Deuterated Ethanol as a Probe for Measuring Equilibrium Isotope

Article pubs.acs.org/JPCA

Deuterated Ethanol as a Probe for Measuring Equilibrium Isotope Effects for Hydroxyl Exchange Hai Xu,*,†,‡ Siqi Zhao,†,§ Xiang Xiong,§ Jiayao Yao,‡,∥ R. James Cross,*,‡ and Martin Saunders*,‡ †

College of Chemistry and Chemical Engineering and §Powder Metallurgy Research Institute, Central South University, Changsha 410083, China ‡ Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States ∥ SINOPEC Research Institute of Petroleum Processing, Beijing 100083, China ABSTRACT: Equilibrium deuterium isotope effects for exchange of hydroxyl deuterons and protons among tert-butanol, phenol, ethanethiol, diethylamine, and ethanol were measured by using NMR and also calculated theoretically. Deuterated ethanol could be used as a probe for measuring equilibrium isotope effects (EIE) for hydroxyl exchange; tert-butanol, phenol, ethanethiol, diethylamine, and pyrrole were used as five representive examples. A procedure called the “one-atom isotope effect” was used to save time in the calculations.

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INTRODUCTION It is easy to get information on transition states for reactions from kinetic isotope effects (KIE).1,2 Information about features of structures and chemical reactions can also be valuable detailed by isotope effects yield.3 Equilibrium isotope effects (EIE) result from bonding and nonbonding interactions in structures that are minima on the energy surface.4 Under normal circumstances, compared to KIE, EIE are too small to be calculated; nevertheless, there are many cases in which they can be measured very accurately.2−4 EIE can be expressed theoretically as more specifically reduced isotopic partition function ratios (or appropriate ratios of partition functions).5 It is useful to compare results from calculations with experimental results for testing the accuracy of the theoretical methods used and gaining detailed information about a variety of qualitative effects on chemical structures.2,6,7 It was well-known that alcohols exchange hydroxyl protons readily. Exchange occurs between molecules of the same or different structures. Because the product of hydroxyl proton exchange is chemically the isotopically same as the starting material, no change can normally be seen in the NMR spectrum except for changes in the spin−spin splitting.8−13 However, if one mixes an alcohol with a different alcohol containing an OD (D means 2H or is named as deuterium, another isotope of H), hydroxyl hydrogen exchange now yields a product which is different. The equilibrium constant for this reaction is called an equilibrium isotope effect (EIE). Measuring the ratio of the area of OH peaks in the proton spectrum and of OD peaks in the deuterium NMR spectrum can yield experimental values for the EIE. The field of EIE has been reviewed several times over many years.14−22 Theory due to Bigeleisen, Mayer, and Wolfsberg14,23−25 yields predicted values for these equilibrium constants as a function of vibrational frequencies and temperatures. The © 2017 American Chemical Society

necessary vibrational frequencies can be predicted using quantum mechanics. Theoretical values for equilibrium isotope effects obtained in this way were found to be in excellent agreement with experimental values.24 If we have N different alcohols, there are N(N − 1)/2 distinct pairs, and we could measure this number of experimental EIE constants. We would need to do the same number of theoretical calculations for comparison. Consider equilibrium between an alcohol and a deuterium atom to give the deuterated alcohol and a hydrogen atom. The EIE for this process can readily be calculated, but there is no way of measuring it. However, the ratio of such values for two different alcohols is exactly the EIE for deuterium exchange between these alcohols. In this way, by doing N theoretical calculations, we can obtain predicted EIE values for N(N − 1)/2 pairs of alcohols. The theoretical values that we obtain for each alcohol exchanging with a deuterium atom can be called one-atom equilibrium isotope effects. This is similar to the expression (S1/S1)F used as an intermediate by Bigeleisen and Mayer.23 Here, we examine deuterium equilibrium isotope effects for ethanol, tert-butanol, phenol, ethanethiol, and pyrrole, all of which have exchangeable protons. Deuterated ethanol is commercial available and it is a nice probe for measuring equilibrium isotope effects (EIE) for hydroxyl exchange and the other molecules.

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CALCULATIONS Here, we examine deuterium equilibrium isotope effects for ethanol, tert-butanol, phenol, ethanethiol, and pyrrole, all of which have exchangeable protons. We did Gaussian 09W Received: January 17, 2017 Revised: March 3, 2017 Published: March 3, 2017 2288

DOI: 10.1021/acs.jpca.7b00514 J. Phys. Chem. A 2017, 121, 2288−2292

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The Journal of Physical Chemistry A

bending modes, which are the most anharmonic. Again, we expect large cancellation of the errors in taking the various ratios. In principle, it is possible to include both solvent effects and anharmonic vibrations, but this would result in an enormous increase in computation time and complexity.26 It seems reasonable to start with a simple theory and see how well it works. The isotopic exchange of deuterium and hydrogen between activated protons occurs rapidly enough to reach equilibrium in seconds. For an H−D exchange equilibrium (3) between compound A and partially deuterated B, one can calculate the equilibrium constant K of the reaction from the eq 4 and can measure the concentration of each species using the NMR to get the equilibrium constant. Many molecules contain functional groups with readily exchangeable protons such as OH, NH, and SH. Ethanol, tertbutanol, phenol, ethanethiol, and pyrrole have been chosen because they are very common and they illustrate five types of active hydrogen, and all of them are soluble in chloroform. Other molecules will also be examined, and the results will be published in the near future. Because C2H5OD is commercially available, we chose this as our common probe molecule, species B in eq 3. It is also convenient because the methyl and methylene protons do not exchange and can be used to measure the concentration of C2H5OD in the proton NMR. It is then dissolved in CDCl3 along with the other molecule of interest. From the areas for the appropriate peaks in the proton and/or deuterium NMR (which should approximate the concentrations) we can obtain experimental values of K. Other molecules will also be examined, and the results will be published in the near future.

calculations at the level RHF/6-311+G(d,p). The output from Gaussian (Cartesian coordinates of atoms, the Cartesian forceconstant matrix) and the temperature are then input to the program THERMISTP,24 which calculates the partition functions and equilibrium constants for the specified isotopomers. This program supplants the earlier program QUIVER.25 We define the one-atom isotope effect for A, K1(A), as the EIE constant for the reaction AD + H ⇋ AH + D K1(A) =

[AH][D] [AD][H]

(1)

(2)

Then, the equilibrium constant for the reaction AD + BH ⇋ AH + BD

(3)

is K=

K (A) [AH][BD] = 1 [AD][BH] K1(B)

(4)

because the concentrations of H and D cancel. The advantage of using eq 1 as a standard is that it requires only one electronic structure calculation, because the electronic wave functions and the resulting potential energy surface are independent of isotopes. It also requires the calculation of only two partition functions. The results are shown in Table 1. Note that only the alcohols have zero-point vibrational energy and the H or D atoms do Table 1. Equilibrium Constants for Replacing One H with D at 295 Ka

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EXPERIMENTAL SECTION C2H5OD and the other compounds to be studied were dissolved in chloroform-d and dried with molecular sieve (4 Å) overnight to remove any water present. We used 0.5 mL of CDCl3 and measured the other components with a microsyringe or a precision microbalance. The mixture was allowed to stand long enough to reach the equilibrium. The T1 of every proton of OH, NH, or SH was checked, and the 1H NMR was measured at d1 = 5T127 to confirm that the concentration measurement was correct on the basis of integrated areas of the peaks. C2H5OD was used as a NMR probe because there are three groups of protons; there are two protons in −CH2− and three protons in − CH3. We could use the program Topspin to integrate automatically and we can check that the ratio of peak areas for −CH2− and −CH3 was 2:3 within 1%; otherwise, the spectra were discarded. Furthermore, this implies that the total area of the peaks for −OH will be one-third of the area for −CH3. Because the area for −OH can be measured, we can get the area for −OD. The integration of peaks for other compounds is treated similarly. The NMR spectra were recorded on a Bruker Avance DPX-400 or DPX-500 spectrometer. Sample tube temperatures were constant with the range 22.0 ± 1.0 °C. Similar experiments have been done by Smirnov et al.28

a

White dot means hydrogen, gray dot carbon, red dot oxygen, yellow dot sulfur, and blue dot nitrogen.

not. This is why K1 is so large. For reaction 3 K is a ratio of K1 values, and so K is much closer to unity. Because the calculations use gas-phase partition functions, solvent effects are neglected. Although solvation energies can be large, much of the effect cancels out in taking the ratio in eq 2. Further cancelation occurs in taking the ratio of two K1’s in eq 4. The program also uses the harmonic-oscillator approximation to calculate the vibrational partition functions. Unfortunately, the largest contribution to the vibrational partition function usually comes from the low-frequency

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RESULTS AND DISCUSSION tert-Butanol and Ethanol. For the isotopic exchange reaction 2289

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= 1.00. This shows good reproducibility and good agreement with theory. Phenol and Ethanol. We next look at the exchange with phenol,

tert ‐butanol‐H + ethanol − D (5)

⇋ tert ‐butanol‐D + ethanol‐H

we assume that activities are proportional to concentrations. The ratio of deuteron to proton concentrations of tert-butanol (A) and ethanol (B) can be obtained from the NMR spectrum by measuring the areas of the peaks for tert-butanol and ethanol. T1 for OH protons of both tert-butanol and ethanol are 3.3 s, so we set d1 = 5T1 = 16.5 s. For pure CH3CH2OH the ratios of peak areas are 3:2:1. In our case the area of the OH peak will be less than this because some of the ethanol is deuterated. By measuring the ratio of areas of the OH peak to the methyl and methylene peaks, we can then get the fraction of protonated ethanol. One minus this fraction is, of course, the fraction of deuterated ethanol. Similar consideration applies to tert-butanol. Putting these fractions into eq 4 gives K. Because K depends on the ratio of concentrations, we do not need to know the absolute concentrations or the amounts of any of the species. It is also important to note that K is not affected by the initial amount of deuteration of the ethanol. Thus, if some H2O is initially present in the sample, it will exchange with the deuterated ethanol, and some of the deuterium will be lost when the sample is dried. This does not change K except for degradation in accuracy. Figure 1 shows an NMR spectrum for

phenol‐H + ethanol‐D ⇋ phenol‐D + ethanol‐H

(6)

The NMR spectrum is shown in Figure 2 for three different amounts of C2H5OD in the sample. The phenol OH peak shifts

Figure 2. 1H-NMR spectra of phenol in chloroform-d: (1) 5 μL of ethanol-D; (2) 15 μL of ethanol-D; (3) 25 μL of ethanol-D. The peak assignments are (A) solvent, (B) meta protons, (C) para protons, (D) ortho protons, and (E) OH on phenol. The OH proton on ethanol is off to the right at 1.24 ppm.

from 6.50 to 7.00 to 7.50 ppm as the amount of C2H5OD increases. The shift is due to the stronger solute−solvent interactions.17,18 T1 for phenol and ethanol are 2.5 and 3.3 s, respectively. We set d1 = 16.5 s. The analysis is done as it was for tert-butanol. The data are shown in Table 3 for the three amounts of C2H5OD. The three measurements give K = 0.925, 0.977, and 0.966 (average 0.955 ± 0.02). From eq 4 and Table 1 we get a calculated value of K = 0.934. According to the results presented, the H/D exchange between aliphatic alcohols (tertbutanol and ethanol) is almost a degenerative process, whereas between aliphatic (ethanol) and aromatic alcohol (phenol) K1 < 1. Ethanethiol and Ethanol. The equilibrium for

Figure 1. 1H-NMR spectra of tert-butanol and ethanol-D in chloroform-d. The peaks are (A) CH2 in EtOH, (B) OH in EtOH, (C) OH in t-BuOH, (D) CH3 in t-BuOH, and (E) CH3 in EtOH.

the mixture. By addition of deuterated ethanol, OH in t-BuOH decreases and OH in EtOH increases, which helps us assign OH signals B and C. Table 2 gives the results for three independent runs. The three runs give K = 1.029, 1.019, and 0.974 (average 1.007 ± 0.03). The calculations, using eq 4 and Table 1, give K

Table 2. Equilibrium Constants Obtained from the 1H-NMR Spectra of Ethanol and tert-Butanol Mixture in Chloroform-d Solution 30 μL of tert-butanol/20 μL of ethanol-D 30 μL of tert-butanol/10 μL of ethanol-D 30 μL of tert-butanol/25 μL of ethanol-D

tert-butanol-Ha

tert-butanol-Db

ethanol-Ha

ethanol-Db

K

0.484 0.571 0.538

0.516 0.429 0.462

0.491 0.576 0.531

0.509 0.424 0.469

1.029 1.019 0.974

a

Concentration obtained by integrated proton NMR signal (arbitrary units). bConcentration obtained by comparing the proton NMR signals for the exchanged protons and the nonexchanged protons (see text). 2290

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The Journal of Physical Chemistry A Table 3. Equilibrium Constants for Phenol and Ethanol phenol-H

phenol-D

ethanol-H

ethanol-D

K

0.714

0.286

0.698

0.302

0.925

0.549

0.451

0.543

0.457

0.977

0.426

0.574

0.449

0.551

0.962

10 mg of phenol/ 5 μL of ethanol-D 5 mg of phenol/ 25 μL of ethanol-D 5 mg of phenol/ 15 μL of ethanol-D

C2H5SH + C2H5OD ⇋ C2H5SD + C2H5OD

(7)

is similar. The NMR spectrum, shown in Figure 3, shows that the SH proton is split into a triplet by the methylene protons.

Figure 4. 1H-NMR spectra of pyrrole and ethanol-D in chloroform-d. The peaks are (A) NH in pyrrole, (B) solvent, (C, D) CH in pyrrole, (E) CH2 in EtOH, (F) OH in EtOH, and (G) CH3 in EtOH.

Table 5. Equilibrium Constant for Pyrrole and Ethanol 20 μL of pyrrole/ 10 μL of ethanol-D 20 μL of pyrrole/ 20 μL of ethanol-D 20 μL of pyrrole/ 30 μL of ethanol-D

pyrrole-D

ethanol-H

ethanol-D

K

0.652

0.348

0.651

0.349

0.995

0.551

0.451

0.549

0.451

0.998

0.464

0.536

0.461

0.540

0.985

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CONCLUSION Deuterated ethanol was used as a proton-NMR probe to measure the equilibrium isotope effect with four other compounds with different activated protons. The results could also be calculated with the program THERMISTP.24 The agreement between theory and examined NMR results is good.

Figure 3. 1H-NMR spectra of ethanethiol and ethanol-D in chloroform-d. The peaks are (A) CH2 in EtOH, (B) CH2 in EtSH, (C) OH in EtOH, (D) SH in EtSH, (E) CH3 in EtSH, and (F) CH3 in EtOH.

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T1 for the SH and OH protons were 3.0 and 3.3 s, respectively. D1 was set to 16.5 s. Data are in Table 4.

AUTHOR INFORMATION

Corresponding Authors

Table 4. Equilibrium Constant for Ethane Thiol and Ethanol 20 μL of EtSH/10 μL of EtSH 20 μL of EtSH/20 μL of EtSH 20 μL of EtSH/40 μL of EtSH

pyrrole-H

*H. Xu. E-mail: [email protected]. *R. J. Cross. E-mail: [email protected]. *M. Saunders. E-mail: [email protected].

C2H5SH

C2H5SD

C2H5OH

C2H5OD

K

0.772

0.228

0.465

0.535

0.340

0.674

0.326

0.451

0.550

0.397

Hai Xu: 0000-0003-1610-9556

0.657

0.343

0.409

0.591

0.361

Notes

ORCID

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to the National Science Foundation for partial support of this research under grant CHE-0809780. H.X. was supported by a T. B. Johnson fellowship at Yale University and NSFC Grants 21002127, 212111120. J.Y. was supported by the Chinese National Building High-Level-University Graduate Student Program. S.Q.Z. was supported by the Mittal Students Innovative Projects of Central South University.

The experiment gives K = 0.340, 0.397, and 0.361 (average 0.366 ± 0.02). The calculated value from eq 4 and Table 1 is 0.358. Pyrrole and Ethanol. We now turn to our final case, pyrrole‐H + ethanol‐D ⇋ pyrrole‐D + ethanol‐H

(8)

T1 for the NH proton on pyrrole and the OH proton on ethanol is 3.1 and 3.3 s, respectively, and we again use d1 = 16.5 s. Figure 4 shows the NMR spectrum, and the results are given in Table 5. The three results are 0.995, 0.998, and 0.985 (average 0.993 ± 0.006). Theory gives 0.989.

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