31P, 1H NMR Relaxation and Molecular Mobility in Layered α

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P, 1H NMR Relaxation and Molecular Mobility in Layered α‑Zirconium Phosphate: Variable-Temperature NMR Experiments

Vladimir I. Bakhmutov* and Abraham Clearfield Department of Chemistry, Texas A&M University, P.O. Box 30012, College Station, Texas 77842-3012, United States ABSTRACT: Internal rotations in HPO4− groups and proton transfer between them have been characterized in static α-zirconium phosphate by variable-temperature measurements of 31P T1 and 1H T1ρ times. The 1H T1ρ times have been obtained by the kinetic of phosphorus−proton crosspolarization treated with the I-I*-S model. The calculations of the temperature T1 relaxation dependences have resulted in the rotational activation energy of 2.6 kcal/mol (or 3.9 kcal/mol in account for the τC distribution) and the proton transfer activation energy of 5.5 kcal/mol. Thus, two types of motions have been found in α-zirconium phosphate: the low-frequency proton transfer with the correlation time τc of 1.5 × 10−5 s at 295 K and the high-frequency rotation in P−OH groups with the correlation time τc of 2.2 × 10−8 s at 295 K.

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The 31P T1 relaxation times of phosphate groups in solids are known to change in very large limits: from >100 s in a natural apatite to 4 s in a synthetic apatite,11 or between 0.8 and 40 s in zirconium phosphates.12 Moreover the 31P T1 relaxation time can even depend on “prehistory” of samples, probably on their morphology. For example, a 31P T1 time of 45 s has been measured for a fresh-prepared α-zirconium phosphate in ref 10 versus 19.3 s reported for the same compound in ref 12. Potentially the above 31P T1 sensitivity can be a good tool for structural diagnostics. However, in the absence of a clear understanding of the molecular dynamics and its influence on the relaxation times in such systems, the application of this tool is obviously problematic.

INTRODUCTION Layered zirconium phosphates1−8 constantly attract attention of researchers due to their wide applications in the industry as biosensors, fuel cells, and catalysts. Intercalation of organic components,7 including biomolecules,6 increases the initial interlayer distance of 7.6 Å in α-zirconium phosphate, Zr(HPO4)2·H2O, to allow uptake of different cationic complexes, pillaring agents, and many others leading to molecular systems used in nanomedicine for drug delivery.4−6,9 Various physical methods such as thermogravimetry, X-ray powder diffraction (XRPD), IR and UV spectra, scanning electron microscopy coupled with energy dispersive X-ray spectroscopy (SEM-EDX), and solid-state NMR2−4,7 have resulted in detailed structural descriptions of the zirconium phosphate materials. However, up to now there is only little knowledge about the molecular dynamics in the zirconium phosphate network which is still not studied. The internal highand low-frequency motions can play an important role in heterogeneous catalysis based on zirconium phosphates, on proton conductivity in these materials, and also in interactions between the phosphate network and intercalated compounds and even in their releasing. Recently,10 the 31P NMR spin−lattice relaxation times (31P T1) measured in a series of modified and intercalated zirconium phosphate materials have allowed to recognize their molecular dynamics as internal rotation of P−OH groups around P−O bonds. The applied 31P T1/31P T2 approach10 has led to estimations of the rotational correlation times. In this work we perform a more detailed study of the rotations based on the variable-temperature measurements of 31P T1 and 1H T1ρ times in a simplest member in the family of such materials, αzirconium phosphate, Zr(HPO4)2·H2O. The 1H T1ρ times have been measured by the phosphorus proton cross-polarization kinetics in static samples. © XXXX American Chemical Society

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EXPERIMENTAL SECTION Material. The α-zirconium phosphate was synthesized following the reflux method reported by Sun and co-workers.13 The procedure consists of the dropwise addition of 200 mL of a 0.05 M ZrOCl2·8H2O aqueous solution to a 200 mL solution of H3PO4 (6 M). The phosphoric acid solution was preheated in an oil bath at 94 °C in a 500 mL round-bottom flask before the addition of the zirconyl chloride. The resulting solution was refluxed with constant stirring at 94 °C for 2 days. The product was filtered and washed several times with water and dried in an oven at 70 °C. The dried phosphate was ground with a mortar and pestle into a fine powder for the NMR study. Instrumentations. The X-ray powder diffraction (XRPD) measurement was performed from 2 to 40° (in the 2θ axis) using a Bruker D8 Advance X-ray power diffractometer with Cu Kα radiation (λ = 1.5406 Å) with Bragg−Brentano assembly Received: November 8, 2016 Revised: December 6, 2016 Published: December 13, 2016 A

DOI: 10.1021/acs.jpcc.6b11247 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C and operated at a potential of 40 kV and a current of 44 mA. Bragg’s law (nλ = 2d sin θ) was used to determine the interlayer distance in the zirconium phosphate layers taking into account the first order diffraction peak, where λ is the wavelength of the X-ray source, is the interlaminar distance between planes in the unit cell, and θ is the diffraction angle. The 31P and 1H static and MAS NMR spectra were obtained with a Bruker Avance-400 spectrometer (400 and 162 MHz for 1 H and 31P nuclei, respectively) equipped with a standard 2.5 mm NMR probe head. Standard 2.5 mm zirconium oxide rotors have been applied. The 1H and 31P chemical shifts are referred to external TMS and H3PO4, respectively. The variable - temperature NMR experiments have been performed with a standard temperature unite of the spectrometer calibrated with liquid methanol placed into a MAS NMR rotor. 1 H and 31P T1 relaxation times were measured by inversion− recovery (180°−τ−90°) experiments where rf pulses were well calibrated and τ delays were widely varied in account for rough T1 estimations. Relaxation (recycle) delays were adjusted to provide full nuclear relaxation in each cycle (from 120 s at high temperatures to 600 s at 176 K). The inversion−recovery method was used instead the saturation recovery method to obtain a more detailed description of recovery curves to recognize a character of NMR relaxation. The experimental 1H and 31P inversion−recovery curves “signal intensity versus τ time” have been treated with a standard nonlinear fitting computer program based on the Levenberg−Marquardt algorithm. According to the statistics, the errors in T1 time determinations were approximately 15%. The latter was confirmed by independent reproductions of the T1 experiments. Kinetics of proton−phosphorus cross-polarization has been studied by variations in contact times between 50 and 10000 μs used for the 31P{1H} CP MAS and static NMR experiments. The kinetic data have been treated with a standard fitting computer procedure based on equations discussed below.

Figure 1. Fragment of the stylized structure of α-zirconium phosphate with phosphate groups experiencing internal rotation around O−P bonds.

Figure 2. 1H NMR spectrum in a static sample of α-zirconium phosphate at 275 K (top) and 328 K (bottom).

proton−proton exchange occurring on the NMR time scale. The proton exchange is often observed in phosphate solids.15−17 The 31P{1H} MAS NMR spectrum of α-zirconium phosphate recorded at a spinning rate of 4 kHz (Figure 3) exhibits a major resonance at −19.1 ppm corresponding to HPO4− groups in zirconium phosphate layers (Figure 1) in full accordance with the data published earlier.10,18

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RESULTS AND DISCUSSION The XRPD pattern of α-zirconium phosphate, prepared in this work as nanoplatelets was identical to those published early14 to show a typical intense peak at low angles (2θ = 11.6°) corresponding to an interlayer distance of 7.6 Å. According to previous estimations,14 this material has about 11 layers per nanoparticle. The stylized structure of α-zirconium phosphate is shown Figure 1, where phosphate groups experience the internal rotation10 and water molecules are not shown for simplicity. In the context of NMR, this rotation around P−O bond reorients dipolar vector P···H effecting on 31P relaxation. Since the goal of the present work is a study of NMR relaxation at different temperatures, the 1H and 31P relaxation experiments have been performed in static α-zirconium phosphate to avoid the well-known problem connected with the remarkable influence of spinning on the temperature in the sample. At the same time, NMR characterizations of the compound have been carried out by static and MAS NMR as well. The 1H NMR spectrum of a static sample of α-zirconium phosphate shows a symmetrical resonance at ∼4.2 ppm (Figure 2) which remarkably broadens on cooling from 1.5 kHz at 328 K to 2.3 kHz at 275 K. Strong broadenings below 273 K complicate the 1H T1 measurements. This signal obviously belongs to protons of water situated between layers and on the surface and also protons P−OH that are averaged due to

Figure 3. Room-temperature 31P NMR spectra of α-zirconium phosphate from top to bottom: the 1H decoupled 31P MAS NMR spectrum recorded at a spinning rate of 4 kHz; the 1H decoupled 31P NMR spectrum in a static sample; the 1H coupled 31P NMR spectrum in a static sample.

The isotropic signal transforms to a wide line in a static sample shaped by phosphorus chemical shift anisotropy (SCA) in accord with data σ11 = 4 ppm, σ22 = −24 ppm, and σ33 = −37 ppm reported in ref 18. In the absence of {1H} decoupling, this signal experiences an additional broadening by 3070 Hz due to proton-phosphorus dipolar coupling. It should be emphasized B

DOI: 10.1021/acs.jpcc.6b11247 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C that the shape of the signal does not change with the temperature from 367 to 175 K, revealing, thus, the absence of motions (even slow) discussed in ref 10, which could affect the SCA. The typical inversion−recovery curve observed for the 31P resonance in a static sample of α-zirconium phosphate, prepared in this work is represented in Figure 4. As seen, the phosphorus relaxation is not exponential but it is well treated with a stretched exponential f(t) = exp(−t/T1)β at a β parameter of 0.57.

Figure 5. NMR relaxation data collected in a static sample of αzirconium phosphate represented in coordinates ln(T1) versus temperature in 1000/T units: (○) phosphorus relaxation in the laboratory coordinate system; (●) proton relaxation in the laboratory coordinate system; (■) proton relaxation in the rotating coordinate system (points ∇ corresponding to 1H T1ρ relaxation in the presence of a paramagnetic contribution are not involved in the calculations). All of the T1 times are expressed in seconds.

5.4 kcal/mol and τ0 of 2 × 10−14 s.20 These values give τC(295 K) = 1.6 × 10−6 s, corresponding to low-frequency motions out of the T1 scale in our case. To characterize quantitatively this rotational motion, the 31P T1 temperature dependence in Figure 5 has been treated with eq 1,21

Figure 4. Inversion recovery curve (○) obtained at 298 K for the 31P resonance in a static sample of α-zirconium phosphate treated with an exponential (dashed line) and a stretched exponential (solid line) at the β parameter of 0.57.

1/T1 = (4/30)(μ0 /4π )2 r(P−H)−6 γP 2γH 2ℏ2IH(IH + 1)

We have found that the β parameter in the treatments of the variable-temperature 31P T1 experiments changes only slightly between 0.55 and 0.66. Such β values rather correspond to a Gaussian distribution (0.67)19 of spin−lattice relaxation times which is typical of powders. This feature provides a correct comparison of the 31P T1 data collected at different temperatures. The relaxation times are shown in Table 1 and Figure 5.

{3τC/(1 + ωP 2τC 2) + 6τC/(1 + (ωP + ωH)2 τC 2) + τC/(1 + (ωP − ωH)2 τC 2)}

Table 1. 31P T1, 1H T1, and 1H T1ρ Times Measured at 295 K in a Static Sample of α-ZrP Phosphate 31

P T1 time (s)/β

14.0 ± 0.8 13.9/(0.56)

1

1

0.18 ± 0.09/0.55

51 ± 6;a 55 ± 7b

H T1 time (s)/β

(1)

where ωP and ωH are the P and H resonance frequencies, ω = 2πν, τC = τ0 exp(ΔE/RT) and ΔE is the activation energy. Figure 5 shows a good agreement between the theory and experiments and the fitting procedures give τ0 = 3 × 10−11 s and ΔE = 2.6 ± 0.3 kcal/mol describing the internal rotation. Moreover the r calculations lead to a quite reasonable P···H distance in the P−O−H groups found as ∼2.5 Å in accounting for the single proton−phosphorus contact. The main problem of the above treatment is eq 1 is valid for isotropic motions, while the P−OH rotation is anisotropic and limited as rotational diffusion in a cone.22,23 However, as it has early been analyzed,24 when an isotropic model is applied for anisotropic motions, for example, for the relaxation in a symmetric ellipsoid, the ΔE value is still meaningful, while the correlation time constant τ0 can become a fictitious parameter. The similar situation takes place at anisotropic motions where a fast motion is diffusion in a cone.22,23 In this case, the spectral density function can be written as22,23 31

H T1ρ time (ms)

a

Found by the cross-polarization experiment at variation in contact times in a spinning sample. bIn a static sample.

It is remarkable that the 31P T1 time of 14 s measured at room temperature in a static sample agrees well with the 31P T1 times of 19.2−12.3 s reported for spinning samples of αzirconium phosphate and its derivative.12 Earlier we have suggested that phosphorus relaxation in zirconium phosphate materials is governed by internal rotation in HPO4− groups around P−O bonds via hetero nuclear proton-phosphorus dipole−dipole interactions between 31P and 1 H nuclei in these groups.10 In fact, potentially the protons of water could affect phosphorus relaxation via the same dipolar interactions. However, the low-field 1H T1 study carried out for α-zirconium phosphate has demonstrated water molecules to experience 180°-flips in the cavities of the phosphate at ΔE of

1

J(ω) = 5/2(S2τM /(1 + (τMω)2 ) + (1 − S2)τ /(1 + (τω)2 )

(2)

where S is the order parameter and τM and τ are correlation times of slow and fast motions, respectively. Taking τM →∞, as in the case of zirconium phosphate, leads to the regular spectral C

DOI: 10.1021/acs.jpcc.6b11247 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C density, which is dependent on S. First, the order parameter does not change with temperature and second, it often takes low values (even 0) in a cone. Another result can be expected in the presence of symmetrical correlation time distributions.24,25 Here the activation energy observed (ΔE(obs)) and the real activation energy (ΔE) are connected via the distribution parameter β in eq 3:24 ΔE(obs) = β ΔE

minimum has to be observed at a temperature which is higher than that corresponding to the 31P T1 minimal time.21 This contradiction can be explained by the fact that the 1H signal belongs to protons P−OH and also protons of water located in the interlayer space and on the surface. All these species can have different mobility. Taking into account for this circumstance, we have performed the variable-temperature experiments on kinetics of proton - phosphorus cross-polarization26 potentially providing measurements of 1H T1ρ times in the rotating coordinate system for protons P−OH participating in the crosspolarization process, as we believe. The variation in crosspolarization contact time between 50 and 10000 μs in a spinning sample of zirconium phosphate (4 kHz) resulted in the kinetic curve in Figure 7, which can be well treated in the framework of a classical spin I−S model according to eq 4.27

(3)

Generally speaking, the wide 31P T1 minimum in Figure 5 can be actually attributed to the presence of a correlation time distribution. Then accepting the β parameter found for the 31P relaxation curves as a parameter of the motional correlation time distribution gives activation energy ΔE of 3.9 kcal/mol which remains still small and reasonable for the rotation. In these terms, the correlation time τc calculated at 295 K as 2.2 × 10−8 s will correspond to a center of this distribution, characterizing the internal rotation. It is remarkable that this τc magnitude is in good agreement with previous estimations obtained on the base of the 31P T1/31P T2 approach.10 Concerning the phosphorus−proton distance of 2.5 Å, it is definitely elongated due to the character of motion as it is always observed in the practice.22−24 Finally the activation barriers for free reorientation of the methyl group in solid diazepam change strongly between 0.5 and 3.0 kcal/mol again due to distributions.26 1 H nuclei are the second relaxation label in the zirconium phosphate. The inversion−recovery relaxation experiments performed for the 1H signal in a static sample (Figure 2) have demonstrated again a nonexponential character of the relaxation (Figure 6) which is well described by a stretched exponential to give the β parameters close to those observed for 31 P nuclei. However, it is interesting that the variable temperature data illustrate a very slight 1H T1 dependence (Figure 5) which could be interpreted in terms of a very wide 1H T1 minimum observed at 295 K. If the 31P and 1H labels characterize the same motion in α-zirconium phosphate, then the 1H T1

I(t ) = I0(1 − TH − P/T1ρ(H))−1(exp(− t/T1ρ(H)) − exp(− t/TH − P))

(4)

Figure 7. Kinetic proton-phosphorus cross-polarization at 295 K in a sample of α-zirconium phosphate spinning at a rate of 4 kHz (treated with eq 4) and a static sample treated with eq 5, dashed line, and eq 6, solid line.

In this equation, I(t), TH−P, T1ρ(H), and t are the signal amplitude, the proton−phosphorus cross-polarization constant, proton relaxation time, and contact time, respectively. The fitting procedure in Figure 7 gives very reasonable magnitudes of TH−P = 0.34 ms and 1H T1ρ = 51 ms. However, the character of the CP curves changes strongly in the static CP experiments performed at different temperatures (Figure 7) revealing clearly a more complex cross-polarization process. The process follows the so-called I-I*-S model, where I and I* are dipolar coupled protons and S represent phosphorus nuclei, respectively.27 The reason for this unexpected phenomenon is the dipolar phosphorus−proton interactions operating in a static sample (see Figure 2, where additional broadening in the absence of {1H} decoupling is estimated as ∼3 kHz). In the frameworks of this model, the crosspolarization kinetic in a static sample could be treated with eq 5

Figure 6. Inversion recovery curve (○) obtained at 358 K for the 1H resonance in a static sample of α-zirconium phosphate treated with an exponential (dashed line) and a stretched exponential (solid line) at β parameter of 0.55. D

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kHz, corresponding to the rotating coordinate system. In turn, correlation time τc is calculated at 295 K as 1.5 × 10−5 s. Finally application of proton−phosphorus dipolar interactions does not change the activation energy leading to 5.8 ± 0.5 kcal/mol. Since the 1H relaxation behavior in the rotating framework characterizes P−OH groups, we identify the observed lowerfrequency motion as a proton transfer between these groups,15−17,26 which has the higher activation energy. Such processes are generally slow and can show, for example, correlation times as long as 1.2 × 10 −3 s (300 K)15 and 1.5 × 10−2 s (340 K),16 in solid KH2PO4 and KD2PO4, respectively. For clear reasons, this slow motion cannot contribute to relaxation of phosphorus nuclei in α-zirconium phosphate. In conclusion, it would be emphasized that correlation times and activation energies of P−O rotations in phosphate groups will be obviously restricted, for example, by H-bonding with water molecules and dependent on morphology of zirconium phosphate materials; and phosphorus relaxation can serve as the tool for their studies.

I(t ) = I0 exp( −t /T H1ρ)[1 − 0.5 exp( −t /THSD) − 0.5 exp( −1.5t /THSD) cos(Ct /2)]

(5)

H

where I, t, T 1ρ, THSD, and C are the amplitude of a CP signal, contact time, proton T1 time in a rotating frame, the proton spin-diffusion constant, and dipolar constant, respectively. Generally speaking, such an I-I*-S cross-polarization is often observed for different nuclei in static samples.27 However, application of eq 5 in Figure 7 naturally results in oscillations expected at short contact times,28 which are not observed in the experiments. According to the cross-polarization theory,27,28 the oscillations can be damped due to a rapid Gaussian decay of the S magnetization at the very beginning of the CP kinetic curve. Under this condition, eq 6 can describe the CP curves, where T2 is the 31P spin−spin relaxation time. I(t ) = I0 exp( −t /T H1ρ)[1 − 0.5 exp( −t /THSD) − 0.5 exp( −1.5t/THSD)exp(− 0.5t 2 /T2 2)]

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(6)

CONCLUSIONS In this work, we have characterized internal rotations in HPO4− groups of α-zirconium phosphate by the variable temperature dependence of the 31P T1 relaxation time measured in a static sample. The phosphorus relaxation was nonexponential and interpreted by the presence of Gaussian distribution of T1 times. The calculations of the 31P T1 temperature dependence have resulted in the rotational activation energy of 2.6 or 3.9 kcal/mol in account for the distribution of motional correlation times. 1 H T1ρ times of protons P−OH in the rotating coordinate system have been determined by the kinetic of phosphorus proton cross-polarization. In contrast to a spinning sample, the static cross-polarization follows the I−I*-S model used for the 1 H T1ρ calculations. The variable temperature 1H T1ρ data have resulted in the activation energy of 5.5 kcal/mol attributed to proton transfer between P−OH groups. Thus, two types of motions have been found in α-zirconium phosphate: the lowfrequency proton transfer with the correlation time τc of 1.5 × 10−5 s at 295 K and the high-frequency rotation in P−OH groups with the correlation time τc of 2.2 × 10−8 s at 295 K.

Figure 7 illustrates good agreement between the theory (eq 6) and the experiment leading to 1H T1ρ times at different temperatures shown in Figure 5. It should be noted that the fitting procedures gave very reasonable values of the proton spin-diffusion constant THSD (around 0.6 ms at T2 times determined as ∼0.2−0.3 ms).27,28 The 1H T1ρ temperature dependence in Figure 5 shows a sharp 1H T1ρmin minimum at 264 K. It is interesting that at the lowest temperatures (between 205 and 175 K) the 1H T1ρ time becomes temperature−independent. This effect is often observed in solids and typically explained by relaxation via paramagnetic centers.15,29,20 Generally they are unidentified. Here, like in the case of the previous study,10 traces of paramagnetic centers in α-zirconium phosphate, prepared in this work, have been found as a wide signal at a g-factor of 2.0− 2.5 in the EPR spectrum. This g-factor corresponds to the presence of paramagnetic ions of Fe(III), Mn(II),30or Cu(II).31 Since the signal is observed after 16 EPR scans, their concentration is obviously small. In accord, the paramagnetic contribution to 1H T1ρ times does not exceed 16%. As seen in Figure 5, this low-temperature effect is not observed in phosphorus relaxation. Nevertheless in this case, paramagnetic centers can cause another mechanism of 31P relaxation controlled by diffusion of 31P spins to paramagnetic ions.32,33 Theoretically spin-diffusion coefficients decrease at rotations of powder samples and thus T1(SD) times should be dependent on MAS rates.32 The 31P T1 time has been measured in a sample of zirconium phosphate spinning at 4 kHz. The experiment has shown a nonexponential relaxation curve which is well treated with a stretched exponential again at β parameter of 0.55 to give T1 = 16 s. In account for the errors, there is no evidence for effectiveness of the spin diffusion supporting again the dipolar mechanism of phosphorus relaxation. The temperature dependence of the 1H T1ρ times can be treated in terms of proton−proton dipole−dipole interactions generally accepted for 1H nuclei in eq 715 1/T1ρ = 3/2K {τc/(1 + 4ω12τC 2)

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AUTHOR INFORMATION

Corresponding Author

*(V.I.B.) E-mail: [email protected]. ORCID

Vladimir I. Bakhmutov: 0000-0002-5011-0385 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Robert A. Welch Foundation Grant A-0673 (Metal Phosphonates as Crystal Engineered Solids and platforms for drug delivery) and the Nuclear Energy University Program (DOE) Grant Award No. DE-NE0000746 (Mixed Metal Phosphonate−Phosphate Resins for Separation of Lanthanides from Actinides), for which grateful acknowledgement is made. We would like to acknowledge Drs. Y. Kan and Javeed Ahmad Sheikh for help in preparation of the αzirconium phosphate and the NMR Laboratory at Texas A&M University for the use of the solid-state NMR facilities.

(7)

where K is the dipolar force constant, frequency ω 1 corresponds to the rotating coordinate system and τC = τ0 exp(ΔE/RT). The calculation gives τ0 = 1.4 × 10−9 s at ΔE = 5.5 ± 0.5 kcal/mol and a very reasonable frequency ν1 of 12 E

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DOI: 10.1021/acs.jpcc.6b11247 J. Phys. Chem. C XXXX, XXX, XXX−XXX