Dissociation of sulfur oxoacids by two water molecules studied...

F U L L P A P E R

Dissociation of sulfur oxoacids by two water molecules studiedusing ab initio and density functional theory calculations

You Kyoung Chung | Seong Kyu Kim

Department of Chemistry and Basic Science

Research Institute, Sungkyunkwan

University, Suwon 16419, Korea

Correspondence

Seong Kyu Kim, Department of Chemistry

and Basic Science Research Institute,

Sungkyunkwan University, Suwon 16419,

Korea.

Email: [email protected]

Funding information

YKC was supported by the Program for

Returners into R&D (KW- 2015-PPD-0175)

of the Center for Women in Science,

Engineering and Technology (in Korea).

AbstractUsing ab initio [SCS-MP2 and CCSD(T)] and density functional theory (M062X) calculations, we

have studied the geometries and energies of sulfur oxoacids H2SmO6 (m52–4) and their monohy-

drated and dihydrated clusters. When including the results from previously reported disulfuric acid

(H2S2O7) cases, the gas phase acidity is ordered as H2S2O6<H2S3O6<H2S2O7<H2S4O6. The

intramolecular H-bonding, which may indicate the degree of structural flexibility in this molecular

series, is an important factor for the order of the gas phase acidity. All these sulfur oxoacids show

dissociated (or deprotonated) geometries with only two water molecules, although the energies of

the dissociated conformers are ranked differently. All of the dissociated conformers form a unique

H-bonding network structure in which the protonated first water (H3O1) is triply H-bonded to

each oxygen atom of two SO3 moieties as well as the second water, which in turn is H-bonded to

a SO3 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.

K E YWORD S

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

and Devlin[7] suggested that as many as three water molecules are needed to form NO23 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

form the ionized species. For HCl(H2O)n, the matrix isolated IR spectra studied by Amirand and Maillard[9] and the mass-selective IR depletion spec-

tra in the helium droplet state studied by Gutberlet et al.[10] identified the deprotonated complex for n54, 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.https://doi.org/10.1002/qua.25419

http://q-chem.org VC 2017Wiley Periodicals, Inc. | 1 of 11

Received: 3 April 2017 | Revised: 25 May 2017 | Accepted: 26 May 2017

DOI: 10.1002/qua.25419

http://orcid.org/0000-0003-0902-3738

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

study by one of the present authors.[23] 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-

tory of finding pKa values for Brønsted acids in solution[25–27] spans over many decades, which is now collected into the NIST database.[28] 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):

DGg5G H1� �

1G A2ð Þ2G HAð Þ; (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.

Otto and Steudel[24] 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 (X5F, 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 (m52–4) 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

TABLE 1 Number of water molecules needed for deprotonation from hydrated acid clusters

Acid nla ng

b

HF 4[13,14] > 10[15]

HCl 4[14] 4[14]

HBr 3[14,16] 4[14,16]

HI 3[14] 3[14]

HNO3 4[8,17] 5[17]

H2SO4 3[18,19] 4[5], 5[18]

HSO3Xc 3[20] 3[20]

CH3SO3H 3[21] 3[21]

HClO4 3[22] 3[22]

H2S2O7 2[23] 2[23]

aFrom local minimum geometries.bFrom global minimum geometries.cX: halogen atom.

2 of 11 | CHUNG AND KIM

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.

While all geometries reported in this article are from the SCS-MP2/aVTZ optimization, their energies were refined by single point energy calcu-

lations using a larger basis set, aug-cc-pVQZ (abbreviated as aVQZ), and/or with higher level coupled cluster theory with single, double, and pertur-

bative triple excitations [CCSD(T)] using the aug-cc-pVTZ basis set. In the SCS-MP2 and the CCSD(T) calculations, the basis set for the core

electrons was fixed and a consistent auxiliary basis set was added for the valence electrons. The SCS-MP2 energy in the complete basis set (CBS)

limit was obtained by the following relation:[46,47]

ESCS-MP2=CBS5 43ESCS-MP2=aVQZ233ESCS-MP2=aVTZ� �

=ð43233Þ; (2)

where the E’s are the uncorrected electronic energies and their superscripts represent the methods of calculations. The CBS limit energy for the

CCSD(T) method was obtained by adding the CBS correction term at the MP2/aVTZ and MP2/aVQZ levels to the CCSD(T)/aVTZ energy.[48] That

is,

ECCSDðTÞ=CBS5ECCSDðTÞ=aVTZ1EMP2=CBS2EMP2=aVTZ: (3)

Vibrational frequencies, which determine the zero-point energy (ZPE) and the thermal energy corrections to provide the Gibbs free energy GT

at temperature T, were obtained via the M062X method for selected low energy conformers. This should result in negligible errors to the correction

since the geometries optimized with the SCS-MP2 and those with the M062X are nearly the same.

For the final analysis of the atomic charges, the Wiberg bond order,[49] bond ionicity, and natural bond orbital (NBO) analysis[50,51] were studied

along with the MP2/aVTZ results. We used the Gaussian 09 program[52] for the M062X calculations and the Turbomole 7.1 program[53] for the

MP2, SCS-MP2, and CCSD(T) calculations. For the NBO analysis, an NBO3.1 module integrated into the Gaussian 09 program was used.

3 | RESULTS

3.1 | Geometries of H2SmO6 and HSmO26 (m52–4)

The geometries of the bare H2S2O6, H2S3O6, and H2S4O6, optimized with the SCS-MP2/aVTZ method are shown in Figure 1. Only the conformers

whose energies are close to that of the global minimum within 3.5 kcal/mol are shown. Selected structural parameters for each conformer are

shown in Table 2, while extensive information on the parameters (including those for hydrated clusters) is found in the Supporting Information. The

electronic part of the uncorrected energy (Ee), its ZPE correction (E0), and Gibbs free energy at 298 K (G298K) relative to each global minimum value

are also reported in Table 2. We also show, for comparison, the values for H2S2O7 from the work presented in Ref. [23].

FIGURE 1 The geometries of H2SmO6 and HSmO26 (m52–4) optimized via the SCS-MP2/aVTZ method. Weak intramolecular H-bonds are

shown with dotted straight lines

CHUNG AND KIM | 3 of 11

First, the following convention for denoting the conformers is provided. a, b, c, or a represents H2S2O6, H2S3O6, H2S4O6, or H2S2O7, respec-

tively, and is followed by wn to denote n water molecules; the wn notation is omitted for bare molecules. The notation ends with an integer, for

example, 0, 1, 2, and so forth, which respectively denotes the conformer of the lowest energy, the second lowest energy, the third lowest energy,

and so forth. For the corresponding anion, a–, b–, c–, or a– is used with no integer since only one conformer for each anion was found.

Second, label numbers on the atoms are assigned to be consistent for all conformers, and so the label numbers 1 to 10 are given to atoms for

the two SO3H moieties, as shown in Figure 1A. The hydrogen to be dissociated is given the number 10. Then, the linking sulfur atoms for H2S3O6

and H2S4O6 are given the numbers 11 and 12, as shown in Figure 1F,H, respectively. For the hydrated clusters, the atoms from the first and the

second water molecules are labeled as O13, H14, H15 and O16, H17, H18, respectively.

The global minimum geometry of H2S2O6 (a0) is consistent with that reported by Otto and Steudel[24] or by Abedi and Farrokhpour.[25] In addi-

tion, three more conformers of H2S2O6 whose SCS-MP2/aVTZ energy is within 3.5 kcal/mol are found. The third lowest and the fourth lowest con-

formers (a2 and a3) are similar to the second lowest and the third lowest conformers, respectively, from the report by Otto and Steudel. However,

the second lowest conformer (a1) is newly found. The global minimum geometry of H2S3O6 (b0) has a shape identical to that of H2S2O7, as reported

in Ref. [23], except the linking atom in the middle. It shows the two intramolecular H-bonds with C2 symmetry. Owing to the stabilization effect

made by the intramolecular H-bonds, its energy is lower than that of the next lowest conformer by more than 7 kcal/mol. The two lowest conform-

ers reported by Otto and Steudel are the second lowest and the third lowest conformers in our case. Therefore, we only report the newly found

and dominantly lowest b0 for H2S3O6. The global minimum conformer of H2S4O6 (c0) also shows the two intramolecular H-bonds, which is slightly

stronger than that of H2S3O6 (b0) or H2S2O7 (a0) based on the interatomic distance. The next lowest conformer (c1) shows one intramolecular H-

bond. These two conformers were absent in Otto and Steudel’s report. The SCS-MP2/aVTZ energy of their global minimum conformer is higher by

more than 5 kcal/mol compared to that found in our study and thus is not reported in this work.

3.2 | Geometries and energies of H2S2O6(H2O)1–2

The geometries of low-lying conformers of H2S2O6(H2O)1–2 are shown in Figure 2, and their energies are summarized in Table 3. In the reported

energy, DEe is the uncorrected electronic energy of the cluster minus the sum of energies of all fragments, so that –DEe represents the binding

energy of the cluster. DE0 and DG298K are defined in the same way.

Particularly interesting geometries are found for H2S2O6(H2O)2, in which the lowest and second lowest conformers (aw20 and aw21, respec-

tively) show undissociated geometries, but the third, fourth, and fifth lowest conformers (aw22, aw23, and aw24, respectively) show dissociated geo-

metries. The binding energy [–DEe (–DE0)] of the dissociated aw22 is smaller than that of the undissociated aw20 by 2.8 (2.8), 2.7 (2.8), 2.6 (2.7), 2.5

(2.5), and 2.4 (2.4) kcal/mol at the SCS-MP2/aVTZ, SCS-MP2/aVQZ, SCS-MP2/CBS, CCSD(T)/aVTZ, and CCSD(T)/CBS levels, respectively. All five

low-lying conformers of H2S2O6(H2O)3, as shown in the Supporting Information, are dissociated.

TABLE 2 Selected geometrical parameters, bond orders, and energy values for the optimized sulfur oxoacids and their corresponding anionsa

H2S2O6 H2S3O6 H2S4O6 H2S2O7b

a0 a1 a2 a3 a– b0 b– c0 c1 c– a0 a1 a–

Bond length (Ǻ)O9AH10 0.972 0.972 0.973 0.971 0.983 0.985 0.971 0.979 0.971O9AH5 4.380 3.838 2.661 4.422 2.021 1.904 1.616 1.848 1.825 1.535 1.989 2.038 1.678S1AZc 2.184 2.187 2.207 2.206 2.245 2.121 2.089 2.151 2.156 2.128 1.653 1.627 1.586

Bond orderd

O9AH10 0.724 0.720 0.720 0.726 0.680 0.675 0.667 0.676 0.682 0.632O7AH5 0.000 0.000 0.000 0.000 0.020 0.026 0.096 0.030 0.016 0.131 0.013 0.002 0.060S1AZc 0.509 0.497 0.497 0.499 0.455 0.777 0.832 0.727 0.794 0.742 0.666 0.704 0.784

Bond ionicity

O9AH10 0.519 0.522 0.522 0.516 0.522 0.548 0.577 0.551 0.564 0.602 0.556 0.552 0.580

Ee-(Ee)mine 0 0.35 0.82 1.26 0 0 0 0 1.95 0 0 3.15 0

E0-(E0)mine 0 0.58 0.74 1.20 0 0 0 0 1.95 0 0 3.30 0

G298K-(G298K)mine 0 0.80 0.25 0.68 0 0 0 0 1.21 0 0 2.05 0

aFor the geometries optimized via the SCS-MP2/aVTZ method.bFrom the work of Ref. [23].cZ denotes an atom in the linking group. That is, Z5 S6 for H2S2O6, Z5 S11 for H2S3O6 and H2S4O6, and Z5O11 for H2S2O7.dThe Wiberg bond order.eEe/E0 is the ZPE-uncorrected/corrected energy and G298K is the Gibbs free energy at 298 K, where Ee used the SCS-MP2/aVTZ value while ZPE andthe thermal energy used the M062X/TZVP values. The subscript ‘min’ denotes the global minimum.



The geometries of low-lying conformers of H2S3O6(H2O)1–2 are shown in Figure 3, and their energies are summarized in Table 3. The three lowest

conformers of H2S3O6(H2O)1 are not dissociated, but all five lowest conformers of H2S3O6(H2O)2 are dissociated.


The geometries of low-lying conformers of H2S4O6(H2O)1–2 are shown in Figure 4, and their energies are summarized in Table 3.

Particularly interesting geometries are found for H2S4O6(H2O)2, in which the global minimum conformer (cw20) shows an undissociated geome-

try, but the second and fourth lowest conformers (cw21 and cw23, respectively) show dissociated geometries. The binding energy [–DEe (–DE0)] of

the dissociated cw21 is smaller than that of the undissociated cw20 by only 0.2 (1.0), 0.1 (0.8), and 0.003 (0.7) kcal/mol at the SCS-MP2/aVTZ, SCS-

MP2/aVQZ, and SCS-MP2/CBS, levels, respectively. However, at the CCSD(T)/aVTZ and CCSD(T)/CBS levels, the binding energy [–DEe (–DE0)] of

cw21 is larger than that of cw20 by 0.4 (–0.26) and 0.7 (–0.05) kcal/mol, respectively.

4 | DISCUSSION

4.1 | Energetic criteria for gas phase activity

We first provide the gas phase acidities (DGg at 1 atm and 298 K) for the sulfur oxoacids calculated at the CCSD(T)/CBS level in Table 4. The tabu-

lated values are averages over all conformers with weighing factors of exp[-{Ee-(Ee)min}/kT]. Here and in follow-up discussions, the (unpublished as

well as published) data for the H2S2O7 system stemming from the work of Ref. [23] are included since they were obtained using the same methods

as the current work. We also used the energies of H1(H2O)1 and H1(H2O)2 as calculated by the same protocol to complete the table.

The DGg values for the four sulfur oxoacids range from 277 to 284 kcal/mol. These values are much lower than those for most well-known

strong acids. For example, the reported DGg values for HClO4,[33] CF3SO3H,

[30,33] and HI[33,35] are 293.5, 292.4, and 309.0 kcal/mol, respectively.

Therefore, the sulfur oxoacids must be stronger than those acids. The DGg values comparable to those for the sulfur oxoacids are found in

(CF3SO2)2NH and (CF3SO2)2CH, whose experimental DGg values are 291.8 and 289.0 kcal/mol, respectively.[54] The DGg values for the four sulfur

oxoacids calculated by Otto and Steudel[24] or by Abedi and Farrokhpour[25] are also shown in parentheses. While our calculated values are in gen-

eral slightly higher than their values, a rather big difference is found in H2S3O6; our value is higher by 5.1 kcal/mol compared to Otto and Steudel’s

FIGURE 2 Geometries of H2S2O6(H2O)1–2 optimized with the SCS-MP2/aVTZ method. The geometries of H2S2O6(H2O)3 are shown in theSupporting Information


value. This is mainly due to a contribution from the newly found global minimum conformer, which is much more stable than that of Otto and Steu-

del (by 7.1 kcal/mol in the SCS-MP2/aVTZ energy). With the DGg values of our calculation, the gas phase acidity for the four sulfur oxoacids is

ordered as H2S2O6<H2S3O6<H2S2O7<H2S4O6, which is different from Otto and Steudel’s report.

For the hydrated acid clusters, the Gibbs free energy for microsolvation (DGs) should be added to give the overall change of Gibbs free energy.

DGs is defined as the free energy of solvating ionized species minus that of solvating neutral acid. For n51, the micro-solvated state is either

H1(H2O)1 or A– (H2O)1. For the sulfur oxoacids considered in this study, the binding energy of H1(H2O)1 is much larger than that of A– (H2O)1. (For

example, the binding energies (–DEe) of H1(H2O)1 and HS2O

27 (H2O)1, calculated at the SCS-MP2/aVTZ level, are 171.5 and 11.4 kcal/mol, respec-

tively.) Therefore, DGs is equal to the free energy of binding H1(H2O)1 minus that of binding HA(H2O)1. Likewise, for n52, DGs is the free energy

of binding H1(H2O)2 minus that of binding HA(H2O)2 since the binding energy of H1(H2O)2 is larger than that of A–(H2O)2 or the sum of the binding

energies of H1(H2O)1 and A– (H2O)1. The order of acidity judged from the DGg1DGs values for HA(H2O)1 and HA(H2O)2 does not change from that

found in the gas phase, as the difference in free energy of binding HA(H2O)1,2 over the series is small.

Since the DGs values are negative, the overall change of Gibbs free energy DGg1DGs is lower than DGg and decreases as the size of the

hydrated acid cluster increases. As the size increases further, the contribution of solvating A– becomes more important, and the DGg1DGs value is

expected to become negative and saturated to the value of solution state. In Abedi and Farrokhpour’ report,[25] the DGg1DGs values for H2S2O6(aq)

and H2S2O7(aq) are 227.0 and221.8 kcal/mol, respectively, at the CCSD/6–31111G(d,p) level.

4.2 | Structural criteria for gas phase acidity

The order of the gas phase acidity, H2S2O6<H2S3O6<H2S2O7<H2S4O6, is consistent with the O9AH10 bond order shown in Table 2; the OH

bond order for H2S2O6 is the highest, that for H2S4O6 is the lowest, and that for H2S3O6 is slightly higher than that for H2S2O7. Here, two criteria

for the bond order can considered; one is the bond ionicity (or polarity) and the other is the bond strength.

TABLE 3 Binding energies and Gibbs free energy of the binding (kcal mol21) for low-lying conformers of H2SmO6(H2O)1–2 (m52–4)a

SCS-MP2 CCSD(T)aVTZ aVQZ CBS aVTZ CBS

–DEe (–DE0) –DG298K –DEe –DEe –DEe –DEe (–DE0) –DG298K

H2S2O6(H2O)1,2aw10 14.9 (12.6) 3.7 14.6 14.5 16.3 16.1 (13.8) 4.9aw11 14.1 (11.9) 3.0 13.9 13.7 15.6 15.2 (13.0) 4.1aw12 13.9 (11.9) 3.1 13.7 13.5 15.3 15.0 (13.0) 4.2aw20 29.2 (24.6) 6.3 28.8 28.4 32.2 31.6 (27.0) 8.6aw21 28.0 (23.7) 5.6 27.6 27.3 32.2 31.7 (27.4) 9.3aw22

b 26.5 (21.8) 3.5 26.1 25.8 29.8 29.2 (24.5) 6.2aw23

b 25.8 (21.4) 3.2 25.1 24.6 28.7 27.6 (23.3) 5.1aw24

b 25.6 (21.0) 2.7 25.2 24.9 28.9 28.3 (23.7) 5.4

H2S3O6(H2O)1,2bw10 12.2 (10.0) 1.9 12.0 11.8 13.3 13.0 (10.8) 2.7bw11 12.0(10.0) 2.0 11.8 11.6 13.0 12.8 (10.7) 2.8bw12 7.5 (6.5) 1.6 7.0 6.6 8.4 7.6 (6.6) 1.6bw20

b 23.5 (18.4) 1.2 23.1 22.8 26.3 25.7 (20.5) 3.4bw21

b 20.9 (15.6) 1.7 20.4 20.1 23.7 22.9 (17.6) 0.3bw22

b 19.3 (14.7) 1.7 19.0 18.8 21.4 21.0 (16.3) 0.2bw23

b 19.0 (14.4) 2.8 18.7 18.5 21.1 20.6 (16.0) 1.4bw24

b 18.7 (14.1) 2.2 18.3 18.0 21.0 20.2 (15.6) 0.9

H2S4O6(H2O)1,2cw10 14.4 (11.5) 3.7 14.2 14.1 15.3 15.1 (12.3) 4.5cw11 12.7 (9.9) 1.7 12.6 12.4 13.8 13.7 (10.9) 2.6cw12 12.4 (9.4) 1.7 12.2 12.0 12.8 12.6 (9.6) 1.9cw13 12.2 (9.5) 1.8 12.0 11.9 12.7 12.6 (9.9) 2.2cw20 25.2 (19.7) 3.2 24.7 24.4 27.0 26.4 (20.9) 4.4cw21

b 24.9 (18.7) 2.4 24.6 24.4 27.4 27.0 (20.8) 4.5cw22 24.4 (19.2) 3.3 24.0 23.8 26.1 25.7 (20.5) 4.6cw23 24.2 (18.6) 2.0 23.9 23.6 26.0 25.5 (19.9) 3.3cw24

b 23.6 (17.9) 0.6 23.2 22.9 26.2 25.7 (20.0) 2.6

aDEe is the difference in electronic energy between the cluster and the individual molecules, while DE0 is the difference in ZPE-corrected energies.Basis set superposition errors were not corrected because of the dissociation phenomena. The ZPE and the thermal correction for DG298K used thebM062X/TZVP values.Dissociated geometry.


The OH bond ionicity is calculated with the natural polarization coefficients cO and cH to generate the natural OH bond orbital from the hybrid

orbital of O and the 1s orbital of H. That is,[50]

ionicity5c2O2c2H� �

c2O1c2H� � : (4)

FIGURE 4 Geometries of H2S4O6(H2O)1–2 optimized with the SCS-MP2/aVTZ method

FIGURE 3 Geometries of H2S3O6(H2O)1–2 optimized with the SCS-MP2/aVTZ method


As shown in Table 2, the OH bond ionicity increases in the order of H2S2O6<H2S3O6<H2S4O6, which is the same order as for the gas phase acid-

ity. However, the OH bond ionicity of H2S2O7 is larger than that of other acids and therefore, from the bond ionicity viewpoint, H2S2O7 should be

the strongest acid. As for the other criteria, the OH bond strength can be judged from the O9AH10 bond length. This increases in the order as

H2S2O6<H2S3O6<H2S4O6. However, the OH bond length for H2S2O7 is between those for H2S2O6 and for H2S3O6. Therefore, the bond strength

criteria lowers the rank for acidity of H2S2O7 that is achieved through the bond ionicity criteria.

H2S3O6 and H2S2O7 have the same shape in which two intramolecular H-bonds are made in a C2 symmetry structure. However, their electronic

structures are very different due to having more electronegative oxygen atoms in the center of H2S2O7 than the corresponding sulfur atom in

H2S3O6. The atomic charges of the central three atoms (SAOAS) in H2S2O7 are 1, –,1while those (SASAS) in H2S3O6 are1,1,1. This difference

in charge distribution implies that the partial negative charge on O9 is delocalized over the other atoms in H2S2O7 more efficiently than in H2S3O6.

As a result, the OH bond ionicity for H2S2O7 is greater than that for the other sulfur oxoacids.

The global minimum geometries for H2S3O6, H2S4O6, and H2S2O7 have two intramolecular H-bonds, whose strength as judged from the

Wiberg bond order (although this may not be strictly correct for nonbonding characters) and the interatomic (O7AH5) distance is ordered as

H2S4O6>H2S3O6>H2S2O7>H2S2O6, as shown in Table 2. This is the same order for the O9AH10 bond length and the reverse order for the

O9AH10 bond strength. Therefore, intramolecular H-bonding is thought to play a role in the gas phase acidity. The degree of intramolecular H-

bonding may be a measure for the molecular flexibility. H2S2O6 has no linking atom, making it difficult to direct two OH bonds to the proper orien-

tation and distance, and thus no intramolecular H-bond is formed. In this sense, H2S2O6 is considered to be the least flexible molecule. H2S4O6 is

the most flexible molecule in this series owing to two kinds of twisting around the two linking sulfur atoms, and two intramolecular H-bonds are

formed in the global minimum geometry. While each of H2S3O6 and H2S2O7 has one linking atom and two intramolecular H-bonds in their respec-

tive global minimum geometry, H2S3O6 appears to be slightly more flexible given that the intramolecular H-bonds are stronger.

4.3 | Number of water molecules for deprotonation

There are three criteria for judging deprotonation in hydrated hydroxy clusters: the OAH bond length, the OAH bond order, and the OAH stretch-

ing frequencies. When the hydrated hydroxyl cluster is deprotonated, the number of vibrational modes in the wavenumber region between 2100

and 2820 cm21 is increased due to the stretching modes in the eigen structure of H3O1.[55–59] All the dissociated conformers that we designated in

Tables 3 satisfy these three criteria, as demonstrated in Supporting Information.

The deprotonation phenomena observed in this study can be summarized as follows. For all the sulfur oxoacids investigated in this work and in

Ref. [23], two water molecules are needed for the dissociation at the low-lying energy states. The degree of dissociation in terms of the rank for the

energy of the dissociated conformer differs as follows. The dissociated geometry for H2S2O6(H2O)2 appears from the third lowest conformer, while

the lowest and the second lowest conformers are not dissociated. The global minimum geometry of H2S2O7(H2O)2 shows dissociation but the ener-

gies of the undissociated second and third lowest conformers are very close.[23] For H2S3O6(H2O)2, all low-lying conformers exhibit dissociated geo-

metries. For H2S4O6(H2O)2, the energies of the lowest undissociated and the lowest dissociated conformers are very close, and their orders vary

TABLE 4 Sum of the Gibbs free energies (kcal/mol) of the gas phase dissociation (DGg) and microsolvation (DGs) at 298 K and 1 atm

DGg1DGsa

H2S2O6 284.0 (282.0)b,c (278.9)d

H2S3O6 282.3 (277.2)b

H2S4O6 277.3 (276.3)b

H2S2O7 280.1 (279.9)b,c (280.1)d

H2S2O6(H2O)1 121.8

H2S3O6(H2O)1 111.9

H2S4O6(H2O)1 115.6

H2S2O7(H2O)1 117.5

H2S2O6(H2O)2 109.3

H2S3O6(H2O)2 102.9

H2S4O6(H2O)2 98.7

H2S2O7(H2O)2 101.7

aFor bare molecules, DGg1DGs 5DGg.bMP2/6–31111G(3df,3pd) results from Ref. [24].cMP2/6–31111G(3df,3pd) results from Ref. [25].dCCSD/6–31111G(d,p) results from Ref. [25].


with the calculation method; with the SCS-MP2 calculation, the undissociated conformer is the global minimum, while with the CCSD(T) calculation,

the dissociated conformer is the global minimum.

If the acidity is judged from the number of water molecules for deprotonation and the degree of dissociation, H2S3O6 must be the strongest.

This is not consistent with the order of gas phase acidity that we stated earlier. Therefore, an additional factor must determine the number of water

molecules for deprotonation and its degree of dissociation. It is interesting that the geometries of all dissociated dihydrated conformers have a com-

mon feature, as is schematically shown in Figure 5A. This common feature also holds for the dissociated conformers of (H2SO4)2(H2O)2[3] and

H2S2O7(H2O)2.[23] In the right side of Figure 5A, the protonated first water (H3O

1) is H-bonded to each oxygen atom of the two SO3 moieties of

the acid. This interaction must be aided by additional H-bonding to the second water, for such a double H-bonding of a H3O moiety to two SO3

moieties does not occur in monohydrated clusters. The second water is then H-bonded to one SO3 moiety to complete the H-bonding network

structure. The resultant protonated (H2O)2 is shaped like the Zundel form[1,57] of H5O12 , and we use (A–)(H5O

12 ) in Figure 5 to denote this state to

emphasize that the dissociated conformer has a di-ionic character.

Assuming that an undissociated precursor state for the deprotonated structure may exist in which the proton is transferred back to the acid,

the M062X/TZVP energy was scanned along the O9AH10 distance coordinate while other internal coordinates were varied for optimization. The

energy curve, shown in Figure 5B for H2S3O6(H2O)2, is typical for all dissociated conformers. Such a curve shows that the undissociated precursor

state is not a local minimum and that the energy variation from the undissociated precursor to the dissociated conformer is repulsive with no barrier.

The proton transfer occurs immediately at the instance when two water molecules and the acid form the precursor state.

The degree of dissociation for two water molecules is another demonstration of the structural flexibility for this series of molecules. With no

linking atom, H2S2O6 is the least flexible and forms the H-bonding network structure with a high strain, while H2S3O6 has the best molecular flexi-

bility for adopting such an H-bonding network structure. H2S4O6 is the most flexible in forming intramolecular H-bonding. However, the structure

of H2S4O6 has a disadvantage in forming the H-bonding network because the two SO3 moieties are so far apart that the bonds to the two linking

sulfur atoms must be heavily twisted to create the double H-bonding to one H3O moiety. Therefore, even if the gas phase acidity of H2S4O6 is the

highest, undissociated and dissociated conformers of H2S4O6(H2O)2 have nearly the same energy.

5 | CONCLUSIONS

In this work, we have studied how a structural variation in a series of Brønsted acids affects the acidity. This is a new approach since the acid

strength is usually compared and discussed within a molecular series in which an atom or a group of atoms is substituted in the same structure.

Through a study with very accurate ab initio theory calculations that were extrapolated up to the CCSD(T)/CBS level, we were able to deter-

mine the order of gas phase acidity for four sulfur oxoacids as follows: H2S2O6<H2S3O6<H2S2O7<H2S4O6. Except for H2S2O6, all the global

FIGURE 5 (A) Schematic drawing for the dissociated conformer [(A–)(H5O12 ), right] and its undissociated precursor state [HA(H2O)2, left].

(B) M062X/TZVP energy change on a relaxed scan over the O9AH10 bond distance coordinate for H2S3O6(H2O)2. (C) The geometries ofthe dissociated conformer [right, R(O9AH10)51.416 Ǻ] and the undissociated precursor state [left, R(O9AH10)51.09 Ǻ]


minimum conformers have two intramolecular H-bonds. We consider the intramolecular H-bonding as a measure for the structural flexibility in this

series of molecules. H2S2O6 is the least flexible molecule with no atom for linking the two SO3H moieties and does not form an intramolecular H-

bond. Conversely, H2S4O6 is the most flexible molecule with two linking sulfur atoms, and its two intramolecular H-bonds are the strongest. The

degree of the intramolecular H-bond, which is a reflection of the structural flexibility, is an important factor when considering the gas phase acidity,

as a strong intramolecular H-bond weakens the O9AH10 bond in the acid.

All the sulfur oxoacids studied in this work exhibit dissociated conformers at the low-lying states of dihydrated clusters. The degree of dissociation is

slightly different for this series. The dissociation of H2S2O6(H2O)2 appears from the third lowest conformer, while all low-lying conformers of H2S3O6(H2O)2

are dissociated. For H2S2O7(H2O)2 and H2S4O6(H2O)2, the energies of the dissociated and undissociated conformers are nearly the same. The degree of dis-

sociation is not consistent with the order of gas phase acidity. While the higher gas phase acidity appears to require a smaller number of water molecules

for deprotonation, it does not seem to determine the degree of dissociation. Therefore, an additional factor must affect the degree of dissociation. This addi-

tional factor must be how well the H-bonding network structure is formed with the two water molecules. In the H-bonding network structure, the proto-

nated first water (H3O1) results in triple H-bonding to the two SO3 moieties of the acid and the second water, which in turn is H-bonded to one of the SO3

moieties of the acid. It appears that the least flexible H2S2O6 forms the H-bonding network structure with a large amount of strain, while H2S3O6 has the

best flexibility for adopting such a structure. In contrast, while H2S4O6 is the most flexible molecule in creating intramolecular H-bonds, it has difficulty form-

ing the H-bonding network, as the bonds linking to the two sulfur atoms should be heavily twisted to reduce the distance between the two SO3 moieties.

ACKNOWLEDGMENTS

YKC was supported by the Program for Returners into R&D (KW- 2015-PPD-0175) of the Center for Women in Science, Engineering and

Technology (in Korea).

REFERENCES

[1] K. R. Leopold, Annu. Rev. Phys. Chem. 2011, 62, 327.

[2] S. Schobesberger, A. Franchin, F. Bianchi, L. Rondo, J. Duplissy, A. K€urten, I. K. Ortega, A. Metzger, R. Schnitzhofer, J. Almeida, A. Amorim, J. Dom-

men, E. M. Dunne, M. Ehn, S. Gagn�e, L. Ickes, H. Junninen, A. Hansel, V.-M. Kerminen, J. Kirkby, A. Kupc, A. Laaksonen, K. Lehtipalo, S. Mathot,

A. Onnela, T. Petäjä, F. Riccobono, F. D. Santos, M. Sipilä, A. Tom�e, G. Tsagkogeorgas, Y. Viisanen, P. E. Wagner, D. Wimmer, J. Curtius, N. M.

Donahue, U. Baltensperger, M. Kulmala, D. R. Worsnop, Atmos. Chem. Phys. 2015, 15, 55.

[3] Y.-P. Zhu, Y.-R. Liu, T. Huang, S. Jiang, K.-M. Xu, H. Wen, W.-J. Zhang, W. Huang, J. Phys. Chem. A 2014, 118, 7959.

[4] H. Henschel, J. C. A. Navarro, T. Yli-Juuti, O. Kupiainen-Ma€A€Tta€, T. Olenius, I. K. Ortega, S. L. Clegg, T. Kurte�n, I. Riipinen, H. Vehkamäki, J. Phys.

Chem. A 2014, 118, 2599.

[5] B. Temelso, T. E. Morrell, R. M. Shields, M. A. Allodi, E. K. Wood, K. N. Kirschner, T. C. Castonguay, K. A. Archer, G. C. Shields, J. Phys. Chem. A

2012, 116, 2209.

[6] B. Temelso, T. N. Phan, G. C. Shields, J. Phys. Chem. A 2012, 116, 9745.

[7] G. Ritzhaupt, J. P. Devlin, J. Phys. Chem. 1995, 95, 90.

[8] P. R. McCurdy, W. P. Hess, S. S. Xantheas, J. Phys. Chem. A 2002, 106, 7628.

[9] C. Amirand, D. Maillard, J. Mol. Struct. 1988, 176, 181.

[10] A. Gutberlet, G. Schwaab, O. Birer, M. Masia, A. Kaczmarek, H. Forbert, M. Havenith, D. Marx, Science 2009, 324, 1545.

[11] S. D. Flynn, D. Skvortsov, A. M. Morrison, T. Liang, M. Y. Choi, G. E. Douberly, A. F. Vilesov, J. Phys. Chem. Lett. 2010, 1, 2233.

[12] S. M. Hurley, T. E. Dermota, D. P. Hydutsky, A. W. Castleman, Jr, J. Chem. Phys. 2003, 118, 9272.

[13] S. Re, J. Phys. Chem. A 2001, 105, 9735.

[14] S. Odde, B. J. Mhin, S. Lee, H. M. Lee, K. S. Kim, J. Chem. Phys. 2004, 120, 9524.

[15] S. Odde, B. J. Mhin, K. H. Lee, H. M. Lee, P. Tarakeshwar, K. S. Kim, J. Phys. Chem. A 2006, 110, 7918.

[16] C. Conley, F.-M. Tao, Chem. Phys. Lett. 1999, 301, 29.

[17] J. R. Scott, J. B. Wright, J. Phys. Chem. A 2004, 108, 10578.

[18] S. Re, Y. Osamura, K. Morokuma, J. Phys. Chem. A 1999, 103, 3535.

[19] H. Arstila, K. Laasonen, A. Laaksonen, J. Chem. Phys. 1998, 108, 1031.

[20] S. Li, F.-M. Tao, R. Gu, Chem. Phys. Lett. 2006, 426, 1.

[21] S. Li, W. Qian, F.-M. Tao, Chem. Phys. Lett. 2007, 438, 190.

[22] K. H. Weber, F.-M. Tao, J. Phys. Chem. A 2001, 105, 1208.

[23] S. K. Kim, H. M. Lee, K. S. Kim, Phys. Chem. Chem. Phys. 2015, 17, 28556.

[24] A. H. Otto, R. Steudel, Eur. J. Inorg. Chem. 2001, 3047.

[25] M. Abedi, H. Farrokhpour, Dalton Trans. 2013, 42, 5566.

[26] F. Bordwell, Acc. Chem. Res. 1988, 21, 456.

[27] J. P. Guthrie, Can. J. Chem. 1978, 56, 2342.


[28] J. E. Bartmess, in Negative Ion Energetics Data in NIST Standard Reference Database Number 69 (Eds: W. G. Mallard, P. J. Linstrom), National Insti-

tute of Standards and Technology, Gaithersburg, MD 1997.

[29] E. Raamat, K. Kaupmees, G. Ovsjannikov, A. Trummal, A. K€utt, J. Saame, I. Koppel, I. Kaljurand, L. Lipping, T. Rodima, V. Pihl, I. A. Koppel, I. Leito,

J. Phys. Org. Chem. 2013, 26, 162.

[30] K. E. Gutowski, D. A. Dixon, J. Phys. Chem. A 2006, 110, 12044.

[31] J. Zhang, Y. Sun, C. Mao, H. Gao, W. Zhou, Z. Zhou, J. Mol. Struct. THEOCHEM 2009, 906, 46.

[32] M. J. McGrath, I.-F. W. Kuo, W. B. F. Ngouana, J. N. Ghogomu, C. J. Mundy, A. V. Marenich, C. J. Cramer, D. G. Truhlar, J. I. Siepmann, Phys.

Chem. Chem. Phys. 2013, 15, 13578.

[33] A. Trummal, L. Lipping, I. Kaljurand, I. A. Koppel, I. Leito, J. Phys. Chem. A 2016, 120, 3663.

[34] D. K. Bohme, E. Lee-Ruff, L. B. Young, J. Am. Chem. Soc. 1972, 94, 5153.

[35] K. M. Ervin, V. F. DeTuri, J. Phys. Chem. A. 2002, 106, 9947.

[36] D. Young, Computational Chemistry: A Practical Guide for Applying Techniques to Real World Problems: Appendix a: SPARTAN, Wiley-Interscience 2001.

[37] Y. Zhao, N. E. Schultz, D. G. Truhlar, J. Chem. Theory Comput. 2006, 2, 364.

[38] A. Schäfer, C. Huber, R. Ahlrichs, J. Chem. Phys. 1994, 100, 5829.

[39] A. Hellweg, S. A. Gr€un, C. Hättig, Phys. Chem. Chem. Phys. 2008, 10, 4119.

[40] C. Møller, M. S. Plesset, Phys. Rev. 1934, 46, 618.

[41] F. Weigend, M. H. Häser, H. Patzelt, R. Ahlrichs, Chem. Phys. Lett. 1998, 294, 143.

[42] T. H. Dunning, J. Chem. Phys. 1989, 90, 1007.

[43] S. Grimme, J. Chem. Phys. 2003, 118, 9095.

[44] J. Antony, S. Grimme, J. Phys. Chem. A 2007, 111, 4862.

[45] A. D. Boese, J. Chem. Theory Comput. 2013, 9, 4403.

[46] T. Helgaker, W. Klopper, H. Koch, J. Noga, J. Chem. Phys. 1997, 106, 9639.

[47] S. K. Min, E. C. Lee, H. M. Lee, D. Y. Kim, D. Kim, K. S. Kim, J. Comput. Chem. 2008, 29, 1208.

[48] P. Hobza, J. �Sponer, J. Am. Chem. Soc. 2002, 124, 11802.

[49] K. B. Wiberg, Tetrahedron 1968, 24, 1083.

[50] A. E. Reed, R. B. Weinstock, F. Weinhold, J. Chem. Phys. 1985, 83, 735.

[51] F. Weinhold, C. R. Landis, Discovering Chemistry with Natural Bond Orbitals, Wiley, Hoboken, New Jersey 2012.

[52] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li,

M. Caricato, A. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Wil-

liams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G.

Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Thros-

sell, J. A. Montgomery, Jr, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J.

Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski,

R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, D. J. Fox, Gaussian 09, Revision B.01, Gaussian, Inc., Wallingford, CT 2010.

[53] F. Furche, R. Ahlrichs, C. Hättig, W. Klopper, M. Sierka, F. Weigend. Turbomole. WIREs Comput. Mol. Sci 2014, 4, 91.

[54] I. A. Koppel, R. W. Taft, F. Anvia, S.-Z. Zhu, L.-Q. Hu, K.-S. Sung, D. D. DesMarteau, L. M. Yagupolskii, Y. L. Yagupolskii, N. V. Ignat’ev, N. V. Kon-

dratenko, A. Y. Volkonskii, V. M. Vlasov, R. Notario, P.-C. Maria, J. Am. Chem. Soc. 1994, 116, 3047.

[55] J.-W. Shin, N. I. Hammer, E. G. Diken, M. A. Johnson, R. S. Walters, T. D. Jaeger, M. A. Duncan, R. A. Christie, K. D. Jordan, Science 2004, 304, 1137.

[56] M. Miyazaki, A. Fujii, T. Ebata, M. Mikami, Science 2004, 304, 1134.

[57] J. M. Headrick, E. G. Diken, R. S. Walters, N. I. Hammer, R. A. Christie, J. Cui, E. M. Myshakin, M. A. Duncan, M. A. Johnson, K. D. Jordan, Science

2005, 308, 1765.

[58] M. Park, I. Shin, N. J. Singh, K. S. Kim, J. Phys. Chem. A 2007, 111, 10692.

[59] H.-C. Chang, C.-C. Wu, J.-L. Kuo, Int. Rev. Phys. Chem. 2005, 24, 553.

SUPPORTING INFORMATION

Additional Supporting Information may be found online in the supporting information tab for this article.

How to cite this article: Chung YK, Kim SK. Dissociation of sulfur oxoacids by two water molecules studied using ab initio and density func-

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