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Received: 3 April 2017 | Revised: 25 May 2017 | Accepted: 26 May 2017 DOI: 10.1002/qua.25419 FULL PAPER Dissociation of sulfur oxoacids by two water molecules studied using ab initio and density functional theory calculations You Kyoung Chung | Seong Kyu Kim Department of Chemistry and Basic Science Research Institute, Sungkyunkwan Abstract University, Suwon 16419, Korea Using ab initio [SCS-MP2 and CCSD(T)] and density functional theory (M062X) calculations, we have studied the geometries and energies of sulfur oxoacids H2SmO6 (m 5 2–4) and their monohy- Correspondence drated and dihydrated clusters. When including the results from previously reported disulfuric acid Seong Kyu Kim, Department of Chemistry < < < and Basic Science Research Institute, (H2S2O7) cases, the gas phase acidity is ordered as H2S2O6 H2S3O6 H2S2O7 H2S4O6.The Sungkyunkwan University, Suwon 16419, intramolecular H-bonding, which may indicate the degree of structural flexibility in this molecular Korea. series, is an important factor for the order of the gas phase acidity. All these sulfur oxoacids show Email: [email protected] dissociated (or deprotonated) geometries with only two water molecules, although the energies of Funding information the dissociated conformers are ranked differently. All of the dissociated conformers form a unique 1 YKC was supported by the Program for H-bonding network structure in which the protonated first water (H3O ) is triply H-bonded to Returners into R&D (KW- 2015-PPD-0175) each oxygen atom of two SO3 moieties as well as the second water, which in turn is H-bonded to of the Center for Women in Science, Engineering and Technology (in Korea). aSO3 moiety. H2S3O6 has the best molecular flexibility for adopting such an H-bonding network structure, and thereby all the low-lying conformers of H2S3O6(H2O)2 are dissociated. In contrast, the least flexible H2S2O6 forms such a structure with a high strain, and dissociation of H2S2O6(H2O)2 is found from the third lowest conformer. Although the gas phase acidity of H2S4O6 is the highest in this series, the lowest dissociated conformer and the lowest undissoci- ated conformer of H2S4O6(H2O)2 are very close in energy. This is because forming the H-bonding network structure is somewhat difficult due to the large distance between the two SO3 moieties. KEYWORDS ab initio,H2S2O6,H2S3O6,H2S4O6, sulfur oxoacid 1 | INTRODUCTION Hydrated clusters of acids can provide information on the molecular-level interaction between an acid solute and a water solvent.[1] Such informa- tion is useful for understanding the aerosol nucleation process that occurs in the atmosphere.[2–6] In particular, the condition required for an acid to transfer a proton to solvated water has been an interesting topic for many theoreticians as well as spectroscopists over decades. They have focused on H-bonding geometries in clusters and the number of water molecules needed for deprotonation from the acid. There have been several experimental findings related to the deprotonation phenomena in hydrated acid clusters. For HNO3(H2O)n,Ritzhaupt [7] 2 and Devlin suggested that as many as three water molecules are needed to form NO3 species in hydrated thin films, as determined by Fourier- transform infrared (FTIR) spectroscopy. Later, in a matrix isolated FTIR study, McCurdy et al.[8] claimed that four water molecules are needed to [9] form the ionized species. For HCl(H2O)n, the matrix isolated IR spectra studied by Amirand and Maillard and the mass-selective IR depletion spec- tra in the helium droplet state studied by Gutberlet et al.[10] identified the deprotonated complex for n 5 4, while the mass-selective IR study by Flynn et al.[11] concluded that five water molecules are needed for deprotonation. In the mass-selective ultrafast pump-probe experiment, Herley et al.[12] suggested that photoexcited hydrated HBr undergoes deprotonation for n 5. Experimental results sometimes involve nonideal sample preparation or ambiguous interpretations, which can be avoided by theoretical approaches. Thereby, a larger body of research on hydrated acid clusters has been conducted through computational methods. Table 1 provides a summary of the number of water molecules needed for deprotonation in the hydrated acid clusters studied so far with ab initio or density functional Int J Quantum Chem. 2017;117:e25419. http://q-chem.org VC 2017 Wiley Periodicals, Inc. | 1of11 https://doi.org/10.1002/qua.25419 2of11 | CHUNG AND KIM TABLE 1 Number of water molecules needed for deprotonation from hydrated acid clusters a b Acid nl ng HF 4[13,14] > 10[15] HCl 4[14] 4[14] HBr 3[14,16] 4[14,16] HI 3[14] 3[14] [8,17] [17] HNO3 4 5 [18,19] [5] [18] H2SO4 3 4 ,5 c [20] [20] HSO3X 3 3 [21] [21] CH3SO3H3 3 [22] [22] HClO4 3 3 [23] [23] H2S2O7 2 2 aFrom local minimum geometries. bFrom global minimum geometries. cX: halogen atom. theory (DFT) calculations. [Unless stated otherwise, the number of water molecules needed for deprotonation, the global (or local) minimum, and the lowest (or low-lying) conformers referred to in this article are derived from the calculated electronic energy.] Except for HF, the acids listed in Table 1 are classified as strong acids. Qualitatively, the stronger acids appear to require a smaller number of water molecules for deprotonation. The smallest number of water molecules for deprotonation studied so far is two for the disulfuric acid (H2S2O7) system, as recently found in a previous [23] study by one of the present authors. Owing to the flexible structure of H2S2O7, an effective H-bonding network structure is formed with only two water molecules, a feature that is absent in the other strong acids in Table 1. This is consistent with the expectation that H2S2O7 must be much stronger than the other acids in Table 1.[24,25] The strength of acids in a solution is usually represented by the pKa value, which varies with solvent, temperature, and concentration. The his- [25–27] [28] tory of finding pKa values for Brønsted acids in solution spans over many decades, which is now collected into the NIST database. As the acids become stronger, obtaining reliable pKa values through experiments becomes more difficult and computational approaches tend to be more reliable. In such computational methods,[25,29–33] the gas phase acidity and the energies of the solvating acids along with their dissociated ions are calculated using numerous continuum solvation models. The gas phase acidity of HA is usually represented by the Gibbs free energy of dissociation (DGg): ÀÁ 1 2 DGg5G H 1GðÞA 2GðÞHA ; (1) – where G is the Gibbs free energy of each species. The lower the DGg value, the stronger the acidity of HA. For the computation, G(HA) and G(A ) are obtained from high-level ab initio electronic energies and thermal corrections for their global minimum geometries, while only the thermal contri- bution is needed for G(H1). For most acids, the computational results are in good agreement[33–35] with spectroscopic data. [24] Otto and Steudel calculated DGg values for global minimum conformers of a few sulfur oxoacids and then used the data to order their acid- ities as follows: H2S2O4 < H2SO3X(X5 F, Cl) H2S2O6 < H2S2O7 < H2S3O6 < H2S4O6. According to this order, we expected that two or less than two water molecules are needed for deprotonation from H2S3O6 or H2S4O6 since they are reportedly stronger than H2S2O7. This motivated us to calculate the hydrated clusters of H2SmO6 (m 5 2–4) and study the deprotonation phenomena. Since they are almost the strongest Brønsted acids, H2S2O6 (dithionic acid), H2S3O6 (trithionc acid), and H2S4O6 (tetrathionic acid) are found only in their anionic forms. Nevertheless, studying the hydrated clusters of these acids would be meaningful since the series experiences variations in structural flexibility. Usually, the acid strength is com- pared and discussed within a molecular series in which an atom or a group of atoms is substituted in the same structure, for example, as in the hydrogen halide series or as in the oxyacid series. However, in this series consisting of sulfur oxoacids, the structural flexibility is varied with no (H2S2O6), one (H2S3O6), or two (H2S4O6) sulfur atoms to link the two SO3H moieties. We were interested in how such a structural variation influen- ces the acidity or the number of water molecules needed for deprotonation. 2 | METHODS To begin the calculation, we employed a conformation distribution function in the Spartan’ 14 program[36] to obtain local geometries of each cluster. By implementing a Monte Carlo search using a molecular mechanical force field or a semiempirical parametrized Hamiltonian, the function provided approximately 20–40 geometries for each cluster. The obtained geometries were then used as the starting geometries for optimization via the DFT CHUNG AND KIM | 3of11 2 5 – FIGURE 1 The geometries of H2SmO6 and HSmO6 (m 2 4) optimized via the SCS-MP2/aVTZ method. Weak intramolecular H-bonds are shown with dotted straight lines calculations by using a hybrid functional M062X[37] and TZVP[38] basis set. Several low-lying conformers from the DFT calculations were then fur- ther optimized by utilizing the spin-component scaled[39] (SCS, scaling factors are 1.2 for the same spins and 0.3 for opposite spins) second order Møller–Plesset perturbation (MP2) theory,[40] implemented by the resolution of identity (RI) method[41] with the aug-cc-pVTZ basis set[42] (abbrevi- ated as aVTZ). The SCS-MP2 is meant to be a general improvement of MP2[43] and was tested successfully for numerous noncovalent systems,[44] although in a test by Boese,[45] the MP2 outperformed the SCS-MP2 for hydrogen bonded systems. When we tested these two theories for this work, no appreciable difference was found in the optimized geometries and the binding energy differences were less than 0.1 kcal/mol.

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