Non-steady-state kinetic studies of the real kinetic isotope effects and Arrhenius activation parameters for the proton transfer reactions of 9,10-dimethylanthracene radical cation with pyridine bases

Article abstract of DOI:10.1039/b102320a

The kinetics of the reactions between 9,10-dimethylanthracene radical cation and 2,6-diethylpyridine (DEP) in dichloromethane-Bu₄NPF₆ (0.2 M) as well as that with 2,6-dimethylpyridine (LUT) in acetonitrile-Bu₄NPF₆ (0.1 M) were studied at temperatures ranging from 252 to 312 K. In the time period before steady-state was reached for both reaction systems at all temperatures, the apparent deuterium kinetic isotope effects (KIE_app) were observed to increase with extent of reaction. The KIE_app-extent of reaction profiles provide strong evidence for a two-step mechanism [eqns. (i),(ii)] consisting of reversible complex formation prior to rate determining proton transfer. (i) ArCH₃^+. + B ? ArCH₃^+./B K_eq = k_f/k_b (ii) ArCH₃^+./B → ArCH₂^. + BH⁺ k_p (iii) ArCH₂^. + ArCH₃^+. + B → Products fast. Resolution of the kinetics into the relevant microscopic rate constants resulted in real deuterium kinetic isotope effects (KIE_real) which are much larger than KIE_app and were observed to increase markedly with decreasing temperature. Values of KIE_real ranged from 62 to 247. It is concluded that a significant degree of quantum mechanical tunneling is involved for both reaction systems. Activation parameters for apparent and microscopic rate constants are discussed with reference to the proton tunneling effect.

Full text of DOI:10.1039/b102320a

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Non-steady-state kinetic studies of the real kinetic isotope effects
and Arrhenius activation parameters for the proton transfer
reactions of 9,10-dimethylanthracene radical cation with pyridine
bases†
2
Yixing Zhao, Yun Lu and Vernon D. Parker*
Department of Chemistry and Biochemistry, Utah State University, Logan, UT 843222-0300,
USA
Received (in Cambridge, UK) 12th March 2001, Accepted 29th May 2001
First published as an Advance Article on the web 6th July 2001
The kinetics of the reactions between 9,10-dimethylanthracene radical cation and 2,6-diethylpyridine (DEP) in
dichloromethane–Bu4NPF6 (0.2 M) as well as that with 2,6-dimethylpyridine (LUT) in acetonitrile–Bu4NPF6 (0.1 M)
were studied at temperatures ranging from 252 to 312 K. In the time period before steady-state was reached for both
reaction systems at all temperatures, the apparent deuterium kinetic isotope effects (KIEapp) were observed to
increase with extent of reaction. The KIEapp–extent of reaction profiles provide strong evidence for a two-step
mechanism [eqns. (i),(ii)] consisting of reversible complex formation prior to rate determining proton transfer.
ϩ
ϩ
ؒ
ؒ
(i)
ArCH3 ϩ B
ArCH3 /B
Keq = kf/kb
ϩ
ϩ
ؒ
ؒ
(ii)
(iii)
ArCH3 /B → ArCH2 ϩ BH
kp
ϩ
ؒ
ؒ
ArCH2 ϩ ArCH3 ϩ B → Products
fast
Resolution of the kinetics into the relevant microscopic rate constants resulted in real deuterium kinetic isotope
effects (KIEreal) which are much larger than KIEapp and were observed to increase markedly with decreasing
temperature. Values of KIEreal ranged from 62 to 247. It is concluded that a significant degree of quantum
mechanical tunneling is involved for both reaction systems. Activation parameters for apparent and microscopic
rate constants are discussed with reference to the proton tunneling effect.
This has implicated complex, rather than single-step, mechan-
Introduction
isms for these reactions. Intermediates have not been observed
in any case and their structures are unknown. We have assumed
that the intermediates in both classes of reactions are likely to
be π-complexes and that all of these reactions follow the same
general mechanism [eqn. (1)], where B(N) acts either as a base
(B) or as a nucleophile (N).
Proton transfer reactions of organic radical cations have
received a great deal of attention from both a kinetic1–9 and a
thermodynamic10,11 viewpoint. The most important difference
between this class of carbon acids and those encountered
in earlier studies is that the radical cations are often very
much stronger acids and are sometimes super-acids. When the
acidic hydrogens reside on carbon the radical cations react
at moderate rates even with relatively strong bases. The latter
allows detailed kinetic studies to be carried out using transient
techniques.
Radical cations are also subject to nucleophilic attack by
both anionic and neutral nucleophiles.12–15 It was recently
pointed out that only nucleophilic attack at the 10-position is
observed for the reaction of 9-methylanthracene radical cation
with pyridine, but that when the base is 2,6-dimethylpyridine
(LUT) initial nucleophilic attack at the 10-position is followed
by elimination of lutidinium ion to give the 9-anthracenyl-
methyl radical.1h When 9,10-dimethylanthracene radical cation
is the proton donor the rate of nucleophilic attack is diminished
and only proton transfer takes place during the reaction with
LUT.
Radical Cation ϩ B(N)
(π-complex) → Products (1)
The acidic protons of interest are often on the side-chain of
the radical cations derived from methylarenes. Since bases are
generally nucleophilic it seems reasonable that the initial inter-
action with a radical cation will involve the most electrophilic
center on the latter, the positive charge. A direct interaction
between the C–H dipole, remote from the positive charge, and
the base would appear less likely.
A major problem in differentiating between the mechanisms
is that under steady-state conditions the mechanisms are
kinetically indistinguishable with rate laws differing only in the
definition of the apparent rate constants. However, we have
recently discovered that, depending upon the relative values
of the microscopic rate constants, reactions following the
mechanism shown as reactions (2)–(4) frequently reach steady-
Small and sometimes negative Arrhenius activation energies
are frequently encountered in both proton transfer1e–i and
nucleophile combination14a,b,d,f,h,j reactions of radical cations.
ϩ
ϩ
ؒ
ؒ
ArCH3 ϩ B
ArCH3 /B Keq = kf /kb
(2)
(3)
ϩ
ϩ
ؒ
ؒ
ArCH3 /B → ArCH2 ϩ BH
kp
† This paper is dedicated to the memory of Professor Lennart Eberson
whose many contributions had an enormous influence on the chemistry
of radical cations and on the work of one of the authors (V. D. P.).
ϩ
ϩ
ؒ
ؒ
ArCH2 ϩ ArCH3 ϩ B → ArCH2B ϩ ArCH3 fast (4)
DOI: 10.1039/b102320a
J. Chem. Soc., Perkin Trans. 2, 2001, 1481–1488
This journal is © The Royal Society of Chemistry 2001
1481

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state late in the first half-life.1i During the pre-steady-state
period the various rate constants affect the overall reaction
rate to different degrees than implied by rate law (5). This gives
simplest complex mechanism consistent with the experimental
data. We cannot rule out the possibility of a more complex
mechanism involving additional steps.
ϩ
ϩ
ؒ
ؒ
Ϫd[ArCH3 ]/dt = 2(kf kp/(kp ϩ kb))[ArCH3 ][B] (5)
Assignment of rate constants
The magnitude of the ratio of the derivative peak heights
(RЈI = IЈb/IЈf) is a measure of the rate of reaction of the
electrode-generated intermediate, ranging from 1.0 for no
reaction to 0 for complete reaction during the time of the
experiment. The experimental variable is v, the voltage sweep
rate. The experimental RЈI/(1/v) response curves may be com-
pared with theoretical data obtained by digital simulation in
order to evaluate rate constants of the homogeneous chemical
reactions coupled to the charge transfer reaction of the
substrate.
rise to apparent kinetic isotope effects (KIEapp) which vary sig-
nificantly with the extent of reaction. The observation of extent
of reaction dependent KIEapp for these reactions establishes
two mechanistic facts; first, that the reactions do not follow the
simple mechanism, and second, that steady-state is not yet
achieved in the time period where KIEapp varies.
The concurrent fitting of theoretical data obtained by digital
simulation to experimental data for the reactions of both
ϩ
ϩ
ؒ
ؒ
ArCH3 and ArCD3 results in a unique set of rate constants;
kf, kb, kpH and kpD.1i The mechanism shown as reactions (2)–(4)
was demonstrated and rate constants were assigned for the
reactions of two different substituted methylanthracene radical
cations with LUT and 2,6-diphenylpyridine in dichloromethane
–Bu4NPF6 (0.2 M) at 291 K. That study demonstrated that
real kinetic isotope effects (KIEreal), equal to kpH/kpD, for all
four reactions are much larger than KIEapp and can only be
accounted for by invoking a considerable degree of quantum
mechanical tunneling. It should be pointed out that the extent
of reaction dependent KIEapp would go undetected treating the
data in the conventional way, in which concentration–time pro-
files are fitted to linear relationships for first- or second-order
kinetics. The latter strategy also assumes steady state for com-
plex mechanisms, which revokes the opportunity to resolve the
kinetics and assign microscopic rate constants.
ϩ
ؒ
The concurrent fitting of data for both ArCH3
and
ϩ
ؒ
ArCD3 results in a unique set of rate constants which give the
best correspondence between the experimental response and
the theoretical data.1i In order to arrive at this unique set of rate
constants, the parameters must be varied over a wide range in a
systematic manner. Arriving at the unique set of rate constants
requires a large number of simulations.
Our data fitting procedure involves calculating (vexpH Ϫ
H
D
vsimH)2/vsim
,
(vexpD Ϫ vsimD)2/vsim
,
and (KIEexp Ϫ KIEsim)2/
KIEsim, where vH and vD are the voltage sweep rates necessary
for a particular RЈI and the subscripts refer to experimental
(exp) and simulation (sim) data, at each RЈI from 0.85 down to
0.50 and summing each of these over the entire range (ΣH, ΣD,
and ΣKIE). Since the dependence of KIEapp on RЈI is the most
important parameter in arriving at a unique fit, ΣKIE is used
directly in the data fit while ΣH and ΣD are monitored to assure
that good fits to the two response curves are obtained.
We have recently shown that the pre-steady-state time period
can be accessed during the stopped-flow study of the kinetics of
the reaction between 1-nitro-1-(4-nitrophenyl)ethane (NNPE)
with hydroxide ion in aqueous acetonitrile.16 The experimental
kinetic data for this reaction were observed to deviate sig-
nificantly from that expected for the simple mechanism. The
kinetics were resolved by concurrent fitting of experimental
extent of reaction–time profiles for NNPEH and NNPED to
appropriate theoretical data for the complex mechanism. Real
deuterium kinetic isotope effects ranging from 17 to 26 were
observed, along with Arrhenius activation parameters con-
sistent with extensive proton tunneling (EaD Ϫ EaH = 2.8 kcal
molϪ1; AD/AH = 4.95).
Since the rate constant for a proton transfer step passing
through a classical transition state is expected to be much
more temperature dependent than that for the fraction of the
reaction taking place by tunneling through the barrier, kinetic
studies over a range of temperatures have been recommended
in order to provide evidence for the latter.17 In this paper we
The fact that the range of kf over which RЈI-dependent
H
KIEapp are observed is limited, i.e. from kapp to 11(kappH),
suggests the following strategy. We typically select about 10 kf
H
over the applicable range starting at kapp and determine the
values of the other rate constants, kpH, kb and kpD, which give
the best fit for that particular kf value. This is done by varying
H
D
kp and adjusting the other two rate constants (kb and kp
)
to conform to eqns. (6)–(8), where the subscript s.s. refers to
H
(kapp
(kapp
)
)
s.s./2kf = (kpH/kb)/(1 ϩ kpH/kb) = CH
s.s./2kf = (kpD/kb)/(1 ϩ kpD/kb) = CD
(6)
(7)
(8)
D
KIEreal = [CH/(1 Ϫ CH)]/[CD/(1 Ϫ CD)]
steady-state. For each kf a series of ΣKIE as a function of kpH is
H
obtained. Plots of ΣKIE vs. kp are parabola-like curves with
present kinetic results for the reactions of 9,10-dimethyl-
minima that reflect the best fit of experimental to theoretical
data for the kf value. Fitting of experimental to theoretical
data is best accomplished by using an iterative approach. The
approximate rate constants obtained using moderate changes
in the variables provide the starting point for more accurate
fitting. The overall result is a series of the fitting parameter at
anthracene radical cations (DMAϩ and DMA-d6 ) with LUT
and 2,6-diethylpyridine (DEP) as a function of temperature in
dichloromethane–Bu4NPF6 (0.2 M) and acetonitrile–Bu4NPF6
(0.1 M). We have successfully resolved the kinetics and have
assigned microscopic rate constants for all of the reactions over
the entire temperature range studied and have evaluated KIEreal
in all cases.
ϩ
ؒ
ؒ
the minimum ((ΣKIE)min) as a function of kf. A plot of (ΣKIE)
min
vs. kf is, again, parabola-like, with a minimum which reflects the
best value of kf. The fitting procedure is illustrated graphically
in Fig. 3 of reference 1i. The factor of 2 which appears on
the left hand side of eqns. (6) and (7) is a consequence of the
stoichiometry of reactions (2)–(4).
Results
The proton transfer reactions of DMAϩ and DMA-d6 with
DEP in dichloromethane–Bu4NPF6 (0.2 M) and with LUT in
accetonitrile–Bu4NPF6 (0.1 M) were studied in the temperature
range 252 to 312 K. The reaction kinetics were studied using
derivative cyclic voltammetry (DCV)18 and the rate constants
were evaluated by fitting experimental DCV data to the theor-
etical data obtained by digital simulation19 using the procedure
recently described.1i Experimental DCV response curves were
closely matched with theoretical data for the two-step proton
transfer mechanism [eqns. (2)–(4)]. The proposed scheme is the
ϩ
ؒ
ؒ
Temperature effects on experimental DCV data for the radical
cation proton transfer reactions
The experimental DCV data for the reactions of DMAϩ and
ؒ
ϩ
ؒ
DMA-d6 as a function of temperature are illustrated in
Figs. 1 and 2 for both solvent–base systems. The solid symbols
are for the DMAϩ data and the open symbols are for the
ؒ
ϩ
ؒ
DMA-d6 data in both figures. The solid lines represent the
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J. Chem. Soc., Perkin Trans. 2, 2001, 1481–1488

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Fig. 2 DCV kinetic data for the reactions of DMAϩ (solid squares)
ؒ
ϩ
ؒ
and DMA-d6 (open squares) with DEP in dichoromethane–Bu4NPF6
(0.2 M) as a function of temperature. The solid lines represent
theoretical data for the complex proton transfer mechanism.
Fig. 1 DCV kinetic data for the reactions of DMAϩ (solid squares)
ؒ
ϩ
ؒ
and DMA-d6 (open squares) with LUT in acetonitrile–Bu4NPF6 (0.1
M) as a function of temperature. The solid lines represent theoretical
data for the complex proton transfer mechanism.
best-fit theoretical data obtained as described in the previous
section. The most significant feature of these data is the fact
that in all cases excellent correspondences between experi-
mental and theoretical data for the mechanism shown by
Fig. 3 Arrhenius plots for the reactions of DMAϩ (solid squares) and
ؒ
ϩ
ؒ
DMA-d6 (open squares) with LUT in acetonitrile–Bu4NPF6 (0.1 M)
derived from apparent rate constants (a) and microscopic rate constants
(b).
reactions (2)–(4) are observed.
D
Arrhenius plots of ln k vs. 1/T , where k are kappH, kapp
,
kpH, and kpD, are illustrated for both solvent systems in
Figs. 3 and 4. Again, the solid symbols refer to data for DMAϩ
ؒ
ϩ
ؒ
steady-state is achieved. For the reactions studied here, this
evidence is illustrated by the data in Tables 1 and 2 for the
reactions of the radical cations with LUT in acetonitrile–
Bu4NPF6 (0.1 M) and with DEP in dichloromethane–Bu4NPF6
(0.2 M), respectively. For these reactions, at all temperatures
studied, KIEapp increases significantly with extent of reaction
in the RIЈ range from 0.85 down to 0.50. In Tables 1 and 2
both experimental (exp) and simulated (sim) KIEapp are listed.
This again shows the excellent fit between experimental and
theoretical data for the reactions over the entire range of
temperature in the two solvent systems.
and the open symbols are for DMA-d6 data. In all cases
excellent linear relationships are observed over the limited
temperature intervals.
The effect of extent of reaction on KIEapp for the proton transfer
reactions of the radical cations
The experimental evidence which differentiates the mechanism
shown as reactions (2)–(4) from a simple second-order proton
transfer mechanism consists of the observation of a KIEapp
dependent on the extent of reaction in the time period before
J. Chem. Soc., Perkin Trans. 2, 2001, 1481–1488
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View Article Online
the range of KIEapp increased with decreasing temperature. For
this system, KIEreal varied from 62 to 189 as the temperature
was decreased from 291 to 252 K.
Activation parameters for the reactions of DMA radical cations
with pyridine bases
Arrhenius activation parameters for the reactions of DMAϩ
ؒ
ϩ
ؒ
and DMA-d6 with LUT in acetonitrile–Bu4NPF6 (0.1 M) and
DEP in dichloromethane–Bu4NPF6 (0.2 M) are gathered in
Tables 5 and 6, respectively. The activation parameters apply to
four distinct rate constants including kappH, kappD, kpH and kpD in
the two solvent–base systems. Although there are differences,
the activation parameters for the two reaction systems appear
to be remarkably similar. The greatest differences are in
the values of the Arrhenius A factors, which are consistently
greater when the base is LUT (Table 5) as compared to that
when DEP (Table 6) is the base. Binding energies in the inter-
mediate complexes can be estimated from the temperature
effect on the equilibrium constants (equal to kf/kb) for the
formation of the complexes (Tables 3 and 4). The binding
energies of the corresponding radical cation–base complexes
were estimated from van’t Hoff plots to be equal to Ϫ1.2 and
Ϫ0.6 kcal molϪ1 for LUT in acetonitrile–Bu4NPF6 (0.1 M)
and DEP in dichloromethane–Bu4NPF6 (0.2 M), respectively.
Fig. 4 Arrhenius plots for the reactions of DMAϩ (solid squares) and
ؒ
ϩ
ؒ
DMA-d6 (open squares) with DEP in acetonitrile–Bu4NPF6 (0.1 M)
derived from apparent rate constants (a) and microscopic rate constants
(b).
The effect of temperature on apparent and real deuterium kinetic
isotope effects
As expected, both KIEapp and KIEreal were observed to depend
markedly on temperature. Rate constants for both reaction
systems are summarized in Tables 3 and 4. The effect of tem-
perature on KIEapp for the reactions of DMAϩ with LUT in
ؒ
Uncertainty in rate constants and kinetic isotope effects derived
from the fitting procedure
acetonitrile–Bu4NPF6 (0.1 M) is similar to that observed above.
However, KIEreal values in this case were larger and were found
to vary from 76 to 247 in the temperature range from 312 to
252 K. For the reactions of the radical cations with DEP in
dichloromethane–Bu4NPF6 (0.2 M) both the magnitude and
The average deviations between experimental data and
theoretical fitting lines, for example those illustrated in Figs.
1 and 2, are about 2%, which is within experimental error for
Table 1 Apparent (KIEapp, Exp = experimental, Sim = simulated) and
real (KIEreal) deuterium kinetic isotope effects for the reactions of
Table 2 Apparent (KIEapp, Exp = experimental, Sim = simulated) and
real (KIEreal) deuterium kinetic isotope effects for the reactions of
DMAϩ with LUT in acetonitrile–Bu4NPF6 (0.1 M) at different
DMAϩ with DEP in CH2Cl2–Bu4NPF6 (0.2 M) at different
ؒ
ؒ
temperatures
temperatures
T /K
T /K
312
292
273
252
292
273
252
RIЈ
Exp
Sim
Exp
Sim
Exp
Sim
Exp
Sim
9.78
RIЈ
Exp
Sim
Exp
Sim
Exp
Sim
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
KIEreal
7.90 7.62
8.55 8.54
8.61 9.04
9.09 9.35
9.28 9.57
9.73 9.71
10.1
10.2
75.6
8.54
8.21 10.1
9.94 11.5
10.9
11.6
11.9
12.3
12.5
12.6
10.1
12.0
13.1
13.7
14.1
14.4
14.6
14.7
9.81
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
KIEreal
6.05
7.23
7.64
7.67
7.77
8.06
8.51
8.65
6.30
7.11
7.61
7.91
8.10
8.26
8.35
8.42
7.14
7.14
8.22
8.87
9.27
9.54
9.74
9.86
9.96
8.44
9.79
10.6
11.3
11.6
11.8
12.7
13.2
8.49
9.93
10.8
10.0
10.5
11.1
11.8
12.3
13.0
13.4
13.0
15.5
16.8
17.6
18.8
19.5
20.3
13.8
15.8
17.0
17.8
18.3
18.7
18.9
7.84
8.73
8.97
9.61
9.75
10.0
10.5
12.4
13.9
14.1
14.4
15.1
15.6
11.3
11.6
11.8
12.0
12.2
9.81
9.90
107
139
247
61.9
106
189
a,b
Table 3 Rate constants for the reactions of DMAϩ with LUT in acetonitrile–Bu4NPF6 (0.1 M) at different temperatures
ؒ
H
D
H
D
T /K
kapp
kapp
kp
kp
kf
kb
ket
KIEapp
KIEreal
312
292
273
252
12090
7160
4080
1984
1307
628
306
120
9190
4430
2930
1470
122.0
41.4
21.1
13960
7940
4480
2120
1143
482
287
67200
51500
28700
13520
7.90–10.2
8.54–13.4
10.1–15.8
9.81–20.3
75.6
107
139
247
5.95
99.3
a [DMA] = 1.0 mM and [LUT] = 10.0 mM. b Units for kappH, kappD, kf and ket are MϪ1 sϪ1; units for kpH, kpD and kb are sϪ1
.
a,b
Table 4 Rate constants for the reactions of DMAϩ with DEP in CH2Cl2–Bu4NPF6 (0.2 M) at different temperatures
ؒ
H
D
H
D
T K
kapp
kapp
kp
kp
kf
kb
ket
KIEapp
KIEreal
292
273
252
3030
1650
860
386.5
182.2
79.6
2690
1912
1380
43.5
18.04
7.30
3420
1788
908
341
159.0
76.1
57100
42200
25300
6.05–8.65
7.14–10.5
8.44–13.2
61.9
106
189
a [DMA] = 0.5 mM and [DEP] = 12.5 mM. b Units for kappH, kappD, kf and ket are MϪ1 sϪ1; units for kpH, kpD and kb are sϪ1
.
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J. Chem. Soc., Perkin Trans. 2, 2001, 1481–1488

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Table 5 Arrhenius parameters for apparent and real proton and deut-
eron transfer reactions of DMAϩ with LUT in acetonitrile–Bu4NPF6
ؒ
(0.1 M)
Apparenta
H
Realb
H
D
D
Ea/kcal molϪ1
EaDϪEaH/kcal molϪ1
106A
4.71
6.19
4.62
14.0
7.66
25.6
1.48
3.04
1.83
23.8
27.7
AD/AH
1.04
a From kappH and kapp
.
b From kpH and kp
.
D
D
Table 6 Arrhenius parameters for apparent and real proton and
deuteron transfer reactions of DMAϩ with DEP in CH2Cl2–Bu4NPF6
ؒ
(0.2 M)
Apparenta
H
Realb
H
Fig. 5 Plots showing percent deviation of theoretical to experimental
data caused by changes in rate constants from the best-fit values; kf
(solid squares) and kp (open squares).
D
D
H
D
Ea/kcal molϪ1
EaDϪEaH/kcal molϪ1
106A
4.60
5.76
7.72
2.43
6.50
3.05
∆
is much more sensitive to changes in kf, kapp and kapp
total
1.16
4.07
17.6
than to changes in kp.
8.13
0.173
The difference in sensitivity toward changes in kf and kp is
further illustrated by the ∆total vs. rate constant profiles in Fig. 5.
The data near the minima of the curves are parabola-like
and may be fit with second-order polynomial equations. The kf
plot is very narrow and steep and any departure from the best-
fit value of kf results in significant change in the % deviation.
The kp plot is much broader and more shallow; changes in kp
from the best fit value result in smaller changes in the %
deviation. When the x-axis is expressed in rate constant values
this suggests that the fitting error would be smaller for kf than
for kp. However, the minimum can be located for both of the
plots with very small degrees of uncertainty.
We use two different methods to locate the best fit depending
upon the stage of refinement of the fit. The first method, which
is used at a lower degree of fit refinement, is to select the lowest
value of the fitting parameter for a series of simulations.
The second, more accurate, method is to treat the data close
to the minima as second-order polynomials and to calculate
the rate constants at the minima from the equations of the
lines. The latter method is used in the final stages of the fitting
procedure. For the data shown in Fig. 5, the difference in best
fit rate constants using the two different methods of finding
the minima is negligible. We find that ∆total is generally very
sensitive to changes in kf from the best fit value. This is of
importance, since KIEreal only depends on kf and the experi-
mental apparent rate constants [eqn. (8)].
AD/AH
0.950
a From kappH and kapp
.
b From kpH and kp
.
D
D
Table 7 The effect of fitting errors in rate constants on the quality of
experimental to theoretical RIЈ – sweep data fitsa
Rate constant
∆
∆
∆
∆
KIE
total
H
D
Best fit
6.58
12.13
13.32
7.04
1.24
1.53
1.50
1.24
1.24
1.24
1.24
1.22
1.27
1.25
1.23
2.17
5.18
5.68
2.60
2.55
5.39
5.14
4.42
3.63
2.55
2.50
3.17
5.42
6.14
3.19
3.33
6.07
5.91
5.24
4.18
3.42
3.18
(kappH/MϪ1 sϪ1) ϩ 1%
(kappH/MϪ1 sϪ1) Ϫ 1%
(kappD/MϪ1 sϪ1) ϩ 1%
(kappD/MϪ1 sϪ1) Ϫ 1%
(kf/MϪ1 sϪ1) ϩ 1%
(kf/MϪ1 sϪ1) Ϫ 1%
(kpH/sϪ1) ϩ 10%
7.13
12.69
12.29
10.88
9.08
7.21
6.91
(kpD/sϪ1) Ϫ 10%
(ket/MϪ1 sϪ1) ϩ 10%
(ket/MϪ1 sϪ1) Ϫ 10%
a Data from the reaction of DMAϩ with LUT in acetonitrile–Bu4NPF6
(0.2 M).
ؒ
the measurement of RЈI. The deviations of experimental and
theoretical KIEapp (Tables 1 and 2), which are the ratios of the
H and D points in Figs. 1 and 2, are slightly greater, at about
3%, but also within experimental error by virtue of the data
from which they are derived.
The effect of changes in rate constants on the percent devi-
ations between experimental and theoretical data is illustrated
in Table 7. The first row in Table 7 summarizes the various
percent deviations, ∆total, ∆H, ∆D and ∆KIE [eqn. (9)] for the
Discussion
General reactions (2) and (3) are illustrated in Scheme 1 using
the reaction between of DMAϩ and LUT as an example. The
ؒ
proton transfer step (3) is followed by rapid product forming
reactions (4). An important feature of the reaction is that pro-
ton transfer is irreversible due to the large equilibrium constant
and the rapid product-forming reactions of the generated free
radical.1h We have previously shown1i that kinetic data for this,
and several related reactions, are inconsistent with a simple
second-order mechanism for the proton transfer reaction. The
mechanism illustrated in Scheme 1 was assigned on the basis of
fitting experimental to theoretical data in the pre-steady-state
period where KIEapp were observed to vary significantly with
the extent of reaction.
The application of non-steady-state kinetics provides the
means to resolve the kinetics of proton transfer reactions
passing through the mechanism shown as reactions (2)–(4).1i
In the time window before steady-state is achieved, rate
equation (5) is not yet applicable and the relative effect of the
∆total = ∆H ϩ ∆D ϩ ∆KIE
(9)
best fit between experimental points measured at 291 K for the
reaction between DMAϩ with LUT in acetonitrile–Bu4NPF6
ؒ
(0.1 M) and theoretical data for the complex mechanism. The
terms on the right-hand side of eqn. (9) refer to the percent
deviation between experimental and theoretical data for the
RЈI –v profiles for proton transfer (∆H), deuteron transfer (∆D)
and that for KIEapp(∆KIE). The remaining lines in the table show
the effect of varying a single rate constant in the simulations
while holding all others at the value of the best fit. Plots of any
one of the percent deviations vs. one of the rate constants are
parabola-like, with the best fit value at the minimum.1i How
shallow or how deep the parabola are depends upon which rate
constant is plotted. From the data in Table 7 it is obvious that
J. Chem. Soc., Perkin Trans. 2, 2001, 1481–1488
1485

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Scheme 1
microscopic rate constants differ from that at steady-state.
acetonitrile–Bu4NPF6 (0.1 M) KIEapp values are sufficiently
An experimental observation characteristic of this situation is
KIEapp that deviate significantly from the steady-state value at
small extent of reaction, converging to it as the reaction pro-
gresses. The data in Tables 1 and 2 demonstrate the variations in
KIEapp for the radical cation proton transfer reactions during
the pre-steady-state period.
large to suggest tunneling, while the activation parameters are
consistent with semi-classical behavior. Thus, a strong case
for significant proton tunneling could not be made for either
reaction from relationships developed from the apparent rate
constants.
We appear to be justified in concluding that the reactions
of DMAϩ with both bases are accompanied by extensive
ؒ
Besides demonstrating that the complex proton transfer
mechanism [reactions (2)–(4)] rather than a simple second-
order mechanism is applicable, the extent of reaction depend-
ence of KIEapp also serves as the experimental tool to resolve
the kinetics into the microscopic rate constants for the various
steps.1i The RЈI vs. log (1/ν) profiles shown in Figs. 1 and 2
demonstrate the goodness of fit between the experimental data
(symbols) and the theoretical data (solid lines) for the complex
proton transfer reaction.
proton tunneling. Also, it is clear that without resolving
the proton transfer kinetics this conclusion could not be
arrived at. The KIEreal observed for these two reactions are
among the largest that have been reported for proton transfer
reactions.
A question may arise as to whether or not the large degree of
tunneling observed for these reactions is connected to some
special property of radical cation proton transfer reactions. On
the basis of the limited data available we are unable to conclude
whether or not radical cation reactions are especially subject
to tunneling effects. It is our opinion that reactions involving
the cleavage of C–H bonds, whether H leaves as a proton,
a hydrogen atom or a hydride ion, may follow two-step
mechanisms, of which eqns. (2)–(4) is an example, where
formation of an association complex is kinetically significant.
Depending upon the relative magnitudes of the microscopic
rate constants, KIEreal/KIEapp can vary from unity to >100,1i
which highlights the importance of insuring that KIEreal are
used when assessing the degree of tunneling in a reaction. Thus,
it appears to be likely that many of the KIEapp which have been
In our earlier study1i we were able to assign microscopic rate
constants for four different radical cation proton transfer
reactions carried out at 291 K. The values of KIEreal in these
four reactions ranged from 31 to 47, all significantly larger
than the semi-classical maximum value of about 10 under the
reaction conditions.19 In the present study we confine our
attention to the reactions of a single radical cation, DMAϩ
,
ؒ
with 2 different pyridine bases (LUT and DEP) over a range of
temperatures.
The experimental criteria most often considered20–22 to
implicate tunneling in proton transfer reactions are still those
listed by Bell (values in parentheses refer to the C–H bond at
298 K); (a) KIE which exceed the value predicted by semi-
reported for C–H proton transfer are not equivalent to KIEreal
.
H
classical theory (≅10), (b) EaD Ϫ Ea which exceed the isotopic
This being the case, the degree of tunneling in these reactions
remains unknown and comparisons with radical cation proton
transfer reactions cannot be made. The proton transfer reaction
between NPPEH(D) and hydroxide ion16 mentioned earlier
supports the latter conclusion. A large number of kinetic
studies have been carried out on the proton transfer reactions
of nitroalkanes,22–46 of which NNPEH(D) is a representative
example, with the common assumption that the mechanism
involves the simple reversible proton transfer without any
intermediates. Our studies on the proton transfer reactions of
NNPEH(D) with hydroxide ion in aqueous acetonitrile16 suggest
that the latter assumption is not justified and that the deuterium
kinetic isotope effects reported are KIEapp which may be very
difference in zero-point energies (≅1.35 kcal molϪ1) and (c)
AD/AH which exceed the corresponding semi-classical values
(0.7–1.2).16 Clearly, as demonstrated by the data in Tables 3 and
4, KIEreal for both reactions comply with criterion (a). The
values of KIEreal for the two reactions range from 62–189 and
76–247 and increase significantly with decreasing temperature.
Likewise, criterion (b) is fulfilled by data for both reactions.
When the base was DEP in dichloromethane–Bu4NPF6 (0.2 M)
H
(Table 4), EaD Ϫ Ea was observed to be equal to 4.07 kcal
molϪ1, which is significantly larger than the semi-classical value.
This quantity was found to be equal to 3.04 kcal molϪ1 for the
reaction of DMAϩ with LUT in acetonitrile–Bu4NPF6 (0.1 M)
ؒ
(Table 5), consistent with criterion (b). Activation data for the
former reaction are clearly consistent with criterion (c), with
AD/AH equal to 17.6. The ratio for the latter reaction (AD/
AH = 1.83) is somewhat lower but still consistent with this
criterion.
much lower than KIEreal.
Another relevant question deals with whether or not radical
cation proton transfer reactions reach steady-state at a later
stage than occurs with other C–H cleavage reactions. This is
very important in terms of being able to assess whether or
It is also of interest to apply the tunneling criteria to KIEapp
not KIEapp values are reasonable approximations to KIEreal.
H
and the activation parameters derived from kapp and
We believe that the answer to this question is a definitive no.
The proton transfer reaction16 of NNPEH(D) mentioned in the
previous paragraph, as well as an apparent hydride transfer
reaction47 that we have observed to follow the complex mech-
anism, are pertinent examples. Both of the latter involve com-
plex mechanisms for reactions that do not reach steady-state
until late in the first half-life.
kappD. When the base was DEP in dichloromethane–Bu4NPF6
(0.2 M), KIEapp values were only slightly greater than the
semi-classical maximum value. The activation energy difference
(EaD – EaH) was equal to 1.16 kcal molϪ1, which is very close to
that predicted by semi-classical theory and this is also the case
for AD/AH (= 0.95). For the reaction of DMAϩ with LUT in
ؒ
1486
J. Chem. Soc., Perkin Trans. 2, 2001, 1481–1488

View Article Online
Some of the largest deuterium kinetic isotope effects which
have been reported involve unimolecular hydrogen atom shift
in free radicals.48–53 In the case of unimolecular reactions the
formation of a reactant complex is not a necessary feature of
the mechanism and it is likely that KIEapp are very nearly the
same as KIEreal for single-step reactions. The fact that tunneling
can be implicated from the very large KIE that are often
observed in these reactions, while tunneling can less frequently
be shown for second-order reactions, suggests that KIEapp
for the latter cannot usually be equated to KIEreal and are not
reliable measures of the degree of tunneling.
of tunneling in radical cation proton transfer reactions are
expected to provide more detail on this phenomenon.
Experimental
Materials
Dichloromethane was allowed to reflux for several hours over
CaCl2 and, after passing through active neutral alumina,
was used without further purification. Acetonitrile was distilled
from P2O5 and used without further purification after passing
through neutral alumina to remove traces of water. DMA
(Aldrich) was recrystallized from propan-2-ol. DMA-d6 was
prepared according to a literature procedure55 using methyl-
d3-magnesium iodide (99.5ϩ%) as the Grignard reagent. 2,6-
Dimethylpyridine (99.5ϩ%, Aldrich) was distilled under
reduced pressure before use. 2,6-Diethylpyridine was prepared
according to a literature method56 and further purified by
column chromotography (silica gel) before use.
Kreevoy and Kotchevar54 have proposed
a two-step
mechanism for hydride transfer reactions. The first step involves
complex–solvent relaxation before the hydride transfer event.
They observed that KIEapp vary by about a factor of two as
the solvent is changed over a range of aprotic and hydroxylic
solvents and attribute the two extremes to slow and fast
relaxing solvents. Their results suggest that extent of reaction
dependent KIEapp may be observed for reactions experiencing
this phenomenon providing that the kinetics can be studied
in the time regime before steady-state is reached. We have
observed24 extent of reaction dependent KIEapp in a formal
hydride transfer reaction and are currently studying the kinetics
of this system.47
Instrumentation and procedures
The instruments and data handling procedures as well as the
procedures used for kinetic measurements were those recently
described.1i The digital simulations and the fitting of experi-
mental to theoretical data were the same as recently reported.1i
The RЈI range for the kinetic measurements was restricted to
that where the experimental data are most reliable (0.85–0.50).
Above 0.85 the RЈI/(1/v) response curve is relatively flat giving
rise to larger experimental errors. At RЈI lower than about 0.5,
the reverse peak on a cyclic voltammogram is no longer
observed and changes in RЈI with v reflect only the increase in
height of the peak for the forward charge transfer process.
There is still far too little resolved kinetic data available to
draw any firm conclusions concerning structural or solvent
effects on the various rate constants [eqns. (2)–(4)] for the
proton transfer reactions between radical cations and bases.
The limited data do suggest some points of interest with regard
to the association reactions between radical cations and bases.
Data are available for the reactions of DMAϩ with LUT
ؒ
in acetonitrile (this study) and in dichloromethane.1i The
association constants (Keq = kf /kb) are equal to 16.5 (292 K)
and 25.0 (291 K), respectively, in the two solvents, indicating a
small solvent effect. In dichloromethane, Keq was observed to be
equal to 25.0 (291 K) when the base is LUT and 10.0 (292 K)
when the base is DEP. The latter suggests a steric effect for
the formation of the radical cation–base complexes. This is
also reflected in the relative values of binding energies of the
corresponding radical cation–base complexes; Ϫ1.2 and Ϫ0.6
kcal molϪ1 for LUT in acetonitrile–Bu4NPF6 (0.1 M) and DEP
in dichloromethane–Bu4NPF6 (0.2 M), respectively.
Acknowledgements
Acknowledgement is made to the donors of The Petroleum
Research Fund, administered by the ACS, as well as to the
National Science Foundation (CHE-970835 and CHE-
0074405) for support of this research.
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ϩ
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