Quantum Chemical Prediction of pKa Values of Cationic Ion-Exchange

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Quantum Chemical Prediction of pKa Values of Cationic Ion-Exchange Groups in Polymer Electrolyte Membranes Vincent De Paul Nzuwah Nziko, Jiun-Le Shih, Santa Jansone-Popova, and Vyacheslav S. Bryantsev J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09828 • Publication Date (Web): 09 Jan 2018 Downloaded from http://pubs.acs.org on January 9, 2018

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The Journal of Physical Chemistry

Quantum Chemical Prediction of pKa Values of Cationic Ion-Exchange Groups in Polymer Electrolyte Membranes Vincent de Paul Nzuwah Nziko, Jiun-Le Shih, Santa Jansone-Popova, and Vyacheslav S. Bryantsev* Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 U.S.A. *[email protected] Notes: The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). ABSTRACT: The durability of anion exchange membranes (AEMs) in alkaline fuel cells is largely determined by the stability of anion-exchange groups. Despite continuous research efforts, the commonly employed cations still have limited stability against hydroxide that can act as a strong base and nucleophile. This work is concerned with base-catalyzed degradation of organic cations initiated by proton abstraction to form reactive ylides or carbenes. We report on the performance of 24 methods combining density functional theory and electronic structure methods with implicit solvation calculations for predicting pKa values of organic cations in water and DMSO. The most accurate computational protocols are obtained using a combination of M06-2X/6-311++G** with the SMD solvation model for water (the mean absolute error of 0.4 pKa units) and B3LYP/aug-cc-pVTZ with the IEFPCM solvation model for DMSO (the mean absolute error of 1.4 pKa units). The aqueous pKa calculation protocol is cross-validated against the experimental C-H acidity constants outside the conventional range of 0−14 pKa values. This study rationalizes alkaline degradation of imidazolium cations with C2-alkyl substituents and provides a theoretical scale of C-H acidity for potential anion-exchange groups in AEMs.

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Introduction Alkaline fuel cells have received considerable interest, largely because the kinetics of oxygen reduction in alkaline environment is much more facile than in the acidic medium and lower cost non–Pt group metals (e.g., Ni and Ag) can be used as electrocatalysts.1–7 An anion exchange membrane (AEM) consisting of organic polymer and the cationic groups that could either be tethered to a polymer chain or embedded into a polymer backbone is a critical component of an anion exchange membrane fuel cell (AEMFC). An AEM membrane enables the conduction of OH− from the positive to the negative electrode, helps with gas separation and electronic isolation, facilitates water transport, and mitigates the formation of carbonate precipitates.8,9 However, the degradation of AEM under target operating conditions10–13 has plagued efforts to develop AEMFC at the technological readiness level of the Proton Exchange Membrane (PEM) fuel cells. Despite continuous efforts worldwide, none of the membranes meets the requirements imposed by US Department of Energy to withstand strongly alkaline medium for 5000 h at the temperatures up to 120 °C and at the same time maintain high hydroxide ion mobility of >100 mS/cm.9 While the degradation of a polymer backbone14 could be avoided by employing inert hydrocarbon linkages (e.g., polystyrene), identifying anion-exchange groups that are sufficiently stable under alkaline conditions is a much more difficult proposition. Quaternary ammonium,15–17 imidazolium,18–20 guanidinium,21 phosphonium,22–24 and sulfonium25 cations, among others, have been incorporated into polymers as pendant anion-exchange groups. Still, all commonly employed cationic head groups have limited alkaline stability. With the hydroxide anion acting as a strong nucleophile and proton acceptor, organic cations are susceptible to nucleophilic attack and deprotonation.26–28 Possible degradation modes include (i) direct nucleophilic substitution at the N-alkyl or N-benzyl carbon (SN2), (ii) nucleophilic addition-elimination at the C2 carbon of imidazolium/benzimidazolium (ring opening), the central carbon atom of guanidinium, and the phosphorous atom of phosphonium, (iii) Hofmann elimination of β-hydrogen atoms, and (iv) deprotonation of α-hydrogen atoms to form ylide intermediates that could further undergo Stevens, Sommelet-Hauser, and oxidative rearrangements.29 Computer-aided screening and accelerated discovery of stable cationic groups can play a critical role in guiding the experimental efforts to identify alkaline-resistant AEMs and reducing a vast number of trial-and-error approaches that have been used in the past. Most of the quantum chemical work has focused on addressing the nucleophilic stability of anion-exchange groups, including the computation of the lowest unoccupied molecular orbitals energies14 and activation energies30–33 in SN2 and nucleophilic addition-elimination reactions. However, the degradation mode in which hydroxide acts as a strong base and induce the initial proton abstraction to form reactive ylides or carbenes has not been thoroughly investigated by computational means. Since


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the deprotonation free energy provides the thermodynamic limit of stability of reactive intermediates after proton abstraction, the C−H acidity constant (i.e., pKa value) is the most important single descriptor that reflects the tendency of the cationic group to lose the proton.34 For the past decades, many reports have been published describing theoretical methods of pKa calculations for small organic and inorganic acids and bases,35–56 but very few studies have included C−H acidities. In one such study,57 a satisfactory linear correlation was established between the experimental and computed aqueous pKa values of a variety of carbon acids. In another study, a methodology for predicting the C−H pKa values of aromatic heterocycles in DMSO solution with an accuracy of 1.1 pKa units was developed by Shen et al.58 In 2013, one of us reported the performance of several computational protocols for predicting pKa values of aliphatic C−H acids in DMSO with an accuracy of 0.65 pKa units.53 To the best of our knowledge, no quantum chemical calculations of the aqueous pKa values of C−H bonds in organic cations have been reported using the computational pKa protocol validated for a wide range of different cationic groups. Motivated by research toward the design of organic cations having exceptionally high alkaline stability, we report on the performance of several computational protocols for predicting aqueous pKa values of organic cations with N−H and P−H bonds spanning nearly 13 orders of magnitude of basicity. Overall, 24 methods combining density functional theory, the second-order MöllerPlesset (MP2)59,60 perturbation theory, and the coupled-cluster theory (CCSD(T))61–63 with implicit solvation calculations have been evaluated. We find that linear least-squares fitting of pKa to the experimental data predicted by combining calculations at the CCSD(T), M06-2X,64 and B3LYP65,66 level with solvent effects computed using the SMD solvation model67,68 gives the most accurate results. In addition, we extend these methodologies to predict the C-H acidity constants of organic cations in DMSO, because an extensive body of experimental pKa values for organic cations in DMSO is available69 to test theoretical predictions. Finally, the most accurate methods identified in this work have been employed to cross-validate computational results for O−H and C−H acidity constants and provide a theoretical scale of C-H acidity for several classes of potential cationic groups that are considered for AEMs. Combined with theoretical evaluation of the other modes of degradation in the presence of hydroxide, this provides a useful theoretical framework for computational screening of alkaline-stable anion-exchange groups. 2. COMPUTATIONAL METHODS 2.1. pKa Calculations The pKa or acid dissociation constant for a given cation HB+ is defined as HB ⇄ B + H , K =

(1)


3


pKa= - logKa =

∆G*sol,deprot (HB+ )

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(2)

RT ln(10)

where concentrations are used in place of activities in the limit of infinite dilution. The solution ∗ , is calculated using the standard phase standard free energy of deprotonation, Δ, thermodynamic cycle shown in Figure 1.70–73

∗ ∆, + ∆ ∗

∗ ∆!

+

∗ ∆!

∗ ∆,

∗ B ∆!

+

Figure 1. Thermodynamic Cycle Used in the Calculation of pKa ∗ ∗ ∗ ∗ = Δ, + ∆G0→∗ + Δ! Δ, + Δ! − Δ!

(3) ∗ Here, Δ, is the gas phase deprotonation free energy and Δ! # is the standard + + solvation free energy of species X, where X = HB , H or B. For the thermodynamic cycle to be properly implemented, each reactant and product must be in the same standard state. The conversion from an ideal gas standard state at 1 atm (24.46 L mol-1) to an ideal solution standard state of 1 M at 298.15 K is given by Eq 4:

∆G0→∗ = RT ln24.46 = 1.89 kcal/mol (T = 298.15 K)

(4)

Applying this conversion to each gas-phase reactant and product yields the correction term given in the upper leg of the thermodynamic cycle in Figure 1. For the standard free energy of the proton in the gas phase we used the Sackur-Tetrode equation: 74 ∆G0 $H+g %= -6.28 kcal/mol

(5)

∗ The proton solvation free energy, Δ! H , was treated as an adjustable parameter to give the best match between computational and experimental results. The statistical correction term log (n), was included in the calculated pKa values to account for the presence of n equivalent protonatable groups in a molecule.

2.2. Theoretical Calculations


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All the geometries were fully optimized using Gaussian 09 Revision D.0175 software package. One hybrid GGA (B3LYP), two hybrids meta-GGA (M06 and M062X) density functionals and MP2 were employed to calculate gas phase basicities. The results from these computations were gauged against high-level coupled-cluster CCSD(T) calculations and the available experimental data. DFT methods were used in conjunction with the 6-311++G** and aug-cc-pVTZ basis sets, while the largest basis set used with MP2 was aug-cc-pVQZ. In cases, where multiple conformers are possible, they were systematically evaluated, and the most stable conformation is solution was used for pKa calculations. The basis set for geometry optimization at the MP2 level was aug-cc-pVDZ. The deprotonation energy at the CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ level was combined with the basis set incompleteness error at the MP2 level ∆∆E(MP2) (6)

=

∆E(MP2/aug-cc-pVQZ)

−

∆E(MP2/aug-cc-pVDZ)

to obtain the estimate of the CCSD(T)/aug-cc-pVQZ reaction energy δCCSD(T)/aug-cc-pVQZ = ∆E(CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ) + ∆∆E(MP2) (7) Zero-point energies and thermal corrections were obtained based on the gas-phase optimized geometries at the B3LYP/6-311++G** level and, when noted, at the M06-2X/6-311++G** level. The standard Gibbs free energy of every species in the gas phase was calculated using the rigid rotor-harmonic oscillator approximation without scaling. Three continuum solvent models were evaluated in this study, namely SMD,67,68 CPCM,76,77 and IEFPCM,78,79 using the default settings in Gaussian 09. Unless noted otherwise, the electronic energies in the solvent reaction field were computed as single point energies on gas-phase optimized geometries at the B3LYP/6-31+G* level. 3.RESULTS AND DISCUSSION 3.1. Gas phase basicity First, we compared the performance of three density functionals, such as B3LYP, M06, and M06-2X, and two post-Hartree-Fock methods, such as MP2 and CCSD(T), in predicting the gas phase basicities at T = 298.15 K (the negative of the protonation free energy) of 16 neutral N-H and P-H bases (Table 1) and 12 C-H bases (Table 2). Structures of these bases are shown in Figure S1 of Supporting Information (SI). B3LYP and M06-family of density functionals were chosen for their reasonably accurate description of main-group thermochemical properties.52,53,55 Since experimental gas phase basicities for neutral C-H bases are not available, the results using CCSD(T) calculations were used as a benchmark data set against which the accuracy of the DFT and MP2 methods was evaluated. The accuracy of each method with respect to experimental or CCSD(T) results is characterized by the mean absolute error (MAE) and the root-mean-square


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deviation (RMSD) listed in the last two rows of Table 1 and Table 2. As expected, the CCSD(T) method with an RMSD of 1.0 kcal/mol and MAE of 0.7 kcal/mol shows the best performance. CCSD(T) calculations yield gas phase basicities that fall within the experimental uncertainty of 1-2 kcal/mol, with one exception. The predicted gas phase basicity of p-nitroaniline exhibits an unusually high deviation from the experimental value (6.8 kcal/mol). Good consistency of computational and experimental results for all other compounds and accurately predicted pKa value of p-nitroaniline suggests that the experimental value80 of gas phase basicity for pnitroaniline could be in error.

Table 1. Comparison of calculated and experimental gas phase basicities of 16 N-H and P-H bases (kcal/mol).a 6-311++G**

aug-cc-pVTZ

aug-ccpVQZ MP2

CCSD Experi (T)b mentalc M06B3LYP M06 M06MP2 2X 2X 1 Pyridine 213.9 212.3 210.9 216.5 215.8 213.1 212.3 212.3 214.6 214.7 2 p-Amino pyridine 226.8 224.9 223.9 229.7 228.9 226.1 224.2 224.3 227.1 226.5 3 Imidazole 216.6 214.6 214.6 219.2 218.4 216.2 215.4 215.4 217.8 217.3 4 2-Methylimidazole 222.3 220.3 220.0 225.0 224.1 222.0 220.6 220.6 223.0 222.2 5 Acetamidoxime 212.6 211.9 211.2 215.7 216.3 213.6 210.9 211.1 213.0 na 6 Benzamidoxime 216.9 216.0 214.8 219.9 220.2 217.1 214.3 214.4 216.4 na 7 Methylamine 206.2 204.5 204.8 206.2 205.1 204.3 205.5 205.4 206.7 206.6 8 Dimethylamine 213.2 211.0 211.6 214.0 211.8 212.2 213.4 213.2 214.7 214.3 9 Trimethylamine 216.9 214.0 215.2 218.4 215.5 216.8 217.8 217.6 219.3 219.4 10 1-Aminoethan-1-imine 227.0 225.9 225.1 229.0 228.7 226.2 224.7 224.9 226.5 na 11 Guanidine 229.7 227.1 227.8 231.9 232.1 228.9 227.5 227.9 229.1 226.9 12 1,1,3,3-Tetramethylguanidine 239.3 237.7 236.6 241.5 240.3 238.5 236.7 236.7 238.2 na 13 Aniline 203.5 201.8 201.8 203.9 202.9 201.6 202.7 202.5 204.5 203.3 14 p-Nitroaniline 188.7 186.8 187.7 190.0 189.3 188.1 191.5 191.2 192.6 199.4 15 Methylphosphine 194.2 193.8 191.3 196.2 195.3 193.9 195.6 196.2 196.2 195.4 16 Trimethylphosphine 218.4 217.1 217.2 221.2 219.1 217.2 218.9 219.8 220.2 221.4 MAEd 1.2 2.5 2.8 1.6 2.0 1.8 1.4 1.5 0.7 RMSDe 1.6 2.8 3.0 2.2 2.5 2.1 1.6 1.6 1.0 a Thermal corrections and ZPE were obtained at the B3LYP/6-311++G** level of theory. bCCSD(T)/aug-cc-pVQZ estimates based on Eqs (6) and (7). cObtained from the NIST database.81 dThe mean average error (MAE) between experiment and calculations. eThe root-mean-square deviation (RMSD) between experiment and calculations. Compound 14 with unusually larger error was excluded from MAE and RMSD. B3LYP

M06

Table 2. Comparison of calculated and experimental gas phase basicities of 12 C-H bases (kcal/mol).a Cationic form

17 18 19 20 21 22 23 24 25 26 27

1,3-Dimethylimidazolium 1-Methyl-3-phenylimidazolium 1,2,5-Trimethylthiazolium 1,5-Dimethylthiazolium Dimethylbenzylsulfonium Tetramethylammonium Trimethylsulfoxonium Benzyltriphenylphosphonium Triphenylmethylphosphonium N-Benzylpyridinium 1,3-Dimethylbenzimidazolium

6-311++G** B3LYP

M06

253.2 254.7 246.4 241.5 254.9 281.5 241.6 264.6 271.4 255.0 252.5

249.4 250.6 243.2 241.0 254.4 279.6 239.6 263.3 270.6 254.8 248.5

aug-cc-pVTZ M062X 249.1 250.1 242.5 239.3 253.9 280.3 238.8 261.8 268.4 256.1 247.5

B3LYP

M06

254.2 255.6 247.7 242.0 254.2 281.3 242.0 264.2 271.5 254.5 253.6

252.3 253.3 245.8 241.4 253.9 278.6 240.5 na na 255.0 251.6


M062X 250.6 251.3 244.0 239.1 252.7 279.1 238.6 na na 255.0 249.3

MP2

aug-ccpVQZ MP2

CCSD(T)b

253.4 254.5 247.3 243.5 253.9 279.6 238.6 na na 251.7 252.5

253.4 254.5 247.4 243.2 253.8 279.6 237.8 na na 251.2 252.5

252.1 253.1 245.4 242.7 254.5 280.7 240.1 na na 257.6 251.2

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Benzyltrimethylammonium 278.5 277.0 278.0 278.0 276.5 276.6 278.0 277.8 279.8 MAEc 1.3 1.9 2.2 1.8 1.2 2.1 1.8 2.1 RMSDc 1.4 2.1 1.8 2.0 1.6 2.2 2.3 2.7 a Thermal corrections and ZPE were obtained at the B3LYP/6-311++G** level of theory. bCCSD(T)/aug-cc-pVQZ estimates based on Eqs (6) and (7). cThe mean average error (MAE) and the root-mean-square deviation (RMSD) are calculated with respect to CCSD(T), because the experimental data are not available.

The reaction energies at the MP2/aug-cc-pVQZ level are reasonably converged with respect to the basis set size, with a slightly lower rate of convergence exhibited by compounds containing the third-row P and S elements. We find that less computationally demanding DFT methods (with optimal basis sets) show overall performance comparable to that of MP2. All these methods with MAE and RMSD ≤ 2.0 kcal/mol provide a satisfactory description of gas phase basicities. We note that extending the basis set from 6-311++G** to aug-cc-pVTZ worsens the performance of B3LYP, but improves the performance of M06 and M06-2X. This behavior is consistent with nearly optimal performance of B3LYP/6-311++G** for neutral and charged water clusters, while the extension to the complete basis set limit is required to obtain the most accurate results with the M06-family of density functionals.82 3.2. pKa calculation Next, we compared the ability of 24 theoretical protocols, combining gas-phase basicities given in the preceding sections with the solvation free energies calculated using SMD, CPCM, and IEFPCM models, to accurately predict the pKa values. The training set was selected to cover a diverse set of 16 N-H and P-H bases, having a small number of conformations, which can be systematically investigated, and covering a wide range of pKa values extrapolated to zero ionic strength. We chose 12 C-H bases, for which the experimental pKa values in DMSO are available from a comprehensive compilation by Bordwell.69 Since implicit solvation calculations are prone to yielding large errors in the solvation free energies of ions, the computed pKa values in general are not expected to give the accurate absolute values, but rather able to capture the trends in pKas. Calibration of the computed against the experimental pKa values can account for the deficiency of the gas-phase and solvation methods and provide a regression model with high predictive power (a and b are fitting parameters) pKapred = a + b x pKacomp (8) ∗ Since the solvation free energy of the proton, Δ! H , was treated as an adjustable ∗ parameter, the value of the fitting parameter a was absorbed into Δ! H . Table 3 and Table 4 summarize the accuracy of each pKa model in water and DMSO, respectively, as gauged by MAE and RMSD (in parentheses) between experiment and calculations. The pKa values and the associated parameters of Eq (8) obtained with all 24 methods are provided in SI (Tables S1-S6).

3.2.1 pKa in water


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Irrespective of the employed solvation model, the M06-2X/6-311++G** functional acquires the highest accuracy in predicting pKa values. The choice of the continuum solvation model also has a strong bearing on the predictive power of pKa models. The SMD solvation model has emerged as the most accurate solvation model for predicting the aqueous pKa of organic cations. As a result, a combination of M06-2X/6-311++G** and SMD has the lowest MAE (0.41 pKa units) and RMSD (0.55 pKa units). B3LYP/6-311++G** and CCSD(T) in combination with SMD also give accurate results, with MAEs of 0.43 and 0.50 pKa units and RMSDs of 0.55 and 0.70 pKa units, respectively. The least performing methods have an error that is 3−4 times larger than that of the best method. An excellent correlation is observed (R2 = 0.991, Figure 2) between the computed (using the best method) and experimental aqueous pKa values of 16 organic cations considered in this study. However, the slope obtained for all 24 pKa methods is significantly less than unity (0.565−0.742, Tables S1−S3). The disparity between the fitted slope and the ideal value is mainly ascribed to significant underestimation of ion hydration free energies computed with implicit solvation models26,83 and in part to the accuracy level of DFT when a DFT method is applied. Indeed, the largest slope of 0.742 is obtained using a combination of the benchmark CCSD(T) method and the SMD solvation model that gives larger absolute ion hydration free energies compared to CPCM and IEFPCM. Excellent results obtained using Eq 8 imply that there is a good proportionality between the computed and experimental hydration free energies of ions. A theoretically more satisfying approach potentially avoiding the use of the empirical correction factor would be to compute the solvation energies of cationic species by explicitly adding water molecule to their structures.84-86 However, this approach has its own challenges associated with convergence of the results with the number of explicit water molecules, identification of the most stable conformation for each water-ion cluster, and anharmonic behavior of fluxional water molecules, that can all add to a relatively high variation of the computed pKa values. Another potential improvement for more flexible and complex molecules would be to perform geometry optimization and frequency calculations in solution.84,87–89 However, for the present set of relatively rigid molecules, entirely solution phase calculations using the best combination of M06-2X/6-311++G** and SMD reduced the mean unsigned difference only slightly from 0.41 (Table 3) to 0.38 (Table S4 of SI) pKa units. Table 3. Accuracy of pKa calculation for 16 organic cations with N−H and P−H bonds in water obtained using a combination of 8 gas phase and 3 implicit solvation models, as gauged by MAE and RMSD (in parentheses). SMD

CPCM

IEFPCM

B3LYP/6-311++G**

0.43(0.55)

0.68(0.80)

0.66(0.80)

M06/6-311++G**

0.67(0.76)

0.85(0.98)

0.80(0.91)

M06-2X/6-311+G**

0.41(0.55)

0.54(0.67)

0.56(0.67)

B3LYP/aug-cc-pVTZ

0.68(0.86)

0.99(1.13)

0.94(1.12)


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M06/aug-cc-pVTZ

0.81(1.04)

1.08(1.27)

1.03(1.26)

M06-2X/aug-cc-pVTZ

0.51(0.65)

0.83(0.97)

0.80(0.95)

MP2/aug-cc-pVQZ

0.69(0.87)

0.72(0.90)

0.66(0.82)

CCSD(T)a

0.50(0.70)

0.70(0.83)

0.65(0.81)

a

CCSD(T)/aug-cc-pVQZ estimates based on Eqs (6) and (7).

M06-2X/6-311++G** and SMD pKa pred = 0.6803pKa comp

20

R2 = 0.978 15

10

5

0 0

5

10

15

20

25

pKa (aqueous), computed

Figure 2. Computed versus experimental pKa values of 16 organic cations with N−H and P−H bonds in water. The computed pKa values were obtained at M06-2X/6-311++G** level of theory with solvent correction obtained using the SMD implicit solvation model. ZPE and thermal corrections were calculated in the gas phase at the B3LYP/6-311++G** level of theory. 3.2.2. pKa in DMSO Error analysis of pKa calculations in DMSO (Table 4) shows that the CCSD(T) method that attains the highest accuracy in predicting basicities in the gas phase, performs relatively poorly and trails behind the other methods in predicting pKa values with C−H bonds. This could be due to higher uncertainty of the experimental data at the higher end of the pKa range, which is outside the reliable range of measurement by conventional methods, and/or deficiencies of the solvation methods that could negate the accurate gas phase data. The B3LYP and M06-2X functionals in conjunction with the aug-cc-pVTZ basis set show the best overall performance. We note that consistently more accurate results are obtained with DFT methods by employing larger basis sets. When coupled with the IEFPCM solvation model, these methods yield MAE and RMSD that are 1.4 and 1.8 pKa units, respectively. MP2/aug-cc-pVQZ together with the SMD solvation model also performs well in reproducing the pKa values (a MAE of 1.8 and an RMSD of 2.2 pKa units), but this method is significantly more expensive. As can be seen in Figure 3, a combination of B3LYP/aug-cc-pVTZ and IEFPCM that gives the most accurate results show a very strong correlation (R2 = 0.948) with the experimental data. Slightly larger


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deviation for three largest pKa values is expected because these values are associated with higher experimental error bars. Unlike in water, the slope for pKa in DMSO in Figure 3 is very close to unity (1.01). The proximity of the slope for several DFT, MP2, and CCSD(T) methods (Tables S4−S6) to the theoretically expected 1:1 line is consistent with our previous report53 on predicting the C−H acidities of neutral molecules in DMSO. These results suggest that implicit solvent models provide better estimates of the solvation free energies of ions in DMSO (as aprotic solvent) than in water (as hydrogen-bonding solvent). Furthermore, the value of ∗ Δ! H = -270.0 kcal/mol in DMSO, fitted to yield zero free term (a = 0 in Eq 8) in the ∗ regression line shown in Figure 3, is surprisingly close to the experimental value of Δ! H 54,55 = -273.3 ± 4.0 kcal/mol derived using the cluster pair approximation. Therefore, the developed method for computing pKa in DMSO gives us confidence that this approach will be applicable for a broad range of C−H bases. Table 4. Accuracy of pKa Calculation for 12 organic cations with C−H bonds in DMSO obtained using a combination of 8 gas phase and 3 implicit solvation models, as gauged by MAE and RMSD (in parentheses) SMD

CPCM

IEFPCM

B3LYP/6-311++G**

2.0(2.3)

1.7(2.0)

1.6(1.9)

M06/6-311++G**

2.6(3.0)

2.2(2.5)

2.2(2.5)

M06-2X/6-311++G**

2.5(2.8)

2.1(2.4)

2.1(2.4)

B3LYP/aug-cc-pVTZ

2.3(2.9)

1.4(1.8)

1.4(1.8)

M06/aug-cc-pVTZ

1.7(2.0)

1.4(1.8)

1.4(1.8)

M06-2X/aug-cc-pVTZ

1.9(2.2)

1.6(1.9)

1.6(1.9)

MP2/aug-cc-pVQZ

1.3(1.6)

1.8(2.2)

1.8(2.2)

CCSD(T)a

2.3(2.6)

2.2(2.4)

2.2(2.4)

a

CCSD(T)/aug-cc-pVQZ estimates based on Eqs (6) and (7).


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B3LYP/aug-cc-pVTZ and IEFPCM pKa pred = 1.010pKa comp

45

R2 = 0.948 pK a (DMSO), experimental

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


38 31 24 17 10 10

17

24

31

38

45

pKa (DMSO), computed

Figure 3. Computed versus experimental pKa Values of 12 organic cations with C-H bonds in DMSO. The computed pKa values were obtained at B3LYP/aug-cc-pVTZ level of theory with solvent correction obtained using the IEF-PCM implicit solvation model. ZPE and thermal corrections were calculated in the gas phase at the B3LYP/6-311++G** level of theory. 3.3. Cross-validation of the aqueous pKa calculation protocol outside the conventional pKa range Potentiometric titration allows reliable pKa measurements in the range of 1.0 to 12.5. This is due to limitations of the pH glass electrodes90 that exhibit nonlinear response at high acid and alkaline concentrations and can be damaged by strong alkaline solutions. The pKa measurements window can be slightly extended to -0.5−14.5 range by employing various spectrometric titration methods (spectrophotometry, NMR, fluorescence, etc.) that can directly detect the formation of protonated/deprotonated species. Therefore, developing and validating a reliable pKa prediction protocol outside the conventional pKa range will provide a tool that could greatly enhance our understanding of superacid and superbase chemistry. In a seminal work by Amyes et al.,27 followed by others,91 a kinetic method was used to obtain pKa values of 16.9−28.2 for the conjugate acids of imidazolyl carbenes and related compounds in water. The equilibrium constant was determined from the ratio of the rate constant for hydroxide catalyzed deprotonation at C(2) position obtained from NMR spectra by a deuterium-exchange method and the rate constant for the reverse protonation of carbene. We have used this dataset to test our theoretical predictions. To demonstrate the applicability of our theoretical approach for a wider range of pKa values, we included two examples with negative pKa values as well. Figure 4 shows the structures of the studied cations along with the experimental (in black) and predicted (in blue) aqueous pKa values. Calculations were carried out at the M06-2X/6-311++G** level with solvent corrections obtained using the SMD solvation model as the most reliable method. As follows from comparison of the predicted and experimental pKa values in Figure 5, there is an


11


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excellent correlation between them (R2 = 0.993), despite a systematic underestimation of pKa values by ~2 pKa units. We have also performed geometry optimization and frequency calculations in solution (M06-2X/6-311++G**), but this has not substantially improved the agreement with experiment (Table S10 of SI). Considering higher uncertainty of the experimental data obtained with the kinetic method, the agreement between the calculated and experimental values is reasonably good. We note that previously calculated pKa values for several imidazolium cations in water, which were not calibrated against the experimental data, deviate from the values obtained by the kinetic method by a larger margin, 3.1−4.4 pKa units.28

Figure 4. Experimental (in black) and predicted (in blue) C−H and O−H acidity constants of organic cations in water. The most acidic protons are shown in blue.


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M062X/6-311++G** and SMD pKa pred = 1.146pKa comp – 0.705 R2 = 0.983 pKa (aqueous), Experimental

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


p K (aqueous),predicted a

Figure 5. Experimental versus predicted C−H and O−H acidity constants of organic cations in water. The pKa values were obtained at M06-2X/6-311++G** level of theory with solvent correction obtained using the SMD implicit solvation model. ZPE and thermal correction were calculated in the gas phase at the B3LYP/6-311++G** level of theory. The solid line is the 1:1 relationship between the experimental and predicted pKa values. The dotted line represents the fitted linear equation shown in the figure. 3.4. Rationalizing Alkaline Stability of Imidazolium Cations with C2-alkly Substituents Based on Their Acidity Constants Predicted pKa values provide a useful metrics for determining relative stability of organic cations that degrade via initial proton abstraction by the hydroxide anion. We then directed our efforts towards demonstrating the utility of this approach in rationalizing the alkaline stability of imidazolium cations with C2-alkly substituents. Analysis of degradation products for this class of cations by Hugar et al.26 suggests that they do not decompose by nucleophilic attack on Nsubstituents or by nucleophilic addition to the C2 position and concomitant ring-opening. Instead, the cation is initially deprotonated, which then leads to the degradation of the molecule via rearrangements. The percent of each cation remaining (x%) after 30 days in CD3OH solution of 1 M KOH at 80 oC together with their predicted pKa values in water are shown in Figure 6. There is a good correspondence between the pKa value of the most acidic hydrogen (shown in blue) and the extent of degradation. This becomes even more apparent by plotting -log(x/1-x) versus pKa (not shown), which yields a linear correlation with R2 = 0.90. We observe that cation 45 whose acidity is the lowest (pKa = 27.1), is still subject to 5% degradation under tested conditions. Since alkaline fuel cell operating conditions are more severe, organic cations with pKa values significantly higher than 27.1 would be required to pass the stringent stability test.


13


20). We find that slope for pKa in DMSO is close to unity (0.84−1.06), but significantly less than unity for pKa in water (0.57−0.74). The data suggests that implicit solvation models provide better estimates of the solvation free energies of the studied cations in aprotic DMSO solvent than in water, which forms strong and directional hydrogen bonds with ionic solutes. The predictive power of the pKa computation protocol in water is further tested outside the conventional pKa range (pKa < 0 and pKa ≥ 20), demonstrating that the developed theoretical


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model provides reliable description of the C−H acidity of organic cations relevant for anion exchange membranes. This approach has been used to rationalize the alkaline stability of imidazolium cations with C2-alkly substituents, signifying a good correspondence between the predicted pKa values of the most acidic hydrogen and the extent of degradation. Using the most accurate pKa computation protocols, we have investigated the C-H acidity of several classes of potential cationic groups for polymer electrolyte membranes. Based on the computed pKa values, the least acidic are guanidinium, quaternary ammonium, and substituted imidizalium cations, where in the latter case the acidic ring protons are replaced by C2-aryl and C4/5 alkyl/aryl groups. In contrast, the alkyl and benzyl phosphonium, pyridinium, and sulfonium, along with the unsubstituted thiazolium and 1,2,3-triazolium exhibit rather low pKa values, which makes them less suitable for applications in strongly basic environment. Combined with theoretical investigation of nucleophilic stability of organic cations, this study provides a convenient means of screening for suitable organic cations as anion-exchange groups in alkaline polymer electrolyte membranes fuel cells. Supporting Information. Structures of the organic cations used in the pKa training set and the pKa values in water and DMSO computed with 24 methods, correlation between the predicted pKa values in water and DMSO, pKa values in DMSO for potential anion-exchange groups, the effect of relaxing geometries and running frequency calculations in solution, and Cartesian coordinates of all cation and deprotonated neutral molecules accompanied by their electronic energies obtained at the M06-2X/6-311++G** level. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgements. This work was funded by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. References (1)

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TOC Graphic high

pKa = 23.4

Alkaline stability

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 28

low

pKa= 39.7

pKa = 27.1

pKa = 20.5

Calculated aqueous pKa

high


28

Quantum Chemical Prediction of pKa Values of Cationic Ion-Exchange

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