Picosecond Dynamics of Nonadiabatic Proton Transfer: A Kinetic Study of Proton Transfer within the Contact Radical Ion Pair of Substituted Benzophenones/N,N-Dimethylaniline

Article abstract of DOI:10.1021/ja991604+

Picosecond absorption spectroscopy has been employed in the study of the dynamics of proton transfer within substituted benzophenones/N,N-dimethylaniline contact radical ion pairs. The reactions were investigated in the solvents cyclohexane, benzene, and dimethylformamide. The correlation of the reaction rates with the change in free energy reveals that the reaction pathway corresponds to a nonadiabatic process, that is the reaction proceeds by proton tunneling. In nonpolar solvents, an inverted region is observed in the proton-transfer process.

Full text of DOI:10.1021/ja991604+

J. Am. Chem. Soc. 2000, 122, 107-113
107
Picosecond Dynamics of Nonadiabatic Proton Transfer: A Kinetic
Study of Proton Transfer within the Contact Radical Ion Pair of
Substituted Benzophenones/N,N-Dimethylaniline
Kevin S. Peters,* Amanda Cashin, and Peter Timbers
Contribution from the Department of Chemistry, UniVersity of Colorado, Boulder, Colorado 80309-0215
ReceiVed May 13, 1999
Abstract: Picosecond absorption spectroscopy has been employed in the study of the dynamics of proton
transfer within substituted benzophenones/N,N-dimethylaniline contact radical ion pairs. The reactions were
investigated in the solvents cyclohexane, benzene, and dimethylformamide. The correlation of the reaction
rates with the change in free energy reveals that the reaction pathway corresponds to a nonadiabatic process,
that is the reaction proceeds by proton tunneling. In nonpolar solvents, an “inverted region” is observed in the
proton-transfer process.
Introduction
exist based on the work of Bell.5 The experimental indicators
of tunneling are taken to be large kH /kD ratios and curved
Arrhenius plots of ln k vs 1/T.
+
+
In 1996, we reported a picosecond kinetic study for the effect
of solvent upon the dynamics of proton and deuteron transfer
between the radical anion of benzophenone and the radical
cation of dimethylaniline, which were produced upon the
irradiation of benzophenone in the presence of dimethylaniline1
(Scheme 1).Examining the temperature dependence of the proton
transfer, kpt, within an Arrhenius framework, we found that the
ratio of A-factors for proton transfer, AH, and deuteron transfer,
AD, are strongly solvent dependent: in benzene AH/AD ) 0.6,
and in THF AH/AD ) 2.4. Surprisingly, the standard theoretical
framework for proton transfer could not accommodate the
solvent dependence for this ratio of A-factors. Thus, given the
importance of proton-transfer reactions in acid-base chemistry2
and enzyme catalysis,3 we have expanded upon our initial study
by examining how the rate of proton transfer depends on driving
force as well as the solvent and have analyzed these results
within newly developed theoretical models for proton transfer.
The standard theoretical framework for the analysis of kinetics
for proton/deuteron transfer is transition-state theory.4-6 In this
theory, a classical transition state is defined by the free-energy
maximum along the reaction coordinate. Isotope effects are
calculated in terms of the difference between the zero-point
energies for the transition state and the reactant. In the absence
of tunneling, the rate constant ratios kH /kD are predicted to
be in the range of 3-7. These predictions are extensively used
as an indicator of mechanism for organic, inorganic, and
biochemical reactions in solution. The additional effect of H+/
D+ tunneling through the barrier is expected to lead to an
enhancement in the isotope effect reflecting the greater ease of
tunneling by the lighter isotope; approximate theories of this
Recently, the basic assumptions that underlie transition-state
theory have been brought into question.7-9 Theory has revealed
that, in the gas phase, tunneling is the dominant reaction mode
for proton transfer, even at ambient temperatures. Extensive
calculations show that the standard theory for kinetic isotope
effects (KIE) and tunneling can be seriously in error, and thus
the entire framework for interpretation of KIE and tunneling in
gas-phase reactions is undergoing revision. The corresponding
theoretical development for solution-phase reactions has been
undertaken by Dogonadze, Kuznetzov, Ulstrup, and co-work-
ers,10 and then extended by Borgis and Hynes,11-13 Cukier,14,15
and Voth.16,17 Collectively, these theories suggest that when a
potential-energy barrier is present in the proton-reaction coor-
dinate, the reaction pathway involves tunneling through the
barrier as opposed to passage over the barrier. If experiments
are found to confirm these theoretical formulations, which depict
the proton-transfer process as occurring exclusively by tunneling
at ambient temperatures, studies that use the kinetic isotope
effect as an indicator of the nature of the transition state in
proton-transfer reactions will need to be reassessed.
There have been in recent years a great number of investiga-
tions into the dynamics of proton transfer in the gas phase, in
clusters, in solution, and in matrixes.18-30 However, none of
+
+
(7) Garrett, B. C.; Truhlar, D. G.; Wagner, A. F.; Dunning, T. J. Chem.
Phys. 1983, 78, 4400.
(8) Babamow, V. K.; Marcus, R. A. J. Chem. Phys. 1981, 74, 1790.
(9) Truhlar, D. G.; Garrett, B. C. Acc. Chem. Res. 1980, 14, 440.
(10) Kuznetsov, A. M. Charge Transfer in Physics, Chemistry and
Biology; Gordon and Breach: Luxembourg, 1995.
(11) Borgis, D. C.; Lee, S.; Hynes, J. T. Chem. Phys. Lett. 1989, 162,
19.
(1) Dreyer, J.; Peters, K. S. J. Phys. Chem. 1996, 100, 19412.
(2) Bell, R. P. The Proton in Chemistry; Chapman and Hall: London,
1973.
(3) Fresht, A. Enzyme Structure and Mechanism; W. H. Freeman: New
York, 1985.
(4) Gandour, R. D.; Schowen, R. L. Transition States of Biochemical
Processes; Plenum: New York, 1978.
(5) Bell, R. P. The Tunnel Effect in Chemistry; Chapman and Hall:
London, 1980.
(12) Borgis, D.; Hynes, J. T. J. Chem. Phys. 1991, 94, 3619.
(13) Borgis, D.; Hynes, J. T. J. Phys. Chem. 1996, 100, 1118.
(14) Cukier, R. I.; Morillo, M. J. Chem. Phys. 1989, 91, 857.
(15) Morillo, M.; Cukier, R. I. J. Chem. Phys. 1990, 92, 4833.
(16) Li, D.; Voth, G. A. J. Phys. Chem. 1991, 95, 10425.
(17) Lobaugh, J.; Voth, G. A. J. Chem. Phys. 1994, 100, 3039.
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10.1021/ja991604+ CCC: $19.00 © 2000 American Chemical Society
Published on Web 12/16/1999

108 J. Am. Chem. Soc., Vol. 122, No. 1, 2000
Peters et al.
Scheme 1
these studies has been able to fully verify recent theoretical
models developed for proton transfer in solution. In the
following paper, we will examine the dynamics of proton
transfer between the radical cation of dimethylaniline and a
series of substituted benzophenone radical anions. This series
of reactions will be studied in the solvents cyclohexane, benzene,
and dimethylformamide. The correlation of the rate constant
for proton transfer with change in energy, as a function of
solvent, will then used to assess the recent theoretical models
for solution-phase proton-transfer reactions.
Experimental Section
Benzophenone, 4,4′-dichlorobenzophenone, 4-chlorobenzophenone,
4-fluorobenzophenone, 4-methylbenzophenone, 4-methoxybenzophe-
none, 4,4′-dimethoxybenzophenone were obtained from Aldrich, and
4,4′-dimethylbenzophenone was obtained from Kodak. Each was
recrystallized from ethanol. N,N-Dimethylaniline (Aldrich) was distilled
from calcium hydride under reduced pressure and stored under argon.
The solvents cyclohexane (Mallinckrodt), benzene (Baker), and di-
methylformamide (Mallinckrodt) were used without further purification.
The picosecond absorption spectrometer, which employs a Con-
tinuum (PY61C-10) Nd:YAG laser producing a 19 ps pulse width, and
the methods of data analysis have previously been described.31 The
sample was continuously flowed through a 1 cm quartz cuvette during
the experiment. All experiments were undertaken at 23 °C.
Figure 1. Transient absorption at 680 nm following 355 nm excitation
of 0.02 M 4-chlorobenzophenone - 0.4 M N,N-dimethylaniline in
benzene. ([) Experimental points, (s) fit to data with kpt ) 4.1 × 109
s-1
.
The dynamics for the decay of the triplet radical ion pair in
cyclohexane and in benzene, which is attributed solely to proton
transfer, were monitored at 680 nm following the 355 nm
irradiation of the corresponding benzophenone.1 For the samples
in cyclohexane and in benzene, the time increments employed
in the data acquisition were 15 ps; a total of 80 points were
obtained for each run, and a total of four runs were averaged
for each sample. The modeling of the kinetic data assumed a
single-exponential decay of the contact radical ion pair giving
rise to the triplet radical pair. An example of the decay of the
4-chlorobenzophenone/dimethylaniline triplet radical ion pair
in benzene and its fit to the model is shown in Figure 1.
For the samples in dimethylformamide (DMF), the time
increment for monitoring the dynamics of the radical ion pair
at 680 nm was 25 ps; a total of 80 points were obtained for
each run, and a total of four runs were averaged for each sample.
Given the polarity of DMF, one must take into account the
diffusional separation of the contact radical ion pair to form
the solvent-separated radical ion pair, as observed in some of
our previous studies.32-36 The modeling of the kinetic data in
DMF assumed that there are two decay pathways for the contact
radical ion pair; decay of the contact radical ion pair (CRIP) to
the radical pair (RP) through proton transfer, kpt, as well as
diffusional separation to the solvent-separated radical ion pair
(SSRIP), kdif, which cannot undergo proton transfer. Allowing
for the collapse of the SSRIP to reform the CRIP did not
improve the fit of the kinetic model to the experimental data.
Also, in the modeling, it was assumed that the extinction
coefficients for the two radical ion pairs are equal, although
this is only an approximation as there should be a small
difference in the absorption profile for the two species.37
Results
For the present experiments, we wished to examine the
dynamics of proton transfer within the triplet radical ion pair
of the various substituted benzophenones and dimethylaniline.
The choice of the triplet state was predicated upon the need to
eliminate the competition of back-electron transfer with proton
transfer. For the triplet radical ion pair, back-electron transfer
is a long time event, >10 ns,31 while proton transfer occurs on
the 100 ps time scale.1 Thus, to ensure that only the dynamics
of triplet radical ion pairs are monitored, it is necessary that
the amine concentration should not be in excess of 0.5 M; at
higher amine concentrations electron transfer may occur between
the excited singlet state of the benzophenones and the amine,
thus producing a portion of singlet radical ion pairs whose rate
constants for back-electron transfer are competitive with proton
transfer. For the following series of experiments, the sample
concentrations employed were set to 0.02 M for the benzophe-
nones and 0.4 M for the dimethylaniline. The observed dynamics
for the decay of the triplet radical ion pair were found to be
independent of the amine concentration over the range of 0.3-
0.5 M.1
(20) Tolbert, L. M.; Nesselroth, S. M. J. Phys. Chem. 1991, 95, 10331.
(21) Moog, R. S.; Maroncelli, M. J. Phys. Chem. 1991, 95, 10359.
(22) Robinson, G. W. J. Phys. Chem. 1991, 95, 10386.
(23) Shida, N.; Almlof, J.; Barbara, P. F. J. Phys. Chem. 1991, 95, 10457.
(24) Pines, E.; Fleming, G. R. J. Phys. Chem. 1991, 95, 10448.
(25) Zewail, A. H. J. Phys. Chem. 1996, 100, 12701.
(26) Hineman, M. F.; Bruker, G. A.; Kelley, D. F.; Bernstein, E. R. J.
Chem. Phys. 1990, 92, 805.
(27) Syage, J. A. J. Phys. Chem. 1995, 99, 5772.
(28) Brucker, G. A.; Swinney, T. C.; Kelley, D. F. J. Phys. Chem. 1991,
95, 3190.
(29) Swinney, T. C.; Kelley, D. F. J. Chem. Phys. 1993, 99, 211.
(30) Parsapour, F.; Kelley, D. F. J. Phys. Chem. 1996, 100, 2791.
(31) Peters, K. S.; Lee, J. J. Phys. Chem. 1993, 97, 3761.
(32) Deniz, A. A.; Li, B.; Peters, K. S. J. Phys. Chem. 1995, 99, 12209.
(33) Dreyer, J.; Peters, K. S. J. Phys. Chem. 1996, 100, 15156.
(34) Lipson, M.; Deniz, A. A.; Peters, K. S. J. Phys. Chem. 1996, 100,
3580.
(35) Peters, K. S.; Lee, J. J. Phys. Chem. 1992, 96, 8941.
(36) Peters, K. S.; Li, B. J. Phys. Chem. 1994, 98, 401.

Picosecond Dynamics of Nonadiabatic Proton Transfer
J. Am. Chem. Soc., Vol. 122, No. 1, 2000 109
kdif
RP 7kpt
9CRIP 8 SSRIP
The optimal value for kdif was was found to be 5.0 × 108 s-1
.
An example of the decay of the 4-methylbenzophenone/
dimethylaniline triplet radical ion pair in DMF is shown in
Figure 2. The decay of the 4,4′-dichlorobenzophenone/di-
methylaniline triplet radical ion pair to the RP in DMF could
not be accurately resolved due to the dominance of the
diffusional separation of the CRIP to the SSRIP. The cumulative
data for the eight triplet radical ion pairs in the three solvents
are displayed in Table 1.
Discussion
In the follow section, we will first present an account of some
of the recent theoretical developments relating to nonadiabatic
and adiabatic proton transfer. This account will then be followed
by a discussion of the procedure for determining the energetics
for proton transfer within each radical ion pair. Finally, the
correlation of the rate of proton transfer with the energetics will
be presented within the context of theory.
Figure 2. Transient absorption at 680 nm following 355 nm excitation
of 0.02 M 4-methylbenzophenone/0.4 M N,N-dimethylaniline in DMF.
([) Experimental points, (s) fit to data with kpt ) 1.5 × 109 s-1 and
kdif) 5.0 × 108 s-1
.
Table 1. Observed Rate Constants for the Decay of Substituted
Benzophenones/Dimethylaniline Triplet Radical Ion Pair (at 23 °C)
Theory of Nonadiabatic Proton Transfer. The model for
proton-transfer developed by Dogonadze, Kuznetzov, Ulstrup,
and their co-workers assumes that the reaction pathway is a
function of the distance of separation, R, between reactants,
AH+‚‚‚A, Scheme 2.10 At large distances of R, the reaction is
thermally activated in the proton-transfer coordinate, r, and at
the top of the reaction barrier there may be a tunneling
contribution of the overall reaction rate. This pathway is that
depicted as curve A in Scheme 2. When the distance of reactant
separation R decreases, the reaction barrier narrows and is
reduced, which then leads to a nonadiabatic proton transfer as
the predominate reaction mode, that is the proton tunnels from
the reactant state to the product state, curve B in Scheme 2.
Upon further decrease in the separation distance R, as a result
of the very strong coupling between the reactant state and
product state, the potential-energy barrier in the proton-transfer
coordinate is eliminated, and the reaction in the proton
coordinate becomes adiabatic, curve C in Scheme 2.
4,4′-benzophenone
cyclohexane
benzene
DMF
a
4
4′
kH (109 s-1
)
kH (109 s-1
)
kH (109 s-1
)
CH3O-
CH3-
CH3O-
CH3-
H
F
Cl
CH3O-
2.9
5.9
5.4
2.4
4.3
3.6
5.8
6.2
5.5
4.1
3.7
1.9
1.8
1.7
1.5
0.7
0.5
0.3
b
CH3-
H
H
H
H
H
8.9
12.0
12.5
12.0
9.1
Cl
Cl
a Estimated uncertainties in rate constants (10% (1σ). b Could not
accurately resolve decay.
Scheme 2
As R decreases, the potential-energy barrier in the proton-
transfer coordinate decreases, leading to an increase in the rate
of reaction but at a cost of increasing the energies of the reactant
and of the product states at short distances. Dogonadze,
Kuznetzov, and Ulstrup thus defined the rate of proton transfer
as10
k ) φ(R)W(R) dR
(1)
∫
where W(R) is the transition probability from reactant to product
at distance R, and φ(R) is the distribution function for the
molecular species in R.
The model for nonadiabatic proton-transfer developed by
Kuznetsov and his colleagues, depicted as curve B in Scheme
2, is very similar to the model for nonadiabatic electron transfer
in its treatment of the involvement of solvent.10 The fundamental
assumption is that when a barrier is encountered in the proton
transfer coordinate, instead of the proton undergoing a thermally
activated crossing of the barrier, the proton tunnels through the
barrier, thus leading to a nonadiabatic process. This assumption
is fundamentally different from the Bell picture where proton
tunneling occurs only in the region at the top of the reaction
barrier. In Kutznetsov model, for the symmetric proton-transfer
reaction, AH+‚‚‚A to A‚‚‚H+A, when the polar solvent is
Scheme 3
equilibrated to the reactant, Scheme 3 , surface A, the proton
will not be transferred due to an energy mismatch in the reactant
and product states. Upon a solvent fluctuation, the energy of
(37) Simon, J. D.; Peters, K. S. J. Am. Chem. Soc. 1983, 105, 4875.

110 J. Am. Chem. Soc., Vol. 122, No. 1, 2000
Peters et al.
the reactant and product states become equal, Scheme 3, curve
B, and it is in this solvent configuration that the proton tunnels
from one side of the well to the other. Finally upon solvent
relaxation, the product state is formed, Scheme 3, curve C.
This model leads to the following theoretical formulation for
the rate of proton transfer:10
k )
P k
(2)
∑∑
n
nm
n
m
where
knm ) 2π(Cnm/2)2(π/h2kBTEs)1/2 exp (-∆Gqnm/kbT) (3)
and
∆Gqnm ) (∆E + Es + ∆Enm)2/4Es
(4)
Figure 3. Graph of free-energy dependence (-∆G kcal/mole) of the
relative rates of proton transfer employing the Borgis-Hynes model,
eqs 2-5. ER ) 2.0 kcal/mol, EQ ) 1.0 kcal/mol, vibrational frequency
300 cm-1, and ∆Qe ) 0.1 Å. Es ) 2.0 kcal/mol for the larger graph
and Es ) 7.0 kcal/mol for the smaller graph.
In eqs 3 and 4, associated with the solvent coordinate is the
solvent reorganization energy Εs. The energy difference between
the solvent equilibrated reactant state and solvent equilibrated
product states is ∆E. The term knm is the rate constant associated
with tunneling of the proton out of the reactant state with n
quanta of vibrational energy and into the product state with m
quanta of vibrational energy; thus the model allows for the
formation of vibrationally excited product. The term Pn is just
the thermal average over the vibrational populations of the
reactant state. In eq 3, Cnm is the proton tunneling probability
from the n state of the reactant to the m state of the product
reaction coordinate coupling to Q vibration, ER ) h2R2/2m. C0
is the tunneling matrix element for the transfer from the 0
vibrational level in the reactant state to the 0 vibrational level
in the product state. The term ∆Qe is the shift in the oscillator
equilibrium position. F[L(EQ, ER, ωQ)] is a function of a
Laguerre polynomial. For a thorough discussion of eq 5, see
ref 13.
when the two states are iso-energetic. Finally for eq 4, ∆Enm
)
Graphs of the free-energy dependence for the rate of proton
transfer within the Borgis-Hynes model, eqs 2-5, assuming a
promoting mode of 300 cm-1, are shown in Figure 3; the
(n - m)hν is the difference between the vibrational energy levels
in the reactant state and in the product state.
The initial ideas put forth by Dogonadze, Kuznetzov, Ulstrup,
and co-workers for nonadiabatic proton transfer have been
extended by Borgis and Hynes where they address the important
issue of low-frequency vibrations in promoting proton trans-
fer.11-13 One striking difference between electron transfer and
proton transfer is the extreme sensitivity of the proton tunneling
matrix element to distance. The functional form of the tunneling
matrix element between the reactant and product state, for
moderate to weakly hydrogen-bonded species, is C(Q) ) C0
2
calculated rate constants, k/C0 , have been normalized. In both
plots, the value for ER is 2.0 kcal/mol and the value for EQ is
1.0 kcal/mol. They only differ in Es, the solvent reorganization
energy, where for the larger of the two graphs, Es is 2.0 kcal/
mol and for the smaller of the two graphs, Es is 7.0 kcal/mol.
With increasing solvent reorganization energy, the maximum
rate constant for a given solvent reorganization energy shifts to
larger negative free-energy change and the maximum amplitude
is reduced in magnitude as well. This reduction in the maximum
rate constant with increasing Es is the result of the term Es-1/2
in eq 3. Thus, the model predicts that there is an “inverted
region” for proton transfer.
Borgis and Hynes have also theoretically examined the
situation where A‚‚‚A internuclear separation is small, so that
the electronic coupling between the reactant and product state
is large, leading to an adiabatic reaction; the reaction barrier in
the proton-transfer coordinate is below the zero-point vibrational
energy level of the hydrogen stretch, and thus, no electronic
barrier is encountered in the transfer.13 The adiabatic limit leads
to the rate expression
exp(-RδQ). The decay parameter R is very large, 25-35 Å-1
,
when compared to the corresponding decay parameter for the
electronic coupling in electron transfer, 1 Å-1. It is this feature
that makes the dynamics of proton transfer so sensitive to the
internuclear separation of the two heavy atoms, A‚‚‚A. Whereas
a decrease of 0.1 Å will increase the rate of electron transfer
by a factor of 1.1, a similar distance change in proton transfer
will increase the rate by a factor of 20. Thus, in the Borgis-
Hynes model, intermolecular vibrations that lead to a decrease
in the A‚‚‚A nuclear separation will significantly enhance the
rate of proton transfer.
The Borgis-Hynes model introduces a low-frequency vibra-
tional mode, Q, whose frequency is ωQ, and the associated
vibrational reorganization energy is EQ.13 On the basis of a
Landau-Zener curve crossing formulation, they derived the
nonadiabatic rate constant, k, similar to that of Kuznetsov and
co-workers but where the tunneling term Cnm is significantly
modified. The tunneling term, Cnm, is dependent upon a
promoting vibration Q
kad ) (ωs/2π) exp(-â∆Gq)
(6)
where ωs is the solvent frequency and ∆Gq is the free energy
of activation. If the proton-transfer reaction is adiabatic, that
is, it does not occur through proton tunneling, then the A-factor
will be of the order of 1013 s-1 or greater.13
Energetics for Proton Transfer. To compare theories for
proton transfer with experiment, it is necessary to examine how
the rate of proton transfer changes with the change in energy
for the reaction. This requires an assessment of both substituent
and solvent effects for the energy change for the proton-transfer
reaction.
2
Cnm2 ) C0 exp(-R∆Qe) exp((ER - EQ)/hωQ)
F[L(EQ, ER, ωQ)] (5)
The energy ER is a quantum term associated with the proton

Picosecond Dynamics of Nonadiabatic Proton Transfer
J. Am. Chem. Soc., Vol. 122, No. 1, 2000 111
To determine the energetics for proton transfer, it is necessary
to estimate the energy of the contract radical ion pair as well as
the energy of the triplet radical pair relative to the initial
reactants so that the difference in energies reflects the energy
change for the reaction. First, the energetics for proton transfer
in the benzophenone/dimethylaniline contact radical ion pair
to form the triplet radical pair in acetonitrile is derived from
thermochemical data. Then, the effect of the solvents DMF,
benzene, and cyclohexane upon the energy of the contact radical
ion pair of benzophenone/dimethylaniline will be estimated from
prior studies of solvent dependencies of ion pair energies; we
assume the energy of the radical product to be independent of
solvent. Then, from redox potentials, we will deduce how the
energy of the contact radical ion pair varies with substituent.
Finally, the effect of substituents upon the stability of the ketyl
radical will be estimated from the kinetic data for the thermal
rearrangement of 2-aryl-3,3-dimethyl-methylenecyclopropanes.
The energy of the benzophenone/dimethylaniline contact
radical ion pair relative to the reactants, in acetonitrile, has
previously been determined by Mataga and co-workers through
oxidation and reduction potentials; the derived value is 59.3
kcal/mol.38 The energy of the radical pair relative to the reactants
is obtained from literatures values for the energy for the
formation of the ketyl radical39 and the C-H bond dissociation
energy of dimethylaniline40 through the following thermody-
namic cycle.
ion pairs. Relative to acetonitrile, we find that the contact radical
ion pair increases in energy by 0.5 kcal/mol in DMF, by 2.8
kcal/mol in benzene, and by 3.6 kcal/mol in cyclohexane. Thus,
with decreasing solvent polarity, the energy released upon proton
transfer increases to -3.1 kcal/mol in DMF, to - 5.4 kcal/mol
in benzene, and to -6.2 kcal/mol in cyclohexane for the
benzophenone/dimethylaniline contact radical ion pair.
The effect of substituent upon the stability of the radical ion
pair was derived from the study of Arnold and co-workers of
the reduction potentials for a variety of 4,4′-substituted ben-
zophenones which included the substituents methoxy, dimethoxy,
methyl, and dimethyl.42 For these substituents they found an
excellent linear correlation between the reduction potential and
the Hammett σ parameter. Unfortunately, they did not examine
benzophenones substituted with either chlorine or fluorine. To
obtain the reduction potentials for 4-fluorobenzophenone,
4-chlorobenzophenone, and 4,4′-dichlorobenzophenone, we
employed the correlation of reduction potentials with σ to obtain
these values. Relative to benzophenone, the subtituents have
the following effects upon the stability of the contact radical
ion pair: 4,4′-dimethoxy (4.4 kcal/mol), 4,4′-dimethyl (2.1 kcal/
mol), 4-methoxy (2.1 kcal/mol), 4-methyl (0.9 kcal/mol),
4-fluoro (-0.5 kcal/mol), 4-chloro (-1.9 kcal/mol) and 4,4′-
dichloro (-4.0 kcal/mol). Thus, 4,4′-dimethoxy substitution
destablizes the contact radical ion pair by 4.4 kcal/mol, while
the 4,4′-dichloro substitution stabilizes the contact radical ion
pair by 4.0 kcal/mol.
(C6H5)2CdO + H2 f (C6H5)2CHOH ∆H ) - 9 kcal/mol
The effect of substituents upon the stability of the ketyl radical
were estimated from the kinetic data obtained by Creary for
the thermal rearrangement of 2-aryl-3,3-dimethylmethylenecy-
clopropanes, where the mechanism for the isomerization as-
sumes a biradical intermediate.43 Assuming the kinetic data
directly reflects the effect of the substituent upon the stability
of the radical intermediate, then the energy associated with the
substituent effect can be obtained from the energy of activation.
To obtain the energy of activation, it is necessary to have a
measure of the A-factor for the thermal rearrangement. Kirmse
and co-workers have measured an A-factor of 1014 s-1 for the
thermal rearrangement of 1-ethoxy-methylenecyclopropane.44
Finally, in our calculation of substituent effects upon the stability
of the ketyl radical, we assumed that the effect of the substituent
would be less for the ketyl radical, given its higher degree of
delocalization; we arbitrarily assigned a 50% reduction in the
substituent effect on the stability of the ketyl radical relative to
the substituent effect upon the thermal isomerization of 2-aryl-
3,3-dimethyl-methylenecyclopropanes. Thus, we find the fol-
lowing substituents stabilize the ketyl radical: 4,4′-dimethoxy
(0.4 kcal/mol), 4,4′-dimethyl (0.2 kcal/mol), 4-methoxy (0.2
kcal/mol), 4-methyl (0.1 kcal/mol), 4-chloro (0.1 kcal/mol), and
4,4′-dichloro (0.2 kcal/mol). The only substituent that destabi-
lizes the ketyl radical is the 4-fluoro (-0.1 kcal/mol).
On the basis of the above analysis of substituent and solvent
effects, we have determined the following energetics for proton
transfer shown in Table 2.
Comparison of Theory-Experiment. Before we begin to
compare the predictions of nonadiabatic proton transfer theory
with the present experiments, we need to establish that the
reaction conditions are such that adiabatic proton transfer does
not intervene. Adiabatic proton transfer may occur when the
internuclear separation between the two heavy atoms involved
in the proton transfer is small, leading to large electronic
2H• f H2
∆H ) -104 kcal/mol
(C6H5)CHOH f H• + (C6H5)2COH ∆H ) 78 kcal/mol
dimethylaniline f H• + (C6H5)N(CH3)(CH2•)
∆H ) 91.7 kcal/mol
benzophenone + dimethylaniline f
(C6H5)2COH + (C6H5)N(CH3)(CH2•)
∆H ) 56.7 kcal/mol
Thus, in acetonitrile, the energy released upon proton transfer
is ∆H ) -2.6 kcal/mol. In the above analysis, the greatest
source of error is associated with the C-H bond energy for
diphenylmethanol for, as to our knowledge, this quantity has
not been directly measured; the error could be as large as ( 3
kcal/mol. However, what is most important in the present
analysis is the change in energy for the proton-transfer reaction
with substituents and solvents, not the absolute value for the
energy change.
To calculate the solvent dependence for the energetics of
proton transfer within the benzophenone/dimethylaniline radical
ion pair, we need to estimate how the energy of the contact
radical ion pair changes with solvent; we assume that the
energies of the product radical species are independent of
solvent. Recently Gould, Goodman, Farid, and co-workers
determined how the energy of the contact radical ion pair of
1,2,4,5-tetracyanobenzene/hexamethylbenzene varies with sol-
vent.41 We have taken their data and correlated it with ET 30 to
obtain an estimate of the effect that the solvents, employed in
the present study, have upon the energies of the contact radical
(38) Miyasaka, H.; Nagata, T.; Kiri, M.; Mataga, N. J. Phys. Chem. 1992,
96, 8060.
(39) Walling, C.; Gibian, M. J. J. Am. Chem. Soc. 1965, 87, 3361.
(40) Dombrowski, G. W.; Dinnocenzo, J. P.; Farid, S.; Goodman, J. L.;
Gould, I. R. J. Org. Chem. 1999, 64, 427.
(42) Leigh, W. J.; Arnold, D. R.; Humphreys, R. W. R.; Wong, P. C.
Can. J. Chem. 1980, 58, 2537.
(41) Gould, I. R.; Noukakis, D.; Gomez-Jahn, L.; Young, R. H.;
Goodman, J. L.; Farid, S. Chem. Phys. 1993, 176, 439.
(43) Creary, X. J. Org. Chem. 1980, 45, 280.
(44) Kirmse, W. J. C. S. Chem. Commun. 1977, 122.

112 J. Am. Chem. Soc., Vol. 122, No. 1, 2000
Peters et al.
Table 2. Effect of Substitutents upon the Energetics for Proton
Transfera
4
4′
DMF
C6H6
C6H12
CH3O
CH3
CH3O
CH3
H
F
Cl
CH3O
CH3
H
H
H
H
H
Cl
-7.9
-5.4
-5.5
-4.1
-3.1
-2.5
-1.3
+0.7
-10.2
-7.7
-7.7
-6.4
-5.4
-4.8
-3.6
-1.6
-11.0
-8.5
-8.5
-7.2
-6.2
-5.6
-4.4
-2.4
Cl
a All values are in kcal/mol. Dimethylformamide - DMF, benzene
- C6H6, cyclohexane - C6H12
coupling between the reactant and product states. The distance
associated with the crossover between nonadiabatic and adiabatic
proton transfer has yet to be defined and will clearly be system
specific. However, from model calculations, distances in excess
of 2.5 Å appear to lead to the realm of nonadiabatic proton
transfer.12
Figure 4. Plot of the rate constant for proton transfer vs free energy
change (-∆G kcal/mol) for solvent cyclohexane.
The geometry of the benzophenone/dimethylaniline contact
radical ion pair that undergoes proton transfer is not known.
However, from numerous studies of excimers and exciplexes,
it is anticipated that the contact radical ion pair would be
π-stacked to maximize the Coulombic attraction.
The separation between the π-stack system should be of the
order of 3.3 Å based upon studies of the pyrene excimer.45 Given
that both the radical ion of benzophenone and the radical cation
of dimethylaniline should be planar molecules, the equilibrium
separation between the two heavy atoms involved in the proton
transfer, C and O, should be of order of 3.3 Å, although this
distance will vary with radical ion pair intermolecular vibrations.
Thus, the expectation is that proton-transfer reaction should be
nonadiabatic.
Figure 5. Plot of the rate constant for proton transfer vs free-energy
change (-∆G kcal/mol) for solvent benzene.
Further support for this proposal can be found in our recent
investigation of the temperature dependence of proton transfer.
For benzophenone/dimethylaniline in benzene and in THF, the
temperature dependence of the rate constant for proton transfer
was examined within an Arrhenius framework.1 The A-factor,
assuming it is independent of temperature, for proton transfer
is 2.6 × 1011 s-1 in benzene and 6.6 × 1010 in THF. If this
reaction were to be attributed to an adiabatic process, as
described by eq 6, the expectation is that the A-factor should
be greater than 1013 s-1 13
Consequently, based upon consid-
.
eration of the geometry of the contact radical ion pair and the
frequency factor for proton transfer, the transfer process should
fall in the nonadiabatic regime.
The correlation of the rate constant for proton transfer with
changes in free energy for the solvents cyclohexane, benzene,
and DMF can be found in Figures 4-6. For the solvents
cyclohexane and benzene, as the reaction becomes increasingly
exergonic, the reaction rate initially increases, reaches a
maximum, and then decreases. Although the free-energy change
associated with the maximum rate in proton transfer is not well
defined, the maximum rate for proton transfer in both cyclo-
hexane and benzene is approximately -6 kcal/mol. In the
Figure 6. Plot of the rate constant for proton transfer vs free-energy
change (-∆G kcal/mol) for solvent dimethylformamide.
solvent DMF, the rate constant for proton transfer increases as
the free energy changes from -1 to -5 kcal/mol and then
appears to reach a maximum beyond -8 kcal/mol. What is
immediately striking when comparing the nonpolar solvents with
the polar solvent is a decrease in the proton-transfer rate with
a free-energy change of -6 to -12 kcal/mol for the nonpolar
solvents, while the rate increases over this range for the polar
(45) Birks, J. B. The Photophysics of Aromatic Excimers; Birks, J. B.,
Ed.; Academic Press: New York, 1975.

Picosecond Dynamics of Nonadiabatic Proton Transfer
J. Am. Chem. Soc., Vol. 122, No. 1, 2000 113
solvent. The standard model for proton transfer cannot account
for this kinetic behavior. Also in the nonpolar solvents, there is
a clear manifestation of the “inverted region” for proton transfer
as predicted by eqs 2-5.
forms, could not account for the observed dynamics of proton
transfer within the benzophenone/dimethylaniline contact radical
ion pair. This initial conclusion was based upon two observa-
tions. First, from temperature-dependent studies, the derived
A-factor for the solvents benzene and THF is of the order of
1011 s-1. Second, the kinetic deuterium isotope effects are small,
ranging from 2.0 to 2.4. The A-factor analysis appeared to
preclude an adiabatic process, for as shown in eq 6 of this paper,
the expected A-factor for an adiabatic process should be of the
order of 1013 s-1 or greater. Regarding the small isotope effect,
we employed a form of the Borgis-Hynes theory whose
analytical form is derived from eqs 2-5 of the present paper
with the assumption that â(h/2π)ωQ , 1, resulting in eq 1 in
ref 1. Since the prefactor of this equation involves the square
of the tunneling matrix element, one would anticipate a large
deuterium isotope effect for nonadiabatic proton transfer.
However, eq 1 in ref 1 is inappropriate for the analysis of the
dynamics of proton transfer under the conditions of our system
for term â(h/2π)ωQ is approximately equal to 1.0 as well as eq
1 in ref 1 does not allow for the reaction channel to produce
vibrationally excited products, which is clearly an important
consideration for proton-transfer reactions that are exothermic.
Thus, the full analytical forms of eqs 2-5 of the present study
should be employed in the analysis of the kinetic data. Also,
recent theoretical studies of kinetic deuterium isotope effects
reveal that with the appropriate parameters, eqs 2-5 can produce
small kinetic isotope effects.46 Thus, the presence of a small
kinetic isotope effect cannot be used to rule out the intervention
of a nonadiabatic proton-transfer process. As a result of these
considerations as well as the observed inverted region for proton
transfer in the present study, we conclude that the reaction
mechanism for proton transfer within the benzophenone/
dimethylaniline contact radical ion pair involves the nonadiabatic
transfer of the proton.
Qualitatively, the shape of these curves are similar to those
predicted by theory, eqs 2-5, although they appear not to be
symmetrical about the maximum as predicted by theory, Figure
2. However the theory employed in the development of Figure
2 assumes that only one active vibration is involved in promoting
proton transfer. However, more than one vibration may be
involved in reducing the two heavy atom, C and O, internuclear
separation; thus, the appropriate expression for the rate constant
should involve a summation over several vibrational modes,
which could lead to an asymmetry in the correlation of the rate
constant for proton transfer with change in free energy.
Another apparent inconsistency between theory and experi-
ment is the expectation that the maximum in the rate constant
for proton transfer in cyclohexane and in benzene should differ,
whereas experiment reveals them to be approximately the same.
One parameter that controls the position of the maximum is
the solvent reorganization energy, for as the solvent reorganiza-
tion energy increases, the maximum in the rate constant for
proton transfer should shift to larger negative free-energy
changes, Figure 2. For the proton-transfer reaction, the solvent
reorganization energies for cyclohexane and benzene are not
known, but the solvent reorganization energy should be larger
for benzene given its somewhat greater polarity. Therefore, it
is the expectation that the maximum in benzene should occur
at a larger negative free-energy change. However, it is important
to note that there is an inherent error in determining the solvent
dependence of the free-energy change for proton transfer, and
it may be this error that accounts for the same maximum in the
two solvents.
Examining how the maximum in the rate constant varies with
solvent polarity reveals that in cyclohexane the maximum rate
is 1.4 × 1010 s-1, which is reduced to 6.2 × 109 s-1 in benzene,
and then further reduced to 1.9 × 109 s-1 in DMF. This in
qualitative accord with the predictions of eqs 2-5 as the
prefactor to the exponential contains the term Es -1/2. As the
solvent reorganization energy increases, the prefactor should
decrease, leading to a reduction in the maximum rate constant.
There is, however, another factor to consider, for as the solvent
polarity increases, the Coulombic attraction in the contact radical
ion pair should decrease, leading to an increase in the inter-
nuclear separation. The increase in the separation of the contact
radical ion pair with an increase in solvent polarity will lead to
a reduction in the tunneling matrix element for proton transfer.
Therefore, increasing the solvent polarity will increase the
solvent reorganization energy and reduce the tunneling matrix
element, both having the effect of reducing the maximum rate
constant for proton transfer.
Conclusion
The goal of the present study was to ascertain if recently
developed theories for nonadiabatic proton transfer could
account for the effect solvent has upon the dynamics of proton
transfer in the benzophenone/dimethylaniline contact radical ion
pair. Although qualitatively the correlation between theory and
experiment was rather good, a quantitative comparison was not
feasible, given the uncertainty in how a number of the
parameters integral to theory vary with solvent. However, the
results from the present study strongly suggest that, in this
particular molecular system, nonadiabatic proton transfer is the
dominant reaction mode.
Acknowledgment. This work is supported by grants from
the National Science Foundation, CHE-9816540, University of
Colorado Council on Research and Creative Work, and the
Cristol Fund administered by the Department of Chemistry,
University of Colorado.
Finally it is important to note that the above conclusions
regarding the applicability of Borgis-Hynes theory for under-
standing the dynamics of proton-transfer stands in contrast to
our earlier conclusions. In our initial study, ref 1, we suggested
that Borgis-Hynes theory, either the adiabatic or nonadiabatic
JA991604+
(46) Professor J. T. Hynes, personal communication. The theory for
kinetic deuterium isotope effects will be present shortly.