The superacidity of closo-dodecaborate-based Brønsted acids: a DFT study
Lauri Lipping*,‖, Ivo Leito‖, Ivar Koppel‖, Ingo Krossing§, Daniel Himmel§ and Ilmar A. Koppel*,‖
*,*
‖University of Tartu, Institute of Chemistry, 14a RavilaSt., Tartu 50411, Estonia
§University of Freiburg, Institute for Inorganic and Analytic Chemistry, 21 Albertstr., Freiburg D-79104, Germany
Abstract
The structures and intrinsic gas-phase acidities (GA) of some dodecaborate acids, the derivatives of YB12H11H (Y = PF3, NH3, NF3, NMe3),B12H12H2 and B12H12H–(HA, H2A and HA-,respectively) have been computationally explored withDFT B3LYP method at 6-311+G** level of theoryas new possible directions of creating superstrong Brønsted acids. Depending on the nature and number of the substituents different protonation geometries were investigated.Also, the pKavalues of B12H12H2 , CB11H12H and their perfluorinated derivatives in 1,2-dichloroethane (DCE) were estimated with SMD and cluster-continuum model.
In general, the GA values of the neutral systems varied according to the substituents in the following order: CF3F Cl and in case of anionic acids: CF3Cl F. The dodecatrifluoromethyl derivative of H2A, B12(CF3)12H1H2, emergesas the strongest among the considered acids and is expected to be in the gas phase at least as strong as the undecatrifluoromethyl carborane, CB11(CF3)11H1H. The GA values of the respective mono-anionic forms of the considered acids remained all, but (CF3)11-derivative,higher thanthe widely used threshold of superacidity. The HAderivatives’ (Y = PF3, NF3) GA’s were approximately in the same range as the H2Aacids’. In case Y = NH3 or NMe3 the GA values were significantly higher.
The derivatives of B12H12H2 are as a rule not significantly weaker acids than the respective derivatives of CB11H12H. This is important for expanding practical applicability of this type of acids and their anions, as they are synthetically much easier accessible than the corresponding CB11H12– derivatives.
Introduction
Practical and fundamental reasons1-4 have motivated scientists to search for molecules and molecular systems that are more acidic than known before. Several strategies5,6have been proposed todesign highly acidic molecules.An obvious route is introducing electron withdrawing substituents (e.g. fluorination or trifluoromethylation)into already strong or superstrong Brønsted acids. Well-known examples are fluorosulfonic and trifluoromethanesulfonic acids, which can be regarded as derivatives of sulfuric acid.Another much used approach is increasing the hydrogen ion donor ability of a Brønsted acid HA by mixing it with a Lewis acid so that the anion A–formed in the ionization of HA is converted into the highly stabilized complex with this Lewis acid. This principle is operational in e.g. magic acid or HSbF6. Although, strong, both of these acids are prone to form reaction side products by means of fluorination.
The electron withdrawing effects of substituents are especially powerful if synergized with the charge delocalization ability of electron-deficient systems, most notably different spherical boron compounds.Decades of work7-10 on boron compounds and their substituted derivatives have resulted in a new generation of anions – derivatives of the closo-dodecaborate and monocarba-closo-dodecaborate anions –superweak (i.e. very weakly coordinating), extremely inert anionic bases whose conjugate acids are the strongest Brønsted acids presently known1-8. These anions have been used as counter-ions for strongly electrophilic cationic species that in dilute solution are not only extremely strong acids11, but also have extremely low nucleophilicity, electrophilicityand oxidizing activity.
The first computational evidence7 that the intrinsic gas-phase superacidity of boron-based acids can exceed that of sulfuric acid the “classical” basis for definition of superacidity by many powers of ten was published in 2000 in the work of some of the present authors with coworkers.7 It was followed by aDensity Functional Theory (DFT) investigation of the intrinsic gas-phase acidities of some smaller carborane derivatives12. Further computational extension and revision of the intrinsic gas-phase super acidity scale was carried out in 20091.
The practical chemical use of these novel reagents has yet to gather impetus. The main obstacle is the high cost and limited availability of the borate and carborate acids and their salts. The quantities that presently can be prepared via complexand time-consuming synthetic pathways are suitable for obtainingsmall quantities of valuable substances, enough for small scale experiments, but not for extensive or large-scale use. In the recent reports13-18some experiments of fundamental interest have been reported made possible by the free acids CB11XnR12-nH (X = Cl, F; R = H, CH3; n = 6, 11). However, the question about the availability of the derivatives of CB11H12–remains. Therefore, the quest for anions of similar inertness and low basicity, but easier to prepare, is constantly on. The interest in the derivatives of H2(B12X12) comes from a fact that the salts of the starting compound B12H122– are commercially available at a reasonable price.Furthermore, as B12X122– are dianions, a useful approach to further increase their acidity could be decreasing the availability of the negative charge by using a single positively charged group, which turns the bianionic closo-dodecaborate into a monoanion. Besides a positive charge this group should have electron-withdrawing properties, should not contain any well-defined protonation centers and should be reasonably stable. Based on these considerations we have chosen the -PF3+, -NF3+, -NH3+, -NMe3+ groups for this purpose.
In a recent report19the solution-phase superaciditiesof two diprotic acids, based on the closo-dodecaborateanionsH2(B12X12) (X = Cl, Br) have been estimated indirectly by Reed et al. using the anions’ ν(NH) basicity scale based on NH stretching frequency shifts of Oct3NH+ in CCl4 induced by H-bond formation between the latter cationic proton donor and the superweak anionic base.20,21Based on theseresults and the ability of the derivatives of H2(B12X12) (X = Cl, Br)to protonate benzene19by forming[C6H7]2[B12X12]salts their acid strength – even corresponding to the detachment of the second proton – was considered to be comparable with the respective carborane acids.Theseresults wereexplained withthe hypothesis19that “halogenosubstituents on both anions form an effective screen for negative charge that is delocalized and buried within the icosahedral cage”. Therefore, for accurate experimental and computational estimation of intrinsic acidity the careful analysis of possible protonation sites is necessary.
However,no direct measurement or computational estimation of these acids in any solvent has been published according to our best knowledge.
Therefore, to give an estimation about the acidity of borane and carborane acids in solution, pKa values were calculated for the parent compounds and for their perfluorinated derivatives in 1,2-dichloroethane (DCE). Although, the computational estimations of the pKa values in solution have large practical importancethe results have to be addressed carefully because of the imperfection of the computational models and difficulties in validating the results against experiment. Even the measurement of these compounds in the gas phase has not been very successful because of the problems in bringing them into gas phase.
DCE is the least polar and basic solvent where a self-consistent ladder of relative acidities (i.e. ΔpKa) has been measured24.C2H4Cl2 is a very weak hydrogen bond acceptor by its Kamlet-Taft hydrogen bond acidity (α) and basicity (β)parameters of 0.0 and 0.1, respectively22. According to its polarity parameter (π*) of 0.81 and dielectric constant23 of 10.38, it is a medium polar solvent and can dissolve ionic compounds.
In this paper we shall focus on the study of the closo-dodecaborate-based superacid derivatives with a range of substituents of different nature using mostly high level DFT calculations. In order to obtain reliable results, different possible protonation geometries and the effects of substituents on the protonation site are compared. First time the pKa values of some borane and carborane acid derivatives are calculated in solution.
Methods
Unless otherwise indicated, density functional theory (DFT) calculations were carried out on B12XnH12-n2- (X = F, Cl, CF3; n = 0, 1, 6, 11, 12) and YB12XnH11-n-(Y = PF3, NH3, NF3, NMe3,X = F, Cl, CF3; n = 0, 1, 6, 11) cages and their protonated forms at B3LYP/6-311+G** level with Gaussian 09 system of programs with full thermal corrections to Gibbs energies at the optimized structures25. In the largest systems where X = CF3 and n = 12 (n = 11 with the Y-borates), the vibrational analysis at the B3LYP/6-311+G** level failed, so thermal corrections were calculatedusing the RI-BP8626,27/def-TZVP28levelwith default RI-J auxiliary basis29on the corresponding optimized structuresusing the Turbomole 6.430-32program system (see the discussion for details).
Figure 1. The numbering ofcloso-dodecaborate’s vertexes.
The starting position of the substituent insertion for the borates without Y-group was considered as position 1 (Figure 1). In case of the Y-substituted borates the position 1 was the vertex with Y-group.Replacement of the hydrogen atoms with substituents was done subsequently in the following groups of vertexes (belts): 1, 2…6, 7…11 and 12.
For most of the acids several input geometries of protonated forms with different protonation sites were composed to determine the most stable one. Full geometry optimizations as well as vibrational analyses were carried out for all acids and anions.
The intrinsic gas-phase acidity (Gacid= GA) of a neutral acid HA was calculated according to the following thermodynamic heterolysis equilibrium:
HA A– + H+, (1)
The Gacid values (at 298 K) were calculated taking into account the zero-point energies, finite temperature (0 to 298 K) and entropy correction and the pressure-volume work term pV. The absence of imaginary frequencies (NImag = 0) was taken as the criterion of finding geometry corresponding to true energy minimum.
By definition, the gas-phase acidity of a neutral acid HA is equal to the gas-phase basicity (toward the proton) of its conjugate base, A–. The lower numerical values of GA’s (in kcal mol-1) mean stronger/higher acidities.
For the calculations in the solution phase SMD model33was used. This is parametrized for calculating Gibbs solvation energies with the inclusion of H-bond and nonelectrostatic interactions. Using a cluster-continuum model35,Gibbs standard solvation energy(-210.5 kcal mol–1)was calculated (i.e. an absolute chemical standard potential) for the proton which is somewhat lower (by 5.1 kcal mol–1) than previously calculated by some of us36(more details in SI). Tissandier et alhave reported the absolute chemical standard potential for the proton in water -264.0 kcal mol–1.37According to this calculationDCE as a bulk solvent is by 53.4 kcal mol–1less basic than water.
Results and Discussion
The computational Gacid values of the conjugate acids of the borate anions B12XnH12-n2–are presented in Table 1. The respective results of the Y-substituted borate acids are presented in Table 2. More detailed information about the results of the DFT calculations is available in the SI or from the authors upon request.
For the unsubstituted (parent) compoundsH2Aand HA-the calculations resulted in the Gacid values 267.5 and 359.8kcal mol-1, respectively. As can be seen, the GA of B12H12H2(Figure 2) iswithin 2 kcal mol-1 range from that of the respective carborane acid CB11H12H (GA = 266.5 kcal mol-1).1 The protonation sites of the neutral acid,H2A were positioned antipodally to each other.
Figure 2.Geometry of the neutral acid B12H12H2.
The derivatives of HAhad the most stable protonation site placed on the spherical boron cage diametrically opposite to the positively charged Y-group and the Gacid values in case of PF3- and NF3-derivativeswere266.6 kcal mol-1 and 269.2 kcal mol-1, respectively.The respective NH3- and NMe3-acids had the GA’s around 281 kcal mol-1. These results nonexistent acidity increase caused by the substitution with the charged Y show means that in the gas phase the electrostatically bound proton is well able to act as a partly covalently interacting and positively charged substituent.On Figure 3 we introduce a scale of computational gas-phase acidities of some borate anions’conjugate acids supplemented by some Brønsted acids as landmarks.
Figure 3. A scale of gas phase acidities from a selection of dodecaborate derivatives accompanied with some Brønsted acids. Blue color denotes the derivatives of B12XnH12-n2– (X = F, Cl, CF3; n = 0, 1, 6, 11, 12) and YB12XnH11-n– (Y = PF3, NH3,X = F, Cl, CF3; n = 0, 1, 6, 11), purple denotes carborane derivatives.
The most favorable protonation site of the unsubstituted carborane anion CB11H12–is determined by the anisotropy33 of the electrostatic potential throughout the molecule and is the boron atom antipodal to the carbon atom. Protonation of its substitution derivatives is additionally influenced by the placement and nature of substituents.1The same is true for YB12H11–. When a positively charged substituent is added to the spherical B12H122–anionthen the charge anisotropy is created and this causes the relocationof the negative charge density in a waysimilar to the case of the carboraneanion CB11H12–. Further addition of substituents makes the interplay of substituents and protonation sites more complex. Below we will present an overview of the most stable protonation sites of theses derivatives and their gas-phase acidities.
Table 1. Results of acidity calculations of B12H12H2 and its F, CF3 and Cl substituted derivatives in the gas phase with DFT B3LYP method at 6-311+G** level as well as for some representative compounds in the 1,2-dichloroethane solution with the SMD method.@Lauri, pane siia palun DCE numbrid sisse (tabeli vasakusse poolde üks veerg juurde), kusjuures need, mis on vahetult võrreldavad ref 24 andmetega (st mitte absoluutsed). Pane selle kohta footnotesse märge ja viita seal seda tööd ka: , kuna selles on ka mõnijagu DCE väärtusi. Palun too vastavad karboraanid ka siia tabelisse, et oleks võrdlusvõimalus.protonation / protonation
acid / sitesa / Gacidb / acid / sitea / Gacidb
B12H12H2 / B1 & B12 / 267.5 / B12H12H― / 1 - 2 - 3 / 359.8
B12(CF3)1H11H2 / B2 & B10 / 259.0 / B12(CF3)1H11H― / 2 - 3 - 7 7 - 8 - 12 / 349.2
B12(CF3)6H6H2 / B7 & B9 / 230.1 / B12(CF3)6H6H― / B12 / 308.4
B12(CF3)11H1H2 / 1 - 2 - 3 & B12 / 177.5 / B12(CF3)11H1H― / B12 / 283.3
B12(CF3)12H2 / 1 - 2 - 3 & 9 - 10 - 12 / 170.8c / B12(CF3)12H― / 1 - 2 - 3 / 253.9c
B12F1H11H2 / B2 & B10 / 265.2 / B12F1H11H― / 2 - 3 - 7 7 - 8 - 12 / 356.6
B12F6H6H2 / B7 & B9 / 243.1 / B12F6H6H― / 7 - 8 - 12 / 339.6
B12F11H1H2 / 1 - 2 - 3 & B12 / 220.0 / B12F11H1H― / B12 / 317.4
B12F12H2 / F1 → F2 & F10 → F12 / 213.4 / B12F12H― / 1 - 2 - 3 / 310.7
B12F12H2 / F1→ F2 & 9 - 10 - 12 / 212.3
B12Cl1H11H2 / B2 & B10 / 261.1 / B12Cl1H11H― / 2 - 3 - 7 7 - 8 - 12 / 353.2
B12Cl6H6H2 / Cl1 → Cl2 & B12 / 246.6 / B12Cl6H6H― / 7 - 8 - 12 B12 / 323.3
B12Cl11H1H2 / Cl2 → Cl3 & Cl9 → Cl10 / 238.8 / B12Cl11H1H― / Cl1 → Cl2 Cl2 → Cl3 / 304.0
B12Cl12H2 / Cl1 → Cl2 & Cl10 → Cl12 / 236.8 / B12Cl12H― / Cl1 → Cl2 / 302.5
aThe 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
substituent C in the position y. The "" mark denotes that there are two protonation sites with approximately the same Gacid value.
bGacid values given in kcal/mol 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.
The monosubstituted derivatives of B12XH11H2 and B12XH11H–where X =F, Cl, CF3
The computational aciditypredictions of the H2A with a single substituent placed on the B12 vertex ranked the systems according to the GA values as follows: F (265.2 kcal mol-1) → Cl (261.1 kcal mol-1) → CF3 (259.0 kcal mol-1). The derivative with more electronegative fluorine is less acidic than its more polarizable chlorine counterpart, i.e. the polarizability effect outweighs the electronegativity in the case of monosubstituted acids. This parallels the situation found with the respective carborane acids CB11H11Y.1 The monosubstituted F- and Cl-derivatives’least acidic (most stable) forms have very similar protonation geometry: the protons are interacting with B2-6 and B7-11 and are placed diametrically opposite to each other,they are equidistant (1.354 – 1.359 Å) from the respective B’s, they are placed 0.825-0.829 Å from the H on the same boron vertex. The geometrical positioning of the protons in CF3-derivative was similar to the F- and Cl-derivative. The notable exception was the protonation site near the CF3-group where H/H+ distances from the B were 1.373 and 1.357 Å. The longer B-H distance resulted in the bond nearer to the CF3. The small distance between the hydrogen nuclei supports the idea of some charge transfer34-39 (covalent) character of the formed H-bond besides the electrostatic component.
The same acidity order applies to the monoprotic anionic acids B12X1H11H–with intrinsic gas-phase acidities around 350 kcal mol-1. Interestingly, in theB12X1H112– anions the most favorable protonation site is not on B12 vertex as one could expect, but on the facets 2 – 3 – 7, 3 – 7 – 8 and 7 – 8 – 12, all in the range of 1.4 kcal mol-1. That refers toa certain “surplus” of negative charge across the anion that has not been significantly diminished by the size of the system nor the substituent.
The hexasubstituted derivatives of B12X6H6H2 and B12X6H6H–where X = F, Cl, CF3
In terms of protonation site geometries the largest variations occurred in hexasubstituted borates. In the case of the diprotic Cl-substituted system one proton is attached on the substituent in the position 1 and chelated by the substituent in the position 2. The second proton is bound to the B12 vertex. In terms of negative charge distribution, the neutral acid B12F6H6H2represents a system with unique features. Although, in similar7,12 systems the one-atom halogen substituents, in general, appear to be the most favorable protonation sites in the form of intramolecular hydrogen bond, low polarizability of fluorine atom makes the proton interaction with the fluorine-shield somewhat less favorable. This can be observed as one protonation site appears on the B7while the second is on the B9 vertex at the opposite side of the cage. In the hexakis-CF3 derivative the most favorable protonation sites arethe same, B7and B9vertexes,which is probably the nearest placement of the protons to each other across the systems, resulting in the gas-phase acidity of 230.1 kcal mol-1 vs 243.1 kcal mol-1for the B12F6H6H2 acid.The initial geometries where proton is placed near the CF3 substituent during the geometry optimization result in abstraction of HF or HCF3 and the formation of two neutral molecules e.g. HCF3 + B12(CF3)5H6H.Based on calculations of monocarba-closo-borane derivatives the resulting geometries with the leaving group can have lower energies compared with the most stable protonated form beginning from few up to tens of kcal mol-1, mostly depending on the number of CF3-groups on the vertexes. However, when HF separated from the PF3B12H11H the resulting system (HF + PF2+ + B12H11-, also PF2+ moved from its position above the boron in the position 1 and formed a system where P was above the B – B bond of positions 1 and 2) was by 48.2 kcal mol-1 less stable.
In the order of the intrinsic gas-phase acidities the neutral clusters with six F- and Cl-substituentsswitched their placescompared with the monosubstituted systems: CF3< F < Cl <H. However, the acidity order of the anionic acids remained the same as in case of the single substituent systems. This could be the result of higher polarizability of the Cl-substituent over F. In case of the F6-derivative the most favorable protonation site was again on the 7 – 8 – 12 facet leaving the B12-protonated system by 1.4 kcal mol-1 less stable. Similar chloroborate had the GA’s of 7 – 8 – 12 and B12-protonated derivatives, both, in 0.6 kcal mol-1 range. The (CF3)6-derivative’s acidities of the respective protonation sites have already 4 kcal mol-1 difference in favor of B12. In comparison with monosubstituent systems this change of protonation sites illustrates well the behavior of the substituents in terms of ability to delocalize the negative charge in the anions and the importance of considering all possible geometries to obtain correct interpretation about the acidity ranking.