The Combination of Superhalogens and Brønsted Acids HX (X = F, Cl

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The Combination of Superhalogens and Brønsted Acids HX (X = F, Cl, Br): An Effective Strategy for Designing Strong Superacids Fu-Qiang Zhou, Wen-Hua Xu, Jin-Feng Li, Ru-Fang Zhao, and Bing Yin* MOE Key Laboratory of Synthetic and Natural Functional Molecule Chemistry, College of Chemistry and Materials Science, Northwest University, Xi’an 710069, China

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ABSTRACT: A series of 27 composite structures, consisting of superhalogen and Brønsted acid, is designed and systematically studied based on combined ab initio and DFT calculations focusing on their potentials as novel superacids. As indicated by high-level CCSD(T) results, all the composites here fulfill the theoretical criterion for superacid and the acidities of two of them are close to the strongest superacid ever reported. The influences of various factors on the superacid properties of these composites were analyzed in detail. Our results demonstrate that the acidity of these superacids is mainly determined by the superhalogen components while the effect of Brønsted acids, irrespective of their number or type, is relatively mild. Therefore, it is probable to design novel composite superacid with enhanced property through the regulation of the superhalogen component. It is encouraging that MP2 and DFT could also provide reliable results when compared with the high-level CCSD(T) method. The reliability of these lowcost methods implies the capability of theoretical calculations for future composite superacid of enlarged size, and thus it is highly probable that an effective guide to the related experimental research could be provided by the theory.

1. INTRODUCTION Since its first appearance in the paper by Hall and Conant in the year of 1927,1 the word “superacid” refers to a compound possessing extremely strong acidity. As defined by Gillespie, the acidity of superacid species is stronger than that of 100% sulfuric acid.2 In other words, the Hammet acidity function of superacid is less than −12.2,3 A superacid is capable of protonating very weak bases, e.g., methane,4 due to its extremely high acidity. With the existence of superacid, certain organic carbenium ions, e.g., HCO+ and glycosyl cation, could be observable.5,6 This point is very important for research on the mechanisms of organic reaction. Due to its uniqueness, superacid species have been successfully applied in the fields of catalysis and synthesis, e.g., cracking, isomerization, and alkylnation, as well as medical chemistry research.7−9 Besides the systems constructed from purely Brønsted-type or Lewis-type acid, the composites of both Brønsted and Lewis acid, e.g., HSO3F/SbF5 and HF/SbF5,10−13 have also been proven to be capable of working as superacids by the research of Olah and Hogeveen.10,13 These findings have enriched the structural versatility of superacid significantly, and thus they promoted the rapid development of superacid chemistry.14 Experimentally, the acidity of various superacid systems could be determined by UV−vis, NMR, and kinetic measurement.15−17 However, these experiments are usually performed for solution phase, and thus the results depend on the properties of the solvent themselves. That is to say, there is some uncertainty in the solution acidity of a superacid.18,19 In © 2017 American Chemical Society

comparison, gas-phase acidity is irrelative with solvent, and thus it could be utilized as a uniform standard to characterize superacid species.19,20 Although there are some examples of which the acidity in gas phase is different from that in solution,21,22 gas-phase acidity has been broadly adopted for the theoretical design of novel superacids.23,24 In principle, the gasphase acidity could be determined by the changes of the Gibbs free energies of the deprotonation reactions of the systems, ΔGacid. Usually, a compound could be characterized as superacid if its ΔGacid is less than 300 kcal/mol.23,24 Besides experimental determination via Fourier transform ion cyclotron resonance (FT-ICR), accurate ΔGacid could also be conveniently obtained from theoretical calculations.20 Due to its extreme acidity, it is not hard to understand the complexity and difficulty in the corresponding experimental measurement of superacid arising from the high requirement for both the equipment and operation. Therefore, theoretical calculations have become more and more important in the study on superacid systems.20,23−35 Reliable prediction on superacid, obtained from theoretical calculations, could provide an effective guide for the subsequent experiments and thus could increase the efficiency of the research. In fact, theoretical calculation has already played an important role in the field of superacids in recent years.20,23−35 Received: July 14, 2017 Published: September 11, 2017 11787

DOI: 10.1021/acs.inorgchem.7b01754 Inorg. Chem. 2017, 56, 11787−11797

Article

Inorganic Chemistry Recently, systematic studies on HMnF3n+1 (M = Al, In; n = 1−4), HSnnF4n+1 and HSbnF5n+1 (n = 1−3) systems23,30 have been performed by the group of Skurski based on ab initio and DFT calculations. Those compounds were verified as superacids according to their results. It is worth noting that the deprotonated forms of these superacids, i.e., [MnFnk+1]− (M = Al, In, Sb), could be characterized as superhalogen anions.30 That is to say, these superacids are composites of superhalogen anions and proton. The subsequent study on hydrogenized superhalogen, by the Misra group, further proves the capability of superhalogen in forming a new type of superacid.31 Usually, superhalogen clusters consist of central atom M and ligand X of high electronegativity.36−38 They possess very strong capability of binding the extra electron, and thus the anionic form of superhalogen is very stable.38,39 The deprotonation process of superacid will lead to the existence of anion eventually.27 If the stability of the anion is high, the related ΔGacid values should be small and thus the acidity of the system will be strong. This should be the main reason for the success of superhalogen in forming new superacids. The stability of the superhalogen anion could be characterized by its vertical electron detachment energy (VDE).40 Abundant reports have demonstrated that the VDE of superhalogens increases as the number of the ligands increases. Compared with traditional monouclear superhalogens MXk+1,41−46 polynuclear superhalogens, MnXnk+1, possess one significant advantage, which is the possibility of increasing the number of ligands while avoiding the increase of interligand repulsion in mononuclear ones.47−51 Previous results have shown that the acidity of hydrogenized superhalogen does get stronger when the number of central atoms of the superhalogen component increases.23,30 Besides in combination with proton, recent studies have pointed out that superhalogen could also form superacid after combination with Brønsted acid,32 e.g., HF. Compared with hydrogenized superhalogens, this new type of composite superacid, e.g., (HF)n/AlF3 and (HF)n/GeF4, possesses lower value of ΔGacid, i.e., stronger acidity. Apparently, as probable candidates of novel superacids, composites based on superhalogen are definitely worthy of further exploration. Actually, these composite superacids consist of two components, which are superhalogen and Brønsted acid/ proton. A thorough comprehension of the influence on the properties of the whole system from each component is clearly crucial for both the understanding of this new type of superacid and the subsequent design of novel superacids. The research of the Skurski group has already indicated that increasing the number of Brønsted acids could lead to a lower value of ΔGacid, i.e., stronger acidity.23,32 However, the studies of hydrogenized superhalogens also demonstrated that the acidity increases along the increase of the number of central atoms of the superhalogen components.23 Therefore, effective regulation of the properties of this type of superacid is available from both of the two components. However, until now, it has not been clear whether there is one dominant component of which the influence on the superacid property of the whole system is superior to that of the other component. Even in the aspect of Brønsted acid, previous results mainly focus on the effect of number on the superacid property; the influence of the types of Brønsted acid has not been systematically explored according to our best knowledge. Apparently these unsolved questions are important, and they deserve in-depth investigation. Therefore, a series of composites based on super-

halogen and Brønsted acid, (HX)m/MgnCl2n (X = F, Cl, Br; m, n = 1−3), is designed and theoretically explored here. Our focus is the potential of these composites as effective superacids and the influence of various factors on the acidity of the whole system. We hope our endeavor via theoretical calculations could provide a useful guide for future related studies. High-level ab initio methods, e.g., CCSD(T), have already been proven to be capable of providing reliable prediction of the gas-phase acidity of composite superacids.23,30 However, the computational cost of these methods is quite high. With the deepening of the research, the size of the potential composite superacid is getting larger, and thus the usage of high-level ab initio methods is probably limited. Therefore, other low-cost methods, e.g., MP2 and DFT, were also utilized in this work. With the results from high-level methods as the reference, the performance of these low-cost methods for composite superacids will be carefully checked, and thus reliable theoretical methods with acceptable cost could be indentified.

2. THEORETICAL METHODS AND COMPUTATIONAL DETAILS The deprotonation process could be described as eq 1:

(HX)m /Mg nCl 2n → [(HX)m − 1 /Mg nCl 2nX)]− + H+ (X = F, Cl, Br; m , n = 1−3)

(1)

Correspondingly the change of the Gibbs free energies of this process, i.e., ΔGacid, is defined by eq 2: ΔGacid = ΔG H + + ΔG[(HX)m − 1/MgnCl2n X]− − ΔG(HX)m /MgnCl2n (2) Generally, the most important contribution to ΔGacid comes from the part of electronic energies, i.e., the deprotonation energy (DE) as shown in eq 3:

DE = E H + + E[(HX)m − 1/MgnCl2n X]− − E(HX)m /MgnCl2n

(3)

The contributions, other than DE, include zero-point energy corrections, thermal corrections, and entropy contributions. The geometry optimizations and vibration analysis of all the designed composites as well as their deprotonated product were performed at the MP2/6-311++G(d,p) level.52−54 All the structures were confirmed to be local minima on the potential energy surface by the nonexistence of imaginary frequency. The reliability of the MP2/6311++G(d,p) level for geometry optimizations and vibration analysis has been clearly verified in previous work on composite superacids based on superhalogens.23,24,31 The vibration analysis also provides all the contributions to ΔGacid with the exception of DE. In order to acquire high accuracy, various methods were adopted to calculate DE based on the geometry at the MP2/6-311++G(d,p) level. Besides MP2, high-level ab initio methods, including MP4, CCSD, and CCSD(T), were utilized too.55−57 In the aspect of DFT calculations, three popular functionals (ωB97XD,58 B3LYP,59,60 and M06-2X61) were selected. Various basis sets, from 6-311+G(d,p) to 6-311+ +G(d,p) and 6-311++G(2df,2pd), were selected in the calculation of DE to ensure that the basis set effect will not lead to uncertainty in accuracy issue. The VDE values of the deprotonated products of the superacids, i.e., the superhalogen anions, were calculated via the indirect approach at the CCSD(T)/6-311++G(d,p) level. The indirect approach consists of subtracting the anion energies from those of the neutral at the same level. The basis set superposition error was neglected in our calculations since its effect on DE as well as on ΔGacid has been shown to be quite small, not exceeding 1−2% of the total value.24 All the calculations in this work were performed with the Gaussian 09 program.62 11788

DOI: 10.1021/acs.inorgchem.7b01754 Inorg. Chem. 2017, 56, 11787−11797

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Inorganic Chemistry

HCl/Mg2Cl4, Mg1−Cl6 (2.59 Å) in (HCl)2/Mg2Cl4, and Mg1− Cl2 (2.61 Å) in (HCl)3/Mg2Cl4. All of the composites of (HCl)m/Mg3Cl6 (m = 1−3) composites possess C2 symmetry. The lengths of the terminal Mg−Cl bonds of the trinuclear superhalogen component generally lie within the range of 2.20−2.27 Å, and the corresponding range of the bridging Mg−Cl bonds is 2.31− 2.58 Å. As shown in Figure 2, the deprotonated products of the composites of HCl/MgnCl2n are just the superhalogen anions of

3. RESULTS AND DISCUSSION 3.1. Structures. Starting from the superhalogen anions [MgnCl2n+1]−, the addition of one proton could lead to the composites of HCl/MgnCl2n. Based on HCl/MgnCl2n, the addition of one or two HCl would result in the composites of (HCl)2/MgnCl2n or (HCl)3/MgnCl2n, respectively. Based on these designing ideas, 33 stable composites were obtained via theoretical calculations. Due to the large number of the possible composites, for a given chemical composition, only the most stable one and the isomers of which the relative energies are less than 4 kcal/mol are selected for the subsequent calculation of the ΔGacid values. The total number of the selected isomers is 23. Owing to the limited space, only the structures of 9 composites, which have the smallest ΔGacid values for each given chemical composition, are presented in Figure 1. All the geometries of the other composites are included in Figures S1 and S2.

Figure 2. Equilibrium structures of the corresponding deprotonation products with selected bond lengths (in Å).

mononuclear, binuclear, and trinuclear structures. For other composites, the structures of their deprotonated products are close to that of HCl/MgnCl2n. They could be considered as corresponding superhalogen anions combined with one or two HCl molecules. Besides the above 9 composites, we also explored the other 18 composites of (HX)m/MgnCl2n (X = F, Br; m, n = 1−3) constructed from the replacement of HCl by HF or HBr. Their structures as well as the structures of their deprotonated products are similar to those of (HCl)m/MgnCl2n (m, n = 1−3) as shown in Figures S3−S7. 3.2. The Gas-Phase Acidities of the Composites (HX)m/ MgnCl2n (X = F, Cl, Br; m, n = 1−3) at the CCSD(T) Level. As will be shown in section 3.4, the basis set effect at the CCSD(T) level could be safely neglected, and thus only the CCSD(T) results obtained with the 6-311++g(d,p) basis set are reported in this section. The ΔGacid values of all the 27 composites, as shown in Figure 3 and Tables 1−3, are less than 300 kcal/mol at the CCSD(T)/6-311++G(d,p) level, and thus the theoretical criterion for superacid is fulfilled for all of them. That is to say, all 27 composites here are probable candidates for novel superacids. Within them, the strongest acidities exist for HCl/Mg3Cl6 and HBr/Mg3Cl6, of which the values of ΔGacid are 246.86 and 246.44 kcal/mol, respectively. These

Figure 1. Equilibrium structures of the composites of (HCl)m/ MgnCl2n (m, n = 1−3) with selected bond lengths (in Å) and relative energies (in kcal/mol).

With the exception of (HCl)2/Mg2Cl4 of the Cs point group, all the (HCl)m/MgnCl2n (m = 1−3; n = 1, 2) composites possess C1 symmetry. For HCl/MgCl2, the lengths of two Mg− Cl bonds are quite close to each other, 2.19 Å of Mg1−Cl3 vs 2.21 Å of Mg1−Cl2. In comparison, the third Mg−Cl bond is apparently elongated as the length is 2.51 Å. In the case of (HCl)2/MgCl2, there are two short Cl···H contacts, i.e., Cl2··· H2 (2.24 Å) and Cl4···H1 (2.30 Å), between the second HCl molecule and the residual HCl/MgCl2. For the composite of (HCl)3/MgCl2, there are short contacts between Mg atom and the Cl atoms of the second and third HCl molecules. In the cases of (HCl)m/Mg2Cl4 composites, the lengths of the terminal Mg−Cl bonds of the binuclear superhalogen component generally lie within the range of 2.18−2.26 Å. The corresponding range of the bridging Mg−Cl bonds is 2.33− 2.40 Å. Similar to HCl/MgCl2, there are also elongated Mg−Cl bonds in these composites, e.g., Mg1−Cl3 bond (2.60 Å) in 11789

DOI: 10.1021/acs.inorgchem.7b01754 Inorg. Chem. 2017, 56, 11787−11797

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Inorganic Chemistry

are different numbers of central atoms, while for Brønsted acid, the type and number differ from each other. Thus, the effects of three factors on the acidity of the composites are analyzed here: (1) the number of central atoms of the superhalogen components, indicated by n; (2) the type of Brønsted acid in the composite, indicated by HX; (3) the number of Brønsted acids in the composite, indicated by m. When analyzing the effect of one certain factor, the other two are fixed. 3.3.1. The Effect of the Number of Central Atoms of the Superhalogen Component and the relationship between ΔGacid and VDE of the Superhalogen Components. When the type and number of Brønsted acids are fixed (Figure 4), in most cases, the ΔGacid values of the composites clearly decrease along the increasing of the number of central atoms of the superhalogen component. These results indicate that the acidity of the systems is getting stronger as the number of central atoms of the superhalogen component increases. Taking HX/MgnCl2n (X = F, Cl, Br) as examples (Figure 4a), when n increases from 1 to 3, ΔGacid values decrease by 32.04, 33.04, and 29.02 kcal/mol for X = F, Cl, and Br, respectively. In the cases of (HX)2/MgnCl2n (X = Cl, Br), the increasing of n also leads to the decreasing of ΔGacid values by 21.41 and 23.23 kcal/mol for X = Cl and Br, respectively (Figure 4b). A similar situation also exists for (HX)3/MgnCl2n (X = Cl, Br; n= 1−3), of which the ΔGacid values decrease by 21.93 and 21.85 kcal/ mol for X = Cl and Br, respectively (Figure 4c). The only exceptions are the composites containing more than one HF, e.g., (HF)2/MgnCl2n and (HF)3/MgnCl2n (n = 1−3). For these composites, the values of ΔGacid do not vary monotonically with the increasing of n as the lowest ΔGacid values occur for the composites with a binuclear superhalogen component. Many previous works have proven that the number of central atoms affects directly the stability of the superhalogen anions, characterized by its VDE value.30,48,51,63 As clearly shown in eq 1, the deprotonation of superacid will definitely lead to the existence of anion, and thus stronger stability of the anion should favor lower value of ΔGacid, equivalent to stronger acidity. In other words, the gas-phase acidity of the composites here may be closely related to the VDE of its superhalogen components. Based on this derivation, the number of central atoms of the superhalogen component would affect the acidity of the composite via its influence on the VDE, i.e., stability of the anion product. Previous works on pure superhalogen systems have shown that, generally, increasing the number of central atoms would lead to larger VDE of the anionic form of superhalogen and thus lead to enhanced anionic stability. This may be the main reason for the above finding that polynuclear superhalogen

Figure 3. Values of ΔGacid at the CCSD(T)/6-311++G(d,p) level (kcal/mol): (a) (HF)m/MgnCl2n (m, n = 1−3), (b) (HCl)m/MgnCl2n (m, n = 1−3), and (c) (HBr)m/MgnCl2n (m, n = 1−3).

values are close to the theoretical values of the strongest superacid ever reported (ΔGacid = 230.3 kcal/mol).30 3.3. Analysis on the Effects of Various Factors on ΔGacid at the CCSD(T) Level. As indicated above, one main purpose of this work is to clarify the effect of different factors on the superacid properties of this type of composite. The systems here are constructed from two components: superhalogen and Brønsted acid. In the aspect of superhalogen, there

Table 1. Values of ΔGacid (kcal/mol) of (HF)m/MgnCl2n (m, n = 1−3) Obtained from Various Theoretical Methods in Combination with the 6-311++G(d,p) Basis Set

HF/MgCl2 (HF)2/MgCl2 (HF)3/MgCl2 HF/Mg2Cl4 (HF)2/Mg2Cl4 (HF)3/Mg2Cl4 HF/Mg3Cl6 (HF)2/Mg3Cl6 (HF)3/Mg3Cl6

MP2

MP4

CCSD

CCSD(T)

ωB97XD

B3LYP

M06-2X

287.70 280.13 277.48 282.32 259.56 260.07 256.02 266.11 261.99

289.50 281.55 279.10 284.17 261.72 262.34 256.92 267.16 262.93

290.06 281.91 279.48 284.72 262.09 262.72 257.39 267.70 263.30

290.13 282.33 279.96 284.71 261.76 262.47 258.09 268.34 264.07

285.42 278.24 274.96 279.92 257.27 257.53 256.49 266.27 261.78

283.86 275.73 270.90 278.68 254.71 255.33 252.11 262.25 258.34

284.92 277.36 277.79 279.51 254.51 256.76 256.20 266.27 261.08

11790

DOI: 10.1021/acs.inorgchem.7b01754 Inorg. Chem. 2017, 56, 11787−11797

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Table 2. Values of ΔGacid (kcal/mol) of (HCl)m/MgnCl2n (m, n = 1−3) Obtained from Various Theoretical Methods in Combination with the 6-311++G(d,p) Basis Set HCl/MgCl2 (HCl)2/MgCl2 (HCl)3/MgCl2 HCl/Mg2Cl4 (HCl)2/Mg2Cl4 (HCl)3/Mg2Cl4 HCl/Mg3Cl6 (HCl)2/Mg3Cl6 (HCl)3/Mg3Cl6

MP2

MP4

CCSD

CCSD(T)

ωB97XD

B3LYP

M06-2X

277.16 271.34 270.93 270.83 260.94 260.40 245.15 250.46 248.57

279.62 273.53 273.42 273.23 265.32 262.81 245.61 251.57 249.96

279.65 273.53 273.42 273.24 265.43 262.84 245.53 251.52 249.93

279.91 274.01 274.07 273.49 263.81 264.40 246.86 252.61 250.84

273.85 268.40 265.13 267.29 258.27 257.45 244.75 248.79 245.85

272.53 266.50 258.95 266.27 254.81 256.22 241.30 245.29 240.42

269.56 264.03 265.85 263.25 254.32 252.59 240.02 244.34 243.91

Table 3. Values of ΔGacid (kcal/mol) of (HBr)m/MgnCl2n (m, n = 1−3) Obtained from Various Theoretical Methods in Combination with the 6-311++G(d,p) Basis Set HBr/MgCl2 (HBr)2/MgCl2 (HBr)3/MgCl2 HBr/Mg2Cl4 (HBr)2/Mg2Cl4 (HBr)3/Mg2Cl4 HBr/Mg3Cl6 (HBr)2/Mg3Cl6 (HBr)3/Mg3Cl6

MP2

MP4

CCSD

CCSD(T)

ωB97XD

B3LYP

M06-2X

272.26 267.99 265.97 266.58 259.38 257.49 244.58 246.84 245.32

275.08 270.46 269.00 269.28 264.11 262.02 245.36 247.88 246.88

274.98 270.53 269.11 269.36 264.29 262.23 245.30 247.87 246.91

275.46 271.10 269.77 269.71 263.85 261.88 246.44 249.18 247.92

271.66 267.92 265.12 265.95 259.06 256.55 244.15 247.74 246.42

269.86 265.54 257.77 264.44 256.59 251.44 240.87 244.23 243.76

265.51 261.59 262.56 260.03 252.13 251.26 239.54 241.88 240.28

type of Brønsted acid being fixed, is shown in Figure 7. In the cases of (HX)m/MgCl2 (X = F, Cl, Br; m = 1−3), along the increasing of m, the values of ΔGacid decrease by 10.16, 5.83, and 5.69 kcal/mol for X = F, Cl, and Br, respectively (Figure 7a). However, the variations of ΔGacid values, from m = 2 to m = 3, are actually quite small as the actual values are 2.37, 0.06, and 1.33 kcal/mol for X = F, Cl, and Br, respectively. The results of (HX)m/Mg2Cl4 (X = F, Cl, Br; m = 1−3) are similar to those of (HX)m/MgCl2. When m is increasing, the ΔGacid values decrease by 22.25, 9.10, and 7.83 kcal/mol for X = F, Cl, and Br, respectively. The differences between ΔGacid values of m = 2 and m = 3 are also small, with the values are 0.70, 0.59, and 1.97 kcal/mol for X = F, Cl, and Br, respectively. As shown in Figure 7c, the lowest ΔGacid values of (HX)m/ Mg3Cl6 composites occur when m = 1. That is to say, the acidities of these composites do not vary monotonically with the increase of m. However, it should be indicated that the total amount of the variation of ΔGacid, along m, is relatively small (5.99, 3.98, and 1.48 kcal/mol for X = F, Cl, and Br, respectively) when compared with (HX)m/MgCl2 and (HX)m/ Mg2Cl4. 3.3.4. Comparison among the Three Factors and Identification of the Dominant One. As indicated above, effective regulation of the acidities of this type of superacid is available via all three factors. However, it is not clear about which factor affects the acidity more effectively or whether there is one factor dominating over the other two. In order to answer these questions, direct comparison between two of the factors with the third one fixed is performed in this section. Figure 8 demonstrates the direct comparison between the number of central atoms of the superhalogen component and the type of Brønsted acid. Taking HX/MgnCl2n (X = F, Cl, Br; n = 1−3) as examples (Figure 8a), the decreases of ΔGacid values, resulting from the change in n, i.e., the number of central atoms of the superhalogen component, are 32.04, 33.05,

components usually result in stronger composite superacid. In order to clarify this point, the relationship between ΔGacid of the composites and the VDE (Table S4) of the corresponding superhalogen components is explored. As shown in Figure 5, for most of the composites here, larger VDE value corresponds to lower ΔGacid value. For (HCl)m/ MgnCl2n (m, n = 1−3), as the VDE values of the superhalogen components increase from 6.17 to 7.64 eV, the values of ΔGacid of the whole composite decrease from 279.91 kcal/mol to 246.86 kcal/mol, and the total amount of the variation is 33.05 kcal/mol. Similar results also take place for (HBr)m/MgnCl2n (m, n = 1−3) as shown in Figure 5c. The only exceptions are HF/MgnCl2n (n = 1−3) and (HF)2/MgnCl2n (n = 1−3), as shown in Figure 5a. 3.3.2. The Effect of the Type of Brønsted Acid. When the superhalogen component and the number of Brønsted acids are fixed (Figure 6), it could be concluded that, generally, the acidities of the composites increase along the order of the Brønsted acid, which is HF < HCl < HBr. Taking (HX)m/MgCl2 (X = F, Cl, Br; m = 1−3) as examples (Figure 6a), from HF to HCl and then HBr, the values of ΔGacid decrease by 17.87, 12.15, and 7.70 kcal/mol for m = 1, 2, and 3, respectively. As shown in Figure 6c, the ΔGacid values of (HX)m/Mg3Cl6 (X = F, Cl, Br; m = 1−3) also decrease, along the sequence from HF to HCl and HBr, by 11.64, 19.17, and 16.15 kcal/mol for m = 1, 2, and 3, respectively. The (HX)m/ Mg2Cl4 (X = F, Cl, Br; m = 2, 3) composites are the only exceptions since the influence of the type of Brønsted acid is very weak, as shown in Figure 6b. It is easy to understand that the effect of the type of Brønsted acid on the acidity of the composite probably arises from the order of the acidities of themselves, which is HF < HCl < HBr. 3.3.3. The Effect of the Number of Brønsted Acids. The effect of the number of Brønsted acids on the acidities of the whole composites, with the superhalogen component and the 11791

DOI: 10.1021/acs.inorgchem.7b01754 Inorg. Chem. 2017, 56, 11787−11797

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Figure 5. Relationship between ΔGacid and VDE of the superhalogen components: (a) (HF)m/MgnCl2n (m, n = 1−3), (b) (HCl)m/MgnCl2n (m, n = 1−3), and (c) (HBr)m/MgnCl2n (m, n = 1−3).

Figure 4. Effect of the number of central atoms of the superhalogen component on ΔGacid: (a) HX/MgnCl2n (X = F, Cl, Br; n = 1−3), (b) (HX)2/MgnCl2n (X = F, Cl, Br; n = 1−3), and (c) (HX)3/MgnCl2n (X = F, Cl, Br; n = 1−3).

examples (Figure 9b), due to the increase of n, the values of ΔGacid decrease by 33.05, 21.40, and 23.23 kcal/mol for m = 1, 2, and 3, respectively. In comparison, the magnitudes of the effect on ΔGacid values, originated from the variation of m, are remarkably small, i.e., 5.84, 9.09, and 5.75 kcal/mol for n = 1, 2, and 3, respectively. In the cases of (HBr)m/MgnCl2n (m, n = 1−3), the decreases of ΔGacid along the increase of n are 29.02, 21.23, and 21.86 kcal/mol for m = 1, 2, and 3, respectively. In the aspect of the effect of various numbers of Brønsted acids, the corresponding magnitudes of the change of ΔGacid are only 5.69, 7.83, and 2.74 kcal/mol for n = 1, 2, and 3. Similar results also occur for the composites of (HF)m/ MgnCl2n (m, n = 1−3). The decreases of ΔGacid values, due to the increase of n, are 32.04, 20.57, and 17.49 kcal/mol for m = 1, 2, and 3, respectively. In comparison, the magnitudes of the influence on ΔGacid values, due to different m, are 10.17, 22.95, and 10.25 kcal/mol for n = 1, 2, and 3, respectively. According to the results of the comparisons above, for the acidity of the composite here, the influence of the number of central atoms of the superhalogen component is stronger than the influences of both the type and number of Brønsted acids. That is to say, superhalogen component is the dominant factor determining the acidity of the composites. This point is consistent with the fact that the composites of the strongest

and 29.02 kcal/mol for X = F, Cl, and Br, respectively. In comparison, the decreases of ΔGacid values, due to the change in HX, are only 14.67, 15.06, and 11.65 kcal/mol for n = 1, 2, and 3, respectively. In the cases of (HX)2/MgnCl2n (X = F, Cl, Br; n = 1−3), the magnitudes of the influence on ΔGacid values, due to different n, are 20.57, 21.40, and 21.85 kcal/mol for X = F, Cl, and Br, respectively (Figure 8b). The corresponding magnitudes of the influence on ΔGacid values, due to different HX, are 11.23, 2.09, and 19.16 kcal/mol for n = 1, 2, and 3, respectively. As shown in Figure 8c, similar results also occur for (HX)3/ MgnCl2n (X = F, Cl, Br; n = 1−3). The magnitudes of the variation of ΔGacid values, along different n, are 17.49, 23.23, and 21.85 kcal/mol for X = F, Cl, and Br, respectively. In comparison, the magnitudes of the influence on ΔGacid values, due to different HX, are 10.19, 2.52, and 16.15 kcal/mol for n = 1, 2, and 3, respectively. Therefore, it is clearly indicated that the magnitudes of the decrease of ΔGacid values, because of the increase of central atoms of the superhalogen components, are remarkably larger than those because of the change in the type of Brønsted acid. The comparison between the number of central atoms of the superhalogen component and the number of Brønsted acids is indicated in Figure 9. Taking (HCl)m/MgnCl2n (m, n = 1−3) as 11792

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Figure 6. Effect of the type of Brønsted acid on ΔGacid: (a) (HX)m/ MgCl2 (X = F, Cl, Br; m = 1−3), (b) (HX)m/Mg2Cl4 (X = F, Cl, Br; m = 1−3), and (c) (HX)m/Mg3Cl6 (X = F, Cl, Br; m = 1−3).

Figure 7. Effect of the number of Brønsted acids on ΔGacid: (a) (HX)m/MgCl2 (X = F, Cl, Br; m = 1−3), (b) (HX)m/Mg2Cl4 (X = F, Cl, Br; m = 1−3), and (c) (HX)m/Mg3Cl6 (X = F, Cl, Br; m = 1−3).

acidity here are HCl/Mg3Cl6 and HBr/Mg3Cl6, of which the values of ΔGacid are 246.86 and 246.44 kcal/mol, respectively. Both of them contain the same superhalogen component of the largest number of central atoms, i.e., n = 3. Although containing different Brønsted acids, HCl vs HBr, the difference in their values of ΔGacid is negligible (0.42 kcal/mol). 3.4. The Performances of Various Theoretical Methods Compared to CCSD(T). As shown in Figure 10a, the trends of the variation of ΔGacid values at the CCSD(T) level along various composites are consistent for the three different basis sets. When compared to the results of the largest 6-311+ +G(2df, 2pd) basis set, the relative errors are only 0.16%− 1.44% and 0.24%−1.43% for the 6-311+G(d,p) and 6-311+ +G(d,p) basis sets, respectively, which are quite small. Their corresponding mean absolute errors (MAE) are only 2.02 and 2.01 kcal/mol, respectively, as shown in Figure S8. Therefore, the basis set effect could be safely neglected here. It should be indicated that previous studies of related superacid systems have also verified the reliability of 6-311++G(d,p).20 As indicated above, the high-level CCSD(T) method is practical for all the composites here and thus the reliabilities of our interpretation and prediction should be sufficient. However, with the deepening of the research, it is highly probable that larger composites become our targets, for which CCSD(T) is not available. Thus, the identification of reliable methods of

both low cost and large range of application is crucial for future theoretical studies of composite superacid. Taking all 27 composites here as the test set, two groups of methods are examined in comparison with CCSD(T). The first group consists of low-cost ab initio methods, which are CCSD, MP4, and MP2. The second group is the DFT method of three XC functionals (ωB97XD, M06-2X, and B3LYP). As shown in Figure 10b, the trends of the variations of ΔGacid of the low-cost ab initio methods are apparently consistent with that of CCSD(T). In the aspect of actual ΔGacid values, the results are also very encouraging. The ranges of the relative errors, compared to CCSD(T), are only −0.59% to 0.61%, −0.60% to 0.57%, and −1.69% to −0.69% for CCSD, MP4, and MP2, respectively. Correspondingly, the magnitudes of the MAE are only 0.67, 0.76, and 2.71 kcal/mol, respectively (Figure S12a and Table S6). The good performance of MP2 should be stressed since its computational cost is significantly lower than that of all the other three ab initio methods. When compared with CCSD(T), the performance of DFT methods is also encouraging as shown in Figure 10c. First, the trends of the variations of ΔGacid of DFT methods are generally consistent with that of CCSD(T) too. Second, both the relative and absolute errors, compared with CCSD(T), are also small. The ranges of relative errors are −3.26% to −0.57%, −4.46% to −0.73%, and −5.52% to −1.68% for ωB97XD, M06-2X, and 11793

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Figure 8. Direct comparison between the number of central atoms of the superhalogen component and the type of Brønsted acid: (a) one Brønsted acid, (b) two Brønsted acids, and (c) three Brønsted acids.

Figure 9. Direct comparison between the number of central atoms of the superhalogen component and the number of Brønsted acids: (a) Brønsted acid is HF, (b) Brønsted acid is HCl, and (c) Brønsted acid is HBr.

B3LYP, respectively. The corresponding values of MAE are 4.26, 7.41, and 7.35 kcal/mol, respectively (Figure S12b and Table S7). It is good news that low-cost methods of both ab initio type, e.g., MP2, and DFT, e.g., ωB97XD, could be capable of providing results approaching the accuracy at the CCSD(T) level. These low-cost methods could be safely applied in the composite superacids of enlarged size.

actually close to the corresponding theoretical value of the strongest superacid ever reported (ΔGacid = 230.3 kcal/mol). The effects of various factors, which may influence the acidity of the composites, are analyzed in detail. These factors are (1) the number of central atoms of the superhalogen components, (2) the type of Brønsted acid, and (3) the number of Brønsted acids. Although effective regulation of the acidities of the superacids here is available via all three factors, the superhalogen component is shown to be the dominant factor as stronger acidity arises from larger value of its vertical electron detachment energy. Contrarily, the effect of the Brønsted acid, either the number or the type, is relatively mild. In light of the rapid increase in the number of reported new superhalogens, the composites constructed from superhalogen and other appropriate companions may continue to provide suitable candidates for novel superacids of stronger acidity. In the aspect of theoretical methods, the reliabilities of lowcost methods for the composite superacids in this current work are verified here for both ab initio type, e.g., MP2, and DFT, e.g., ωB97XD. For the future targets of larger composite superacids, these low-cost methods may be suitable choices of the reliable source of theoretical guide as the sizes of the systems would go beyond the capabilities of CCSD(T) or other similar methods of high computational cost. However, the

4. CONCLUSIONS A systematic study, based on combined ab initio and DFT calculations, is performed here on a series of 27 composite structures consisting of superhalogen and Brønsted acid. The potentials of these composites as novel superacids and various factors affecting the acidity of the whole systems are the central points of this work. As indicated by high-level CCSD(T) results, the values of the changes of the Gibbs free energies of the deprotonation reactions, i.e., ΔGacid, are all less than 300 kcal/mol here. In other words, the theoretical criterion for superacid is fulfilled for all of these designed structures, and thus they are all probable candidates for novel superacids. The ΔGacid values of the strongest superacids here, HCl/Mg3Cl6 and HBr/Mg3Cl6, are 246.86 and 246.44 kcal/mol, respectively. These values are 11794

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grant No. 21103137) and Natural Science Foundation of Shaanxi Province (Grant No. 2016JQ2038). B.Y. is grateful to the “Excellent Young Scholar Plan” of Northwest University (Grant No. 338050094). W.H.X. thanks the Education Department of Shaanxi Provincial Government for financial support (No. 15JK1749).

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Figure 10. Performances of various methods compared to CCSD(T): (a) basis set effect at the CCSD(T) level, (b) the comparison between CCSD(T) and other low-cost ab initio methods, and (c) the comparison between CCSD(T) and DFT.

reliabilities of MP2 and DFT for new composite superacids still need to be carefully checked, and this endeavor will not be neglected in our following works. We hope this work will provide useful guidance for the research of novel superacids with enhanced properties and thus could promote related experimental study in the near future.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01754. Listings of all the optimized structures, Cartesian coordinates, lowest normal-mode frequencies, and supplementary numerical details (PDF)

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Bing Yin: 0000-0001-8668-9504 Notes

The authors declare no competing financial interest. 11795

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