First Observation of Ultrafast Intramolecular Proton Transfer Rate

Article pubs.acs.org/JPCA

First Observation of Ultrafast Intramolecular Proton Transfer Rate between Electronic Ground States in Solution Yuichi Masuda,* Tomoko Nakano, and Midori Sugiyama Department of Chemistry, Faculty of Science, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan S Supporting Information *

ABSTRACT: Despite the importance of ultrafast (time scale exceeding 10−11 s) intramolecular proton transfer (PT) events between electronic ground states in solution, experimental determination of the rates of such reactions has not yet been accomplished because of the limitations of the utilized methods. The objective of this study was to evaluate the PT rates of intramolecular O···H···O hydrogen-bonded systems in solution through the 1H spin-lattice relaxation times of the hydroxyl protons, induced by the 1H−17O dipolar interactions (T1dd(OH)), taking into account the contribution of the OH reorientational motion to T1dd(OH). Solutions of the benzoic acid dimer (BA dimer), 1-benzoyl-6-hydroxy-6-phenylfulvene (Fulvene), and dibenzoylmethane (DBM) were chosen as test systems. For Fulvene in CCl4, the PT time, τPT, was deduced to be 7 × 10−11 s. In the case of the BA dimer in CCl4, the τPT value was considerably greater than the OH reorientational correlation time, τR(OH) = 4.3 × 10−11 s. In contrast, the experimental results for DBM in CCl4 indicated that the proton is located about midway between the two oxygen atoms, that is, the PT potential energy surface is a single well or a double well with a PT barrier near or below the zero-point energy. lattices in terms of fluctuating interactions in time caused by the rotational and translational motions of the solvent molecules. The contribution of the solvent to the PT rate is similar to that of electron transfer (ET).11−14 First, additional reorganization energy is produced by a change in the equilibrated solvent orientation or configuration of the reactant and the product. The reorganization energy increases the reaction barrier, and, as a consequence, leads to a decrease in the rate within the regime of the transition state theory.15,16 Second, the rotational and translational dynamics of the solvent play a critical role in PT when the intrinsic barrier of PT is comparable to or even lower than the solvent reorganization energy, and the PT rate is often controlled by the dynamics of the solvent.2,17−21 Accordingly, understanding the contribution that the solvent makes to the PT rate in a static and dynamic manner is a central issue for ultrafast (i.e., low-barrier) PTs, which often occur along hydrogen bonds. Theoretical studies such as molecular dynamics simulations have been conducted.17−20,22−25 In addition, recent progress in hybrid quantum mechanics/ molecular dynamics methods has paved the way for the investigation of the effects of solvents on electronic structures as well as the quantum mechanical behavior of vibrations.26−30 Importance of Intramolecular PT between Electronic Ground States. In contrast to the intensive theoretical and computational studies on intramolecular PT in solution with an

1. INTRODUCTION Intramolecular proton transfer (PT) in solution (Scheme 1) plays an important role as an embodiment of the elementary Scheme 1

steps of acid−base reactions as well as in the fields of chemistry, physics, and biology.1−7In this paper, we present the first observation of the rates of the type of intramolecular PT with an ultrafast time scale exceeding 10−11 s in solution that occurs between electronic ground states where the reactant and the product achieve a thermal equilibrium. Despite the importance of this type of PTs, their rates have not yet been experimentally determined because of the limitations of the methods used to determine these rates. Uniqueness of PT Rate in Solution. Precise X-ray and neutron diffraction analyses carried out recently have revealed that crystal lattices have a significant effect on hydrogen-bond structures.8−10 As a result, PT potential is easily affected by the environment through factors such as intermolecular interactions. In solution, the solvent, especially a polar solvent, also affects the PT potential because the migration of the protonic charge or change in the charge distribution accompanying the PT is strongly coupled with the solvent. However, the effects of the solvent on the PT rate are different from those of the crystal © 2012 American Chemical Society

Received: November 17, 2011 Revised: March 29, 2012 Published: April 17, 2012 4485

dx.doi.org/10.1021/jp2110874 | J. Phys. Chem. A 2012, 116, 4485−4494

The Journal of Physical Chemistry A

Article

Scheme 2

systems are presumed to belong to one of three types based on the results of 1H/2H/3H isotope shifts48 and the 2D quadrupole coupling constants,49 namely, considerably deep double-well potential, shallow double-well potential, and single-well or almost-barrierless potential, for the BA dimer, Fulvene, and DBM, respectively (See Scheme 2). Measurements of nuclear magnetic relaxations have been applied to determine the PT rates in a solid because the proton jumps accompanying the PTs cause fluctuations in the magnetic dipolar couplings, which are sometimes the primary source of magnetic relaxations of nuclei with 1/2 spins such as protons because the couplings depend on the inverse of the cube of the distance between the nuclear magnetic moments.41−44 In contrast, molecular rotation is usually the main cause of the fluctuation contributing to nuclear magnetic relaxations in solution.50,51 However, the fluctuation caused by the PT should contribute to the spin-lattice relaxation when the time scale of the proton jump approaches that of the molecular rotation. Picosecond-order PTs are expected to occur in lowPT-barrier hydrogen-bond systems. The time scale in such systems is believed to be comparable to or even faster than that of the molecular rotation in regular liquid. In such a situation, a PT rate with a 10−11−10−12 s time scale in solution can be determined by extracting the contribution of the fluctuation caused by the proton jump to the nuclear relaxation. Evidence of the contribution of ultrafast chemical processes to spin-lattice relaxation times in a solution has been presented by Merbach et al. for dynamic Yharn-Tailor of copper(II) complex ions.52 Among intramolecular charge transfer reactions, the rates of the intervalence transition (ET) of mixed-valence biferrocene derivatives and the solvent dependences have been obtained by our group by measuring the nuclear relaxation rates caused by fluctuations in local magnetic fields originating from electron hopping between two iron atoms.38,39 The effects of PT on the spin-lattice relaxation time through magnetic dipolar coupling or quadrupole coupling have already been discussed in detail.53,54 However, these studies do not evaluate the PT rates, probably because the PT rates are much slower than the molecular rotations or because delocalization of the protons occurs owing to the low-barrier double-well or single minimum PT potentials in the studied hydrogen-bond systems.

ultrafast time scale, intramolecular PT rates have been experimentally observed only for reaction systems that include photoexcited state(s) through the use of an ultrashort pulse laser technique.31−37 However, the solvent-dependent behavior of PT rates in systems that include photoexcited state(s) does not necessarily indicate that a similar behavior occurs in PT systems between electronic ground states where thermal equilibria between the products and reactants are achieved. Consider the following examples. (i) Most PT systems that include photoexcited state(s) are associated with large driving forces. In such cases, multichannel transitions between the reactant and the product through the highly vibrationally excited states will be the prevailing reaction path.34−37 Such reaction paths are not primarily considered in PT systems between electronic ground states because the reaction systems are associated with small or even no driving forces.(ii) PT systems that include photoexcited state(s) are usually associated with a large change in electron distribution or dipole moment when compared with PT systems between electronic ground states. Such a difference in the magnitude of perturbation to the solvent would transmute the features involved in the dynamic response of the solvent. For example, in the solvent dependence of the intramolecular ET rates, the contribution of the response of the solvent as a dielectric continuum to the ET rates becomes more prominent as the change in the dipole moment between the reactant and product increases.38,39 Similar differences in the solvent response behavior have also been reported for the solvation energy relaxation after the photoexcitation of dye molecules with different magnitudes of dipole moment changes.40 Thus, the observation of the PT rates between electronic ground states in solution is indispensable for understanding how a solvent affects the PT rate. Nevertheless, experimentally observed quantitative information has not been obtained to date for the PT rates of this type in solution; experimental information is only available for the gas and solid states, which has been obtained by methods such as microwave, infrared spectra, nuclear magnetic relaxation, and inelastic neutron scattering.41−47 In this paper, we present the first observation of the rates of PT of the above-mentioned type; the PT rates were obtained by measuring nuclear magnetic relaxations. To accomplish this, we used three intramolecular PT systemsbenzoic acid dimer (BA dimer), 1-benzoyl-6-hydroxy-6-phenylfulvene (Fulvene), and dibenzoylmethane (DBM)each of which contained O··H··O hydrogen bonds, considering a variation in the expected PT potentials (Scheme 2) (Benzoic acid quantitatively forms a dimer through selection of the appropriate concentrations in solvents with less high polarity). The hydrogen-bond

2. BASIC CONCEPT FOR DETERMINING PT RATE In this section, we briefly describe the concept of the procedure used to determine the PT rate from the spin-lattice relaxation time. For simplicity, a linear 17O−H···17O hydrogen-bond system is considered. More general discussions and the formulation for the spin-lattice relaxation time in connection 4486



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T1dd(OH). In such cases, the PT time, τPT, can be determined from T1dd(OH) with a given τR(OH) and the distances of OH and O···H. (See Figure 1) The contribution of intramolecular

with PT in detail are available elsewhere.53,54 The proton jump between the two 17O nuclei (I = 5/2) produces fluctuation in the local magnetic field at the proton because the magnitude of the field is proportional to the inverse of the cube of the distance between the interacting nuclei. At the same time, the magnetic field, which is fluctuating in magnitude because of the proton jump, is changed in angular orientation against the external magnetic field by the OH reorientational motion. The general treatment of the contribution of chemical exchange and molecular rotation to nuclear relaxation is given by Wennerström.54 The time-dependent local magnetic field at the proton, Hloc(t), is then expressed by

Hloc(t ) = hPT(t )hR (t )

(1)

where hR(t) and hPT(t) represent the angular-dependent local magnetic field associated with the orientation of the O−H vector and the magnitude of the field that changes with the OH distance associated with the proton jump, respectively. Assuming no correlation between hR(t) and hPT(t) and single exponential decays for both dynamics, the time-correlation function of the local magnetic field can then be written with the relaxation time of the OH vector rotation for the second rank of the spherical harmonics, τR(OH), and the PT time, τPT, which is equal to 1/(2kPT), where kPT is the PT rate constant.

Figure 1. Calculated 1H spin-lattice relaxation rates caused by magnetic dipolar interaction with 17O nuclei based on eq 3a, considering the contribution of PT relative to relaxation rates for which PT was not considered, for the linear 17O−1H···17O hydrogenbond model system, assuming rOH and rO···H to be 1.00 and 1.50 A, respectively. Dotted and dashed lines indicate values obtained assuming τPT ≫ τR(OH) and τPT ≪ τR(OH), respectively.

⟨Hloc(0)Hloc(t )⟩ = ⟨hPT(0)hPT(t )⟩⟨hR (0)hR (t )⟩

PT to 15N and 2D spin-lattice relaxation rates has already been discussed.49,53,54 However, these studies did not determine the intramolecular PT rates because the PT rates were assumed to have values at the extremes, that is, τPT ≫ τR(OH) or τPT ≪ τR(OH).

⟨hR (0)hR (t )⟩ = exp( −t /τR(OH)) ⟨hPT(0)hPT(t )⟩ = K m(1/2)[(rOH−3 − rO···H−3)2 exp( −t /τPT) + (rOH−3 + rO···H−3)2 ] K m = (35/3)ℏ2γH 2γO2

3. EXPERIMENTAL SECTION 3.1. Synthesis of 17O-Labeled Compounds. The 17Oenriched compounds (∼30% enriched by 17O) were prepared using acid-catalyzed oxygen-exchange reactions56 with 17Oenriched water. Benzoic acid and dibenzoylmethane (DBM) were obtained from Wako Ltd., and used after recrystallization. 1-Benzoyl-6-hydroxy-6-phenylfulvene (Fulvene) was synthesized according to the method given in the literature.57 The 17O enrichment for each compound was carried out by heating a mixture of the corresponding unenriched compound, 42%− 46% 17O-enriched water (Cambridge Isotope Laboratories, Inc.), and hydrochloric acid under the conditions given in the Supporting Information, Table S1. The crude 17O-enriched compounds were then purified by recrystallization. The percentages of the 17O enrichment were determined from the 17 O-signal intensity using 17O-enriched water with a normalized 17 O content. The water concentrations of the sample solutions were determined from the respective signal intensities of the water proton. 3.2. NMR Measurements. The values of the 1H-spinlattice relaxation times caused by the magnetic dipolar interaction with 17O, T1dd(OH) were determined from the 1 H-T1 of the 17O-enriched samples and the corresponding natural abundance. The rotational correlation times, τR(OH), were determined by measuring the 13C-T1 and the nuclear Overhauser enhancements, taking into consideration rotational anisotropy. All measurements were carried out using a JEOL EX400 or Lambda400 Fourier-transform spectrometers operating at 9.4 T with 10 mm (o.d.) sample tubes for the 13C and 17O measurements and 5 or 4 mm (o.d.) tubes for the proton.

(2)

where γO and γH are the gyro-magnetic ratios of 17O and 1H, respectively, and rOH and rO···H indicate the distances of OH and O···H, respectively. The 1H spin-lattice relaxation rate caused by the magnetic dipolar interaction with 17O, T1dd(OH) −1, is related to the Fourier transform of ⟨Hloc(0)Hloc(t)⟩.50,51 T1dd(OH)−1 is then represented under an extreme narrowing limit, τR(OH)−2, τPT−2 ≫ ωH2, ω17O2.55 ̲ −1 = K m(1/2)[(rOH−3 − rO···H−3)2 τ′ T1dd(OH) + (rOH−3 + rO···H−3)2 τR(OH)], τ′−1 = τPT−1 + τR(OH)−1.

(3a)

Equation 3a is basically equivalent to equations given in the literature.53 In the case of the slow PT limit, τPT ≫ τR(OH), T1dd(OH)−1 does not depend on τPT as shown in eq 3b. ̲ −1 = K m(rOH−6 + rO···H−6)τR(OH) T1dd(OH)

(3b)

On the other hand, under the fast PT limit, τPT ≪ τR(OH), the proton feels an averaged local magnetic field by the directly bonded and the hydrogen-bonded 17O nucleus. T1dd(OH) is then represented by eq 3c. ̲ −1 = K m(1/2)[(rOH−3 + rO···H−3)2 τR(OH)] T1dd(OH)

(3c)

As shown in eqs 3b and 3c, in the cases of the two extremes, τPT ≫ τR(OH) and τPT ≪ τR(OH), the obtained T1dd(OH) value only depends on τR(OH). In contrast, if the time scale of the PT is equivalent to that of the molecular rotation (10−11−10−12 s for small or medium molecules), the PT dynamics contribute to 4487



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Figure 2. Observed OH proton magnetization recoveries, Mz(t), in a solution of (a) 0.08 M DBM (17O: 29.5% enriched) in CCl4, (b) 0.05 M Fulvene (17O: 30.5% enriched) in CCl4, (c) 0.08 M Fulvene (17O: 30.5% enriched) in acetonitrile-d6, and (d) 0.05 M Fulvene (17O: 30.5% enriched) in triacetine at 25.0 °C versus pulse intervals, tp (open circles).Mz° in the figure indicates equilibrium magnetization. Dashed, dotted, and dash-dotted lines indicate single exponential Mz recovery with time constants of T1(H:16O, 16O), T1(H:17O, 16O), and T1(H:17O, 17O), respectively.

Fulvene using the Spartan 10 molecular structural analysis program package.

The spin-lattice relaxation times were measured using an inversion recovery method with a pulse sequence of π pulse − tp −π/2 pulse, where tp is the pulse interval time. For the 13CT1 measurements, 200−1000 free induction decays (FIDs) were accumulated for each tp, and 15−20 different tp values were used. The T1 measurements were repeated 3−5 times, and the observed T1 values were reproduced within several percent. The factors of the 13C nuclear Overhauser enhancement, χNOE, were measured using a gated decoupling method. The values were determined from four or more sets of peak areas with and without NOE. The dispersion of the measured χNOE values was within 0.05. For the T1 measurements of the hydroxyl proton, the FIDs with 15−20 tp values for the natural abundance and 40−60 tp values for the 17O-enriched samples were accumulated 16−64 times for each tp. The method for determining the proton T1 for the 17O-enriched samples is described in the next section. The maximum tp was set at ∼10 T1 for the 13C- and 1 H-T1 measurements. The temperature was controlled within 25 ± 0.2 °C with a JEOL GVT2 temperature control unit. The increase in the temperature of the sample solutions caused by proton irradiation of the 13C measurements was minimized by making the proton irradiation power as low as possible. The sample temperatures were calibrated with a thermistor set in a dummy sample under the corresponding NMR measurement conditions such as proton irradiation. The solvents were dried prior to use by standard methods. The sample solutions were degassed by freeze−thaw cycles and then sealed under vacuum. The concentrations of the compounds were 0.025−0.08 mol L−1. Monomers, trimers, and higher aggregates were negligible at the concentrations of BA used for the NMR measurements (∼0.07 mol L−1).58,59 3.3. Molecular Orbital Calculations. Molecular orbital (MO) calculations (MP2: 6-311++G(d,p)) were performed to determine the geometric structure and the dipole moment of

4. NMR DATA ANALYSIS 4.1. Determination of Spin-Lattice Relaxation Time of Proton Caused by Magnetic Dipolar Interaction with 17 O. The 1H-spin-lattice relaxation times caused by the magnetic dipolar interaction with 17O, T1dd(OH) were determined from combinations of the 1H-T1 measurements of the 17O-enriched and natural-abundance samples. The hydroxyl proton signal of each 17O-enriched sample was observed as only one signal despite the existence of three isotopomers with different 17O/16O combinations, 16O···1H···16O, 16O···1H···17O, and 17O···1H···17O because of the small 17O/16O isotope shift. For the BA dimer, a single exponential recovery of the signal intensity after the π pulse was observed owing to the rapid exchange of protons between the three isotopomers with different T1 values. On the other hand, nonexponential recoveries of the longitudinal magnetizations were observed after the π pulse for Fulvene and DBM (Figure 2). These results indicate that the intermolecular proton exchange is not as rapid as the intrinsic relaxation rates of the respective isotopomers. At the slow exchange limit, the recovery of the signal intensity shows superposition of the three exponential recoveries of the three isotopomers with the respective T1's, whereas the recovery depends on the intermolecular proton exchange rate as well as the T1's when the time scales of the exchange and T1's are similar.60 It is assumed that the intermolecular proton exchange is mediated by the trace amount of water (1−10 mM order) in the sample solution.61 Then, for the 17O···1H···16O isotopomer, the change in longitudinal magnetization at time t after a π pulse within a short period dt, that is, dMz(H:17O, 16O)(t), is represented by the intrinsic T1 of the isotopomer, T1(H:17O,16O), and the 4488



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intermolecular proton exchange rate constant between the hydrogen-bonding proton and water, kw, as follows: 17

̲ −1 = P(17O, 17O)T1(H:17O, 17O)−1 T1obs(OH) + P(17O, 16O)T1(H:17O, 16O)−1

16

dMZ(H: O, O)(t )

+ P(16O, 16O)T1(H:16O, 16O)−1

= dt[T1(H:17O, 16O)−1(P(17O, 16O) − MZ(H:17O, 16O) 17

+ P(water)T1(water)−1

16

(t )) − k wP(water)MZ(H: O, O)(t ) + k wP(17O, 16O)MZ(H:water)(t )]

Thus, the T1dd(OH) value was determined from the measured 1H-T1 values for the 17O-enriched and naturalabundance samples, and the water included in CCl4 by using the relationships in eqs 6 and 7. These values are presented in Table 1. The resultant errors for T1dd(OH) were estimated to be within ±2−3% including the measurements of MZ(t) and the fitting errors. 4.2. Determination of Rotational Relaxation Times of OH Vector. The values of 13C-T1 resulting from magnetic dipolar interactions with the directly bonded protons, T 1dd(CH), are determined from the observed 13 C-T 1 , T1obs(C) values and the nuclear Overhauser enhancement factors, χNOE, using the following relationship: T1dd(CH)−1 = T1obs(C) −1(χNOE/1.99).62 The obtained T1dd(CH) can be related to the rotational correlation times of the corresponding C−H vectors, τR(CH), at the extreme narrowing limit as follows:62

(4)

Here, P(X) indicates the fraction of a species, X. The short time changes in the magnetizations of the other species are similarly denoted. The time-dependent magnetization for each species was obtained by successive numerical calculations with a small time step, δt ∼ 10−4 s. The time-dependent total magnetization of the hydrogen-bonding proton at t, Mz(t), is denoted by eq 5. MZ(t ) = MZ(H:16O, 16O)(t ) + MZ(H:17O, 16O)(t ) + MZ(H:17O, 17O)(t ) 17

17

17

(5)

16

T1(H: O, O) and T1(H: O, O) are related to T1dd(OH) and T1(H:16O,16O), which are equal to the observed 1H-T1 values for a natural-abundance sample as follows: ̲ −1 + T1(H:16O, 16O)−1 T1(H:17O, 17O)−1 = T1dd(OH) 17

16

−1

T1(H: O, O)

(6a)

T1dd(CH)−1 = γH 2γC 2ℏ2rCH−6τR(CH)

̲ −1 + T1(H:16O, 16O)−1 = (1/2)T1dd(OH)

The values of T1dd(OH) and kw were determined by fitting the numerically calculated Mz(t) with the experimental values for T1(H:16O,16O), T1(water), and the respective fraction, P(X)s, using the relationships in eq 6 to the experimentally observed Mz(t) recoveries for the 17O-enriched samples. The fitting results and the experimental values used are shown in Figure 1 and Table 1. For the BA solution, a single exponential recovery of the intensity with a T1 value of 0.568 s was observed because of the rapid proton exchange between BA and water protons. The observed relaxation rate, T1 obs(OH) −1, is then expressed considering the intermolecular proton exchange with trace amounts of water entrained in the sample solution as follows: Table 1. Fitting Parameters for Mz Decays Considering Proton Exchange with Residual Water (25.0°C)

solvent kw T1(H:16O,16O)a/s T1dd(OH)/s T1(water)c/s cs/mMd cw/mMd 17 O abundance (%)

fulvene

DBM

CCl4

CCl4

acetonitriled3

triacetine

CCl4

6.12 0.195b 5.47 80 6.0 32.8

0.21 11.4 0.191 5.47 50 5.1 30.5

0.010 22.2 0.47 13.2 80 40 30.5

0.025 1.29 0.0264 0.52 50 21 30.5

0.24 5.47 0.357 5.47 80 7.2 29.5

(8)

where rCH indicates the C−H bond length. The respective correlation times of the OH bond reorientation, τR(OH), of the subject compounds were obtained from the observed T1dd(CH) values through τR(CH) taking into account the rotational anisotropy.63 To analyze the rotational anisotropy, simplified structures of DBM, Fulvene, and the BA dimer were used. For Fulvene, the C(3)-H, C(5)-H, and C(4)-H bonds and the OH··O hydrogen bond were considered to be on an average plane formed by the carbon atoms comprising the five-membered ring and the oxygen atoms because the deviation of the hydrogen atoms from the plane is less than 0.2 Å. On the other hand, the 13C-T1 of each carbon was observed to be the average value of the PT tautomers because they were characterized by a much faster proton jump than that of the 13C-T1. The average structure of the two PT tautomers with a pseudo C2 axis connecting the center of the two oxygens and the C(4) atom was assumed because the difference in the angles between the CH bond and the axis in both of the tautomers was negligibly small, for example, 71° and 70° for C(3) and C(5), respectively. Accordingly, the rotational correlation time for the OH bond was determined from the measured T1dd(CH) values for C(4) and C(3,5), and the averaged angles between the pseudo C2 axis and the C−H bonds given in Table 2. The τR(OH) value for

(6b)

BA dimer

(7)

Table 2. Geometrical Parameters for C−H and OH Bond Angles to Reference Axesa of DBM and Fulvene Used in Determination of Reorientational Correlation Times for OH Vectors

a1

1-benzoyl-6 -hydroxy-6-phenylfluvene (Fulvene) O−H: 86°, C(3)-H: −109°, C(5)-H: 110°, C(4)-H: −179° dibenzoil methane (DBM) O−H: 78.0°, C(2)-H: 180°, C(p)-H: −118°, C(p′)-H: 117°

H-T1 values for samples with 17O natural abundance (0.037 atom %). bValue determined based on the observed 1H-T1 for the 32.8% 17 O-enriched sample (0.568 s), T1(H:16O,16O), and T1(water) according to eqs 6 and 7 (see text). cValues determined by measuring T1 of water protons containing similar concentrations of water in corresponding solvents. dConcentrations of substances, cs, and water, cw.

a

The angles from the axes connecting the center of the two oxygens and the C(4) atom for Fulvene and the C(2) atom for DBM.

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rO···H values for given rOH values, the empirical relationship between rOH and rO···H proposed by Gilli et al. was used for this estimation based on a large collection of crystallographic data for O···H···O hydrogen-bonded systems.68 Although this method of estimation is rather crude, the effects of inaccuracy for the estimations of the rO···H values on the resultant rOH values are minor in the case of the BA dimer and Fulvene.69 The OH bond distances thus obtained are plotted against τPT/ τR(OH). The results are shown in Figure 3 with the inaccuracies

DBM was also obtained with the similar procedure using the measured T1dd(CH) values for the C(2) and C(p) carbons with regard to the C(2)-H and C(p)-H bonds and the O−H··O hydrogen bond on an average plane made by the carbon atoms and the oxygen atoms. The 13C relaxation of the ortho and meta carbons of Fulvene and DBM were not used for the rotational anisotropy analyses because of concern regarding the phenyl group rotation and the out-of-plane position of the protons. The correlation time of the OH bond reorientation, τR(OH), of the BA dimer was assumed to be coincident with that for C(p)-H because the direction of the OH and the C(p)-H bond differed only slightly (3°−4°).64 All of the CH bond lengths were set to 1.11 Å based on the vibrationally averaged distance found for the aromatic CH bonds.65 The molecular structural information was taken from the crystal structural data for the BA dimer64 and DBM.66 For Fulvene, the results of the MO calculations (MP2: 6-311+ +G(d,p)) were used (Supporting Information, Table S2). The geometrical values used for the T1 data analysis are summarized in Table 2. The τR(OH) values were thus determined from the τR(CH) values and the geometrical parameters according to the procedure given by Jackman et al.49 and are listed in Table 3. Table 3. 13C-NMR Results and Rotational Correlation Times (25.0°C) substance (solvent) BA dimer (CCl4) C(p) fulvene (CCl4) C(3,5) C(4) C(o) C(m) C(p) fulvene (acetonitrile-d6) C(3,5) C(4) C(p) fulvene (triacetine) C(3,5) C(4) C(p) DBM (CCl4) C(2) C(p) C(o) C(m)

T1(CH)/s

χNOE

T1dd(CH)/s

1.08

1.97

1.19

0.81 1.34 2.88 3.02 1.02

1.68 1.79 1.71 1.73 1.75

0.96 1.48 2.60 2.75 0.94

2.80 4.49 2.57

1.69 1.76 1.70

2.37 3.98 2.31

0.203 0.272 0.190

1.03 1.38 1.04

0.211 0.253 0.198

3.53 1.46 2.42 2.51

1.71 1.65 1.66 1.63

3.88 1.76 2.90 3.12

τR(OH)/10−11 s 4.3

Figure 3. Values of rOH calculated from T1dd(OH) and T1dd(CH) observed for each subject compound in CCl4 assuming various τPT/ τR(OH) (thick solid lines). Vertical stripes indicate inaccuracies in rOH, ± 0.01 Å, considering errors in observed T1dd(OH) and T1dd(CH), ±2−3%. For DBM inaccuracies in rOH include effects of inaccuracies in estimating rO···H (see ref 69). Arrows on halftones indicate spans of τPT/τR(OH) for BA dimer and Fulvene respectively assuming rOH = 0.99 Å and 1.02 Å (represented by thin solid lines), considering the inaccuracies in rOH. Arrows outside of the figure labeled (a), (b), and (c) indicate the rOH values respectively for BA dimer in crystal (ref 64), Fulvene in isolated state (MO calculations: MP2 6-311++G(d,p)), and DBM in crystal (ref 8).

5.3

2.17

44

in rOH (ca. ± 0.01 Å), which are estimated from the errors in the experiments of T1dd(OH) and T1dd(CH) (±2−3%) considering the dispersion in the measurements of 13C-T1, χNOE, and MZ(t), and the fitting results for MZ(t). Bond distances determined based on magnetic dipolar couplings are known to be somewhat inflated owing to the vibrational averaging effect, and the typical overestimation in a hydrogen-bond system is reportedly ∼3%.70 Therefore, a 3% correction was made to the obtained OH bond distances based on the 17O−1H dipolar couplings to facilitate comparison with the values obtained from crystallographic data and molecular orbital calculations. 5.1. PT Rate of Benzoic Acid Dimer in CCl4. For the BA dimer, the obtained OH bond distances deduced from T1dd(OH)−1 were 0.99 and 0.92 Å under the conditions τPT ≫ τR(OH) and τPT ≪ τR(OH), respectively (Table 4). Meanwhile, single-crystal X-ray, neutron diffraction,64 and MO calculations at the MCG3//MC-QCSD/3 level for the isolated dimer (i.e., that in gas phase)71 indicate values of 0.990 to 0.995 Å and 1.004 Å for the respective OH bond distances. These OH bond distances can be considered to be consistent with those

3.5

5. RESULTS AND DISCUSSION First, to presume the PT rates, the OH bond distances, rOH, for each subject compound were calculated from the experimentally obtained T1dd(OH) and T1dd(CH) values assuming various τPT values with eq 3a.67 In the calculations, the hydrogen bond distances, rO···H, were determined by the following manner. Because rOH was significantly shorter than rO···H in the cases of the BA dimer and Fulvene, the contribution of the hydrogenbonded 17O nucleus to T1dd(OH)−1 was less than 10%, given that the inverse of the proton relaxation time is virtually proportional to the sixth power of the distance. Considering this situation, to facilitate the evaluation of the corresponding 4490



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Table 4. Obtained τPT Values and Calculated OH Distances (25.0°C) BA dimer solvent −11

CCl4

Fulvene CCl4

DBM

acetonitrile-d3

triacetine

CCl4

τR(OH)/10 s τPT/10−11 s (τR(OH)≪ τPT) rOHc,d/Å rO···Hd,e/Å (τR(OH)≫ τPT) rOHc,d/Å rO···Hd,e/Å

4.3 b

5.3 7 ± 2a

2.17 2.5 ± 0.5a

44 b

3.5 b

0.99 (1.02) (1.58)

1.05 (1.08) (1.40)

1.06 (1.09) (1.39)

1.11(1.14) (1.34)

1.22 1.26

0.92 (0.95) (1.78)

0.94 (0.97) (1.58)

1.02(1.05) (1.47)

1.21 1.27

rOH/Å rO···H/Å rO··O/Å ∠OH··O/deg

1.00 1.63 2.63 178

0.95 (0.98) (1.57) Crystal/Ab Initio MO Structuref 1.02 1.47 2.48 172

1.16 1.38 2.46 156

For Fulvene in CCl4 and in acetonitlile the τPT values are determined with rOH of 1.02 Å, which is obtained in triacetine assuming the condition τR(OH)≫ τPT (see text). Errors for τPT are estimated based on inaccuracies in rOH, ±0.01 Å, (see Figure 3). bSee text. cValues obtained from T1dd(OH) and T1dd(CH) assuming the conditions, τR(OH)≪ τPT or τR(OH)≫ τPT. Errors for BA dimer and Fulvene are estimated to be ± 0.01 Å considering the experimental errors for T1dd(OH) and T1dd(CH), ±2−3%. For DBM inaccuracies in rOH (reaching ca. ± 0.02 Å) include effects of inaccuracies in estimating rO···H (see ref 69). dValues indicate those obtained after correction for the vibrational averaging effect. The values before corrections are given in parentheses. The correction is not made for DBM because the proton location was almost halfway between the two oxygens. e The corresponding rO···H values for given rOH values were estimated using the empirical relationship between rOH and rO··H based on a large collection of crystallographic data for O···H···O hydrogen-bonded systems (see text and ref 69). fValues taken from crystal structural analysis results in ref 64 for BA dimer and in ref 8 for DBM. Value for Fulvene taken from the results of ab initio MO calculations (MP2 6-311++G(d,p)). a

with a single-well potential surface or a double well with a PT barrier near or below the zero-point energy as pointed out by Gilli et al.75 The T1dd(CH) values for the ortho and meta carbons are similar to the others. This indicates that the phenyl rotation is much slower than the overall rotation of DBM (see Table 3). The nearly planar structure66 and the considerably rigid phenyl conformation are probably responsible for the significant extent of proton delocalization in DBM.75 The feature is in contrast with the case of Fulvene with the faster phenyl rotation. (See next section) Recent neutron diffraction results in the crystalline state indicate a sufficiently asymmetric position of the hydrogen atom in the hydrogen bond, with rOH and rO··H values of 1.16 and 1.39 A, respectively.8 Moreover, a precise X-ray singlecrystal diffraction analysis suggests that the hydrogen position migrates to midway between the two oxygen atoms with increases in temperature.8 These results indicate that the PT potential of DBM is easily deformed by intermolecular interaction. The nearly symmetric structure of the hydrogen bond in CCl4 may be attributed to a nearly symmetric solvation-structure . 5.3. PT Rate of Fulvene in CCl4. The OH bond distances of Fulvene in CCl4 assuming various τPT values were evaluated in a manner similar to that used for the BA dimer.(Figure 3) The values obtained in the fast and slow PT limits are shown in Table 4. Certain features of these results differed from those of the BA dimer and DBM. The expected OH distances of 1.05 and 0.94 Å for the respective extreme conditions of τPT ≫ τR(OH) and τPT ≪ τR(OH) were both significantly different from the value of 1.024 Å predicted from ab initio MO calculations (MP2: 6-311++G(d,p)) even when the inaccuracy in the expected values was considered (Table 4 and Figure 3). These findings suggest that the PT rate of Fulvene in CCl4 is on a time scale similar to that of the reorientational correlation time. In contrast, the resultant OH bond distance in triacetine, which is a highly viscous solvent (viscosity = 16 cP at 25 °C),76 was

expected from the present experiments assuming the condition, τPT ≫ τR(OH) by taking into account the inaccuracy in the distance (ca. ± 0.01 Å). Therefore, it can be deduced that the intramolecular PT rate in the BA dimer in CCl4 at 25 °C is at least several times lower than the inverse of the OH reorientational correlation time, τR(OH)−1 = 2.3 × 1010 s−1, considering the inaccuracies in rOH (see Figure 3). In comparison, a theoretical PT rate of ∼1 × 1011 s−1 is expected in solid and isolated BA dimers based on calculations using the approximate instanton method as implemented in the DOIT program (AIM/DOIT) and from the barrier height obtained using B3LYP/6-31+G(d) calculations within the TST regime.71 1H NMR relaxometry and quasielastic neutron scattering studies of solid BA dimers also give similar rates.72−74 Thus, the PT rate in CCl4 obtained in the present study seems to be significantly lower than those in the solid and isolated states. Compression of the hydrogen-bond distance by crystal packing and vibrational excitation of the lattice induced by photons are suggested as factors involved in acceleration of the PT rate in the crystalline state despite depletion of the tunnel coupling owing to the asymmetric PT potential surface induced by the crystal packing.72 The reason for the slower PT rate in CCl4 (at least to a certain extent) compared with that in the isolated state is an unresolved question. Although slight geometrical changes in hydrogen bonds affect the PT rates, in the present experiments such geometrical changes cannot be discussed because of the level of accuracy of the determined resultant OH bond distance. 5.2. PT Rate of DBM in CCl4. The obtained OH bond distances for DBM in CCl4 are shown in Table 4 and Figure 3. The OH bond distances of DBM in both extremes, τPT ≫ τR(OH) and τPT ≪ τR(OH), were almost the same and close to half of the O−O distance of 2.46 Å.(The degree of the inaccuracies in rOH is probably reaching ±0.02 Å.)69 In other words, the proton was located about midway between the two oxygen atoms. These findings indicate that DBM in CCl4 is associated 4491



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1.02 Å assuming the condition τPT ≪ τR(OH), which agrees with the value predicted by the present MO calculations. The correlation time of OH orientation in triacetine is much greater than that in CCl4, as indicated by the τR(OH) values of 44 and 5.3 ps in triacetine and in CCl4, respectively. On the other hand, it is suspected that the difference in τPT in these solvents is not very pronounced because the permittivities of these solvents are similar and relatively low (2.3 and 3 for CCl4 and triacetine, respectively),77 which eventuates in the relatively small and similar solvent reorganization energies. Accordingly, the PT rate in triacetine can be regarded as being much faster than the orientational motion of the OH bond. The correspondence between the OH bond distances of Fulvene from the MO calculations and from the present experiments in triacetine under the condition, τPT ≪ τR(OH), thus stands to reason. The effect of solvent polarity on the OH bond distance in hydrogen-bonded systems can be negligibly small except in the case of a very highly polar solvent. For example, DFT/ BLYP MO studies on the acetic acid dimer indicate an elongation of the OH distance by only 0.003 Å in dimethylsulfoxide relative to the isolated state.78 Therefore, the Fulvene OH bond distance in CCl4 was set to 1.02 Å, which is the value obtained from the experiments in triacetine under the condition τPT ≪τR(OH). The τPT value in CCl4 of 7 ± 2 × 10−11 s was then obtained using eq 3a. Thus, the PT potential features of Fulvene are intermediate between those of the BA dimer and DBM, which is qualitatively in accordance with the reported 2D quadrupole coupling constants observed in chloroform.47 A proton tunneling time of ∼10−13 s is reported for malonaldehyde in the gas phase in a microwave study46 as well as for 9-hydroxyphenalen-1-one based on fluorescence spectra in a Ne and Ar matrix near 4 K.47 PTs on a time scale of 10−13 s are also presumed based on ab initio MO calculations for βdiketones, for example, 9-hydroxyphenalen-1-one,79 malonaldehyde,80 and acetylacetone.81 It seems that the observed PT rate of Fulvene, which is classified as a γ-diketone, is more than 2 orders of magnitude lower than the previously reported experimental observation for β-diketones. The reason for the considerable reduction in the evaluated PT rate of Fulvene is not clear at present; however, some possible explanations are presented below. First, interaction with the solvent CCl4 may contribute to a deceleration in the PT rate to some extent, although negligible solvent reorganization is expected in CCl4 as long as the solvent is regarded as a dielectric continuum. Second, the difference in the strain and flexibility of the seven- and six-membered ring formed by the intermolecular hydrogen bond in γ- and βdiketones, respectively,82 may contribute to the deceleration in the PT rate of Fulvene. Another possible reason is derived from the rotational conformation and the freedom of the phenyl groups. The torsion angle of the phenyl groups relative to the hydrogen-bond plane is approximately 35° based on MO calculations. The twisted conformation of the phenyl groups restricts the acceleration of the PT rate through a resonance assist effect.1,75,83 Moreover, the rotation of the phenyl groups is expected to occur on a time scale comparable to the rotational correlation time of Fulvene (∼10−11 s), which is also comparable to the time scale of the PT. This is presumed based on the significantly greater T1dd(CH) values for the ortho and meta carbons than the other carbons, including the para carbon62 (see Table 3). These results suggest that the PT couples with the phenyl rotation given that ab initio molecular

orbital calculations predict retardation of the PT rate because of coupling between the methyl rotation and the proton-transfer process in acetylacetone.84 This conjecture does not conflict with the much shorter time scale (∼0.1 ps) of PT for 6hydroxy-1-formylfulvene, in which both of the phenyl groups in Fulvene are substituted with hydrogens, presumed from the detailed vibrational analysis carried out using ab initio MO calculations85 and from microwave measurements.86 5.4. Solvent Effect on PT Rates of Fulvene. The intramolecular PT rate would be strongly affected by solvents because the charge in migration accompanying the PT strongly couples with a polar medium. The solvent reorganization slows down the rates in standard charge-transfer reaction theories in the static sense.15,16 The solvent also slows down the rate in a dynamic sense through dielectric friction along the solvent coordinate for the reaction.2,17−20 Theoretical approaches for solvents have been presented by many groups, including Hynes et al.22−25 Measurements in acetonitrile were also performed to examine the contribution of the solvent to the PT rate. As shown in Table 4, the present experiment indicated a higher PT rate in acetonitrile than in CCl4, even though acetonitrile is a typical dipolar solvent with a higher dielectric constant than CCl4. The reason for deceleration not being observed in acetonitrile can be at least partially attributed to the considerably low reorganization energy. This energy is estimated to be ∼1.6 kJ mol−1 for a 40° change in dipole orientation on the PT with a 2.22 D dipole moment of Fulvene as determined from the ab initio MO calculations (MP2: 6311++G(d,p) level) when the solvent is regarded as a dielectric continuum. The stabilization by the local interaction between the positive charge of the hydrogen and acetonitrile, which is known to be a typical electron donor solvent,87 is expected to be larger around the transition state than at the reactant or the product because the hydrogen positive charge in a OH··O hydrogen bond tends to increase as the OH bond increases and the O···H distance decreases.1Thus, the acceleration of the rate in acetonitrile when compared with that in CCl4 can likely be attributed to the larger stabilization caused by interaction with the donor site of acetonitrile around the transition state exceeding the solvent reorganization energy. Such a situation is similar to the situation in which the activation energies for double intramolecular PTs of carboxylic acids and amide dimers in water are lower than the energies of the isolated dimers obtained from ab initio MO calculations. Solvent reorganization energies are negligible in these reaction systems because no apparent dipole moment change occurs between the products and the reactants. In addition, stabilization in the transition states is induced to some extent by the solvation to hydrogen or oxygens with the change in charge distribution during the course of the reaction.88

6. CONCLUSION The contribution of intramolecular PT to the hydroxyl proton spin-lattice relaxation rate through 1H−17O dipolar coupling was analyzed for the BA dimer, Fulvene, and DBM in CCl4. The results indicated that the PT rate of the BA dimer in CCl4 is much slower than the molecular rotation, τR ∼ 10−11 s. Conversely, the hydrogen of DBM is located about midway between the two oxygen atoms, indicating that DBM in CCl4 is associated with a single-well potential surface or a double well with a PT barrier near or below the zero-point energy. In Fulvene, PT dynamics were found to contribute to the proton 4492



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relaxation, and the PT time, τPT, was found to be 7 × 10−11 s in CCl4. To examine the solvent effects of Fulvene on the PT rate, measurements were also performed in acetonitrile. A higher rate was observed in acetonitrile than in CCl4, despite the higher dielectric constant of acetonitrile. The results for Fulvene are the first experimentally determined intramolecular PT rates in a solution with a time scale of 10−11 s that occurs between electronic ground states where the reactant and the product achieve a thermal equilibrium. Considering the importance of the PT rate in solution, the results presented in this paper could be benchmark values for examining various theories and computer simulations in this field. The present method can be universally applied for investigating the solvent dependence of an ultrafast PT rate because the method can be extended to other PT systems, such as N···H···N and N···H···O, by monitoring the 1 H- and the 15N-spin-lattice relaxation through the magnetic dipolar interaction between 15N or 17O and 1H.

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(10) Bienko, A. J.; Latajka, Z.; Sawka-Dobrowolska, W.; Ozeryanskii, V. A.; Pozharskii, A. F.; Grech, E.; Nowicka-Scheibe. J. Chem. Phys. 2003, 119, 4313−4319. Grech, E.; Malarski, Z.; Sawka-Dobrowolska, W.; Sobczyk, L. J. Phys. Org. Chem. 1999, 12, 313−318. (11) Mataga, M., Okada, T., Masuhara, H., Eds.; Dynamics and Mechanisms of Photoinduced Electron Transfer and Related Phenomena; Elsevier: Amsterdam, The Netherlands, 1992. (12) A Special Issue on “Electron Transfer”, Chem. Rev. 1992, 92. (13) Marcus, R. A. J. Chem. Phys. 1956, 24, 979−989. (14) Newton, M. D.; Sutin, N. Annu. Rev. Phys. Chem. 1984, 35, 437−480. (15) Marcus, R. A. J. Chem. Phys. 1965, 43, 679−701. (16) Kurz, J. L.; Kurz, L. C. J. Am. Chem. Soc. 1972, 94, 4451−4461. (17) Kuznetsov, A. M. Charge Transfer in Physics, Chemistry and Biology; Gordon and Breach: Luxembourg, 1995. (18) German, E. D.; Kuznetsov, A. M.; Dogonadze, R. R. J. Chem. Soc., Faraday II 1980, 76, 1128−1146. (19) Ghosh, S. K. J. Mol. Liq. 1993, 57, 75−90. (20) Keifer, P. M.; Hynes, J. T. Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase; Elsaesser, T., Bakker, H. J., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2002; Chapter 4. (21) Sumi, H.; Marcus, R. A. J. Chem. Phys. 1986, 84, 4272−4276. Nadler, W.; Marcus, R. A. J. Chem. Phys. 1987, 86, 3906−3924. (22) Hanna, G.; Kapral, R. Acc. Chem. Res. 2006, 39, 21−27. (23) Cukier, R. I.; Morillo, M. J. Chem. Phys. 1989, 91, 857−863. (24) Brogis, D. C.; Lee, S.; Hynes, J. T. Chem. Phys. Lett. 1989, 162, 19−26. (25) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2002, 106, 1834− 1849. (26) Borgis, G.; Tarjus, H.; Azzouz. J. Chem. Phys. 1992, 97, 1390− 1400. (27) Bala, P.; Grochowski, P.; Lesyng, B. J.; McCammon, A. J. Phys. Chem. 1996, 100, 2535. (28) Tunõn, I.; Martins-Costa, M. T. C.; Millot, C.; Ruiz-López, M. F. J. Chem. Phys. 1997, 106, 3633−3642. (29) Kim, S. Y.; Hammes-Schiffer, S. J. Chem. Phys. 2003, 119, 4389. (30) Yamada, A.; Okazaki, S. J. Chem. Phys. 2006, 124, 094110. (31) Peters, K. S. Acc. Chem. Res. 2009, 42, 89−96. (32) Elsaesser, T. Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase; Elsaesser, T., Bakker, H. J., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2002; Chapter 6. (33) Kosower, E. M. Annu. Rev. Phys. Chem. 1986, 37, 127−156. (34) Heitele, H.; Michel-Beyerle, M. E.; Finckh, P. Chem. Phys. Lett. 1987, 134, 273−278. (35) Tominaga, K.; Kliner, D. A. V.; Johnson, A. E.; Levinger, N. E.; Barbara, P. F. J. Chem. Phys. 1993, 98, 1228−1243. (36) Bolton, J. R.; Mataga, N.; McLendon, G. Electron Transfer in Inorganic, Organic, and Biological Systems; American Chemical Society: Washington, DC, 1991. (37) Jortner, J.; Bixon, M. Protein Structure; Molecular and Electronic Reactivity; Austin, R., Buhks, E., Chance, B., Voult, D., Dutton, P. L., Fauenfelder, H., Gol’danski, V. I., Eds.; Saringer: New York, 1987. (38) Masuda, A.; Masuda, Y.; Fukuda, Y. J. Phys. Chem. A 1997, 101, 2245−2253. (39) Masuda, Y.; Shimizu, C. J. Phys. Chem. A 2006, 110, 7019−7027. (40) Su, S.-G.; Simon, J. D. J. Phys. Chem. 1989, 93, 753−761. Nishiyama, K.; Hirata, F.; Okada, T. J. Chem. Phys. 2003, 118, 2279− 85. (41) Vener, M. V. Hydrogen-Transfer Reactions; Hynes, J. T., Ed.; John Wiley & Sons: New York, 2007; Vol. 1, pp 273−299. (42) Ortlieb, M.; Havenith, M. J. Phys. Chem. A 2007, 111 (31), 7355−7363. (43) Wassermann, T. N.; Luckhaus, D.; Coussan, S.; Suhm, M. A. Phys. Chem. Chem. Phys. 2006, 8 (20), 2344−2348. (44) Neumann, M.; Brougham, D. F.; McGloin, C. J.; Johnson, M. R.; Horsewill, A. J.; Trommsdorff, H. P. J. Chem. Phys. 1998, 109 (17), 7300−7311.

ASSOCIATED CONTENT

S Supporting Information *

Conditions of 17O enrichment for benzoic acid, 1-benzoyl-6hydroxy-6-phenylfulvene, and dibenzoylmethane (Table S1); Geometrical parameters of 1-benzoyl-6-hydroxy-6-phenylfulvene determined by molecular orbital calculations (MP2: 6311++G(d,p)) (Table S2). This material is available free of charge via the Internet at http://pubs.acs.org..

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-3-5978-5350. Fax: +81-3-5978-5350. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially supported by a Grant-in-Aid for Scientific Research, No. 19550012, from the Ministry of Education, Science and Culture. The authors thank Ms. R. Shinbori for her help with the synthesis of the materials and the preliminary NMR measurements.

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REFERENCES

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(45) Rowe, W. F.; Duerst, R. W.; Wilson, E. B. J. Am. Chem. Soc. 1976, 98, 4021−4023. (46) Baughcum, S. L.; Duerst., R. W.; Rowe, W. E.; Smith, Z.; Wilson, E. B. J. Am. Chem. Soc. 1981, 103, 6296−6303. (47) Rossetti, R.; Haddon, R. C.; Brus, L. E. J. Am. Chem. Soc. 1980, 102, 6913−6916. (48) Altman, L. J.; Laungani, P.; Gunnarsson, G.; Wennerstrom, H.; Forsen, S. J. Am. Chem. Soc. 1978, 100 (26), 8264−8265. (49) Jackman, L. M.; Trewella, J. C. R.; Haddon. J. Am. Chem. Soc. 1980, 102, 2519−2525. (50) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, U.K., 1961; Chapter VIII. (51) Farrar, T. C.; Becker, E. D. Pulse and Fourier Transform NMR; Academic Press: New York, 1971; Chapter 4 (52) Powell, D. H.; Furrer, J. P.; Pittet, P.; Merbach, A. E. J. Phys. Chem. 1995, 99, 16622−16629. (53) Bernatowicz, P.; Kowalewski, J.; Sandstrom, D. J. Phys. Chem. A 2005, 109, 57−63. (54) Wennerström, H. Mol. Phys. 1972, 24, 69−76. (55) Equation 13 in ref 53 for 15NH···15N hydrogen-bond systems is reduced to eq 3a if one assumes a linear hydrogen bond and replaces the 15N nuclei with 17O nuclei. Similarly, eqs 3b and 3c for the slow and fast PT limits are equivalent to eqs 14 and 15 in ref 53. (56) Risley, J. M.; Van Etten, R. L. J. Am. Chem. Soc. 1981, 103, 4389−4392. (57) Linn, W. J.; Sharkey, W. H. J. Am. Chem. Soc. 1957, 79, 4970− 4972. (58) Satchell, D. P. N; Wardell, J. L. Trans. Faraday Soc. 1965, 61, 1199−1201. (59) Abraham, M. H.; Duce, P. P.; Schultz, R. A.; Morris, J. J.; Taylor, P. J.; Barratt., D. G. J. Chem. Soc., Faraday Trans. I 1986, 82, 3501− 3510. Fujii, Y.; Yamada, H.; Mizuta, M. J. Phys. Chem. 1988, 92, 6768− 6774. (60) Forsen, S.; Hoffman., R. J. Chem. Phys. 1963, 39, 2892−2901. (61) The recovery of the features of the intensity depended on the concentrations of water in the sample solutions. For example, nearly single exponential recovery with a time constant that was close to the weighted average of the relaxation rates of the isotopomers and water was observed for the sample solution with a high concentration of water. The determined proton exchange rates given in Table 1 were comparable to previously reported values. Diratsaoglu, J.; Hauber, S.; Hertz, H. G.; Mueller, K. J. Z. Phys. Chem. (Muenchen, Ger.) 1990, 168, 13−25. Pfeifer, R.; Hertz, H. G. Ber. Bunsen-Ges. 1990, 94, 1349−1359. (62) Lyerla, J. R.; Levy, G. C. Topics in Carbon-13 NMR Spectroscopy; Levy, G. C., Ed.; John-Wiley & Sons: New York, 1974; Chapter 3. (63) Huntress, W. T. Adv. Magn. Reson. 1970, 4, 1−45. (64) Feld, R.; Lehmenn, M. S.; Muir, K. W.; Speakman, J. C. Z. Kristallogr. 1981, 157, 215−219. Wilson, C. C.; Shankland, N.; Florence, J. J. Chem. Soc., Faraday Trans. 1996, 92, 9051−9058. (65) Jackman, L. M.; Trewella, J. C. J. Am. Chem. Soc. 1976, 98, 5712−5714. Kowalewski, J.; Effemey, M.; Jokisaari, J. J. Magn. Reson. 2002, 157, 171−177. (66) Jones, R. D. G. Acta Crystallogr. 1976, B32, 1807−1811. (67) For the bending hydrogen bond, OH···O, the proton jump from one oxygen atom to the other is associated with the angular change in the magnetic dipolar interaction vector relative to the external magnetic field (ref 53). However, the effect on T1dd(OH) is negligible in the present hydrogen-bond systems because the bent angles are close to 2π. As a result, the effect is estimated to be 1% for DBM with an O··H··O angle of 156°, which is the largest among the three subject compounds. (68) Gilli, P.; Bertolasi, V.; Ferretti, V.; Gilli, G. J. Am. Chem. Soc. 1994, 116, 909−915. (69) The relation between rOH and rO···H given by eq 2 in ref 68 was slightly shifted to adjust the respective crystallographic or MO calculation data for the subject compounds. When an intended rOH value is not far from the crystallographic or MO results, the inaccuracy in rO···H thus obtained is estimated to be ± 0.01−0.02 Å, considering the scatter of the data in ref 68. The effect of the inaccuracy in rO···H on 4494


First Observation of Ultrafast Intramolecular Proton Transfer Rate

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