile increase slightly with solvent polarity because
hydrogen bonding is unimportant and the highly polarized
changes in the rate constant ratio, ksRH/ROO•/ks
(RH )
•
ArOH/ROO
styrene), which were “determined by the strength of the
hydrogen bond between the phenol and the solvent”.47,48 Steric
protection of the phenol’s hydroxylic group reduced the KSE,
for example, 2,6-di-tert-butyl-4-methylphenol was a “much more
efficient (antioxidant) than 4-methylphenol” in tert-butyl alcohol
and acetic acid, but it was less efficient in n-decane and
chlorobenzene.47 These observations, which have been con-
firmed for several phenols50 help provide a rationale for why
nature “chose” R-tocopherol as the major lipid-soluble, radical-
trapping antioxidant in mammals.51,52 This phenol resides in
phosphatidylcholine bilayers with its phenolic hydroxyl group
close to the model membrane/water interface52 where H-bonding
would reduce the antioxidant activity of a less sterically hindered
phenol.
41
transition state is stabilized by more polar solvents.
Effects of HBA Solvents on Some Important Properties
of Hydroxylic Substrates. (i) Modulations of Reaction
Products. Minisci and co-workers42-45 have exploited KSEs
to direct certain reactions down chosen pathways.46 For
example,43 tert-butoxyl radicals generated in the presence of
cyclohexene/tert-butyl hydroperoxide (5:1 to 20:1) in benzene
yield tert-butylperoxyl and cyclohexenyl radicals in roughly
equal amounts. Since this peroxyl radical is persistent, the
persistent radical effect (PRE) ensures that only the cross radical
coupling product is formed, tert-butyl cyclohexenyl peroxide.
However, in the strong HBA solvent, pyridine, H-atom abstrac-
tion from the hydroperoxide is suppressed, and the major product
then becomes dicyclohexenyl formed by cyclohexenyl/cyclo-
hexenyl radical coupling. Similarly, in the Fe(III)-catalyzed
reaction of Me3COOH with R-methylstyrene the main product
in benzene is epoxide:44
(iii) Hammett Correlations for Substituted Phenols. Rate
constants for H-atom abstraction from substituted phenols by,
for example, peroxyl radicals are well correlated via the
Hammett equation using Brown and Okamoto’s σ+ substituent
constants,37,53 that is,54
Me3COOH
9
Fe8 Me3CO• Me3COOH8 Me3COO•
kSArOH/Y
•
Me3COO• + CH2dC(Me)Ph f
log
) Fk+inet σ+ (Y• ) ROO•)
(ix)
∑
S
(
)
kPhOH/Y
•
Me3COOCH2C•(Me)Ph f Me3CO• + OCH2C(Me)Ph
Recent experimental and theoretical studies of the gas-phase
O-H bond dissociation enthalpies (BDEs) of substituted phenols
have demonstrated that phenolic O-H BDEs can also be
correlated by Σσ+.55 In a non-HBA solvent the relative rates of
H-atom abstraction from a series of sterically nonhindered
phenols by a particular radical, Y•, will be determined solely
by differences in the activation enthalpies, which must be
proportional to the differences in reaction enthalpies (Evans-
Polanyi principle),56 and these must be proportional to the
differences in phenolic O-H BDEs. The generality of eq ix
was confirmed for Y• ) DPPH• and a fairly good Hammett
However, in the presence of pyridine the main reaction takes a
different course thanks to retardation of the Me3CO•/Me3COOH
reaction and the PRE:
Me3CO• + CH2dC(Me)Ph f
•
Me3COCH2C•(Me)Ph Me COO 8
3
Me3COCH2C(OOCMe3)MePh
Oxidation of alkanes by aromatic peracids occurs with high
regio-, chemo-, and stereoselectivity, probably via the following
radical chain reaction.45 However, primary and secondary
(50) Barclay, L. R. C.; Edwards, C. E.; Vinqvist, M. R. J. Am. Chem.
Soc. 1999, 121, 6226-6231. See also: Barclay, L. R. C.; Vinqvist, M. R.;
Antunes, F.; Pinto, R. E. J. Am. Chem. Soc. 1997, 119, 5764-5765.
Iwatsuki, M.; Tsuchiya, J.; Komuro, E.; Yamamoto, Y.; Niki, E. Biochim.
Biophys. Acta 1994, 1200, 19-26.
(51) Burton, G. W.; Joyce, A.; Ingold, K. U. Lancet 1982, 2, 327. Burton,
G. W.; Joyce, A.; Ingold, K. U. Arch. Biochem. Biophys. 1983, 221, 281-
290. Ingold, K. U.; Webb, A. C.; Witter, D.; Burton, G. W.; Metcalfe, T.
A.; Muller, D. P. R. Arch. Biochem. Biophys. 1987, 259, 224-225.
(52) Burton, G. W.; Ingold, K. U. Acc. Chem. Res. 1986, 19, 194-201.
(53) Brown, H. C.; Okamoto, Y. J. Am. Chem. Soc. 1958, 80, 4979-
4987.
(54) (a) Howard, J. A.; Ingold, K. U. Can. J. Chem. 1963, 41, 1744-
1751. (b) Howard, J. A.; Ingold, K. U. Can. J. Chem. 1963, 41, 2800-
2806.
alcohols are not oxidized by aromatic peracids when the alcohols
are used as solvent despite their relatively weak H-COH bonds
because the alcohols form HB complexes with the peracid and
protect its labile hydrogen atom from abstraction by ArCO2•

Kinetic SolVent Effects on H-Atom Abstractions
J. Am. Chem. Soc., Vol. 123, No. 3, 2001 475
Scheme 3
(iv) Phenolic O-H BDEs Estimated from Measurements
in Solution. A 1995 paper from this laboratory6 reported
photoacoustic calorimetric (PAC) measurements of phenol’s
O-H bond dissociation enthalpy in a number of solvents, BDE-
(O-H)sol, from which gas-phase BDEs were derived by (among
other things) correcting for the enthalpies of H-bonding by
phenol in the different solvents, BDE(O-H)gas mean 87.4 (later
corrected to 87.3)55d kcal mol-1 in good agreement with various
gas-phase values of ∼87 kcal mol-1. It was pointed out6 that
“there are some limitations to the EC (electrochemical cycle)
method which result from the attempt to use solution free-energy
measurements to obtain gas-phase enthalpies”. For some EC
work on phenol in DMSO59 it was also noted that an empirical
equation had been used which “failed to properly account for
the solvent effect” and the reported “gas phase” O-H BDE of
89.9 kcal mol-1 was recalculated as 86.4 kcal mol-1. Further-
more, it was concluded6 that there were “likely to be systematic
errors for BDE(O-H) values measured by the EC method in
DMSO” for a series of phenols having various pKa’s simply
because the constant in the above-mentioned empirical equation
“CDMSO(ArOH) will not be constant.” These criticisms were
vigorously rebutted and “gas-phase” O-H BDEs for 15 phenols
were calculated using the same empirical equation and constant,
for example, for phenol 90.4, 4-methoxyphenol 84.6 and
Figure 4. Plots of calculated log(kSArOH/DPPH•/M-1 s-1) values vs Σσ+
for 19 phenols in an alkane (O, âH2 ) 0.00), anisole (b, â2H ) 0.26),
and HMPA ([, âH2 ) 1.00). Phenols 1-8 and 11 are identified in
Table 4. The substituent(s) and number for the remainder are 3-Cl (12),
4-Me (13), 4-F (14), 4-Br (15), 4-CN (16), 4-NO2 (17), 4-Ph (18), 2-Me
(19), 2,6-Me2 (20), 4-Me2N (21).
type correlation was obtained (see Table 3 and Figure S1).57
log(kAOrOH/DPPH•/M-1 s-1) ) 0.10 -2.4 σ+ (r2 ) 0.95)
∑
3
7
(x)
If the kinetic data had been obtained in an HBA solvent, the
rate constants for phenols, having relatively high and relatively
low RH2 values, would be affected to different extents by
H-bonding, and this would change F+. As far as we are aware,
this point has not been previously addressed. We have therefore
used eqs vii and x to calculate rate constants for H-atom
abstraction by DPPH• from 19 phenols having Σσ+ ranging from
-1.70 to 0.80 and RH values ranging from 0.261 (2-MeOC6H4-
4-cyanophenol 94.2 kcal mol-1 60
However, from literature
.
2
OH)58 to 0.824 (4-NO2C6H4OH) in five different solvents: an
alkane (âH2 ) 0.00), benzene (â2H ) 0.14), anisole (âH2 ) 0.26),
pyridine (âH2 ) 0.62) and HMPA (âH2 ) 1.00) (see Table
S8).Three sets of these data have been used to construct Σσ+
Hammett plots which in the alkane solvent necessarily give a
perfect correlation (F+ ) -2.47, r2 ) 1.00), but as the solvent
becomes a stronger HBA, the scatter increases and F+ becomes
more negative, for example, in anisole F+ ) -2.81 (r2 ) 0.99)
and in HMPA F+ ) -3.97 (r2 ) 0.93), see Figure 4. It is clear
that KSEs can have a significant effect on F+ for the ArOH +
DPPH• reaction and these effects should always be taken into
account when trying to assess the significance of different F+
values for different ArOH + Y• reactions.
data,38 the free energy changes, ∆G°, for the DMSO/4-
methoxyphenol and DMSO/4-cyanophenol hydrogen bonds can
be calculated to be smaller by 0.2 and greater by 1.5 kcal mol-1
,
respectively, than ∆G0 for the DMSO/phenol H-bond. These
differences in free energies for the hydrogen bonds are,
presumably, essentially identical to the enthalpy differences
which implies that the O-H BDE of 4-methoxyphenol was
overestimated by 0.2 kcal mol-1, and that of 4-cyanophenol was
underestimated by 1.5 kcal mol-1. Indeed, if 1.5 kcal mol-1 is
added to the EC ∆BDE(4-NCC6H4O-H - PhO-H) value of
3.8 kcal mol-1 60
,
the ∆BDE rises to 5.3 kcal mol-1, in much
better agreement with our earlier PAC measurement of this
55d
quantity, viz., 5.0 kcal mol-1
.
Application of the General KSE Equation to Proton
Transfer. As noted in the Introduction,10,11 our work on KSEs
for H-atom abstraction from phenols was foreshadowed by
Nielsen’s work on proton transfer from phenols to an aromatic
radical anion. Scheme 3 appears reasonable for proton transfer
and is essentially identical to Scheme 1 for H-atom transfer.
Provided the three assumptions regarding H-atom abstraction
(see Introduction) apply to proton transfer, the KSE equation
for proton transfer should identical to that for atom transfer,
that is,
(55) Experiment: (a) Lind, J.; Shen, X.; Eriksen, T. E.; Mere´nyi, G. J.
Am. Chem. Soc. 1990, 112, 479-482. (b) Jonsson, M.; Lind, J.; Eriksen,
T. E.; Mere´nyi, G. J. Chem Soc., Perkin Trans. 2 1993, 1567-1568. (c)
Bordwell, F. G.; Zhang, X.-M.; Satish, A. V.; Cheng, J.-P. J. Am. Chem.
Soc. 1994, 116, 6605-6610. (d) Wayner, D. D. M.; Lusztyk, E.; Ingold,
K. U.; Mulder, P. J. Org. Chem. 1996, 61, 6430-6433. (e) See also,
Lucarini, M.; Pedrielli, P.; Pedulli, G. F.; Cabiddu, S.; Fattuoni, C. J. Org.
Chem. 1996, 61, 9259-9263. Theory: (f) Wu, Y.-D.; Lai, D. K. W. J.
Org. Chem. 1996, 61, 7904-7910. (g) Wright, J. S.; Carpenter, D. J.;
McKay, D. J.; Ingold, K. U. J. Am. Chem. Soc. 1997, 119, 4245-4252. (h)
DiLabio, G. A. J. Phys. Chem. A 1999, 103, 11414-11424.
(56) Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1938, 24, 11-24.
(57) For 4-methoxyphenol the rate constant was initially measured in
DMSO (âH2 ) 0.780), kDMSO ) 4.78 × 10-2 M-1 s-1, which gave a
calculated ko ) 174 M-1 s-1, in excellent agreement with a subsequently
measured value of 240 M-1 s-1 in n-heptane.
log (kXS H/Y-/M-1 s-1) ) log (kXOH/Y-/M-1 s-1) -8.3 R2Hâ2H
(58) DFT calculations indicate that the transition state for H-atom
abstraction from 2-methoxyphenol differs from that for 4-methoxyphenol.39
Its Arrhenius A-factor will therefore be different from that of 3- and
4-substituted phenols (i.e., break down of the Evans-Polanyi principle)
and thus it does not properly “belong” in Figure 4.
(xiii)
To check this equation we make use of the best available data,
viz., Nielsen and Hammerich’s11b rate constants for deproto-

476 J. Am. Chem. Soc., Vol. 123, No. 3, 2001
SnelgroVe et al.
Table 5. Rate Constants (M-1 s-1) for Deprotonation of Phenol
and 2,4,6-Trimethyl-phenol by the Anthracene Radical Cation at 25
by one single equation:
°C
log(kS/M-1 s-1) ) log(kO/M-1 s-1) - 8.3R2HâH2 (xiv)
S
•-b
10-3 kArOH/An
where kS and kO are the rate constants in solvent S and in a
saturated hydrocarbon, respectively, RH2 and â2H are Abraham’s
parameters which describe the ability of XH to act as a HBD
and S as a HBA, respectively. KSEs due to H-bonding can play
an important role in determining the products of a reaction, the
antioxidant activities of phenols, the magnitude of p+ in
Hammett type correlations and, no doubt, in numerous other
areas. The ability to forecast their magnitude should have far
reaching consequences.
solvent
âH2 a
phenol
2,4,6-Me3C6H2OH
MeCN
PCc
DMF
DMSO
0.44 (0.41)
0.50d (0.47)
0.66 (0.68)
0.78 (0.78)
281
126
5.77
3.41
17.1
5.92
1.53
0.656
a From ref 23a except as noted. Numbers in parentheses are â2H
values calculated from the reported11 equilibrium constants for H-bond
formation by phenol, a “calibrated” HBD for which LPhOH ) 0.946
and DPhOH ) - 0.057 (ref 23a), these âH values being calculated from
2
the relationships, log KH2 ) (log K - DPhOH)/LPhOH and âH ) (log KH2
+ 1.1)/4.636. b From ref 11b. c Propylene carbonate. d Fr2om ref 61.
Experimental Section
Materials. The following solvents, of the purest grade available,
were used as received: acetonitrile, tetrachloromethane and ethyl acetate
(OmniSolve); acetic acid, benzene, heptane, octane, pentane, methyl
acetate, methyl formate, and tert-butyl alcohol (Aldrich). Chlorobenzene
(BDH) was purified by repeated washings with concentrated H2SO4,
H2O, aqueous sodium bicarbonate, and H2O, followed by drying over
CaCl2 and finally by distillation from P2O5. Anisole (Aldrich) was
washed with equal volumes of 2 M NaOH (×2) and H2O (×2), dried
over CaCl2, and then distilled from sodium taking the center cut.
γ-Valerolactone (Aldrich) was purified as described previously.12 With
one exception, the phenols used in this work were from Aldrich. They
were purified by recrystallization from pentane or pentane/ether,
followed by sublimation. The 4-methoxyphenol also had to be
decolorized with charcoal. 2R,4′R,8′R-R-Tocopherol (natural vitamin
E, Chemalog) was purified by chromatography as described previ-
ously.12
Diphenylpicrylhydrazyl, DPPH• (BDH, Poole, U.K.) was 98% pure.12
Di-tert-butyl peroxide (Aldrich, 98%) was percolated through activated
basic alumina, and dicumyl peroxide (Aldrich) was purified by
recrystallization from methanol.
High purity acetophenone, cumyl alcohol, and 1,4-dichlorobenzene
(Aldrich) were used as received. Dimethyl sulfoxide (Aldrich) was dried
over calcium hydride prior to use.
Figure 5. Nielsen and Hammerich’s11b kinetic data for proton transfer
from phenol (b) and 2,4,6-trimethylphenol (9) to the anthracene radical
anion plotted against literature values of âH2 for the four solvents
employed. The data are from Table 5, and the two straight lines have
the same slopes as those found for H-atom abstraction by CumO•, viz.,
MXH ) - 5.15 for phenol and - 3.22 for trimethylphenol (see Table
4).
Laser Flash Photolysis (LFP). The equipment and experimental
procedures have been thoroughly described in earlier papers from this
laboratory.62 Tert-butoxyl and cumyloxyl radicals were generated by
308 nm LFP of solutions of 0.22 M di-tert-butyl peroxide and 0.13 M
dicumyl peroxide, respectively. (These concentrations give an OD ≈
0.3 at the laser wavelength in the 7 × 7 mm2 Suprasil quartz cells.)
All solutions of peroxide and phenol (or other H-atom donor) were
deoxygenated by purging with nitrogen for >5 min prior to LFP.
Pseudo-first-order rate constants (kSexptl) were determined at 298 ( 2 K
using digitally averaged decay or growth curves (from up to 10 laser
flashes). Absolute second-order rate constants (kSXH/Y•) were calculated
by least-squares fitting of plots of kSexptl vs [XH] for at least five
different XH concentrations.
Cumyloxyl Radical Kinetics by Product Analysis. Dicumyl
hyponitrite, synthesized by a literature procedure,63 was decomposed
at 25 °C in the dark in argon-purged, sealed Pyrex vessels for 10 days
in the chosen solvent and known concentrations of an H-atom donor
(e.g., 4-methoxyphenol). Yields (absolute and relative) of acetophenone
and cumyl alcohol were then determined by GC/FID on a Hewlett-
Packard 5890 instrument using a 25 m × 0.02 mm (i.d.) HP-Ultra-2
column and using 1,4-dichlorobenzene as the internal standard. The
mass balance in each experiment (ignoring the dicumyl peroxide formed
by collapse of the geminate cumyloxyl radical pairs in the solvent cage
which was not determined) was calculated as 100× ([acetophenone]
+ [cumyl alcohol])/ [hyponitrite], see Supporting Information. The
nation of phenol and 2,4,6-trimethylphenol by the anthracene
radical anion, kSArOH/An•-, in the four solvents they employed
(see Table 5). Values of âH2 calculated from the reported11
equilibrium constants for hydrogen-bond formation between
phenol and these four HBAs were in good agreement with
literature values23a,61(see Table 5). Plots of log(kSArOH/An
)
•-
versus the literature âH2 values are shown in Figure 5. The two
straight lines have been drawn with slopes identical to those
for H-atom abstraction from phenol (MPhOH ) -5.15) and 2,4,6-
trimethylphenol (MMe C H OH ) -3.22). The good fit of these
3
6 2
lines to experiment is a fairly strong indication that H-atom
transfer and proton transfer from the same substrate have the
same KSE.
Conclusions
Rate constants at room temperature for H-atom (and proton)
abstraction from substrates, XH, in solvents, S, can be correlated
(59) Bordwell, F. G.; Cheng, J.-P.; Harrelson, J. A., Jr. J. Am. Chem.
Soc. 1988, 110, 1229-1231.
(62) Scaiano, J. C. J. Am. Chem. Soc. 1980, 102, 7747-7753. Chatgil-
ialoglu, C.; Ingold, K. U.; Scaiano, J. C. J. Am. Chem. Soc. 1981, 103,
7739-7742. Scaiano, J. C.; Tanner, M.; Weir, D. J. Am. Chem. Soc. 1985,
107, 4396-4403. Kazanis, S.; Azarani, A.; Johnston, L. J. J. Phys. Chem.
1991, 95, 4430-4435.
(60) Bordwell, F. G..; Liu W.-Z. J. Am. Chem Soc. 1996, 118, 10819-
10823.
(61) Besseau, F.; Laurence, C.; Berthelot, M. J. Chem. Soc., Perkin Trans.
2 1994, 485-489.
(63) Dulog, L.; Klein, P. Chem. Ber. 1971, 104, 895-901.

Kinetic SolVent Effects on H-Atom Abstractions
J. Am. Chem. Soc., Vol. 123, No. 3, 2001 477
mean mass balances in chlorobenzene, benzene, anisole, acetic acid,
and acetonitrile were 94, 95, 90, 90, and 97%, respectively. If the yields
of dicumyl peroxide are assumed to be same as Kiefer and Traylor’s64
measured yields of di-tert-butyl peroxide formed in the thermal
decomposition of di-tert-butyl hyponitrite in solvents of the same
viscosities, viz., 0.772, 0.601, 1.25, 1.15, and 0.345 cP, respectively,
for the solvents mentioned above, the estimated total mass balances
rise to 108, 103, 109, 108, and 106%, respectively. It would appear
that cage escape during hyponitrite decomposition of geminate cumy-
loxyl radicals is more efficient than escape of geminate tert-butoxyl
radicals.
point in a 10 × 10 mm2 quartz cuvette placed in a Hewlett-Packard
8425A diode array spectrophotometer equipped with an HP 98090A
programmable heater. Concentrated, deoxygenated stock solutions of
more reactive phenols were rapidly mixed with thermostated, deoxy-
genated solutions of DPPH•. For less reactive phenols, concentrated
deoxygenated stock solutions of DPPH• were rapidly mixed with
thermostated, deoxygenated solutions of XH. Values of kSexptl were
measured for at least five different phenol concentrations, and absolute
second-order rate constants, kSXH/DPPH•, were calculated by least-
squares fitting of plots of kSexptl vs [XH].
Infrared Measurements of R2H. Experiments were done in CCl4
(distilled over P2O5) using DMSO (dried with CaH2) as the hydrogen-
bond acceptor and a Bomem FTIR spectrophotometer 120 series using
a CaF2 cell with a path length of ∼2.5 mm. The concentration of non-
H-bonded XH was determined via a calibration curve (i.e., no DMSO).
This curve was constructed to ensure that experiments with DMSO
were carried out only at XH concentrations below those where
measurable self-association occurred, that is, at concentrations where
Acknowledgment. We thank Professor M. H. Abraham for
some very helpful discussions and the National Foundation for
Cancer Research for partial support of this work.
Supporting Information Available: Derivation of
the general KSE eq viii from Scheme 1 and Abraham’s
thermodynamic equations for hydrogen bonding, plot of
log(kOArOH/DPPH•/M-1 s-1) for nine phenols versus ∑σ+ for their
substituents (Figure S1), detailed kinetic data for the reactions
of CumO• with three selected phenols in various solvents: 2,4,6-
Me3, 4-Cl and 3,5-Cl2-phenol (Tables S1-S3), product data for
the reactions of CumO• with 4-MeO-phenol in various solvents
and with c-C6H12 in anisole (Table S4), data from which R2H
the Beer-Lambert law obtained. At least five different [XH]total
/
[DMSO]total ratios were used to determine the equilibrium constant for
H-bond formation (from the slopes of the straight lines obtained by
plotting [(XH‚‚‚DMSO)]H-bonded/[XH]free against [DMSO]free). Values
of RH2 were calculated using the relation:
log K ) LDMSO log KHA + DDMSO
values were calculated (Table S5), values of kSXH/CumO in
•
various solvents (mainly from the literature) for XH ) tert-
butyl hydroperoxide, aniline and 2-methoxyphenol (Table S6),
detailed kinetic data for the reactions of DPPH• with eight
phenols in heptane and 4-MeO phenol in DMSO (Table S7),
and calculated rate constants for reactions of DPPH• with 19
phenols in an alkane, benzene, anisole, pyridine, and HMPA
(Table S8) (PDF). This material is available free of charge via
the Internet at http://pubs.acs.org.
and
(log KHA + 1.1)
RH2 )
4.636
where LDMSO ) 1.2399 and DDMSO ) 0.2656 (see ref 38).
Kinetic Measurements with DPPH• Radicals. The experimental
procedure has been described in earlier publications from this labora-
tory.12,65 Briefly, the concentration of DDPH• was monitored at its band
maximum (512-530 nm, solvent-dependent) relative to an isosbestic
JA002301E
(64) Kiefer, H.; Traylor, T. G. J. Am. Chem. Soc. 1967, 89, 6667-6671.
(65) Bowry, V. W.; Ingold, K. U. J. Org. Chem. 1995, 60, 5456-5467.