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

Subscriber access provided by SUNY DOWNSTATE

Article

Acidity of Strong Acids in Water and Dimethyl Sulfoxide Aleksander Trummal, Lauri Lipping, Ivari Kaljurand, Ilmar A. Koppel, and Ivo Leito J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b02253 • Publication Date (Web): 26 Apr 2016 Downloaded from http://pubs.acs.org on April 29, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 10

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

The Journal of Physical Chemistry

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

ABSTRACT: Careful analysis and comparison of the available acidity data of HCl, HBr, HI, HClO4 and CF3SO3H in water, 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.

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 DMSO. The acidities – in terms of proton activity of their dilute aqueous solutions – of these acids are leveled. This does not mean, however, that the acidities of their molecules – in terms of proton donating abilities – in water or DMSO 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 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 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 .. -7.4; -8 .. -9; -9 .. -9.5 and -1.5 .. -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 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 experimental aqueous

ACS Paragon Plus Environment


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.

Scheme 1. Thermodynamics of proton abstraction in gas phase and solution.

∆Gacid,g

∆Gacid,s

∆Gs

A-g + H+g

AHg

∆Gs

pKa value, since the experiments were actually carried out in a mixture of liquid SO2 and water. Dimethyl sulfoxide (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, ∆Gtr(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.

∆Gs

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 2 of 10

A-s + H+s

AHs

To calculate pKa values Equation (1) was applied together with the corresponding expansion for ∆Gacid,s:

pK a =

∆Gacid,s RTln(10)

(1)

∆Gacid,s = ∆Gacid,g(AH) – ∆Gs(AH) + ∆Gs(A-) + ∆Gs(H+) + RTln(24.46) (2) The first term in Equation (2) is either experimental or calculated gas-phase acidity (GA) of AH, 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 L1 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 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 Gas-phase acidity of HI was obtained from the raw coupled cluster theory with single, double and non-iterative 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 set33 which includes diffuse exponents on iodine atom. The values of ∆Gs(AH) and ∆Gs(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 SMVLE41 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 additional local electrostatics


Page 3 of 10

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


term to improve 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 conjunction with DKH2 approach to account for relativistic effects associated with core electrons of iodine atom. In some calculations, alternative approach with 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 software.44 SVPE and SMVLE calculations were based on GAMESS implementation.45,46 The aqueous ∆Gs(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 ∆Gs(H+) value -270.0 kcal mol-1 was used.48 The similar value of ∆Gs(H+) in DMSO (-270.5 kcal mol1 ) was also obtained by Fawcett.49 The experimental values of ∆Gs(A-) for Cl-, Br- and I- were taken from refs 47 and 49. RESULS 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 ∆Hacid(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 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. 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 a 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 ∆Hacid,g value of 299.9 ± 5.7 kcal mol-1 obtained by Meyer and Kass53. The ∆Hacid,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 mol1 (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 highlevel calculations carried out for this acid4. 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 downwards 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 ∆Gs values of corresponding anions and either CPCM or SMD ∆Gs values of AH. The pKa values based on calculated CPCM ∆Gs values of HCl and HBr combined with experimental GA



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 4 of 10

values and solvation Gibbs free energies of corresponding anions are -5.86 and -8.83, respectively. The same approach based on SMD ∆Gs values of HCl and HBr results in pKa values of -6.12 (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 -9.7. The results of Table 1. Gas-phase acidities and pKa values in water and DMSO.a Methods

Acids HCl

HBr

HI

HClO4

TfOH

-1

Gas phase

GA values (kcal mol )

G3MP2

328.2

318.6

293.2

292.4

G4MP2

329.2

318.6

294.2

292.5

G4

329.3

318.1

293.5

291.8

CBS-QB3

326.8

318.4

292.1

290.8

CBS-4M

330.1

319.6

291.6

289.4 292.7

CCSD(T)/aug-cc-PVQZ-dk

310.8

W1BD

327.8

293.5

W1RO

327.7

293.5

Expt.

328.0 328.1 ± 0.1

318.3 318.3 ± 0.2

309.2 309.3 ± 0.1

Recommended value

328.1 ± 0.1

318.3 ± 0.1

309.3 ± 0.1

b

Water

e

c

299.5 d 298.8 293.5 ± 0.5 292.7 ± 0.5

pKa values

SMVLE/HF/6-31+G(d)

-8.64

-12.05

-14.01

-15.40

SVPE/HF/6-31+G(d)

-0.56

-5.19

-11.43

-10.58

CPCM/HF/6-31G(d)

-5.08

-9.70

-15.23

-14.65

CPCM/HF/6-31+G(d)

-2.86

-6.45

-14.67

-13.80

CPCM/HF/6-31G(d)//6-31+G(d)

-5.09

-9.70

-15.24

-14.65

SMD/M05-2X/6-31+G(d,p)

0.92

1.68

-15.91

-14.61

-15.2 ± 2.0

-14.7 ± 2.0

f

-14.68

-13.86

f

-15.10

-14.68

-11.96

Expt./SMD/M05-2X/6-31+G(d,p)

-6.12 (-6.16)

-9.69 (-9.58)

Expt./CPCM/HF/6-31G(d)

-5.86 (-5.90)

-8.83 (-8.72)

f

f

-8.80 f (-8.28 )

Expt./CPCM/HF/QZP-DKH

-9.88 (-9.36)

Expt./CPCM/B3LYP/QZP-DKH

-9.98 (-9.46)

Recommended value

-5.9 ± 0.4

-8.8 ± 0.8

e

pKa values

DMSO

SMD/M05-2X/6-31+G(d,p)

-9.5 ± 1.0

-1.58

-0.86

-14.16

SMD/M05-2X/6-31G(d)

-3.55

-1.81

-14.08

Expt./SMD/M05-2X/6-31+G(d,p)

-1.95

-6.73

-10.27

Expt./SMD/M05-2X/6-31G(d)

-2.00

-6.76

-10.19

f

f

Expt./SMD/M06-2X/QZP-DKH

-10.93

Expt./SMD/B3LYP/QZP-DKH

-10.93


Page 5 of 10

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

Recommended value

The Journal of Physical Chemistry -2.0 ± 0.6

-6.8 ± 0.8

-10.9 ± 1.0

-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 b of the different approaches together with their expected reliability. HCl, HBr, HI: first GA value from ref 51, second from ref c d e 50. Experimental GA value from ref 54. Experimental GA value from ref 55. The pKa values designated as Expt. are based f on experimental GA values and Gibbs free energies of solvation of respective anions from ref 49 or ref 47 (in parentheses). LANL2DZ basis set and ECP on iodine atom.

SVPE calculations are probably less reliable for both HCl and HBr. The same conclusion is obviously valid for the case where the ∆Gs 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 ∆Gs values for I- is in the range of -9.36 to -9.98. The corresponding value based on SMD/M05-2X/631+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 probably varies between -14.01 (SMVLE) and -15.23 (CPCM). The value obtained from SVPE procedure is less acidic (-11.43) while 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 CPCM value (-14.61). However, it should be noted that discrepancy in GA of TfOH is rather significant and, therefore, using NIST experimental value of 299.5 kcal mol-1 would change 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 COSMO-RS value of pKa in water was estimated as -4.45 while SMD method provided aqueous pKa range of -12.9 to -18.12. 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 300K using direct thermodynamic cycle from experimental values of GA and Gibbs free energy of solvation of chloride and the proton while ∆Gs value for HCl was calculated using the SM8T method. The resulting pKa value was -7.08. The experimental ∆Gaq value for the deprotonation equilibrium at 300K57 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 free energy of solvation of HClO4 and render it approximately 5 kcal mol-1 less negative than in the similar calculation with G03 defaults. In combination with 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 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) ∆Gs 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 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, 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 combined approach while SMD/M05-2X/6-31+G(d,p) method yields pKa value close to the one obtained from combined approach. The combined approach implementing relativistic DKH-2 Hamiltonian and QZP-DKH basis set for HI results in pKa value of -10.93. The estimated pKa range for perchloric acid is -14.68 -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



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

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 clear signal that the proposed pKa values, even though carefully obtained, are certainly not high-accuracy values.

Page 6 of 10

ASSOCIATED CONTENT Supporting Information. Gibbs free energies, solvation free energies, and structures of the studied acids and corresponding anions. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors *[email protected], phone: +372 6398 311 *[email protected], phone: +372 7375 259

Author Contributions CONCLUSIONS For each acid being in 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 ∆Gs(Hal-) values with the CPCM approach. It is worth mentioning that 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, full SMD approach yields extremely low acidities for both HCl and HBr. 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 ∆Gs(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 quite expected. However, for HClO4 and TfOH the difference is rather small and in 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.

The manuscript was written through contributions of all authors.

Funding Sources Grants IUT14-20 and IUT23-7 from the Estonian Ministry of Education and Research and European Regional Development Fund projects TK134 and TK141.

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENT 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.

ABBREVIATIONS REFERENCES 1. 2.

3.

4.

5.

6.

7.

8.

Dissociation Constants of Inorganic Acids and Bases in Aqueous Solution. Perrin, D. D., ed. Pergamon, Toronto, 1982. 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. 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 Relationship between Free Energy of Hydrolysis and pKa holding over a Range of 20 pK Units. Can. J. Chem. 1978, 56, 2342-2354. Gutowski, K. E.; Dixon, D. A. Ab Initio Prediction of the Gasand Solution-Phase Acidities of Strong Brønsted Acids: The Calculation of pKa Values Less Than -10. J. Phys. Chem. A 2006, 110, 12044-12054. McGrath, M. J.; Kuo, I-F. W.; Ngouana, B. F.; Ghogomu, J. N.; Mundy, C. J.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.; Siepmann, J. I. Calculation of the Gibbs Free Energy of Solvation and Dissociation of HCl in Water via Monte Carlo Simulations and Continuum Solvation Models. Phys. Chem. Chem. Phys. 2013, 15, 13578−13585. Zhang J.; Sun, Y.; Mao, C.; Gao, H.; Zhou, W.; Zhou, Z. Theoretical Study of pKa for Perchloric Acid. J. Mol. Struct.: THEOCHEM 2009, 906, 46-49. Brownstein, S.; Stillman, A. E. Proton Resonance Shifts of Acids in Liquid Sulfur Dioxide. J. Phys. Chem. 1959, 63, 20612062. Reichardt, C.; Welton, T. Solvents and Solvent Effects in Organic Chemistry, 4th ed., Wiley-VCH, Weinheim, 2011.


Page 7 of 10 9.

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

10. 11. 12.

13. 14.

15.

16.

17.

18. 19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

The Journal of Physical Chemistry Marcus, Y.; Kamlet, M. J.; Taft, R. W. Linear Solvation Energy Relationships. Standard Molar Gibbs Free Energies and Enthalpies of Transfer of Ions from Water into Nonaqueous Solvents. J. Phys. Chem. 1988, 92, 3613−3622. McCallum, C.; Pethybridge, A. D. Electrochim. Acta 1975, 20, 815-818. Fujinaga, T.; Sakamoto, I. J. Electroanal. Chem. 1977, 85, 185201. Kortüm, G.; Vogel, W.; Andrussow, K. Dissotziationskonstanten Organischen Säuren in wasseriger Lösung, Butterworths, London, 1961. Bordwell, F. G. Equilibrium Acidities in Dimethyl Sulfoxide Solution. Acc. Chem. Res. 1988, 21, 456–463. Kolthoff, I. M.; Chantooni, J. K., Jr.; Bhowmik, S. Dissociation Constants of Uncharged and Monovalent Cation Acids in Dimethyl Sulfoxide. J. Am. Chem. Soc. 1968, 90, 23-28. Kaupmees, K.; Tolstoluzhsky, N.; Raja, S.; Rueping, M.; Leito, I. On the Acidity and Reactivity of Highly Effective Chiral Brønsted Acid Catalysts: Establishment of an Acidity Scale. Angew. Chem. Int. Ed. 2013, 52, 11569-11572. Curtiss, L. A.; Redfern, P. C.; Raghavachari, K.; Rassolov, V.; Pople, J. A. Gaussian-3 Theory Using Reduced Møller-Plesset Order. J. Chem. Phys. 1999, 110, 4703-4709. Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 Theory Using Reduced Order Perturbation Theory. J. Chem. Phys. 2007, 127, 124105. Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 Theory. J. Chem. Phys. 2007, 126, 084108. Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VI. Use of Density Functional Geometries and Frequencies. J. Chem. Phys. 1999, 110, 2822-2827. Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VII. Use of the Minimum Population Localization Method. J. Chem. Phys. 2000, 112, 6532-6542. Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A., Jr. A Complete Basis Set Model Chemistry. V. Extensions to Six or More Heavy Atoms. J. Chem. Phys. 1996, 104, 2598-2619. Barnes, E. C.; Petersson, G. A.; Montgomery, J. A., Jr.; Frisch, M. J.; Martin, J. M. L. Unrestricted Coupled Cluster and Brueckner Doubles Variations of W1 Theory. J. Chem. Theor. Comput. 2009, 5, 2687-2693. Martin J. M. L.; de Oliveira, G. Towards Standard Methods for Benchmark Quality Ab Initio Thermochemistry - W1 and W2 Theory. J. Chem. Phys. 1999, 111, 1843-1856. Cížek, J. in Advances in Chemical Physics, (Eds.: R. LeFebvre, C. Moser), Vol. 14, pp. 35-89, Wiley Interscience, New York, 1969. Purvis, G. D. III; Bartlett, R. J. A Full Coupled-Cluster Singles and Doubles Model - the Inclusion of Disconnected Triples. J. Chem. Phys. 1982, 76, 1910-1918. Scuseria, G. E.; Janssen, C. L.; Schaefer, H. F. III An Efficient Reformulation of the Closed-Shell Coupled Cluster Single and Double Excitation (CCSD) Equations. J. Chem. Phys. 1988, 89, 7382-7387. Scuseria, G. E.; Schaefer, H. F. III Is Coupled Cluster Singles and Doubles (CCSD) More Computationally Intensive than Quadratic Configuration-Interaction (QCISD)? J. Chem. Phys. 1989, 90, 3700-3703. Pople, J. A.; Head-Gordon, M.; Raghavachari, K. Quadratic Configuration Interaction - a General Technique for Determining Electron Correlation Energies. J. Chem. Phys. 1987, 87, 59685975. Douglas M.; Kroll, N. M. Quantum Electrodynamical Corrections to Fine-Structure of Helium. Ann. Phys. (N.Y.) 1974, 82, 89-155. Hess, B. A. Applicability of the No-Pair Equation with FreeParticle Projection Operators to Atomic and Molecular-Structure Calculations. Phys. Rev. A 1985, 32, 756-763.

31. Hess, B. A. Relativistic Electronic-Structure Calculations Employing a 2-Component No-Pair Formalism with External-Field Projection Operators. Phys. Rev. A 1986, 33, 3742-3748. 32. Jansen G.; Hess, B. A. Revision of the Douglas-Kroll Transformation. Phys. Rev. A 1989, 39, 6016-6017. 33. Bross, D. H.; Peterson, K. A. Correlation Consistent, Douglas– Kroll–Hess Relativistic Basis Sets for the 5p and 6p Elements. Theor. Chem. Acc. 2014, 133, 1434. 34. Ho, J.; Klamt, A.; Coote, M. L. Comment on the Correct Use of Continuum Solvent Models. J. Phys. Chem. A 2010, 114, 13442−13444. 35. Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 29993093. 36. Barone, V.; Cossi, M. Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model. J. Phys. Chem. A 1998, 102, 1995-2001. 37. Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. Energies, Structures, and Electronic Properties of Molecules in Solution with the C-PCM Solvation Model. J. Comp. Chem. 2003, 24, 669681. 38. Chipman, D. M. Charge Penetration in Dielectric Models of Solvation. J. Chem. Phys. 1997, 106, 10194-10206. 39. Zhan, C.-G.; Bentley, J.; Chipman D. M. Volume Polarization in Reaction Field Theory. J. Chem. Phys. 1998, 108, 177-192. 40. Chipman, D. M. New Formulation and Implementation for Volume Polarization in Dielectric Continuum Theory. J. Chem. Phys. 2006, 124, 224111-1/10. 41. Liu, J.; Kelly, C. P.; Goren, A. C.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.; Zhan C.-G. Free Energies of Solvation with Surface, Volume, and Local Electrostatic Effects and Atomic Surface Tensions to Represent the First Solvation Shell. J. Chem. Theory Comput. 2010, 6, 1109-1117. 42. Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113, 6378−6396. 43. Ceolin, G. A.; de Berrêdo, R. C.; Jorge, F. E. Gaussian Basis Sets of Quadruple Zeta Quality for Potassium through Xenon: Application in CCSD(T) Atomic and Molecular Property Calculations. Theor. Chem. Acc. 2013, 132, 1339. 44. Gaussian 09, Revision B.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian, Inc., Wallingford CT, 2009. 45. Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. et al. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347-1363. 46. Gordon, M. S.; Schmidt M. W. in Theory and Applications of Computational Chemistry: the first forty years (Eds.: C. E. Dykstra, G. Frenking, K. S. Kim, G. E. Scuseria), pp. 11671189, Elsevier, Amsterdam, 2005. 47. Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. J.; Earhart, A. D.; Coe, J. V. The Proton’s Absolute Aqueous Enthalpy and Gibbs Free Energy of Solvation from Cluster-Ion Solvation Data. J. Phys. Chem. A 1998, 102, 77877794. 48. Trummal, A.; Rummel, A.; Lippmaa, E.; Burk, P.; Koppel, I. A. IEF-PCM Calculations of Absolute pKa for Substituted Phenols in Dimethyl Sulfoxide and Acetonitrile Solutions. J. Phys. Chem. A 2009, 113, 6206-6212. 49. Fawcett, W. R. The Ionic Work Function and its Role in Estimating Absolute Electrode Potentials. Langmuir 2008, 24, 98689875. 50. Bartmess, J. E. in Negative Ion Energetics Data in NIST Standard reference Database Number 69, (Eds.: W. G. Mallard, P. J. Linstrom), National Institute of Standards and Technology, Gaithersburg, MD, 1997, 20899 (http://webbook.nist.gov).



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

51. Ervin, K. M.; DeTuri, V. F. Anchoring the Gas-Phase Acidity Scale. J. Phys. Chem. A 2002, 106, 9947-9956. 52. Feller, D.; Peterson, K. A.; de Jong, W. A.; Dixon, D. A. Performance of Coupled Cluster Theory in Thermochemical Calculations of Small Halogenated Compounds. J. Chem. Phys. 2003, 118, 3510-3522. 53. Meyer, M. M.; Kass, S. R. Experimental and Theoretical GasPhase Acidities, Bond Dissociation Energies, and Heats of Formation of HClOx, x = 1–4. J. Phys. Chem. A 2010, 114, 4086−4092. 54. Koppel, I. A.; Taft, R. W.; Anvia, F.; Zhu, S.-Z.; Hu, L.-Q.; Sung, K.-S.; DesMarteau, D. D.; Yagupolskii, L. M.; Yagupolskii, Y. L.; Ignat’ev, N. V. et al. The Gas-Phase Acidities of Very Strong Neutral Brønsted Acids. J. Am. Chem. Soc. 1994, 116, 3047-3057. 55. Viggiano, A. A.; Henchman, M. J.; Dale, F.; Deakyne, C. A.; Paulson J. F. Gas-Phase Reactions of Weak Brønsted Bases I-, PO3-, HSO4-, FSO3-, and CF3SO3- with Strong Brønsted Acids H2SO4, FSO3H, and CF3SO3H - A Quantitative Intrinsic Superacidity Scale for the Sulfonic Acids XSO3H (X= HO, F, and CF3). J. Am. Chem. Soc. 1992, 114, 4299–4306. 56. Leito, I.; Raamat, E.; Kütt, A.; Saame, J.; Kipper, K.; Koppel, I. A.; Koppel, I.; Zhang, M.; Mishima, M.; Yagupolskii, L. M. et al. Revision of the Gas-Phase Acidity Scale below 300 kcal mol1 . J. Phys. Chem. A 2009, 113, 8421-8424. 57. Pokrovskii, V. A. Calculation of the Standard Partial Molal Thermodynamic Properties and Dissociation Constants of Aqueous HCl0 and HBr0 at Temperatures to 1000°C and Pressures to 5 kbar. Geochim. Cosmochim. Acta 1999, 63, 1107−1115. 58. Kaupmees, K.; Trummal, A.; Leito, I. Basicities of Strong Bases in Water: A Computational Study. Croat. Chem. Acta 2014, 87, 385–395.


Page 8 of 10

Page 9 of 10

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


Insert Table of Contents artwork here


9


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

82x44mm (300 x 300 DPI)


Page 10 of 10

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

Recommend Documents