Research 1..9

Article

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1 Superacidity of closo-Dodecaborate-Based Brønsted Acids: a DFT

2 Study ,† † † ‡ ‡ ,† 3 Lauri Lipping,* Ivo Leito, Ivar Koppel, Ingo Krossing, Daniel Himmel, and Ilmar A. Koppel* † 4 Institute of Chemistry, University of Tartu, 14a Ravila St., Tartu 50411, Estonia ‡ 5 Institute for Inorganic and Analytic Chemistry, University of Freiburg, 21 Albertstr., Freiburg D-79104, Germany

6 *S Supporting Information

7 ABSTRACT: The structures and intrinsic gas-phase acidities (GA) of some dodecaborane − 8 acids, the derivatives of YB H H(Y= PF ,NH,NF, NMe ), B H H , and B H H − 12 11 3 3 3 3 12 12 2 12 12 9 (HA, H2A, and HA , respectively) have been computationally explored with DFT B3LYP 10 method at the 6-311+G** level of theory as new possible directions of creating 11 superstrong Brønsted acids. Depending on the nature and number of the substituents 12 different protonation geometries were investigated. In general, the GA values of the neutral 13 systems varied according to the substituents in the following order: CF3 < F < Cl and in fl 14 case of anionic acids: CF3 < Cl < F. The dodecatri uoromethyl derivative of H2A, 15 B12(CF3)12H1H2, emerges as the strongest among the considered acids and is expected to 16 be in the gas phase at least as strong as the undecatrifluoromethyl carborane, 17 CB11(CF3)11H1H. The GA values of the respective monoanionic forms of the considered 18 acids all, but the (CF3)11 derivative, remained higher than the widely used threshold of ’ ’ 19 superacidity. The HA derivatives (Y = PF3,NF3)GAs were approximately in the same ’ fi 20 range as the H2A acids . In the case Y = NH3 or NMe3 the GA values were signi cantly fl 21 higher. Also, the pKa values of B12H12H2,CB11H12H, and their per uorinated derivatives in 1,2-dichloroethane (DCE) were fl 22 estimated with SMD and cluster-continuum model calculations. The obtained estimates of pKa values of the per uorinated 23 derivatives are by around 30 units lower than that of trifluoromethylsulfonylimide, making these acids the strongest ever fi 24 predicted in solution. The derivatives of B12H12H2 are as a rule not signi cantly weaker acids than the respective derivatives of 25 CB H H. This is important for expanding practical applicability of this type of acids and their anions, as they are synthetically 11 12 − 26 much more accessible than the corresponding CB11H12 derivatives.

27 ■ INTRODUCTION dinating), extremely inert anionic bases whose conjugate acids 51 1−9 1−4 are the strongest Brønsted acids presently known. These 52 28 Practical and fundamental reasons have motivated scientists anions have extremely low nucleophilicity, electrophilicity and 53 29 to search for molecules and molecular systems that are more 5,6 oxidizing activity and have been used as counterions for 54 30 acidic than known before. Several strategies have been strongly electrophilic cationic species that are also extremely 55 31 proposed to design highly acidic molecules. An obvious route is 12 8 strong acids. The first computational evidence that the 56 32 introducing electron withdrawing substituents (e.g., fluorination intrinsic gas-phase superacidity of boron-based acids can exceed 57 33 or trifluoromethylation) into already strong or superstrong that of sulfuric acid, the “classical” basis for definition of 58 34 Brønsted acids. Well-known examples are fluorosulfonic and superacidity, by many powers of ten was published in 2000 in 59 35 trifluoromethanesulfonic acids, which can be regarded as the work of some of the present authors with co-workers. It was 60 36 derivatives of sulfuric acid. Another much used approach is 61 37 increasing the hydrogen ion donor ability of a Brønsted acid followed by a density functional theory (DFT) investigation of − the intrinsic gas-phase acidities of some smaller carborane 62 38 HA by mixing it with a Lewis acid so that the anion A formed 13 63 39 in the ionization of HA is converted into the highly stabilized derivatives. Further computational extension and revision of the intrinsic gas-phase superacidity scale was carried out in 64 40 complex with this Lewis acid. This principle is operational in, 1 2009. 65 41 e.g., magic acid or HSbF6. Although, both of these acids are 42 strong they are prone to forming reaction side products by The practical chemical use of these novel reagents has yet to 66 43 means of fluorination. gather impetus. The main obstacle is the high cost and limited 67 44 The electron-withdrawing effects of substituents are availability of the monocarba-closo-borane acids and their salts. 68 45 especially powerful if synergized with the excellent charge The quantities that presently can be prepared via complex and 69 46 delocalization ability of the different spherical boron com- time-consuming synthetic pathways are suitable for obtaining 70 7−11 47 pounds. Decades of work on boron compounds and their 48 substituted derivatives have resulted in a new generation of Received: June 30, 2014 49 anions−derivatives of the closo-dodecaborate and monocarba- Revised: December 14, 2014 50 closo-dodecaborate anions−superweak (i.e., very weakly coor-

71 small quantities of valuable substances, enough for small scale calculations. In order to obtain reliable results, different possible 134 72 experiments, but not for extensive or large-scale use. However, protonation geometries and the effects of substituents on the 135 7 fi fi 73 there are developments taking place in this eld, as well. protonation site are compared. For the rst time the pKa values 136 14−19 74 In the recent reports some experiments of fundamental for the borane and carborane acid derivatives of that strength 137 75 interest have been reported made possible by the free acids are reported for 1,2-dichloroethane. 138 76 CB11XnR12‑nH (X = Cl, F; R = H, CH3; n = 6, 11). However, 77 the question about the availability of the derivatives of ■ METHODS 139 − 78 CB11H12 remains. Therefore, the quest for anions of similar Unless otherwise indicated, density functional theory (DFT) 140 2− 79 inertness and low basicity, but easier to prepare, is constantly calculations were carried out on B X H ‑ (X = F, Cl, and 141 12 n 12 n − 80 on. The interest in the derivatives of H2(B12X12) comes from a CF3; n = 0, 1, 6, 11, and 12) and YB12XnH11‑n (Y = PF3,NH3, 142 2− 81 fact that the salts of the starting compound B12H12 are NF3, and NMe3,X= F, Cl, CF3; n = 0, 1, 6, and 11) cages and 143 82 commercially available at a reasonable price. Furthermore, as their protonated forms at the B3LYP/6-311+G** level with the 144 2− 83 B12X12 are dianions, a useful approach to further increase Gaussian 09 system of programs with full thermal corrections 145 29 84 their acidity could be decreasing the availability of the negative to Gibbs energies at the optimized structures. In the largest 146 85 charge by using a single positively charged group, which turns systems where X = CF3 and n = 12 (n = 11 with the Y-borates), 147 86 the bianionic closo-dodecaborate into a monoanion. Besides a the vibrational analysis at the B3LYP/6-311+G** level failed, 148 30,31 87 positive charge this group should have electron-withdrawing so thermal corrections were calculated using the RI-BP86 / 149 32 33 88 properties, should not contain any well-defined protonation def-TZVP level with default RI-J auxiliary basis on the 150 89 centers and should be reasonably stable. Based on these corresponding optimized structures using the Turbomole 151 − + − + − + 34−36 90 considerations we have chosen the PF3 , NF3 , NH3 , and 6.4 program system (see the Discussion for details). 152 − + 91 NMe3 groups for this purpose. The starting position of the substituent insertion for the 153 20 92 In a recent report the solution-phase superacidities of two clusters without Y-group was considered as position 1 (Figure 154 f1 93 diprotic acids, based on the closo-dodecaborate anions 1). In the case of the Y-substituted borates the position 1 was 155 f1 94 H2(B12X12) (X = Cl, Br) have been estimated indirectly by 95 Reed et al. using the anions’ ν(NH) basicity scale based on NH + 96 stretching frequency shifts of Oct3NH in CCl4 induced by H- 97 bond formation between the latter cationic proton donor and 21,22 98 the superweak anionic base. Based on these results and the 99 ability of the derivatives of H2(B12X12) (X = Cl, Br) to 20 100 protonate benzene by forming [C6H7]2[B12X12] salts their 101 acid strength, even corresponding to the detachment of the 102 second proton, was considered to be comparable with the 23 103 respective carborane acids. These results were explained with 20 104 the hypothesis that “halogeno substituents on both anions 105 form an effective screen for negative charge that is delocalized ’ 106 and buried within the icosahedral cage”. Therefore, for accurate Figure 1. Numbering of closo-dodecaborate s vertexes. 107 experimental and computational estimation of intrinsic acidity 108 the careful analysis of possible protonation sites is necessary. the vertex with the Y-group. Replacement of the hydrogen 156 109 However, no direct measurement or computational estima- atoms with substituents was done subsequently in the following 157 110 tion of these acids in any solvent has been published according groups of vertexes (belts): 1, 2···6, 7···11, and 12. 158 111 to our best knowledge. For most of the acids several input geometries of protonated 159 112 Therefore, to give estimation about the acidity of closo- forms with different protonation sites were composed to 160 113 borane and carborane acids in solution, pKa values were determine the most stable one. Full geometry optimization as 161 114 calculated for the parent compounds and for their perfluori- well as vibrational analysis was carried out for all neutral and 162 115 nated derivatives in 1, 2-dichloroethane (DCE). Although, the ionic species. 163 Δ 116 computational estimations of the pKa values in solution have The intrinsic gas-phase acidity ( Gacid = GA) of a neutral 164 117 large practical importance the results have to be addressed acid HA was calculated according to the following thermody- 165 118 carefully because of the imperfection of the computational namic heterolysis equilibrium: 166 119 models and difficulties in validating the results against HA⇆+ A− H+ (1) 120 experiment. Even the measurement of these compounds in 167 Δ 121 the gas phase has not been very successful because of the The Gacid values (at 298 K) were calculated taking into 168 122 problems in bringing them into gas phase. account the zero-point energies, finite temperature (0 to 298 169 123 DCE is one of the least polar and basic solvents where a self- K) and entropy correction and the pressure−volume work term 170 Δ 124 consistent ladder of relative acidities (i.e., pKa) has been pV. The absence of imaginary frequencies (NImag = 0) was 171 24−26 fi 125 measured. C2H4Cl2 is a very weak hydrogen bond donor taken as the criterion of nding geometry corresponding to true 172 126 and acceptor by its Kamlet−Taft hydrogen bond acidity (α) energy minimum. 173 27 127 and basicity (β) parameters of 0.0 and 0.1, respectively. By definition, the gas-phase acidity of a neutral acid HA is 174 128 According to its polarity parameter (π*) of 0.81 and dielectric equal to the gas-phase basicity (toward the proton) of its 175 28 − 129 constant of 10.60, it is a medium polar solvent and can conjugate base, A . The lower numerical values of GA’s (in kcal 176 −1 130 dissolve ionic compounds. mol ) mean stronger/higher acidities. 177 37 131 In this paper we shall focus on the study of the closo- For the calculations in the solution phase the SMD model 178 132 dodecaborate-based superacid derivatives with a range of with structural relaxation at SMD/B3LYP/6-311+G** level 179 133 substituents of different nature using mostly high level DFT was used. Gibbs solvation energies were corrected by 1.9 kcal 180

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Table 1. Results of Acidity Calculations with DFT B3LYP Method at the 6-311+G** Level a Δ b a Δ b acid protonation sites Gacid pKa acid protonation site Gacid pKa d ― − − d B12H12H2 B1 and B12 267.5 28 B12H12H 1 2 3 359.8 26 ― − − ≈ − − B12(CF3)1H11H2 B2 and B10 259.0 B12(CF3)1H11H 2 3 7 7 8 12 349.2 ― B12(CF3)6H6H2 B7 and B9 230.1 B12(CF3)6H6H B12 308.4 − ― B12(CF3)11H1H2 1 2 - 3 and B12 177.5 B12(CF3)11H1H B12 283.3 − − − c ― − − c B12(CF3)12H2 1 2 - 3 and 9 10 12 170.8 B12(CF3)12H 1 2 3 253.9 ― − − ≈ − − B12F1H11H2 B2 and B10 265.2 B12F1H11H 2 3 7 7 8 12 356.6 ― − − B12F6H6H2 B7 and B9 243.1 B12F6H6H 7 8 12 339.6 − ― B12F11H1H2 1 2 - 3 and B12 220.0 B12F11H1H B12 317.4 → → d ― − − d B12F12H2 F1 F2 and F10 F12 213.4 0 B12F12H 1 2 3 310.7 5 → − − B12F12H2 F1 F2 and 9 10 12 212.3 ― − − ≈ − − B12Cl1H11H2 B2 and B10 261.1 B12Cl1H11H 2 3 7 7 8 12 353.2 → ― − − ≈ B12Cl6H6H2 Cl1 Cl2 and B12 246.6 B12Cl6H6H 7 8 12 B12 323.3 → → ― → ≈ → B12Cl11H1H2 Cl2 Cl3 and Cl9 Cl10 238.8 B12Cl11H1H Cl1 Cl2 Cl2 Cl3 304.0 → → ― → B12Cl12H2 Cl1 Cl2 and Cl10 Cl12 236.8 B12Cl12H Cl1 Cl2 302.5 24 24 Tf2NH 286.9 33 1 d CB11H12H 266.5 20 1 − d CB11F12H 212.8 2 a The sites of protonation for the most stable forms. Bx denotes a boron vertex with proton arranged to it symmetrically with the substituent. X - Y- Z → denotes a facet of the boron cage. Ax Cy denotes a geometry where proton is on a substituent A in the position x having HB interaction with ″≈″ Δ bΔ substituent C in the position y. The mark denotes that there are two protonation sites with approximately the same Gacid value. Gacid values given in kcal mol−1 at 298 K, calculated at 6-311+G** level if not noted diﬀerently. cThe acidity is obtained by combining B3LYP/6-311+G** SCF d energy and BP86 thermal correction. Calculated absolute pKa values in DCE.

Table 2. Results of Acidity Calculations with the DFT B3LYP Method at the 6-311+G** level a Δ b a Δ b acid protonation site Gacid acid protonation site Gacid → PF3B12H11HB12 266.6 PF3B12Cl6H5HCl11 Cl12 245.0 → PF3B12(CF3)1H10HB7 254.9 PF3B12Cl11HCl11 Cl12 235.2

PF3B12(CF3)6H5HB2 217.3 NH3B12H11HB12 280.7 − − c − − PF3B12(CF3)11H78 12 180.9 NH3B12F11H78 12 232.2 d PF3B12F1H10H B7 260.4 NF3B12H11HB12 269.2 − − − − ≈ → PF3B12F6H5H23 7 237.8 NF3B12F11H78 12 F12 F11 221.3 − − ≈ → PF3B12F11H78 12 F12 F11 221.0 NMe3B12H11HB12 281.9 − − PF3B12Cl1H10HB7 258.7 NMe3B12F11H78 12 236.6 a − − The sites of protonation for the most stable forms. Bx denotes a boron vertex with proton arranged to it symmetrically with the substituent. X Y Z → denotes a facet of the boron cage. Ax Cy denotes a geometry where proton is on a substituent A in the position x having HB interaction with “≈” Δ bΔ substituent C in the position y. The mark denotes that there are two protonation sites with approximately the same Gacid value. Gacid values given in kcal mol−1 at 298 K, calculated at 6-311+G** level if not noted diﬀerently. cThe acidity is obtained by combining B3LYP/6-311+G** SCF energy and BP86 thermal correction. dF atom is in position 12.

−1 181 mol (= RT ln 24.47) to obtain 1 bar ideal gas (denoted as respective results of the Y-substituted borane acids are 201 182 (g)) to 1 molar ideal solution (denoted as (solv)) standard presented in Table 2. More detailed information about the 202 t2 −1 183 values. An additional correction by 1.5 kcal mol (= RT ln results of the DFT calculations is available in the SI or from the 203 184 12.6) was applied for DCE, as the pure (i.e., 12.6 molar) authors upon request. 204 − 185 solvent (denoted as (l)) was used as standard state. The SMD For the unsubstituted (parent) compounds H2A and HA 205 Δ 186 model is parametrized for calculating Gibbs solvation energies the calculations resulted in the Gacid values 267.5 and 359.8 206 −1 187 with the inclusion of H-bond and nonelectrostatic interactions. kcal mol , respectively. As can be seen, the GA of B12H12H2 207 38 −1 188 Using a cluster-continuum model, Gibbs standard solvation (Figure 2) is within 2 kcal mol range from that of the 208 f2 − −1 −1 1 189 energy ( 210.5 kcal mol ) was calculated (i.e., an absolute respective carborane acid CB11H12H (GA = 266.5 kcal mol ). 209 190 chemical standard potential) for the proton which is somewhat The protonation sites of the neutral acid, H2A were positioned 210 −1 191 lower (by 5.1 kcal mol ) than previously calculated by some of antipodally to each other. 211 39 192 us (more details in the SI). Tissandier et al. have reported the The derivatives of HA had the most stable protonation site 212 193 absolute chemical standard potential for the proton in water − placed on the spherical boron cage diametrically opposite to the 213 − 1 40 + 194 264.0 kcal mol . According to this calculation DCE as a positively charged Y-group. The H /H···B distances of the 214 −1 195 bulk solvent is by 53.45 kcal mol less basic than water. This PF3-, NF3-, NMe3-, NH3-derivatives without substituents were 215 + 196 means that in DCE at a pH of 39.2 the proton has the same 1.365, 1.355, 1.350, and 1.352 Å, respectively. The H ···H 216 197 acidity than in water at pH 0! distances for the same compounds were 0.823, 0.828, 0.831, 217 Δ and 0.830 Å, respectively. The Gacid values in case of PF3 and 218 198 ■ RESULTS AND DISCUSSION −1 NF3 derivatives were 266.6 and 269.2 kcal mol , respectively. 219 Δ ’ 199 The computational Gacid values of the conjugate acids of the The respective NH3 and NMe3 acids had the GA s around 281 220 2− −1 t1 200 borate anions B12XnH12‑n are presented in Table 1. The kcal mol . When considering the acidities of the boranes with 221

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+··· Figure 2. Geometry of the neutral acid B12H12H2. D(H H) = 0.826 Å, D(H+/H···B) = 1.358 Å, and D(H···B) = 1.183 Å.

222 and without charged Y-group in the gas phase it is evident that 223 the electrostatically bound proton is well able to act as a partly 224 covalently interacting and positively charged substituent. In f3 225 Figure 3 we introduce a scale of computational gas-phase 226 acidities of some borate anions’ conjugate acids supplemented 227 by some common Brønsted acids as landmarks. 228 The most favorable protonation site of the unsubstituted − 41 229 carborane anion CB11H12 is determined by the anisotropy of 230 the electrostatic potential throughout the molecule and is the 231 boron atom antipodal to the carbon atom. Protonation of its 232 substitution derivatives is additionally influenced by the 1 233 placement and nature of substituents. The same is true for − 234 YB12H11 . When a positively charged substituent is added to 2− 235 the spherical B12H12 anion then the charge anisotropy is 236 created and this causes the relocation of the negative charge − 237 density in a way similar to the case of the CB11H12 anion. 238 Further addition of substituents makes the interplay of 239 substituents and protonation sites more complex. Below we 240 will present an overview of the most stable protonation sites of 241 these derivatives and their gas-phase acidities. 242 Monosubstituted Derivatives of B12XH11H2 and − 243 B12XH11H where X = F, Cl, and CF3. The computational 244 acidity predictions of the H2A with a single substituent placed 245 on the B12 vertex ranked the systems according to the GA −1 246 values as follows: F (265.2 kcal mol ) → Cl (261.1 kcal −1 → −1 247 mol ) CF3 (259.0 kcal mol ). The derivative with more 248 electronegative fluorine is less acidic than its more polarizable 249 chlorine counterpart, i.e., the polarizability effect outweighs the 250 electronegativity in the case of monosubstituted acids. This 251 parallels the situation found with the respective carborane acids 1 ’ 252 CB11H11Y. The monosubstituted F and Cl derivatives least 253 acidic (most stable) forms have very similar protonation 254 geometry: the protons are interacting with B2−6 and B7−11 and 255 are placed diametrically opposite to each other, they are 256 equidistant (1.354−1.359 Å) from the respective B’s, and they 257 are placed 0.825−0.829 Å from the H on the same boron 258 vertex. The geometrical positioning of the protons in CF3 259 derivative was similar to the F and Cl derivative. The notable 260 exception was the protonation site near the CF3 group where + Figure 3. Scale of gas-phase acidities from a selection of dodecaborane 261 H/H distances from the B were 1.373 and 1.357 Å. The longer derivatives accompanied by some Brønsted acids. Blue color denotes 262 − 2− B H distance resulted in the bond nearer to the CF3. The the derivatives of B12XnH12‑n (X = F, Cl, and CF3; n = 0, 1, 6, 11, and − 263 small distance between the hydrogen nuclei supports the idea 12) and YB12XnH11‑n (Y = PF3 and NH3;X= F, Cl, and CF3; n =0,1, 42−47 264 of some charge transfer (covalent) character of the formed 6, and 11), purple denotes carborane derivatives. 265 H-bond besides the electrostatic component. 266 The same acidity order was found in case of the monoprotic − − − − − − − 267 anionic acids B12X1H11H with intrinsic gas-phase acidities could expect, but on the facets 2 3 7, 3 7 8, and 7 8 12, 270 −1 2− −1 268 around 350 kcal mol . Interestingly, in the B12X1H11 anions all in the range of 1.4 kcal mol . That refers to a certain 271 “ ” 269 the most favorable protonation site is not on B12 vertex as one surplus of negative charge across the anion that has not been 272

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− − − fl Figure 4. Mulliken atomic charges of CB11H12 ,PF3B12H11 , and B12H12H . The atomic charges of the hydrogens and uorines have been presented as the average values of the belts. fi − − 273 signi cantly diminished by the size of the system nor the was again on the 7 8 12 facet leaving the B12-protonated 313 −1 − 274 substituent. system by 1.4 kcal mol less stable. The B12Cl6H6H had the 314 ’ − − 275 Hexasubstituted Derivatives of B12X6H6H2 and GA sof7 8 12 and B12-protonated derivatives, both, in 0.6 315 − −1 ’ 276 B12X6H6H where X = F, Cl, CF3. In terms of protonation kcal mol range. The (CF3)6 derivative s acidities of the 316 −1 277 site geometries the largest variations occurred in hexasub- respective protonation sites had 4 kcal mol difference in favor 317 278 stituted derivatives. In the case of the diprotic Cl-substituted of B12-protonated species. In comparison with monosubstituent 318 279 system one proton is attached on the substituent in the position systems this change of protonation sites illustrates well the 319 280 1 and chelated by the substituent in the position 2. The second behavior of the substituents in terms of ability to delocalize the 320 281 proton is bound to the B12 vertex. In terms of negative charge negative charge in the anions and the importance of 321 282 distribution, the neutral acid B12F6H6H2 represents a system considering all possible geometries to obtain correct 322 8,13 283 with unique features. Although, in similar systems the one- interpretation about the acidity ranking. 323 − 284 atom halogen substituents, in general, appear to be the most Derivatives of B12X11HH2 and B12X11HH where X = F, 324 285 favorable protonation sites in the form of intramolecular Cl, CF3. The B12(CF3)11HH2 acid has the most stable 325 fl − − 286 hydrogen bond, low polarizability of uorine atom makes the protonation sites above the 1 2 3 facet and B12 vertex of 326 −1 287 proton interaction with the fluorine-shield somewhat less the boron cage. The acidity of the system is 177.5 kcal mol . 327 −1 288 favorable. This can be observed as one protonation site appears That is about 5 kcal mol less acidic than the corresponding 328 1 289 on the B7 while the second is on the B9 vertex at the opposite carborane derivative. Similar protonation geometry is visible in 329 −1 290 side of the cage. In the hexakis-CF3 derivative the most the neutral F11-system with GA 220.0 kcal mol .Cl11- 330 291 favorable protonation sites are the same, B7 and B9 vertexes, derivative, in turn, had the most stable protonation sites, 331 292 which is probably the nearest placement of the protons to each both, at the opposite sides of the molecule placed between the 332 293 other across the systems. This results in the gas-phase acidity of chlorines of the vertexes 2−6 and 7−11. The Cl−H distances 333 −1 294 230.1 vs 243.1 kcal mol for the B12F6H6H2 acid. The initial of each protonation site were 1.814/1.439 Å and 1.746/1.471 334 295 geometries where proton is placed near the CF3 substituent Å. 335 − − 296 during the geometry optimization result in abstraction of HF or The monoanionic acids B12F11H1H and B12(CF3)11H1H 336 297 HCF3 and the formation of two neutral molecules, e.g., HCF3 + have the most favorable protonation site on B12 vertex while 337 298 B12(CF3)5H6H. Based on calculations of these monocarba-closo- Cl11-derivative protonates with almost equal energies on the 338 299 borane derivatives the resulting geometries with the leaving chlorine atoms on all vertexes. The acidity order of both levels 339 −1 300 group can have few up to tens of kcal mol lower energies of protonation remained the same compared with the 340 301 compared with the most stable protonated form, mostly respective X6 derivatives. 341 − 302 depending on the number of CF3 groups on the vertexes. Derivatives of B12X12H2 and B12X12H where X = F, Cl, 342 303 However, when HF separated from the PF3B12H11H the CF3. Several attempts failed to calculate the vibrational 343 + − 304 resulting system (HF + PF2 +B12H11 , see Figure S2 in the SI) frequencies of the (CF3)12-borate derivatives with B3LYP/6- 344 −1 305 was by 48.2 kcal mol less stable. 311+G**, so that it remained unclear if the obtained structures 345 306 In the order of the intrinsic gas-phase acidities the neutral were true minima or not. To minimize the risk of, e.g., running 346 307 clusters with six F and Cl substituents switched their places into a transition state during optimization, these systems were 347 fi 308 compared with the monosubstituted systems: CF3

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353 have one electron withdrawing group less. To have a better carborane acids. With the chlorine derivatives the difference is 416 ** −1 354 comparability with the existing DFT B3LYP/6-311+G scale about 3 kcal mol . The comparison with H2A(B12X6H6H2,X 417 fl 355 the optimized geometries from BP86/def-TZVP computations = F, Cl, and CF3) shows rather interesting results. The uorine 418 −1 356 were used as input structures for subsequent B3LYP/6- derivative of the H2A is by 5.3 kcal mol less acidic than the 419 ** −1 357 311+G optimization. The BP86 thermal corrections were respective PF3B12F6H5H (GA = 237.8 kcal mol ), the CF3- 420 −1 358 applied to these SCF energies after the verification that no derivative is by 12.8 kcal mol weaker (GA = 230.1 kcal 421 −1 −1 359 significant changes of geometries had taken place during this mol ), and Cl-derivative only by 1.6 kcal mol weaker (GA = 422 −1 360 procedure. This resulted in GA values of 170.8 and 253.9 kcal 246.6 kcal mol ). 423 −1 361 mol , respectively. The same method was applied also to the The GA computations of PF3B12(CF3)11H required the same 424 ff 362 computations of CB11(CF3)12H that has eluded the e orts to procedure as the respective H2A derivative. The SCF energies 425 363 calculate it is frequencies with Gaussian 09, as well. These from B3LYP 6-311+G** calculations with BP86-thermal 426 −1 −1 364 calculations resulted in GA of 172.3 kcal mol that is in the corrections resulted in gas-phase acidity of 180.9 kcal mol . 427 −1 365 same range with the respective dodecaborane derivative. That is about 10 kcal mol less acidic than the respective 428 366 The B12F12H2 had the most favorable protonation sites on derivative of H2A. 429 −1 367 the opposite sides of the molecule (GA = 212.3 kcal mol ). In case of the perfluorinated and perchlorinated systems of 430 fl 368 The energy of the system where one proton was on the boron B12X12H2 and PF3B12X11H the uorinated H2A was 1 kcal 431 −1 −1 369 facet and another on the fluorine chelated with the neighboring mol stronger and the chlorinated H2A 3.6 kcal mol weaker 432 −1 370 fluorine was in a 0.9 kcal mol range of the isomeric structure than the respective HA. The acidities of YB12F11H(Y=PF3 and 433 371 where both protons were between the fluorines placed NF3) were about the same. The respective systems where Y = 434 − −1 372 antipodally to each other. A similar result was also observed NH3 and NMe3 were about 11 15 kcal mol weaker than the 435 373 in the case of the respective Cl derivative (GA = 236.8 kcal Y=PF3 and NF3 derivatives. 436 −1 374 mol ). Acidity Calculations in Solution. We carried out 437 375 The most favorable proton locations for the anionic F12 and estimation of pKa values in 1,2-dichloroethane (DCE) for 438 − − −1 fl 376 Cl12 acids were on the 1 2 3 facet (GA = 310.7 kcal mol ) B12H12H2,CB11H12H, and their per uorinated derivatives. For 439 −1 fl 377 and between the substituents (GA = 302.5 kcal mol ), comparison also the pKa of bis-tri uoromethylsulfonylimide 440 38 378 respectively. (HNTf2) was calculated as HNTf2 is one of the strongest 441 379 Derivatives of YB12XnH11‑nH where Y = PF3,NH3,NF3, common acids with experimentally determined GA of 286.5 442 n −1 − 24−26 380 and NMe3; X = F, Cl, and CF3; and = 1, 6, and 11). In kcal mol and pKa 11.9 in DCE (against picric acid). 443 381 order to decrease the negative charge of the anions we have The calculations show that in the gas phase HCB11F12 has 444 382 created a series of monoanions by introducing positively strong interaction with DCE molecule via a hydrogen bond 445 + Δ ° − −1 Δ ° − −1 383 charged Y group as a substituent. However, the less negative with H = 19.6 kcal mol ( G = 9.5 kcal mol ). 446 447 384 charge of these anions compared to the respective B12H11 Similarly, H2B12F12 exothermically binds two DCE molecules in Δ ° − −1 Δ ° 385 derivatives without Y group does not lead to a significant the gas phase with overall H = 30.8 kcal mol and G = 448 − −1 386 increase of the gas-phase acidity. 12.6 kcal mol . Strong hydrogen bonds with DCE are very 449 − fi 450 387 The anion PF3B12H11 is characterized by signi cantly lower uncommon. Therefore, they may not have been adequately 388 dipole moment (in this case characterizing the uneven parametrizised in SMD. Thus, also a cluster-continuum 451 389 distribution of charge in the anion) compared to the respective calculation model was applied in which the DCE adducts of 452 − f4 390 carborane anion CB H (1.26 D vs 2.73 D; Figure 4). the acids were used for the Gibbs solvation energy calculation 453 11 12 − − 391 In the Y-borate the largest positive partial charge resides on (see the Born Fajans Haber cycles in the SI). 454 392 the Y atom hence the most favorable protonation site for the Furthermore, it was noticed that contrary to the gas phase 455 393 unsubstituted system is the B vertex. Because of this and also where the proton is located on a B1B2B3 facet, in solution the 456 12 − − 394 for the steric reasons one could expect for the insertion of Cs-symmetric structure of HB12F12 with an F H bond is more 457 395 electron withdrawing atoms and groups the most favorable stable. This energy of interconversion between the structures 458 459 396 position is also B12. However, comparing the energies of two was included in the Gibbs solvation energy (see the SI). − fl − − 460 f5 397 PF3B12F1H10 isomers with uorine placed on positions 12 and Figure 5 presents the Born Fajans Haber protolysis cycle −1 398 2, the former anion is only about 1.9 kcal mol more stable. (BFHC) of HNTf2. Mainly due to the very low basicity of DCE 461 399 Nevertheless, the derivatives in Table 2 follow substitution 400 levels starting from the vertex antipodal to the Y group. − 401 The monosubstituted systems: H2A, HA ,thePF3- 1 402 derivatives of HA and carboranes follow the same GA order: 403 F > Cl > CF3, meaning the F derivative has the weakest GA. 404 This acidity order refers to the additional destabilization of the Δ ° 405 anion by stronger resonance donor effect of the fluoro Figure 5. BFHC for HNTf2 protoysis in DCE. G values in kcal −1 406 substituent (compared to the chloro substituent). In the case mol . 407 of the singly substituted PF3-halogen derivatives the F- −1 408 derivative is by about 1.7 kcal mol weaker acid than the as bulk solvent the calculations resulted in a very high absolute 462 409 respective Cl-derivative and results in the GA value of 260.4 pKa of 32.6. From this it could be concluded that also other 463 −1 −1 410 kcal mol . This is by 3.2 kcal mol weaker than the respective common Brønsted acid molecules like H2SO4, HSO3F, or 464 1 −1 411 carborane acid and by 4.8 kcal mol stronger than the HClO4 may have pKa values in DCE around 30 or above. 465 412 B12FH11H2. The most favorable protonation site for the One can calculate a pH of 17.8 and a protolysis degree of 1.6 466 × −15 fi 413 monosubstituted PF3-anion where X = F, Cl, and CF3 was B7. 10 for a 1 mM solution of HNTf2 in DCE. At rst sight 467 414 The gas-phase acidities of the PF3B12X6H5H acids where X = this appears not very acidic, but remembering the (above- 468 −1 415 F, CF3 are both by ca. 5 kcal mol weaker than the respective discussed) shift of 39.2 units between the aqueous and the 469

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Δ ° −1 Figure 6. BFHC for H2B12H12 protoysis in DCE. G values in kcal mol .

470 DCE pH scales, the proton’s chemical potential is by 29.2 kcal around zero for the first dissociation step which would classify 506 −1 39 “ ” 471 mol higher compared to water at pH 0 and by absolute it as a strong acid in DCE. Again, as discussed above, the pKa 507 472 acidity this solution would correspond to an aqueous solution for the second dissociation step should be taken with caution, 508 − Δ ° 2− 473 with pH of 21.9. as the solvG (B12F12 ) is questionable. An even slightly lower 509 − fl f6 474 The calculated protolysis cycle for H2B12H12 (Figure 6) pKa of 1.6 was calculated for the per uorocarborane acid 510 475 reveals an interesting result. The large gain from solvation whose protolysis BFHC is shown in Figure 9. 511 f9 ff 476 energy overcomes the GA di erence between H2B12H12 and − 477 HB12H12 ; thus, the second pKa is calculated to be lower than 478 the first one! 479 We would like to point out that dianions were not included 480 in the parametrization of SMD. Thus, it is possible that the 2− 481 calculated Gibbs solvation energy of the B12H12 dianion −1 482 (−145.8 kcal mol ) may have a considerably less negative Δ ° Figure 9. BFHC for HCB11F12 protoysis in DCE. G values in kcal − 483 value than calculated. At this time it is unclear whether this mol 1. 484 result is an artifact of the applied model or not. Indeed, the fi 485 second pKa being lower than the rst one would be highly These estimated pKa values can be compared with the 512 486 unusual, but we would like to point out that there is no 24−26,49 published experimental values in DCE if one takes into 513 487 thermodynamic law which forbids that the second pKa may be fi fi account that the experimental values in refs 24−26 and 49 have 514 488 lower than the rst one. The rst and second pKa values refer to been arbitrarily anchored to picric acid (HPi) with pK taken as 515 489 different acidic species and their conjugate bases. True, the a zero. The experimental pKa of HNTf2 relative to HPi is 516 490 second pKa refers to species with more negative charge than the 24−26 −11.9. Based on the pK of HNTf 32.6 computed in this 517 491 first one, thus presumably holding the proton stronger. At the a 2 work the pKa values of the acids investigated in this paper are 518 492 same time the anion formed from such species on − − relative to HPi as follows: H2B12H12, 17.8; HCB11H12, 24.1; 519 493 deprotonation also has more negative charge and is thus − − H2B12F12, 44.6; and HCB11F12, 46.1. The most acidic acid 520 494 presumably better solvated in the liquid phase. Some examples 24−26 fi on the experimental scale is CF3SO(=NTf)NHTf with 521 495 of situations very near to this exist: the rst two pKa values of pK −18 relative to HPi. Thus, even though the pK values 522 496 nitrilotriacetic acid are 3.03 and 3.07 for nitrilotriacetic acid in a a found in this work are estimates (with error bars at least an 523 497 water, the second, third and fourth pKa values of H4SiO4 are 48 order of magnitude), it is clear that the borate- and carborate- 524 498 11.8, 12, and 12, respectively. based acids can offer acidities by many orders of magnitude 525 499 The HCB11H12 is calculated to be somewhat more acidic stronger than any class of acids this far measured in DCE or in 526 500 than its borane counterpart with absolute pKa in DCE of 20.4 any other solvent. 527 f7 501 (Figure 7). Due to the enormous acidities of the more acidic closo- 528 dodecaboranes and monocarba-closo-boranes, it can be 529 concluded that DCE is not fully suited as superacid chemistry 530 solvent for these compounds, not only because of its leveling 531 effect but also because the rearrangement and decomposition 532 reactions of the protonated DCE may limit its practical use. 533 Δ ° Figure 7. BFHC for HCB11H12 protoysis in DCE. G values in kcal − ■ CONCLUSION 534 mol 1. In this investigation two new directions of designing super- 535 strong Brønsted acids, which are potentially better available 536 f8 502 The BFHC for the protolysis of H2B12F12 is shown in Figure than the acids of the CB11H12H family, were studied. The 537 f8 503 8. acidities of, both, B12H12H2 and PF3B12H11H are very similar to 538 504 As H2B12F12, is much more acidic in the gas phase compared the CB11H12H. However, when the substituents are inserted the 539 − 505 to the previously discussed compounds, we calculated a pKa respective derivatives of B12H12H2 are in most cases about 5 8 540

Δ ° −1 Figure 8. BFHC for H2B12F12 protolysis in DCE. G values in kcal mol .

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−1 541 kcal mol less acidic than the respective derivatives of the (10) Meyer, M. M.; Wang, X.-B.; Reed, C. A.; Wang, L.-S.; Kass, S. R. 602 542 CB11H12H family. However, in the case of B12(CF3)6H6H2 the Investigating the Weak to Evaluate the Strong: An Experimental 603 −1 543 difference is about 18.4 kcal mol and in the case of the Determination of the Electron Binding Energy of Carborane Anions 604 − 1 and the Gas Phase Acidity of Carborane Acids. J. Am. Chem. Soc. 2009, 605 544 B12F12H2 only 0.6 kcal mol . ff 131, 18050−18051. 606 545 Although, for the PF3B12H11H derivatives the di erences in (11) Krossing, I.; Raabe, I. Noncoordinating AnionsFact or 546 acidities are smaller, the decrease of the anion’s charge with a 607 Fiction? A Survey of Likely Candidates. Angw. Chem. Int. Ed. 2004, 43, 608 547 positively charged substituent group does not have a significant 2066−2090. 609 548 effect on the gas-phase acidity. (12) Reed, C. A. Carborane Acids. New “Strong yet Gentle” Acids for 610 549 According to the model pK calculations, the most acidic a Organic and Inorganic Chemistry. Chem. Commun. 2005, 1669−1677. 611 550 borane and carborane derivatives may be strong acids and fully (13) Lipping, L.; Koppel, I. A.; Koppel, I.; Leito, I. Some Small 612 551 dissociated even in very low basic 1,2-dichloroethane (with “ ” Weakly Coordinating Anions Based on Carboranes. Proc. Estonian 613 552 absolute pKa values <0), while common strong acids like Acad. Sci. Chem. 2006, 55, 145−154. 614 553 HNTf2 may have absolute pKa values around 30 or higher. (14) Küppers, T.; Bernhardt, E.; Eujen, R.; Willner, H.; Lehmann, C. 615  W. [Me3Si][R-CB11F11] Synthesis and Properties. Angew. Chem., Int. 616 554 ■ ASSOCIATED CONTENT − Ed. 2007, 46, 6346 6349. 617 555 *S Supporting Information (15) Stoyanov, E. S.; Gunbas, G.; Hafezi, N.; Mascal, M.; Stoyanova, 618 +··· + 556 Full details of quantum chemical calculations of Tables 1 and 2 I. V.; Tham, F. S.; Reed, C. A. The R3O H Hydrogen Bond: 619 557 (S1, S3, and S5); complete ref 29; details for the pK Toward a Tetracoordinate Oxadionium(2+) Ion. J. Am. Chem. Soc. 620 a − 558 calculations. This material is available free of charge via the 2012, 134, 707 714. 621 559 (16) Nava, M.; Reed, C. A. Triethylsilyl Perfluoro-Tetraphenylborate, 622 Internet at http://pubs.acs.org. + − [Et3Si ][F20-BPh4 ], a Widely Used Nonexistent Compound. Organo- 623 2011 − 624 560 ■ AUTHOR INFORMATION metallics , 30, 4798 4800. (17) Tsurumaki, E.; Hayashi, S.; Tham, F. S.; Reed, C. A.; Osuka, A. 625 561 Corresponding Authors Planar Subporphyrin Borenium Cations. J. Am. Chem. Soc. 2011, 133, 626 562 *E-mail: [email protected]. − * 11956 11959. 627 563 E-mail: [email protected]. (18) Stoyanov, E. S.; Stoyanova, I. V.; Reed, C. A. Oligomeric 628 564 Notes Carbocation-like Species from Protonation of Chloroalkanes. J. Am. 629 565 The authors declare no competing financial interest. Chem. Soc. 2011, 133, 8452−8454. 630 (19) Stoyanov, E. S.; Stoyanova, I. V.; Tham, F. S.; Reed, C. A. 631 − 566 ■ ACKNOWLEDGMENTS Dialkyl Chloronium Ions. J. Am. Chem. Soc. 2010, 132, 4062 4063. 632 (20) Avelar, A.; Tham, F. S.; Reed, C. A. Superacidity of Boron Acids 633 567 This work was supported by the Grant 8162 from the Estonian H (B X ) (X=Cl, Br). Angew. Chem., Int. Ed. 2009, 48, 3491−3493. 634 568 Science Foundation and also by the Centre of Excellence 2 12 12 ́ (21) Stoyanov, E. S.; Kim, K.-C.; Reed, C. A. An Infrared iNH Scale 635 569 HIGHTECHMAT (SLOKT117T), by the targeted financing for Weakly Basic Anions. Implications for Single-Molecule Acidity and 636 570 SFO180089008 as well as the institutional funding IUT20-14 Superacidity. J. Am. Chem. Soc. 2006, 128, 8500−8508. 637 571 (TLOKT14014I) from the Ministry of Education and Research (22) Juhasz, M.; Hoffman, S. P.; Stoyanov, E. S.; Kim, K.-C.; Reed, C. 638 572 of Estonia and by the ERC in the Advanced Grant UniChem. A. 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