J. Phys. Chem. B 2008, 112, 219-226
219
Nonadiabatic Proton/Deuteron Transfer within the Benzophenone-Triethylamine Triplet Contact Radical Ion Pair: Exploration of the Influence of Structure upon Reaction† Libby R. Heeb and Kevin S. Peters* Department of Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309 ReceiVed: May 1, 2007; In Final Form: August 30, 2007
The dynamics of proton transfer within a variety of substituted benzophenone-triethylamine triplet contact radical ion pairs are examined in the solvents acetonitrile and dimethylformamide. The correlation of the proton-transfer rate constants with ∆G reveals an inverted region. The kinetic deuterium isotope effects are also examined. The solvent and isotope dependence of the transfer processes are analyzed within the context of the Lee-Hynes model for nonadiabatic proton transfer. Theoretical analysis of the experimental data suggests that the reaction path for proton/deuteron transfer involves tunneling, and the origin of the inverted region is attributed to a curved tunneling path.
Introduction Kinetic isotope effects for proton-, hydrogen-atom-, and hydride-transfer reactions have been extensively employed in the determination of reaction mechanisms. As with any kinetic measurement, their mechanistic interpretation always lies within the context of a model for the process of interest.1-12 The first model for the kinetic deuterium isotope effect that found wideranging application in the study of organic and biochemical reactions is attributed to Westheimer.13 This model is based on transition-state theory, where the activated complex is located along the proton-transfer coordinate. The origin of the kinetic isotope effect is traced to the difference in the isotopic dependence of the zero-point energies in the reactant state and in the transition state. From the magnitude of the kinetic isotope effect, the position of the transition state along the reaction coordinate is estimated. In this treatment, the quantum nature of the proton/deuteron is manifested only in the vibrational frequencies of the reactive modes. The quantum nature of the proton/deuteron was explicitly incorporated into the Westheimer model by Bell.2 In the Bell tunneling correction to transition-state theory, tunneling at the top of the reaction barrier accelerates the transfer process. Prescriptions for the calculation of this tunneling correction have been formulated. Currently, this model is finding extensive application in molecular dynamic simulations of proton and hydride transfer in enzymatic processes.14,15 A different perspective for the description of the reaction coordinate for proton transfer in the condensed phase was developed by German, Kuznetsov, and Dogonadze in the 1960s.5,16,17 They proposed that the initial molecular process associated with proton transfer is a fluctuation in the solvent structure that brings the reactant and product states into resonance. At this critical solvent configuration, if there is an electronic barrier separating the reactant and product states in the proton-transfer coordinate and if the zero-point energy of the vibration associated with the transferring proton lies below the electronic barrier, then the proton tunnels through the reaction barrier into the product state, leading to a nonadiabatic reaction pathway. A particularly intriguing result of German, †
Part of the “James T. (Casey) Hynes Festschrift”.
Kuznetsov, and Dogonadze’s theoretical analysis is found in the correlation of the kinetic deuterium isotope effect with ∆G. Employing very reasonable molecular parameters, they found that as ∆G decreases from 0 to -12 kcal/mol, the kinetic deuterium isotope effect falls from a value of 8 to a value of 2.17 The magnitudes of these isotope effects are characteristic of the predictions of the classical formulation developed by Westheimer, and yet, in this nonadiabatic model, the protontransfer process proceeds exclusively by tunneling. Thus, small values for the kinetic deuterium isotope effect, 2 to 8, cannot be used to distinguish between a classical reaction path and a nonadiabatic pathway. For a given molecular potential, the question that naturally arises is which reaction pathway kinetically dominates, the classical model for proton transfer with the Bell tunneling correction or the nonadiabatic formalism involving the fluctuation of the solvent that brings the reactant and product states into resonance, thus allowing for proton tunneling. Azzouz and Borgis examined the reaction dynamics for the proton transfer in the model system OH-N, where the molecular parameters for the system corresponded to a weak hydrogen-bonded complex.18 Modeling the quantum hopping process within the context of the Landau-Zener theory, they found the reaction pathway incorporating the nonadiabatic process, kLZ, completely dominates the classical reaction pathway incorporating the Bell correction term, kC, for kLZ/kC ) 200. Thus, their model study suggests that the dominant reaction pathway for proton transfer with an intervening electronic barrier proceeds by tunneling through the barrier. The nonconventional view of proton/hydrogen/hydride transfer has been significantly advanced by Hynes and co-workers over the past 15 years.3,19-24 In addition to further elucidating the importance of the solvent coordinate in bringing the reactant and product states into resonance, a coordinate not found in conventional theories, they also expanded the theory to include both adiabatic and nonadiabatic transfer processes in the protontransfer coordinate. The demarcation between these two regimes depends upon whether the zero-point vibration associated with the transferring mode in the reactant state is above or below the electronic barrier in the transfer coordinate; the adiabatic regime is often associated with strong hydrogen-bonded com-
10.1021/jp073340g CCC: $40.75 © 2008 American Chemical Society Published on Web 10/11/2007
220 J. Phys. Chem. B, Vol. 112, No. 2, 2008 plexes, while the nonadiabatic regime is found in weak hydrogen-bonded complexes.3 For nonadiabatic transfer, Hynes and co-workers identified the importance of a low-frequency vibrational mode in promoting the transfer.3 In the transfer of a proton between two heavy atoms, the vibrational frequency associated with the internuclear separation of the two heavy atoms greatly accelerated the rate of the transfer; the origin of this effect is traced to the rapid fall off of the tails of the proton wave function. This feature is not found in electron-transfer theory, given the much slower decay of the tails of the electronic wave function when compared to that of the proton wave function. Finally, Hynes and co-workers have carried out an extensive theoretical study of the origin of the kinetic deuterium isotope effect for both adiabatic and nonadiabatic transfer processes. They found that the isotope effects for both regimes can vary between 1 and 7.23 In the nonadiabatic regime, the magnitude of the kinetic isotope effect and its variation with driving force is strongly dependent on the low-frequency vibrational promoting mode. Over the past 10 years, we have presented a series of studies that examined the free-energy dependence of the rate constant for proton transfer within the triplet contact radical ion pairs composed of variously substituted benzophenone radical anions and N,N-disubstituted aniline radical cations.25-31 Surprisingly, the correlation of the rate constants with ∆G reveals both a normal region and an inverted region. The position of the maximum in the rate constant in the correlation is a sensitive function of the solvent polarity as well as the vibrational reorganization energy of the radical cation of the substituted aniline, a kinetic behavior reminiscent of nonadiabatic electron transfer. Indeed, in order to rationalize the proton kinetic behavior, we proposed that the reaction pathway must involve nonadiabatic proton transfer. We were able to model the reaction kinetics for proton transfer within the triplet contact radical ion pair employing the theoretical formulation of Lee and Hynes, provided that the proton tunneling occurred out of the zero-vibrational level of the reactant state (V ) 0) and into the zero-vibrational level of the product state (V′ ) 0).31 Recently, Kiefer and Hynes presented a theoretical study for nonadiabatic proton transfer involving a linear configuration between the two heavy atoms and the proton that reveals that the tunneling rate constant from the zero-vibrational energy level of the reactant (V ) 0) into the first-vibrational energy level of the proton stretch (V′ ) 1) will exceed the rate constant for reactant V ) 0 to product V′ ) 0; the result is the correlation of the observed rate constant with driving does not display an inverted region.23 In view of this most recent theoretical study, we speculated that the origin of the observed inverted region must reside in a curved protontunneling reaction pathway.31 The origin of the curved reaction path is traced to the probable π-stacking of the benzophenone radical anion with the radical cation of the substituted aniline. Molecular modeling of the π-stack suggests that the shortest distance for proton transfer out of the reactant state and into the product state produces the product state where the H-OC-C dihedral angle is twisted 90° with respect to the equilibrium geometry for the product, Scheme 1. Following the transfer to the product state with the 90° configuration, the system thermally relaxed to the equilibrium configuration. To further explore the effect of the geometry of the reactive complex upon the correlation of the rate constant for proton transfer with driving force, we now present an investigation into the kinetics of proton/deuteron transfer within the triplet contact radical ion pair of benzophenone/triethylamine. Unlike N,N-
Heeb and Peters SCHEME 1
disubstituted anilines, the radical cation of triethylamine cannot form a π-stacked complex; thus, the geometry of the reactive complex will differ from our previous study. As before, we find an inverted region in the correlation of the rate constant for proton/deuteron transfer with driving force for the triplet contact radical ion pair of benzophenone/triethylamine. Experimental Section The solvents acetonitrile (99.93+%), and N,N-dimethylformamide (DMF) (99.8%) were purchased from Aldrich and used as received. The nine different substituted benzophenone compounds were obtained from Aldrich: 4,4′-dimethoxybenzophenone (DiMeO) (97%); 4,4′-dimethylbenzophenone (DiMe) (99%); 4-methoxybenzophenone (MeO) (97%); 4-methylbenzophenone (Me) (99%); benzophenone (H) (99%); 4-fluorobenzophenone (F) (97%); 4-chlorobenzophenone (Cl) (99%); 4,4′dichlorobenzophenone (DiCl) (99%); and 4-(trifluoromethyl)benzophenone (CF3) (97%). Triethylamine (99.5%) and triethyld15-amine (98%) were also purchased from Aldrich. The picosecond laser system, described previously, employs a Continuum Leopard D-10 Nd:YAG laser with an 8 ps pulse length.32 The samples were contained in a 1 cm path-length quartz cuvette at room temperature with a magnetic stir bar. All samples were composed of 0.02 M benzophenone and varying concentrations of triethylamine, 0.4 M for acetonitrile samples and 0.6 M for DMF samples. The samples were irradiated at 355 nm and probed at 725 nm. The calculated electrostatic potentials, surface areas, and Mulliken charge densities are based upon B3LYP density functional theory at the 6-31G* level using Spartan 04. The calculated vibrational frequencies employed AM1 using Spartan 04; the derived values for the vibrational frequencies were scaled by a factor of 0.9.33 The procedure for deriving the kinetic parameters from the experimental kinetic data has been discussed previously.34 Briefly, the time-dependent absorbance A(t) obtained from the experiments results from the convolution of the instrument response function, I(t), with the molecular kinetics, F(t)
A(t) )
∫t -∞ I(τ)F(t - τ)dτ
(1)
where the instrument response function I(τ) is the result of the convolution of the pump and probe beams and is assumed to have the analytical form of a Gaussian
I(t) ) (2πσ)-0.5exp(-(t - t0)/2σ2)
(2)
The parameters characterizing the Gaussian are obtained from the calibration compounds pyrene and perylene. The kinetic parameters are solved for simultaneously employing the downhill simplex method of Nelder and Mead for minimization.34 Results and Discussions Reaction Pathways. The first mechanistic study of the photochemical reduction of benzophenone by triethylamine on the picosecond time scale first appeared in 1980.35 Excitation
Proton/Deuteron Transfer with Benzophenone-Triethylamine SCHEME 2
of benzophenone at λexc ) 355 nm produces the first-excited singlet state, 1Bp*, which decays by intersystem crossing, kisc, to produce the first-excited triplet state of benzophenone, 3Bp*, within 10 ps. The 3Bp* has an absorption maximum at λmax ) 525. The 3Bp* is quenched by the transfer of an electron from triethylamine to form the triplet contact radical ion pair (3CRIP), ket, with the radical anion of benzophenone absorbing at λmax ) 710 nm. At high concentrations of triethylamine in acetonitrile, the electron transfer occurs on the 30 ps time scale, although a precise determination of the rate constant was not determined in our 1980 study. The triplet contact radical ion pair decays by two pathways.25 The first is the transfer of a proton from the amine radical cation to the benzophenone radical anion forming the triplet geminate radical pair (3GRP), kpt, with the benzophenone ketyl radical absorbing at λmax ) 545 nm. The second decay pathway is the diffusional separation of the triplet contact radical ion pair into the triplet solvent-separated radical ion pair (3SSRIP), kdiff. These kinetic processes are depicted in Scheme 2. The time-dependent concentrations of the intervening molecular species are readily accessible, given their unique absorption spectra: benzophenone triplet state, λmax ) 525 nm, benzophenone radical anion, λmax ) 710 nm, and benzophenone ketyl radical, λmax ) 545 nm. The form of the triplet radical ion pair, either contact or solvent-separated, produced upon electron transfer has been the subject of much discussion.36 Given that the free-energy change for the electron transfer is approximately ∆G ) -10 kcal/mol, such a small driving force should favor the formation of the triplet contact radical ion pair, a conclusion based upon the pioneering studies of Gould and Farid.37 Benzophenone Triplet Quenching. To facilitate the determination of the rate constant for proton transfer within the triplet contact radical ion pair, kpt, it is desirable that kpt < ket, where ket is the rate constant for quenching of the triplet state of benzophenone by electron transfer and is a function of the amine concentration. Since the rate constants for proton transfer within the various triplet contact radical ion pairs are found to vary from 330 ps to 2 ns, it is desirable that the quenching of 3Bp* is essentially complete by 300 ps. To determine the appropriate concentration of triethylamine leading to kpt< ket, we utilized 1,4-diazabicyclo[2.2.2]octane (DABCO) as an electron-transfer quencher of 3Bp* as DABCO has the virtually same oxidation potential as that of triethylamine, 0.71 eV versus SCE in acetonitrile, but importantly, the radical cation of DABCO does not undergo proton transfer on the picosecond-nanosecond time scales.36,38 Monitoring the time dependence of the transient absorption spectra of 3Bp* and the radical anion of benzophenone over the wavelength range of 506 to 756 nm, we found that 3Bp* is effectively quenched on the 300 ps time scale utilizing 0.4 M DABCO in acetonitrile and 0.6 M DABCO in DMF, thus establishing the appropriate concentrations of triethylamine for the present kinetic studies.
J. Phys. Chem. B, Vol. 112, No. 2, 2008 221 Kinetics for Proton/Deuteron Transfer. Following 355 nm excitation of the various substituted benzophenones in the presence of triethylamine, the dynamics for the formation and decay of the contact radical anion pair is probed at 725 nm, an absorption attributed only to the radical anions of the various benzophenones. An example of the kinetic data for 4,4′dimethylbenzophenone with triethylamine in acetonitrile is shown in Figure 1. The data is analyzed within the following model
The rise in the transient absorption at 725 nm is associated with the rate constant for electron transfer, ket ) 6.8 × 1010 s-1. Given the limited number of data points characterizing the rise in absorption, the error in the derived rate is large, on the order of (50%. Also, this rate process as modeled is pseudo-first order as the concentration dependence of ket was not examined, and hence, it does not reflect the intrinsic rate of electron transfer. The decay of the contact radical ion pair (3CRIP) is attributed to two processes, proton transfer, kpt )1.1 × 109 s-1, where the resulting triplet geminate radical pair (3GRP) does not absorb at 725 nm, and the diffusional separation into the triplet solventseparated radical ion pair (3SSRIP), kd ) 1.4 × 108 s-1, modeled as having an identical absorption spectrum to that of the 3CRIP. Both of these latter processes are assumed to be unimolecular. The rate constants for proton transfer and deuteron transfer for the variously substituted benzophenones are given in Table 1. Energetics for Proton/Deuteron Transfer. The analysis of the kinetic data within the context of the Lee-Hynes model requires the correlation of the rate constants for proton/deuteron transfer with ∆G.19 This driving force is the difference in the free energy between the 3CRIP and the 3GRP. The protocol for the determination of the driving force has been described.29 Briefly, the free energy for the formation of the 3CRIP relative to the initial reactants, ∆GCRIP, is given by RED ∆GCRIP ) (EOX D - EA ) + ∆CRIP
(3)
OX where EOX D is the oxidation potential of triethylamine, ED ) RED 0.71 versus SCE, and EA is the reduction potential of the ) various benzophenones, which for benzophenone is ERED A -1.86 versus SCE.38 The parameter ∆CRIP is the solvent correction factor based on the Onsager dipole model for the solvent dependences of the energetics of the contact radical ion pair.29,39 The change in free energy for the formation of the 3GRP relative to the initial ground-state reactant is determined by addition of the enthalpy of formation for the triplet state of benzophenone (69.2 kcal/mol), the enthalpy for the addition of a hydrogen atom to the triplet state of benzophenone (-110.8 kcal/mol), and the value for the CH bond dissociation enthalpy for triethylamine (90.7 kcal/mol).29,40 To the enthalpy change is added the entropy change associated with the formation of the 3GRP relative to the ground-state reactants. The entropy change associated with the spin statistics is R ln 3, which, at room temperature, is less than 1 kcal/mol and thus is neglected. The determination of the effect of substituents upon the energy of the 3CRIP and the 3GRP has been described previously.29 The resulting driving forces for proton transfer within the various benzophenone/triethylamine 3CRIP are given
222 J. Phys. Chem. B, Vol. 112, No. 2, 2008
Heeb and Peters
Figure 1. Transient absorption for 0.02 M 4,4′-dimethylbenzophenone and 0.4 M triethylamine in acetonitrile at 23 °C. Excitation: 355 nm. Probe: 725 nm. Experimental data: squares. Fit: solid line. Fitting parameters: kpt ) 1.06 × 109 s-1, kdiff ) 1.36 × 108 s-1, and ket ) 6.88 × 1010 s-1.
TABLE 1: Rate Constants for Proton (kpt, s-1) and Deuteron (kdt, s-1) Transfer Solvent
Acetonitrile
Acetonitrile
Acetonitrile
DMF
DMF
DMF
benzophenone substituents
kptb
kdt
kpt/kdt
kpt
kdt
kpt/kdt
DiMeO DiMe MeO Me H F Cl DiCl CF3
4.73E+08 1.06E+09 7.40E+08 1.62E+09 2.00E+09 1.46E+09 2.19E+09 3.12E+09 3.01E+09
3.84E+08 a 5.99E+08 1.02E+09 1.13E+09 1.44E+09 1.43E+09 1.65E+09 a
1.23
5.66E+08 1.27E+09 8.93E+08 1.48E+09 1.96E+09 2.33E+09 2.32E+09 2.81E+09 2.65E+09
5.47E+08 a 7.94E+08 1.53E+09 1.89E+09 1.65E+09 1.97E+09 1.99E+09 1.90E+09
1.03
a
1.24 1.59 1.77 1.01 1.53 1.89
1.12 0.97 1.04 1.41 1.18 1.41 1.39
Isotope studies were not completed for these compounds due a limited supply of deuterated triethylamine. b Estimated error ( 10%
TABLE 2: Driving Forces for Proton Transfer benzophenone substituents
driving force in acetonitrile (kcal/mol)
driving force in DMF (kcal/mol)
DiMeO DiMe MeO Me H F Cl DiCl CF3
-15.6 -13.1 -13.1 -11.8 -10.8 -10.2 -9.0 -7.0 -5.6
-16.0 -13.5 -13.5 -12.2 -11.2 -10.6 -9.4 -7.4 -6.0
in Table 2. They range from -5.6 kcal/mol for 4-(trifluoromethyl)benzophenone to -15.6 kcal/mol for 4,4′-dimethoxybenzophenone in acetonitrile. In DMF, the driving force increases by -0.4 kcal/mol for each of the contact radical ion pairs. Lee-Hynes Model. Numerous theoretical models have been introduced for the description of nonclassical barrier crossings following the initial formulation of transition-state theory by Eyring, modified by Wigner to include a quantum correction.41,42 One such recent development is the formulation of the pathintegral quantum transition-state theory, a quantum analogue of transition-state theory.43 Another is variational transitionstate theory with a semiclassical tunneling as a correction; this method has been widely applied to the elucidation of enzyme reaction mechanisms involving proton/hydride tunneling.14,15,44 Finally, recent theoretical studies of proton tunneling in malon-
aldehyde reveals that one-dimensional models are inadequate for the accurate description of the tunneling splitting; instead, a multidimensional surface must be utilized in conjunction with WKB tunneling probabilities.45-47 For the analysis of the present set of experimental data, the application of these various theoretical methods is problematic. The main difficulty is in the modeling of the solvent effect upon proton tunneling as the solvent not only modifies the potential of mean force but also the rearrangement of the solvent is critical for bringing the reactant and product states into resonance to facilitate tunneling. The reorganization of solvent as a critical component of the reaction path is not readily incorporated into the above-mentioned theoretical models in such a way as to make a facile connection to experimental studies. One theoretical model that is readily applicable for the analysis of the present experimental data is the Lee-Hynes model for proton transfer, although the models of Kuznetsov and of Cukier, which have many points in common with LeeHynes, could also be implemented for analysis.6,16,19 The theory of Lee -Hynes reduces the complexity of the problem down to a simple set of reaction coordinates consisting of the solvent reorganization, the vibrational modulation of the tunneling distance, and the proton-tunneling coordinate. Given the importance of the multidimensional nature of the tunneling reaction path found for malonaldehyde, the simplification invoked by Lee-Hynes theory should, at best, give only qualitative insights into the nature of the reaction path for proton transfer. The Lee-Hynes model for nonadiabatic proton transfer determines the rate constant for the tunneling of a proton out
Proton/Deuteron Transfer with Benzophenone-Triethylamine
J. Phys. Chem. B, Vol. 112, No. 2, 2008 223
of the nth vibrational level of the reactant state into the mth level of the product state19
k(nr f mp) ) kmp,nr(0)(π/2A2)1/2 exp(-A21/2A2)
(4)
where kmp,nr(0), A1, and A2 are defined as
kmp,nr(0) ) 2(2π/h)2[Cmp,nr(Q)]2 exp{(ER/hωQ)*2 coth(βhωQ/2)} (5) A1 ) (2π/h){∆E + ES + EQ + ER + [hmpωP - hnrωR] + 2∆Q/|Q|(EREQ)1/2*coth(βhωQ/2)} (6) A2 ) 2(2π/h)2kBT{ES + (EQ + ER)(βhωQ/ 2π coth(βhωQ/2π)) + ∆Q/|∆Q|(EREQ)1/2βhωQ} (7) The terms are defined as follows: ωR, the frequency of the vibration associated with the proton transfer in the reactant state; ωP the frequency of the vibration associated with the proton transfer in the product state; ∆Q, the change in the equilibrium distance in the intermolecular separation of the reaction complex upon going from the reactant state to the product state; EQ, the energy associated with the change in ∆Q; ES, the solvent reorganization energy; nr, the vibrational quantum number in the reactant state; mp, the vibrational quantum number in the product state; ωQ, the low-frequency normal mode associated with the intermolecular vibration of the reaction complex; and ∆E, the driving force for proton transfer. The tunneling matrix element from the nth vibrational level of the reactant state to the mth vibrational level of the product state is Cmp,nr(Q) and is defined as
Cmp,nr(Q) ) (h/4π2)(ωRωP)1/2 exp{(-2π2/hωq)[Vq - 1/2(VnR + VmP)]} (8) The barrier height is Vq, the energies of the reactant and product states are Vnr and Vmp, and ωq is the mass-weighted imaginary frequency associated with the inverted parabola of the transitionstate reaction coordinate. Finally, the term ER is an energy term associated with R that characterizes the distance dependence of the wave function overlap associated with the tunneling process; it is dependent on the mass of the transferring particle. From theoretical modeling, the values of R for proton transfer vary from 25 to 35 Å-1. ER is given by ER ) h2R2/2m, where m is the mass of the tunneling particle; for proton transfer, ER is on the order of 1 kcal/mol.3 Applying the Lee-Hynes formalism to deuteron transfer, five terms are dependent upon the mass: the reactant frequency, ωR; the product frequency, ωP; the imaginary frequency at the transition state, ωq; the energy of the quantum term, ER; and the distance dependence of the overlap of the tails of the wave function, R. Upon deuteration, the three vibrational frequencies, ωR, ωP, and ωq, are reduced by a factor of 1/x2. From the model studies of Hynes and co-workers, ER is on the order of 1 kcal/mol for proton transfer and increases to 2 kcal/mol for deuteron transfer.23 Geometry of the Contact Radical Ion Pair. To complete the analysis of the data using Lee-Hynes theory, an approximate geometry of the CRIP must be determined in order to properly select the proton-donating and -accepting vibrational frequencies. All of the molecular systems employed in our prior
Figure 2. Electrostatic potential for the triethylamine radical cation and benzophenone radical anion calculated based upon B3LYP density functional theory at the 6-31G* level. Positive potential: blue. Negative potential: red.
SCHEME 3
studies of nonadiabatic proton transfer have been based upon various analogues of benzophenones and N,N-disubstituted anilines.31 The reaction geometries of the triplet contact radical ion pairs are assumed to be π-stacked, leading to the protontransfer coordinate depicted in Scheme 1. To change the reaction geometry of the 3CRIP, the radical cation of triethylamine is employed as the proton donor. To gain insight into the nature of the reactant geometry, the electrostatic potentials of the triethylamine radical cation and the benzophenone radical anion are calculated employing B3LYP density functional theory at the 6-31G* level for each species separately. The results of the calculation are shown in Figure 2, where the radical anion and the radical cation have been schematically arranged; this geometry is not the result of a computational minimization. The positive-charged density resides mainly on the N in the radical cation, while the negativecharged density resides mainly on the O of the radical anion. The proposed reactant geometry based upon the optimization of the Coulombic interaction is given in Scheme 3, which is to be contrasted with the reactant geometry displayed in Scheme 1. Given the nature of the Coulombic interaction between the nitrogen cation and the oxygen anion, the reaction complex is free to fluctuate about some equilibrium structure. The distribution of the reactant structures, which in principle can be obtained computationally, although with great difficulty due to the effects of solvent, has not been determined.48 Since a distribution of reactant structures is likely to contribute to the overall protontransfer process, it is reasonable to assume that both stretching and bending modes in both the reactant and product states are active in proton transfer. The modeling of the proton transfer within the Lee-Hynes theory will examine these various reaction pathways.
224 J. Phys. Chem. B, Vol. 112, No. 2, 2008
Heeb and Peters
TABLE 3: Substituent Effect upon Oxygen Charge Density p substituents
oxygen charge
DiMeO DiMe MeO Me H F Cl DiCl CF3
-0.560280 -0.551672 -0.545793 -0.537608 -0.528402 -0.536459 -0.527659 -0.531162 -0.518945
The analysis of the experimental data assumes that the distribution of reactant states is independent of the nature of the substituent at the para positions on the aromatic rings. However, substituents will modify the electric charge distribution on the oxygen due to the donation or withdrawal of electron density by the substituent. To gain insight into this effect, a Mulliken population analysis of the charge density on oxygen of the variously substituted benzophenone radical anions was undertaken, the results of which are given in Table 3. As the reaction driving force decreases, from DiMeO to CF3, there is a general decrease in charge density at the oxygen. This decrease in charge density will decrease the Coulombic interaction between the anion and cation, leading to an increase in the internuclear separation of the reactants. Thus, in considering distance alone, the kinetics of proton transfer for DiMeO should exceed the kinetics of proton transfer for CF3, contrary to observation; the inverted region cannot be the result of a substituent affecting the distance for proton transfer. Application of the Lee-Hynes Model. Modeling the data within the context of the Lee-Hynes model for nonadiabatic proton transfer, we examined four different combinations of vibrational reaction modes that could be actively involved in proton tunneling: a C-H stretch (2645 cm-1) to an O-H stretch (2386 cm-1), a C-H stretch (2645 cm-1) to an O-H bend (768 cm-1), a C-H bend (1183 cm-1) to an O-H stretch (2386 cm-1), and a C-H bend (1183 cm-1) to an O-H bend (768 cm-1). These vibrational frequencies were obtained from AM1 calculations and represent normal modes whose largest amplitude of vibration is associated with the designated stretch or bend. The vibrational frequency associated with the barrier top of the transition state was set to ωq ) 2500 cm-1, a value adopted from a prior theoretical study of hydrogen-atom transfer.31 The energy term ER was set to 1.0 kcal/mol, based upon theoretical modeling.23,31 Since the increase or decrease in the intermolecular separation of the 3CRIP upon proton transfer was unknown, ∆Q was initially set to ∆Q ) 0, making EQ ) 0. A global fit of the Lee-Hynes model to both proton and deuteron transfer in a given solvent is a function of three variable parameters: Vq, the barrier height; ωQ, the intermolecular vibrational frequency of the 3CRIP; and ES, the solvent reorganization energy. The mass dependence of the various parameters was taken into account as described earlier. The barrier height Vq is defined as the energy separation between the zero-point energy of the transferring vibrational mode in the reactant state and the energy of the transition state. Upon deuteration, Vq will increase by the difference in the zero-point energies associated with the C-H- and C-D-transferring modes in the reactant state. An example of the results for the model that assumes the stretch to stretch is active is given in Figure 3, while the bend to bend as the transferring modes is given in Figure 4. The fits to all of the kinetic data can be found in the Supporting Information. The quality of the fits is basically independent of the combination of vibrational promoting modes.
Figure 3. Correlation of the experimental rate constants for proton transfer (solid diamonds) and deuteron transfer (solid triangles) with driving force in acetonitrile. Driving force is defined as -∆G. Solid line: fit of the Lee-Hynes model with Vq ) 25.8 kcal/mol, Es ) 6.6 kcal/mol, ωQ ) 180.5 cm-1, reactant stretch ) 2645 cm-1, and product stretch ) 2386 cm-1. See text for details.
Figure 4. Correlation of the experimental rate constants for proton transfer (solid diamonds) and deuteron transfer (solid triangles) with driving force in acetonitrile. Driving force is defined as -∆G. Solid line: fit of the Lee-Hynes model with Vq ) 18.5 kcal/mol, Es ) 6.6 kcal/mol, ωQ ) 215.0 cm-1, reactant bend ) 1183 cm-1, and product bend ) 768 cm-1. See text for details.
However, the derived fitting parameters are dependent upon the combination of vibrational promoting modes employed for the analysis. The three fitting parameters are given in Table 4 as a function of the nature of the reaction modes. In acetonitrile, the derived barrier heights Vq vary from 18.5 kcal/mol for the bend-bend model to 25.8 kcal/mol for the stretch-stretch model. The low-frequency promoting mode ωQ varies from 215 cm-1 for the bend-bend model to 180 cm-1 for the stretchstretch model. The value of the solvent reorganization energy ranging from 6.5 to 7.0 kcal/mol is rather insensitive to which vibrational model is employed. A general comment on the variations found in the fitting parameters follows. For a given set of donating and accepting vibrational frequencies, the solvent reorganization energy ES is virtually independent of the other fitting parameters and is mainly determined by the position of the maximum in the correlation, leading to a range in values of (0.2 kcal/mol. The barrier height Vq and the low-frequency promoting mode ωQ are highly correlated. However, the simultaneous fitting of the proton rate constants and the deuterium rate constants greatly constrains the value ωQ to within (2.0 cm-1, which in turn leads to a range in Vq of (0.4 kcal/mol.
Proton/Deuteron Transfer with Benzophenone-Triethylamine TABLE 4: Fitting Parameters Based upon Lee-Hynes Theory solvent: acetonitrile promoting frequencies used barrier (kcal/mol) Es (kcal/mol) ωQ
R stretcha to R stretch to R bendc to R bend to P bend P stretchb P stretch P bendd 25.8 6.6 180.5
21.5 7.0 199.5
22.6 6.5 193.0
18.5 6.6 215.0
solvent: DMF promoting frequencies used barrier (kcal/mol) Es (kcal/mol) ωQ
R stretch to R stretch to R bend to R bend to P stretch P bend P stretch P bend 26.7 7.3 174.0
22.3 7.4 191.3
23.4 7.3 185.5
19.0 7.3 207.8
a Reactant stretch, 2645 cm-1. b Product stretch, 2386 cm-1. c Reactant bend, 1183 cm-1. d Product bend, 768 cm-1.
In the above modeling, it is assumed that a change in the internuclear separation of the reacting molecules does not change upon proton transfer. However, as the reactant contact radical ion pair transforms into the radical pair product, the loss of charge should decrease the energy of interaction of the complex, leading to an increase in the internuclear separation upon going from the reactant to the product. However, this separation will be opposed by the necessity to restructure the surrounding solvent to accommodate the expansion. The net increase in the internuclear separation is difficult if not impossible to determine experimentally. The Lee-Hynes model does allow for examination of the effect for a change of internuclear separation on the kinetics for proton tunneling. If the separation is small, ∆Q ) 0.01 Å, the change in the fitting parameters is rather modest; for the bend-bend transition in acetonitrile, Vq and ωQ remain unchanged, while ES decreases from 6.6 to 6.1 kcal/mol, Figure 7S (Supporting Information). If ∆Q ) 0.05 Å, a fit to the data is extremely poor, Figure 8S. Thus, viewing the data within the context of Lee-Hynes theory, the change in ∆Q upon proton transfer is exceedingly small. Analysis of the Modeling. The Lee-Hynes model, based upon a reaction path that is exclusively a V ) 0 to V′ ) 0 transition, gives a qualitative account of the observed kinetic behavior for both proton transfer and deuteron transfer, although there are deviations between the model and the experimental data, particularly at a large driving force. One source for the discrepancy between the model and the data may reside in the participation of a geometrical distribution of reactive species in the overall reaction, which is not taken into account by the model which assumes one fixed geometry. Also, the quality of the fits are not sensitive to the various combination of promoting vibrations; the fitting of the Lee-Hynes model to the experimental data provides no insight into which vibrations in the reactant and product states are involved in the tunneling. That only a V ) 0 to V′ ) 0 transition is required for the model to give a qualitative correlation with the experimental data is surprising in view of the recent study by Kiefer and Hynes.23 In their latest study, they found that for nonadiabatic proton transfer, where the reaction complex constrains the proton tunneling to a linear path between the two heavy atoms, the excited vibrations in the product state make a significant contribution to the tunneling reaction paths. Indeed, allowing for vibrational excitation in the product state by incorporating the V ) 0 to V′ ) 0, V ) 0 to V′ ) 1, and V ) 0 to V′ ) 2 transitions in their model system, the correlation of the reaction
J. Phys. Chem. B, Vol. 112, No. 2, 2008 225 rates with driving force does not reveal an inverted region. Instead, as the driving force increases, the rate of tunneling continues to increase. We found the same effect when we attempted to model the experimental data by employing the Lee-Hynes theory that incorporated the V ) 0 to V′ ) 0, V ) 0 to V′ ) 1, and V ) 0 to V′ ) 2 transitions. Our calculations, based on Lee-Hynes theory, reveal that with an increase in driving force, there is a continuous increase in the rate of proton transfer; no inverted region is manifested upon inclusion of excited vibrations in the product state. Thus, the only way to reconcile the experimental observation of an inverted region with the Lee-Hynes model is to assume that only V ) 0 to V′ ) 0 tunneling predominates; tunneling to higher vibrational levels in the product state must make a negligible contribution to the rate of proton transfer, contrary to the predictions of eq 8. Thus, the use of eq 8 for the determination of the tunneling matrix element is called into question for our chemical system. In the above-mentioned calculations, the tunneling matrix element assumes a linear tunneling geometry, resulting in a onedimensional tunneling pathway, eq 8. However, in light of the discussion regarding the geometry of the reaction complex, the coordinate for proton transfer could involve a curved tunneling pathway, in which case the tunneling matrix element found in eq 8 is inappropriate. The tunneling matrix element for a curved reaction path would entail the implementation of a threedimensional description for the proton wave function in the reactant and product states; an analytical formulation of the tunneling matrix element associated with a curved reaction path appears not to be available. However, in view of the above experiments, it is reasonable to speculate that there will be regimes defined by the reactant geometry where the tunneling amplitude for a V ) 0 to V′ ) 0 transition exceeds that of a V ) 0 to V′ ) 1 transition in a curved reaction path, which would account for the observation of an inverted regime. Validation of this conjecture awaits theoretical inquiry. The conventional view of the kinetic deuterium isotope effect is that if reaction occurs by tunneling, the isotope effect will be large, generally greater than 7.2 Kiefer and Hynes have examined the kinetic deuterium isotope effect for a nonadiabatic process with a linear geometry of transfer.23 The isotope effect is a sensitive function of the vibrational frequency associated with intermolecular separation of the reacting pair, ωQ. Of particular importance to the present study is that as the driving force increases, the kinetic isotope effect decreases, and values of kH/kD )1 are approached. That such low values are achieved is traced to the coupling of ωQ to the tunneling process; for a full exposition on this effect, the reader is referred to the original work of Kiefer and Hynes.23 In the present study, kinetic deuterium isotope effects are found to vary from 1.8 to 1.0. Again, the single reaction mode Lee-Hynes model captures this variation; see Figures 3 and 4. Comparing the solvent reorganization energies, ES, for the benzophenone/triethylamine system with the ES from prior studies of benzophenone with N,N-disubstituted anilines, the present values are smaller. In acetonitrile, ES values range from 13.2 to 21.1 kcal/mol for the N,N-disubstituted anilines, while ES is only 6.7 kcal/mol for triethylamine.31 The smaller value of ES for triethylamine may be traced to its relatively smaller size. In the Marcus formulation of the solvent reorganization energy for electron transfer, as the size of the reactive species decreases, the solvent reorganization energy decreases.49,50 The calculated surface area for triethylamine is 168 Å2, while the surface area for N,N-diethylaniline is 205 Å.2 How the solvent reorganization energy should vary in a quantitative manner with
226 J. Phys. Chem. B, Vol. 112, No. 2, 2008 size for these molecular systems is not readily amenable to analysis; a spherical model of neither the Marcus nor the dielectric ellipsoidal cavity model is applicable to the present molecular system.50 Summary The kinetics for proton transfer within substituted benzophenones/triethylamine contact radical ion pairs have been examined as a function of driving force, solvent, and deuterium substitution. The correlation of the rate constants for proton transfer with driving force reveals an inverted region, results similar to our prior studies of benzophenone/N,N-disubstituted anilines. The Lee-Hynes nonadiabatic proton-transfer singlemode model can qualitatively account for both the correlation with driving force and the kinetic deuterium isotope effect if one assumes that only the V ) 0 to V′ ) 0 tunneling dominates. In view of the recent study of Kiefer and Hynes for linear nonadiabatic proton transfer, where an inverted region is not observed, we conclude that the origin of the inverted region is the result of curvature in the tunneling coordinate. This conclusion awaits verification by theory. Acknowledgment. This work is supported by a grant from the National Science Foundation, No. CHE-0408265. L.R.H. acknowledges support from the University of Colorado OSEP, an NSF-IGERT program. Supporting Information Available: Additional figures relating the rate constants for proton and deuteron transfer to the driving force in acetonitrile and DMF. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Bell, R. P. The Proton in Chemistry; Chapman and Hall: London, 1973. (2) Bell, R. P. The Tunnel Effect in Chemistry; Chapman and Hall: London, 1980. (3) Borgis, D.; Hynes, J. T. J. Phys. Chem. 1996, 100, 1118. (4) Kohen, A.; Klinman, J. P. Acc. Chem. Res. 1998, 31, 397. (5) Kuznetsov, A. M. Charge Transfer in Physics, Chemistry and Biology; Gordon and Breach: Luxembourg, 1995. (6) Morillo, M.; Cukier, R. I. J. Chem. Phys. 1990, 92, 4833. (7) Hammes-Schiffer, S. Acc. Chem. Res. 2001, 34, 273. (8) Barbara, P. F.; Walsh, P. K.; Brus, L. E. J. Phys. Chem. 1989, 93, 29. (9) Pines, E.; Fleming, G. R. Chem. Phys. 1994, 183, 393. (10) Zewail, A. H. J. Phys. Chem. 1996, 100, 12701.
Heeb and Peters (11) Brucker, G. A.; Swinney, T. C.; Kelley, D. F. J. Phys. Chem. 1991, 95, 3190. (12) Genosar, L.; Cohen, B.; Huppert, D. J. Phys. Chem. A 2000, 104, 6689. (13) Westheimer, F. H. Chem. ReV. 1961, 61, 265. (14) Truhlar, D. G.; Gao, J.; Alhambra, C.; Garcia-Viloca, M.; Corchado, J.; Sanchez, M. L.; Villa, J. Acc. Chem. Res. 2002, 35, 341. (15) Garcia-Viloca, M.; Gao, J.; Karplus, M.; Truhlar, D. G. Science 2005, 303, 186. (16) German, E. D.; Kuznetsov, A. M.; Dogonadze, R. R. J. Chem. Soc., Faraday Trans. 2 1980, 76, 1128. (17) German, E. D.; Kuznetsov, A. M. J. Chem. Soc., Faraday Trans. 1 1981, 77, 397. (18) Azzouz, H.; Borgis, D. J. Chem. Phys. 1993, 98, 7361. (19) Lee, S.; Hynes, J. T. J. Chim. Phys. Phys. Chim. Biol. 1996, 93, 1783. (20) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2002, 106, 1834. (21) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2002, 106, 1850. (22) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2003, 107, 9022. (23) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2004, 108, 11793. (24) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2004, 108, 11809. (25) Peters, K. S. AdVances in Photochemistry; John Wiley & Sons: New York, 2002; Vol. 27. (26) Peters, K. S.; Cashin, A. J. Phys. Chem. A 2000, 104, 4833. (27) Peters, K. S.; Cashin, A.; Timbers, P. J. J. Am. Chem. Soc. 2000, 122, 107. (28) Peters, K. S.; Kim, G. J. Phys. Chem. A 2001, 105, 4177. (29) Peters, K. S.; Kim, G. J. Phys. Chem. A 2004, 108, 2598. (30) Peters, K. S.; Kim, G. J. Phys. Org. Chem. 2004, 17, 1. (31) Heeb, L. R.; Peters, K. S. J. Phys. Chem. A 2006, 110, 6408. (32) Peters, K. S.; Lee, J. J. J. Phys. Chem. 1992, 96, 8941. (33) Hehre, W. J.; Yu, J.; Klunzinger, P. E.; Lou, L. A Brief Guide to Molecular Mechanics and Quantum Chemical Calculations; Wavefunction, Inc.: Irvine, CA, 1998. (34) Peters, K. S.; Gasparrini, S.; Heeb, L. R. J. Am. Chem. Soc. 2005, 127, 13039. (35) Shaefer, C. G.; Peters, K. S. J. Am. Chem. Soc. 1980, 102, 7566. (36) Peters, K. S.; Lee, J. J. Phys. Chem. 1993, 97, 3761. (37) Gould, I. R.; Farid, S. Acc. Chem. Res. 1996, 29, 522. (38) Pischel, U.; Nau, W. M. J. Am. Chem. Soc. 2001, 123, 9727. (39) Arnold, B. R.; Farid, S.; Goodman, J. L.; Gould, I. R. J. Am. Chem. Soc. 1996, 118, 5482. (40) Dombrowski, G. W.; Dinnocenzo, J. P.; Farid, S.; Goodman, J. L.; Gould, I. R. J. Org. Chem. 1999, 64, 427. (41) Eyring, H. J. Chem. Phys. 1935, 3, 107. (42) Wigner, E. P. Trans. Faraday Soc. 1938, 34, 1938. (43) Li, D.; Voth, G. A. J. Phys. Chem. 1991, 95, 10425. (44) Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J. J. Phys. Chem. 1996, 100, 12771. (45) Makri, N.; Miller, W. H. J. Chem. Phys. 1989, 91, 4026. (46) Tucherman, M. E.; Marx, D. Phys. ReV. Lett. 2001, 86, 4946. (47) Tautermann, C. S.; Voegele, A. F.; Loerting, T.; Liedl, K. R. J. Chem. Phys. 2002, 117, 1962. (48) Sinnokrot, M. O.; Sherrill, C. D. J. Phys. Chem. A 2006, 110, 10656. (49) Marcus, R. A. J. Chem. Phys. 1956, 15, 155. (50) Li, B.; Peters, K. S. J. Phys. Chem. 1993, 97, 13145.
