Acidity of Strong Acids in Water and Dimethyl Sulfoxide - The Journal

Apr 26, 2016 - Acid dissociation is among the most frequently used model reactions for validating and parametrizing a great variety of computational m...
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Acidity of Strong Acids in Water and Dimethyl Sulfoxide Aleksander Trummal,*,† Lauri Lipping,‡ Ivari Kaljurand,‡ Ilmar A. Koppel,‡ and Ivo Leito*,‡ †

National Institute of Chemical Physics and Biophysics, 23 Akadeemia tee, Tallinn 12618, Estonia Institute of Chemistry, University of Tartu, 14a Ravila Street, Tartu 50411, Estonia

‡

S Supporting Information *

ABSTRACT: Careful analysis and comparison of the available acidity data of HCl, HBr, HI, HClO4, and CF3SO3H in water, dimethyl sulfoxide (DMSO), and gas-phase has been carried out. The data include experimental and computational pKa and gas-phase acidity data from the literature, as well as high-level computations using different approaches (including the W1 theory) carried out in this work. As a result of the analysis, for every acid in every medium, a recommended acidity value is presented. In some cases, the currently accepted pKa values were revised by more than 10 orders of magnitude.

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INTRODUCTION Strong (mineral) acids are among the most frequently used chemicals in research and industry. In aqueous solution they are practically fully dissociated and several of them also in dimethyl sulfoxide (DMSO). The acidities of these acidsin terms of the proton activity of their dilute aqueous solutionsare leveled. This does not mean, however, that the acidities of their molecules in water or DMSOin terms of proton-donating abilitiesare equal. In fact, the aqueous acidities of these molecules, expressed as pKa values, are very different.1 One might think that if the solutions have the same acidity, then the difference in pKa values does not have much practical importance. This is not so, for at least the following reasons: (1) The solution acidities are the same only in dilute solutions, not in more concentrated ones, which are used in many practical applications, such as acid catalysis. (2) Acid dissociation is among the most frequently used model reactions for validating and parametrizing a great variety of computational methods in solutions. For this it is very useful to have data over an as wide as possible acidity range, and the stronger the acids for which pKa data are available, the wider the range. In spite of their high importance and numerous reported aqueous pKa values,1−5 reliable pKa values of most mineral acids in water are still not available. The reason is related to experimental problems. Most of the methods of measuring pKa values need such conditions in solution whereby comparable amounts of the neutral acid and its anion are at equilibrium. This is not difficult to achieve in aqueous solution in the pKa range of 1 to 13. However, if the pKa value is below, say, −3, then very high concentration of some strong acid is needed for achieving noticeable protonation of the measured acid’s anion. As a result, the solvent, strictly speaking, is not water any more © 2016 American Chemical Society

but is a solvent mixture of water and the strong acid. An outcome of this is that the obtained pKa values do not refer to water as solvent and differ, depending on the strong acid used. Furthermore, a number of indirect and/or theoretical modeling approaches have been applied for obtaining aqueous pKa values. Each has its own assumptions and weaknesses, leading to still greater diversity of the available data. In the Perrin’s classical compilation1 of aqueous pKa values of inorganic acids the pKa values have been obtained using a wide range of approaches, both experimental (conductometry, vapor pressure measurements, NMR, etc.) as well as theoretical (calculations based on thermodynamic cycles, Pauling’s rules, etc.). The pKa values of HCl, HBr, HI and HClO4 are reported in ref 1 and vary in the following ranges: −5.1 to −7.4; −8 to −9; −9 to −9.5 and −1.5 to −14, respectively. Similarly to perchloric acid, a wide range of aqueous pKa values has been reported for triflic acid (CF3SO3H or TfOH), ranging from −5 to −14.2 A comprehensive investigation of pKa values of strong acids was carried out by Guthrie.3 He combined the available theoretical information about a number of acids from the literature and supported by relations between acid pKa values and hydrolysis rate constants of methyl esters. He arrived at a consistent set of aqueous pKa values for a number of strong acids, including HClO4 (−5.0) and CF3SO3H (−5.9). A serious computational effort of establishing the aqueous pKa values of strong acids was undertaken by Gutowski and Dixon.4 They arrived at pKa values within ±2 pKa units from experimental with nearly all investigated acids. Their pKa value for triflic acid is −14.2. This value is in excellent agreement with one of the literature values and in stark disagreement with the value from Received: March 3, 2016 Revised: April 14, 2016 Published: April 26, 2016 3663

DOI: 10.1021/acs.jpca.6b02253 J. Phys. Chem. A 2016, 120, 3663−3669

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The Journal of Physical Chemistry A ref 3. The aqueous pKa value of HCl has been estimated by McGrath et al.,5 using a combined Monte Carlo simulation/ quantum chemical approach. Values −7.1 and −7.5 were obtained, on the basis of different assumptions. Zhang et al. investigated gas-phase and aqueous acidities of HClO4 using a variety of computational methods.6 The authors claim that they were successful in reproducing experimental aqueous pKa of perchloric acid (−10) as reported by Brownstein and Stillman.7 However, it is unclear whether this value can indeed be called an experimental aqueous pKa value, since the experiments were actually carried out in a mixture of liquid SO2 and water. DMSO is probably the second most widely used solvent for pKa determination. Being aprotic and polarizable, DMSO is by its chemical nature very different from water. Nevertheless, like water, it has high dielectric constant (ε = 46)8 to favor charge separation. In addition, DMSO has high basicity. If judged by the proton transfer energy, ΔGtr(H+, H2O → DMSO) = −4.6 kcal mol−1,9 then DMSO is in fact more basic than water. These properties make DMSO an excellent ionizing solvent. The situation with pKa values of strong acids in DMSO is even more problematic than in water. The available experimental pKa values of strong acids in DMSO mostly come from the works of McCallum and Pethybridge,10 as well as Fujinaga and Sakamoto.11 Both groups report some of the strong acids as fully dissociated in DMSO and the pKa values of others slightly above and around zero. At first the pKa values around zero might seem reasonable: it is well-known that the large majority of acid pKa values in DMSO are (significantly) higher than in water. However, this refers first of all to weak and medium-strength acids, which in water receive substantial stabilization of their anions via solvation. As acids get stronger and charge better delocalized in their anions, the difference between aqueous and DMSO pKa values decreases. For example, the pKa of phenol is 10.0 in water,12 which is much lower than 18.0 in DMSO.13 At the same time, the pKa value of 2,4,6-trinitrophenol is 0.4 in water12 and around 0 in DMSO,14 i.e., roughly equal. Based on this and considering the higher proton solvation energy in DMSO than in water, it could be expected that the pKa values of strong acidsespecially ones with efficient charge stabilization in their anions, i.e., HClO4 and CF3SO3Hshould be much lower than zero in DMSO and possibly even lower than in water. In addition, there are experimental reasons, why measurements of pKa values below zero can easily yield erroneously elevated values, which are discussed in ref 15. The aim of this work is to collect the available data on the aqueous and DMSO pKa values of the following strong acids HCl, HBr, HI, HClO4, CF3SO3Hand carry out high-level computations using a range of methods for computations both in the gas phase and in solution. The resulting pool of data is then critically examined and for every acid the most probable aqueous and DMSO pKa values are proposed together with uncertainty estimates.

Scheme 1. Thermodynamics of Proton Abstraction in Gas Phase and Solution

pK a =

ΔGacid,s RT ln(10)

(1)

ΔGacid,s = ΔGacid,g (AH) − ΔGs(AH) + ΔGs(A−) + ΔGs(H+) + RT ln(24.46)

(2)

The first term in Equation 2 is either experimental or calculated gas-phase acidity (GA) of AH, the next three terms are Gibbs free energies of solvation for the standard state of mol L−1 of the neutral acid, its anion, and the proton, respectively, and the last term reflects the change in the standard conditions from 1 atm to 1 mol L−1 for the gas-phase part of the cycle. The GA values of HCl, HBr, HClO4, and TfOH were calculated from the thermodynamics of acid dissociation equilibrium using a variety of high-level compound energy calculation methods including G3MP2,16 G4MP2,17 G4,18 CBS-QB3,19,20 CBS-4M,20,21 W1BD,22 and W1RO.22,23 Gasphase acidity of HI was obtained from the raw coupled cluster theory with single, double, and noniterative triple substitutions (CCSD(T))24−28 using the second-order Douglas−Kroll−Hess (DKH-2) scalar relativistic Hamiltonian29−32 and corresponding aug-cc-pVQZ-DK basis set,33 which includes diffuse exponents on an iodine atom. The values of ΔGs(AH) and ΔGs(A−) were calculated as the differences in SCF energy of the structure in solution and in the gas phase.34 Polarized continuum approach35 was selected to account for the changes in solute environment upon solvation. Various combinations of CPCM,36,37 SVPE,38−40 SMVLE,41 and SMD42 implicit solvation models with Hartree−Fock, B3LYP and M05-2X methods were applied in water while in DMSO SMD/B3LYP, SMD/M05-2X, and SMD/M06-2X methods were used. Because of its intrinsic conductor boundary approach the CPCM model is expected to have some advantages over other methods in high permittivity limit of aqueous solvation. On the other hand, SMVLE, unlike other methods selected in the present study, includes an additional local electrostatics term to improve the description of solute− solvent interaction in the first solvation shell and, therefore, is also a method of choice in the case of water because of its potential ability to provide viable alternative to the complicated cluster-continuum approach. 6-31G(d), 6-31+G(d) and 6-31+G(d,p) split valence basis sets of double ζ quality with and without diffuse exponents on heavy atoms were used for all studied structures except HI. For the latter, QZP-DKH basis set from Jorge’s group43 was used in

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COMPUTATIONAL METHODS The calculation of aqueous and DMSO acidities (expressed as pKa values) of HCl, HBr, HI, HClO4, and TfOH is based on the direct thermodynamic cycle of proton abstraction equilibrium presented in Scheme 1. To calculate pKa values, Equation 1 was applied together with the corresponding expansion for ΔGacid,s: 3664

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The Journal of Physical Chemistry A Table 1. Gas-Phase Acidities and pKa Values in Water and DMSOa acids methods Gas Phase G3MP2 G4MP2 G4 CBS-QB3 CBS-4M CCSD(T)/aug-cc-PVQZ-dk W1BD W1RO expt.b recommended value Watere SMVLE/HF/6-31+G(d) SVPE/HF/6-31+G(d) CPCM/HF/6-31G(d) CPCM/HF/6-31+G(d) CPCM/HF/6-31G(d)//6-31+G(d) SMD/M05-2X/6-31+G(d,p) expt./SMD/M05-2X/6-31+G(d,p) expt./CPCM/HF/6-31G(d) expt./CPCM/HF/QZP-DKH expt./CPCM/B3LYP/QZP-DKH recommended value DMSOe SMD/M05-2X/6-31+G(d,p) SMD/M05-2X/6-31G(d) expt./SMD/M05-2X/6-31+G(d,p) expt./SMD/M05-2X/6-31G(d) expt./SMD/M06-2X/QZP-DKH expt./SMD/B3LYP/QZP-DKH recommended value

HCl

HBr

HI

HClO4

TfOH

293.2 294.2 293.5 292.1 291.6

292.4 292.5 291.8 290.8 289.4

293.5 293.5

292.7

‑1

GA Values (kcal mol ) 328.2 329.2 329.3 326.8 330.1

318.6 318.6 318.1 318.4 319.6 310.8

327.8 327.7 328.0 328.1 ± 0.1 328.1 ± 0.1

318.3 318.3 ± 0.2 318.3 ± 0.1

−8.64 −0.56 −5.08 −2.86 −5.09 0.92 −6.12 (−6.16) −5.86 (−5.90)

−12.05 −5.19 −9.70 −6.45 −9.70 1.68 −9.69 (−9.58) −8.83 (−8.72)

−5.9 ± 0.4

−8.8 ± 0.8

−1.58 −3.55 −1.95 −2.00

−0.86 −1.81 −6.73 −6.76

−2.0 ± 0.6

−6.8 ± 0.8

309.2 309.3 ± 0.1 309.3 ± 0.1 pKa Values

−11.96f −8.80f (−8.28f) −9.88 (−9.36) −9.98 (−9.46) −9.5 ± 1.0 pKa Values −14.16f −14.08f −10.27f −10.19f −10.93 −10.93 −10.9 ± 1.0

293.5 ± 0.5

299.5c 298.8d 292.7 ± 0.5

−14.01 −11.43 −15.23 −14.67 −15.24 −15.91

−15.40 −10.58 −14.65 −13.80 −14.65 −14.61

−15.2 ± 2.0

−14.7 ± 2.0

−14.68 −15.10

−13.86 −14.68

−14.9 ± 2.0

−14.3 ± 2.0

a

Uncertainties of recommended values correspond to ca. 90% probability and are estimated taking into account the results of the different approaches together with their expected reliability. bHCl, HBr, HI: first GA value from ref 51, second from ref 50. cExperimental GA value from ref 54. dExperimental GA value from ref 55. eThe pKa values designated as expt. are based on experimental GA values and Gibbs free energies of solvation of respective anions from ref 49 or ref 47 (in parentheses). fLANL2DZ basis set and ECP on iodine atom.

software.44 SVPE and SMVLE calculations were based on GAMESS implementation.45,46 The aqueous ΔGs(H+) value −264.0 kcal mol−1 at 1 atm, reported by Tissandier et al.,47 was corrected for the change in standard conditions (−265.9 kcal mol−1 at 1M). The DMSO ΔGs(H+) value −270.0 kcal mol−1 was used.48 The similar value of ΔGs(H+) in DMSO (−270.5 kcal mol−1) was also obtained by Fawcett.49 The experimental values of ΔGs(A−) for Cl−, Br− and I− were taken from refs 47 and 49.

conjunction with the DKH-2 approach to account for relativistic effects associated with core electrons of iodine atom. In some calculations, an alternative approach with the LANL2DZ basis set and the corresponding ECP on iodine atom was applied. The geometries of all AH and A− structures were optimized in water and DMSO with the exception of SVPE and SMVLE calculations of HClO4 and TfOH in water, where gas-phase optimized geometries were used instead because excessive values estimated by numerical gradient evaluation at a random step during the search prevented localization of the proper minima for these acids in the presence of solvent. Using the same computational method and basis set combinations the optimized geometries and reference energies were obtained in the gas phase. All stationary points were verified by vibrational analysis to be true minima on the potential energy surface. The default cavities based on the intrinsic atomic Coulomb radii or UFF radii were applied in SMD and CPCM calculations, respectively. For SVPE and SMVLE calculations, the default isodensity value of 0.001 was used. The CPCM and SMD calculations were carried out using the Gaussian09

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RESULTS AND DISCUSSION The results of the GA and pKa calculations are presented in Table 1. Gas-Phase Acidities. The experimental gas-phase acidity values of hydrogen halides were taken from the NIST Standard Reference Database.50 For these acids, another set of GA values closely matching the corresponding NIST data is available from ref 51. The experimental gas-phase acidity of HCl is based on the ΔHacid(HCl) value from threshold ion-pair production spectroscopy. The experimental GA values of HBr and HI were obtained using a thermochemical cycle composed of H−Hal 3665

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The Journal of Physical Chemistry A

(HCl) and −9.69 (HBr). For HCl, SMVLE and CPCM treatment for both neutral and anionic species results in pKa values of −8.64 and −5.08, respectively. For HBr, the same approach provides aqueous pKa values of −12.05 and −9.70. The results of SVPE calculations are probably less reliable for both HCl and HBr. The same conclusion is obviously valid for the case where the ΔGs values of both neutral and anionic structures were calculated using the SMD method. The pKa of HI calculated using CPCM method combined with relativistic DKH-2 approach for HI and experimental ΔGs values for I− is in the range of −9.36 to −9.98. The corresponding value based on SMD/M05-2X/6-31+G(d,p)/ LANL2DZ treatment for HI is −8.80, while the same treatment of both HI and I− provides more acidic value of −11.96. The pKa of perchloric acid is probably between −14.01 (SMVLE) and −15.23 (CPCM). The value obtained from SVPE procedure is less acidic (−11.43), while the SMD approach gives somewhat higher acidity (−15.91). The results of CPCM and SMVLE calculations of triflic acid are −14.65 and −15.40 pKa units, respectively. Again, the SVPE result is less acidic (−10.58), while the SMD result is very close to the CPCM value (−14.61). However, it should be noted that the discrepancy in GA of TfOH is rather significant and, therefore, using the NIST experimental value of 299.5 kcal mol−1 would change the pKa value remarkably in the less acidic direction (pKa estimate −9.64 using CPCM). Comparison of the present results with the data from other sources could provide some additional insight into acidic properties of the investigated strong acids. The COSMO-RS calculations2 indicated that pKa values are −14 for HCl and −15 for HBr, being probably far too acidic. For TfOH, the COSMO-RS value of pKa in water was estimated as −4.45, while SMD method provided an aqueous pKa range of −12.9 to −18.1.2 The latter estimate is generally consistent with results of the present CPCM, SMD, and SMVLE calculations. Gutowski and Dixon calculated the aqueous pKa of TfOH using the combination of G3(MP2) and COSMO implicit solvation model.4 Their pKa value of −14.2 is within 0.5 pKa units from the present CPCM and SMD pKa values. McGrath et al.5 estimated aqueous pKa of HCl at 300 K using direct thermodynamic cycle from experimental values of GA and Gibbs free energy of solvation of chloride and the proton, while the ΔGs value for HCl was calculated using the SM8T method. The resulting pKa value was −7.08. The experimental ΔGaq value for the deprotonation equilibrium at 300 K57 is less negative than the value obtained by McGrath et al. (−8.4 kcal mol−1 vs −9.7 kcal mol−1) and the corresponding experimental pKa value is −6.1. This experimental value compares well with our quasi-experimental estimate of −5.9 pKa units. Zhang et al. obtained aqueous pKa value of perchloric acid of around −10.6 For all reported combinations of gas-phase and solvation methods except gas-phase HF/6-31G(d) the pKa spans the range of −6.8 to −11.1. The least acidic pKa value from the present study is −11.4 from SVPE calculation. A closer look at calculated solvation free energies reveals significant differences between the values for neutral HClO4 from the present study and those reported by Zhang et al. while the corresponding values for ClO4− are rather similar in both studies. These differences can be traced down to the changes in default parameters of PCM implementation introduced in Gaussian09 as compared to the older Gaussian03 version used by Zhang et al. The changes in default calculation settings apparently affect the free energy of solvation of HClO4 and

bond homolytic dissociation, ionization energy of the hydrogen atom, and electron affinity of the halogen atom.51 The high accuracy of the GA values is demonstrated by their uncertainties, which in the case of HHal acids are in the range of 0.002 to 0.048 kcal mol−1.51 The calculated GA values for HCl compare well with the experimental value of 328.1 kcal mol−1. The best match is observed for G3MP2 and W1BD methods. A similar conclusion is valid for HBr, where the difference between the calculated value and experimental value of 318.3 kcal mol−1 is 0.3 kcal mol−1 or less with one notable exception - CBS-4M method overestimates GA by 1.3 kcal mol−1. In the case of HI, the GA value of 310.8 kcal mol−1 based on high-level CCSD(T)/aug-cc-PVQZ-dk calculations is reasonably close to the experimental value of 309.3 kcal mol−1. To achieve even better agreement with experiment, more rigorous treatment including the second order spin−orbit correction could be required for HI.52 The good agreement of high-level calculations with the GA values from refs 50 and 51 serves as further evidence of their high reliability. In the case of HClO4, besides GA also the standard enthalpy of deprotonation at 298.15K was calculated in order to enable comparison with the ΔHacid,g value of 299.9 ± 5.7 kcal mol−1 obtained by Meyer and Kass.53 The ΔHacid,g value 300.2 kcal mol−1, obtained with both W1BD and W1RO, is in excellent agreement with the experiment. This agreement supports the perchloric acid GA value of 293.5 kcal mol−1 obtained using the same methods. Similar computational GA values were reported in ref 6. The results of GA calculation for TfOH disagree with the reported experimental values of 299.5 ± 2.0 kcal mol−1 (ref 54) and 298.8 ± 2.5 kcal mol−1 (ref 55). However, the present TfOH calculation results are in good agreement with the published results of other high-level calculations carried out for this acid.4 In addition, the acidic part of the gas-phase acidity scale, originally presented in ref 54, has been recently reexamined56 and the GA values of a number of strong acids were systematically revised downward by up to 5 kcal mol−1. TfOH was not included in the revision but it is in the same acidity range, and therefore some downward revision of its experimental GA is expected. For this reason, the value of 292.7 kcal mol−1 from W1BD calculation can be considered currently as one of the best available estimates for the GA of TfOH besides the values of 293.0 kcal mol−1 and 292.9 kcal mol−1 from CCSD(T)/CBS calculations with and without additional tight d function on S atom, respectively, as reported by Gutowski and Dixon.4 It follows that obtaining fresh experimental GA values for TfOH and also for HClO4 is a matter of high priority. Aqueous Acidities. The computational pKa values for HCl, HBr, and HI were based on experimental GA values. GA values for perchloric and triflic acids are set to the best computational values of 293.5 kcal mol−1 and 292.7 kcal mol−1, respectively. The pKa values of HCl, HBr, and HI designated in Table 1 as experimental are based on experimental ΔGs values of corresponding anions and either CPCM or SMD ΔGs values of AH. The pKa values based on calculated CPCM ΔGs values of HCl and HBr combined with experimental GA values and solvation Gibbs free energies of corresponding anions are −5.86 and −8.83, respectively. The same approach based on SMD ΔGs values of HCl and HBr results in pKa values of −6.12 3666

DOI: 10.1021/acs.jpca.6b02253 J. Phys. Chem. A 2016, 120, 3663−3669

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The Journal of Physical Chemistry A render it approximately 5 kcal mol−1 less negative than in the similar calculation with G03 defaults. In combination with the less negative value of Gibbs free energy of aqueous solvation of the proton (−264.61 kcal mol−1) used by Zhang et al. to calculate pKa, the differences in Gibbs free energy of solvation of HClO4 were among the main factors that shifted their value of pKa by 5.5 units in the less acidic direction as compared to the present study. Acidities in DMSO Solution. The computational procedure follows the same protocol as it was specified for aqueous acidities. The combination of experimental solvation free energies of Cl− and Br− with SMD/M05-2X/6-31+G(d,p) ΔGs values of the respective acids results in the acidity values of −1.95 and −6.73 pKa units. For HI, the similar approach with LANL2DZ basis set on iodine atom yields a pKa value of −10.27. Omission of diffuse exponents on chlorine and bromine atoms and polarization exponents on hydrogen results in marginal changes to pKa values. However, the full computational approach provides less acidic pKa estimates for HBr and more acidic pKa values for HI. For HCl SMD/M05-2X/6-31G(d) method provides clearly more negative pKa than the combined approach, while the SMD/M05-2X/6-31+G(d,p) method yields a pKa value close to the one obtained from the combined approach. The combined approach implementing the relativistic DKH2 Hamiltonian and the QZP-DKH basis set for HI results in a pKa value of −10.93. The estimated pKa range for perchloric acid is −14.68 to −15.10, while the acidity of triflic acid varies between −13.86 and −14.68 pKa units. Uncertainties of the pKa Values. The uncertainty bars of the pKa values were obtained taking into account the accuracies of the used GA values, the accuracies of the used solvation models, the agreement between the pKa values obtained with different approaches, and the expected accuracy of the experimental pKa values, if they exist. Not all of these accuracies are explicitly available as numerical values. Hence, it is not possible to carry out a rigorous uncertainty calculation, and the obtained uncertainties can be viewed first of all as expert estimates of approximate nature, similar to what has been used in ref 58. In spite of the approximate nature these estimates are expected to be useful for the users of the pKa values of this report and most importantly, will give the readers a clear signal that the proposed pKa values, even though carefully obtained, are certainly not high-accuracy values.

The recommended pKa values for HClO4 and TfOH were obtained from the recommended computational GA values, combined with the CPCM approach (the advantages of CPCM in relation to aqueous solvation are detailed in Computational Methods). For these acids, the pKa values from SMD calculations are well within uncertainty margins of the recommended pKa values. In the case of hydrogen halides in DMSO it was estimated that the most reliable, and recommended by us, pKa values are obtained by combining the experimental GA and ΔGs(Hal−) values with the SMD approach. The recommended pKa values for HClO4 and TfOH were obtained from the recommended computational GA values, combined with the SMD approach, which is the Gaussian default and recommended method for calculation of the free energy of solvation and is well suited for calculations outside the high permittivity limit where, in contrast to aqueous solvation, the advantages of CPCM method are not as pronounced. The comparison of the recommended pKa values in water and DMSO reveals that acidities of HCl and HBr are higher in water than in DMSO which is expected. However, for HClO4 and TfOH the difference is rather small, and in the case of HI, the acidic strength is even reversed. The possible reason is the high polarizability of the iodide ion, which therefore receives significant additional stabilization in DMSOa high-polarizability solventvia dispersion forces. This is not the case with the other, less polarizable, anions studied in this work.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b02253. Gibbs free energies, solvation free energies, and structures of the studied acids and corresponding anions. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: aleksander.trummal@kbfi.ee; phone: +372 6398 311. *E-mail: [email protected]; phone: +372 7375 259. Author Contributions

The manuscript was written through contributions of all authors. Notes

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The authors declare no competing financial interest.

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CONCLUSIONS For each acid chosen as the focus of this study, the recommended acidity values together with uncertainty estimates in the gas phase, water, and DMSO are presented in Table 1. In the gas phase, GA values from the NIST database have been adopted for hydrogen halides, while the values from high-level W1BD calculations were selected for perchloric and triflic acids. In the case of hydrogen halides in water, it was estimated that the most reliable, and recommended by us, pKa values for HHal are obtained by combining the experimental GA and ΔGs(Hal−) values with the CPCM approach. It is worth mentioning that a similar approach based on SMD treatment of HHal resulted in pKa estimates being within 1.2 pKa units from the recommended values in all cases. However, the full SMD approach yields extremely low acidities for both HCl and HBr.

ACKNOWLEDGMENTS This work was in part supported by institutional research funding IUT14-20 (TLOKT14014I) and IUT23-7 from the Estonian Ministry of Education and Research and European Regional Development Fund Projects TK134 and TK141.

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REFERENCES

(1) Dissociation Constants of Inorganic Acids and Bases in Aqueous Solution; Perrin, D. D., Ed.; Pergamon: Toronto, 1982. (2) Raamat, E.; Kaupmees, K.; Ovsjannikov, G.; Trummal, A.; Kütt, A.; Saame, J.; Koppel, I.; Kaljurand, I.; Lipping, L.; Rodima, T.; et al. Acidities of Strong Neutral Brønsted Acids in Different Media. J. Phys. Org. Chem. 2013, 26, 162−170. (3) Guthrie, J. P. Hydrolysis of Esters of Oxy Acids: pKa Values for Strong Acids; Brønsted Relationship for Attack of Water at Methyl; Free Energies of Hydrolysis of Esters of Oxy Acids; and a Linear 3667

DOI: 10.1021/acs.jpca.6b02253 J. Phys. Chem. A 2016, 120, 3663−3669

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DOI: 10.1021/acs.jpca.6b02253 J. Phys. Chem. A 2016, 120, 3663−3669