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Theoretical study of hydrated sulfuric acid: clusters and periodic modeling
Journal of Molecular Structure: THEOCHEM 718 (2005) 71–76 www.elsevier.com/locate/theochem
Theoretical study of hydrated sulfuric acid: clusters and periodic modeling C. Arrouvela,b, V. Viossatb, C. Minota,* a
Laboratoire de Chimie The´orique, UMR 7616 UPCM/CNRS, boıˆte 137, Universite´ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France b Laboratoire des Syste`mes Interfaciaux a` l’Echelle Nanome´trique, UMR 7142, Universite´ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France Received 6 October 2004; revised 15 December 2004; accepted 16 December 2004
Abstract This study was supported by DFT calculations analyses clusters and periodic systems describing the first hydration of the sulfuric acid. We are interested in the relative stability of the ionic and neutral forms. Several factors, like the number of water molecules and the topology of the hydrate, monitor the proton transfer from the acid molecule to water. q 2005 Elsevier B.V. All rights reserved. Keywords: Weakly hydrated sulfuric acid; SAD; SAT; NMR; DFT-B3LYP; DFT-GGA; Transfer of protons; Cluster models; Periodic models
1. Introduction Sulfuric acid is a strong acid at the limit of superacidity [1]. It is an important product for industry and environment. Its production is very large. The demand reached 18.2 million tons in 1997 [2]; it is mainly used to make fertilizers; in chemistry it is used in acidic catalysis [3]. The human activity plays a key role in the increase the acidification of the ecosystem such as emission from industry (via some industrial processes, energetic combustion) from fossil combustion (coal, fuel). In nature, H2SO4 can appear under aerosol of acidic stratospheric clouds [4]. H2SO4 can also be produced from natural reaction: volcano ejects SO2 that is oxidized under solar ray to SO3, which reacts with H2O and forms H2SO4. A biologic activity from bacterium (Thiobacillus) under anaerobic environment produces also H2SO4 [5]. There, crystal structures exist due to very low temperatures and the high acidity of SAD and SAT are primordial factor in this chemistry. The clouds contribute to the ozone disappearing in Antarctic [6]. The acid rains that have corrosive effects originate from the chemistry in stratospheric clouds. It acidifies the lakes and ground; * Corresponding author. Tel.: C33 1 44 27 25 05; fax: C33 1 44 27 41 17. E-mail address: [email protected] (C. Minot). 0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2004.12.032
this concerns the corrosion of buildings including for example the Athens Acropolis and the Rome coliseum [7]. The knowledge of the existing structures of the hydrates is a first necessary step to study the reactivity of the sulfuric acid. According to the number of water molecules per H2SO4 (we call here r the ratio nH2O/nH2SO4) and to the topology, the relative stability of the neutral structure and of the ion pairs is different. Successive Brønsted acidities induce one or two proton transfers. The conjugated bases Z are HOSOK 3 or SO4 while the protonated water could be C C H3O or H5 O2 . The acid cloud stoichiometry has been characterized by Mahe [8]: (H2O)0–0.2 H2SO4. In the phase diagrams, several structures in sulfuric acid clouds were presented. The sulfuric acid molecules exist as hydrates in vapor phase. The number of isolated molecules (monomers) is small relative to the total number of acid molecules [9]. The monomeric species is supposed to be neutral [10] whereas the hydrate forms should be made of ion pairs. The solid phases are ionic, except for the anhydrous one. For the dehydrate form, two protons are transferred from H2SO4 to the H2O molecules. X-ray data provide the geometry of the crystals: anhydrous [11], monohydrated [12], dihydrated [13] and tetrahydrated [14] sulfuric acid. Many calculations on (H2SO4)(H2O)n have been published using MP2 [15], BLYP [16], B3LYP [15,17,18] or
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SCF-MO-LCGO [19] methods. Kurdi et al. [19] have done first calculations on the monohydrated sulfuric acid. They conclude the gas form is neutral, which agrees with experiments [10]. The study by Larson et al. [15] is focused on the formation of sulfuric acid up to the trihydrated from SO3 and (H2O)1–4. Arstila et al. [16] have done calculations on sulfuric acid up to the trihydrated but their results do not clearly exhibit the proton transfer phenomenon. Bandy et al. [18] and Re et al. [17] have more explicitly investigated the proton transfer performing systematic studies. Bandy and Ianni [18] have considered the hydration of a single H2SO4 molecule with B3LYP/6-311GCC** and concluded that the ionic species became more stable than the neutral one when the number n of H2O was 5 or more. Re et al.’s results [17] are based on the B3LYP/D95** and the B3LYP/ D95CC** basis set. The neutral form is more stable up to nZ3. The energy difference between the two species is not very large especially for nZ3 and depends on the quality of the basis set. However, the difference is small and depends on the basis set; the difference is larger and more meaningful for nO4. Clusters restricted to the hydration of a single H2SO4 molecule are too small to be representative of the experimental media. In order to explain the binary systems, we need to consider at least dimers of H2SO4 and insert water in between. In comparison to the studies on the monomeric species, no systematic study has been done on with two molecules of H2SO4. Bandy and Ianni [18] have calculated [H2SO4(H2O)3]2 and they have found that this cluster is neutral. Another study by Kusaka et al. [20] has been done on highly hydrated sulfuric acid ((H2SO4)1–3, (H2O)100–300) using a Monte Carlo simulation [20]. They have found different conformations (ionic and neutral), which are close in free energy. Among them, the dissociation is not observed on small clusters. The environment plays a key role for the nucleation. The dissociation of sulfuric acid molecules is favored with the addition of water molecules. For the dimer of sulfuric acid, they have found that the dissociation occurs when the number of water molecules is high (240H2O) and when there is no water molecule between the dimer. In this paper, we considered weakly hydrated sulfuric acid for different stoichiometries from the monohydrated to the tetrahydrated sulfuric acid. We investigate the difference of acidity between gas phase and solid phase using DFT calculations, focusing on the comparison between the stability of the ionic and the neutral complexes. We also determine the nature of protonated water generated by the proton transfer in the hydrates: H3OC or H5 OC 2 . Our calculations have been carried out for clusters, (H2SO4)1–2 (H 2O) 1–4 , and periodic systems, H 2SO4 (H2 O) 2 and H2SO4(H2O)4. Clusters represent the gas phase and periodic systems represent the solid phase. For periodic systems, we have considered the dihydrated sulfuric acid (SAD) and the tetrahydrated sulfuric acid (SAT) using Vienna Ab initio Simulation Package (VASP)
[21]. In this work, the initial structure used to construct the crystal structures is taken from the X-ray values of the sulfuric acid [14].
2. Calculation methods 2.1. Cluster calculations To calculate the clusters we have used the Gaussian 98 code [22]. We have chosen B3LYP [23] functional because this functional gives good results for the water clusters. The 6-31G** basis set is sufficient to compare ionic pairs and neutral forms of cluster conformers and allows to compute larger clusters. However, we have also used the D95CC** basis set to test the effect of the size of the basis set and to compare our results with those obtained by Re et al. [17]. We have also used this basis set for the most stable structures for (H2SO4)2(H2O)2 and (H2SO4)2(H2O)4. The calculations by Re et al. with Zero-Point Vibration do not change the relative stability between each configuration. Therefore, we do not have calculated the ZPC for our models. 2.2. Periodic calculations To calculate the periodic systems we used VASP [21]. We have chosen the Density Functional Hamiltonian (DFT) using the Generalised Gradient Approximation (GGA) and the Perdew–Wang formalism [24,25]. Ultrasoft pseudopotentials were used [26,27] together with plane wave basis sets. The cutoff energy is 396 eV. The integrations in the Brillouin Zone are performed on a grid of 4!4!4 Monkhorst–Pack special k-points. To build the sulfuric acid tetrahydrated (rZ4, with r the number of H2O molecules per H2SO4 molecule), we have taken crystallographic values [14]. The space group is 1 c. The initial cell contains 38 atoms (2H2SO4 and P42 8H2O) repeated in x, y, and z direction. The structure is ˚ and cZ6.349 A ˚ , V exp.Z quadratic (aZbZ7.484 A ˚ 3). 355.61 A The cell for the sulfuric acid dihydrated that has been determined by X-ray diffraction [13] (space group C2/c) is too large, consisting of 156 atoms (12H2SO4 and 24H2O) and we decided to reduce the amount of calculation. Therefore, we have used a simplified model; we have derived a reasonable structure from that of the tetrahydrated C one by replacing each H5 OC 2 ion by H3O . The SAT structure obtained is smaller than the experimental one, the number SAD units per cell being decreased by a factor 4. We have optimized the resulting structure. For the SAD and the SAT, we have also constructed the neutral forms from the optimized ionic structures by back-transferring protons from the hydronium to the acid and we have run the optimization again.
C. Arrouvel et al. / Journal of Molecular Structure: THEOCHEM 718 (2005) 71–76
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Table 1 Relative energies of the neutral and ionic form of (H2SO4)(H2O)2–4 Basis sets [H2SO4, (H2O)2] rZ2 (H2SO4), (H2O)2 C ðHSOK 4 Þ, ðH5 O2 Þ [H2SO4, (H2O)3] rZ3 (H2SO4), (H2O)2, (H2O) C ðHSOK 4 Þ, ðH7 O3 Þ [H2SO4, (H2O)4] rZ4 (H2SO4), (H2O)2, (H2O)2 C ðHSOK 4 Þ, (H2O)2, (H2O) (H3O ) a
6-31G** E (kcal/mol)
D95** E (kcal/mol)
D95CC** E (kcal/mol)
0.00 C6.77a
0.00 /(H2SO4), (H2O)2
0.00 /(H2SO4), (H2O)2
1.29 0.00
0.98 0.00 (C0.35 [17])
0.00 1.04 (0.46 [17])
2.88 0.00
1.60 [17] 0.00
0.90 [17] 0.00
Saddle point.
3. Results 3.1. Cluster models, monomers Table 1 presents our results for the hydration of a single H 2SO4 molecule (monomer) by two to four water molecules. Energy differences associated to the variations of conformation are weak. Several structures are very close C in energy. For example, for ðHSOK 4 Þ, ðH7 O3 Þ, we have found two structures with different OH conformation (in HSOK 4 ); one is lower energy by K0.35 kcal/mol with the D95** basis set and becomes higher by 0.58 kcal/mol using the D95CC** basis set. Results are essentially the same than found in Ref. [17] and thus validate using 6-31G** basis set. The optimization of the ionic structure for two water molecules led to a saddle point or to the neutral species. Those for four molecules led unambiguously to ionic forms of lower energy. The case of three water molecules is intermediate. The 6-31G** basis set provides this trend correctly. In one limit case (rZ3), the result is opposite to that obtained using the D95CC** basis set, however, the difference in energy is extremely small. The use of the D95** basis set would be similarly insufficient. Using the smallest basis set, the ionic species is that of lowest energy. The stabilization of the ionic trihydrated species is favored when a H2O–H3OC–H2O sequence is formed. The hydronium
ion is stabilized by two adjacent H2O molecules. This species is attached by three hydrogen bonds to three oxygen atoms of HSOK 4 (see Fig. 1a). The neutral structure implies the same total number of hydrogen bonds; however, one H2O has left the sequence of three water molecules to bind exclusively to the acid. Then the hydronium ion is not enough stabilized and the structure remains neutral. The topology of the hydrate seems to require sequences of three water molecules to allow the formation of H3OC. The stability of the different structures increases when the number of hydrogen bonds is higher especially between the water molecule and the acid. However, the total number of hydrogen bonds is not enough to explain the stability between the ionic form and the neutral form. The sequence of three H2O seems to facilitate the proton transfer. For rZ4, the ionic form is unambiguously the more stable form. The energy difference between the neutral form and the ionic form is higher (2.88 eV with 6-31G** basis set). The ionic cluster gets a sequence of 3H2O and 1H3OC. The H3OC ion is solvated by the three water molecules. 3.2. Cluster models, dimers Considering dimeric clusters (two H2SO4 molecules) leads to the appearance of the ionic form at lower stoichiometry. It is indeed possible to optimize a stable ionic form for a ratio C (H2O/H2SO4) rZ1, ðHSOK 4 Þ2 ðH3 O Þ2 (Fig. 2) whereas it was
Fig. 1. (a) Ionic form of H2SO4, (H2O)3; (b) neutral form.
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Fig. 2. Stability between the neutral and the ionic form of (H2SO4)2(H2O)2.
impossible for the monomeric species, (H2SO4)(H2O). This ionic form is, however, not the most stable one and the neutral species still has a lower energy. The neutral pair is stable by 1.16 kcal/mol using the 6-31G** basis set and by 0.75 kcal/ mol using the D95CC** basis set. For rZ2, ((H2SO4)2(H2O)4—Fig. 3a), the structure of lowest energy is the ionic pair where H3OC is stabilized by an adjacent H2O molecule. When neutral water molecules are initially between the two sulfuric acid molecules (neutral forms) the system spontaneously evolves to the ionic form during the optimization process. For the monomers, rZ2 the ionic structure did not correspond to an energy minimum. A neutral from with four independent water molecules, two bridging the two acid molecules and two bound to one acid molecule (Fig. 3b) is a metastable structure, 8.72 kcal/mol compared to the ionic one. C The ½ðHSOK 4 ÞðH3 O –H2 OÞ2 structure is stabilized by three hydrogen bonds. The moiety (H3OC–H2O) clearly C differs from a H5 OC would bridge 2 species where H symmetrically two OH2 molecules. 3.3. Crystalline hydrates First, we will first comment the result for rZ4 (SAT, sulfuric acid tetrahydrated) since it corresponds to existing crystallographic data [14].
3.3.1. Sulfuric acid tetrahydrated, rZ4 The ionic structure corresponds to the complete deprotonation of the sulfuric acid The SAT structure contains C 4ðSO2K 4 C 2H5 O2 Þ ions per unit cell. The optimized cell ˚ (exp. 7.484 A ˚ ), parameters (Fig. 4) are: aZbZ7.40 A ˚ ˚ cZ6.17 A (6.349 A). Fig. 5 shows a symmetric H5 OC 2 structure, at variance with the results obtained in cluster calculations. The neutral structure is not stable: we have back2K transferred the proton from the H5 OC 2 ions to SO4 creating neutral species. During the optimization, this structure returned to the ionic form. The transfer of half of them creating HOSOK 3 ions also led back to the fully ionic structure. 3.3.2. Sulfuric acid dihydrated, rZ2 As explained in Section 2.2, we have built a sulfuric acid dihydrated structure (SAD) starting from a tetrahydrated one containing 26 atoms by removing one H2O per H5 OC 2. The structure contains hydronium ions, H3OC. Under optimization, the structure (Fig. 6) remained fully ionic K (SO2K 4 and not HOSO3 anions). The optimized parameters ˚, of the orthorhombic structure (Fig. 6) are aZ6.40 A C ˚ ˚ bZ6.52 A and cZ6.93 A. Each H3O ion is surrounded C 2K by 3SO2K ions. We also 4 and each SO4 ion by 6H3O imposed a proton transfer to generate a neutral complex
Fig. 3. (a) Ionic form of (H2SO4)2(H2O)4 with 6-31G** basis set, (b) neutral form of (H2SO4)2(H2O)4 with 6-31G** basis set.
C. Arrouvel et al. / Journal of Molecular Structure: THEOCHEM 718 (2005) 71–76
C Fig. 4. 2!2!2 cell of 2SO2K 4 , 4H5 O2 . * Dark gray balls, oxygen atoms; light gray balls, sulfur atoms; white balls, hydrogen atoms.
(Fig. 7) and, as for the SAT structure, the optimization led back to the ionic structure.
4. Discussion and conclusion Hydration of a single acid molecule leads to ionic structures from rR3 in agreement with Re et al.’s [17]. The first acidity of H2SO4 is only involved. H3OC and HOSOK 3 2K are formed, never H5 OC 2 and SO4 . The hydration of dimer (H2SO4)2 always leads to ionic forms. Again, the first acidity of H2SO4 is only involved. Symmetric H5 OC 2 ions
Fig. 5. Surrounding of H5 OC 2 in the SAT structure.
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Fig. 6. Structure of the ionic form of a SAD.
are not generated even though the hydronium ions are solvated. The dissociation is easier for larger systems increasing the number of water molecules [20] or even increasing the number of sulfuric acid molecules. The dissociation is easier when pairs of acid molecules are considered. For the cluster with 2H2SO4, the neutral structure is more stable for 2H2O (rZ1) while it is the ionic for 2H2O (rZ2). The H5 OC 2 is a solvated hydronium species
Fig. 7. Structure of the neutral form of a SAD.
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and not a symmetrical structure. We can also note that there are different systems close in energy. In the crystal structures the ionic forms are always more stable than the neutral ones. The acid dissociation is always complete (second acidity). The cooperative effects are present since there is an alternation of ions of opposite charge (inducing a favorable Madelung field). The SAD crystal structure (rZ2) is ionic despite the lack of solvation of H3OC species. This was not the case for the molecule H2SO4, 2H2O but was already observed for the dimer 2H2SO4, 4H2O. The hydronium in these structures is stabilized by several sulfate ions. In the SAT crystal, HC is solvated by 2H2O molecules and forms a symmetrical H5 OC 2 species. The proton transfer then depends both on r and on the structure (isolated molecules, dimers or extended system). An isolated sulfuric acid molecule needs at least a ratio of three water molecules whereas the dimer needs a ratio of 2. The increase of cluster models shows that the better structures have insertion of water molecules between sulfuric acid molecules. The periodic systems are always zwitterionic. For rZ2 and 4, the neutral form cannot be stabilized.
Acknowledgements This work has been accomplished in the framework of the GDRs ‘re´ activite´ de surface de la glace dans l’environnement naturel et en danger’ and ‘Dynamique Mole´culaire Quantique Applique´e a` la catalyse’. Authors also are grateful to IDRIS and CCR centers for computational facilities.
References [1] G. Olah, G.K.S. Prakash, J. Sommer, Superacids, Wiley, New York, 1985.
[2] http://www.encyclopedia.com/html/section/sulfuric_ProductionofSulfuricAcid.asp [3] M. Liler, Organic Chemistry, Reaction Mechanisms in Sulphuric Acid, vol. 23, Academic Press, London, 1971. [4] C.E. Junge, C.W. Chagnon, J.E. Manson, J. Meteorol. 18 (1961) 81. [5] E. Fjerdingstad, Water Res. 3 (1969) 21. [6] E.W. Wolff, R. Mulvaney, Geophys. Res. Lett. 18 (1991) 1007. [7] http://www.geocities.com/boss_be_99/pollution_air.htm (in french). [8] F. Mahe, Thesis, University of Orle´ans, France, 1999. [9] R.H. Heist, H. Reiss, J. Chem. Phys. 61 (1974) 573. [10] R.L. Kuczkowski, R.D. Suenram, F.J. Lovas, J. Am. Chem. Soc. 103 (1981) 2561. [11] C. Pascard-Billy, Acta. Crystallogr. 18 (1965) 827. [12] P. Pascal, Nouveau traite´ de Chimie Mine´rale, tome XIII, Masson, 1961. [13] I. Taesler, I. Olovsson, J. Chem. Phys. 51 (1969) 4213. [14] T. Kja¨llman, I. Olovsson, Acta. Crystallogr. B 28 (1972) 1692. [15] L.J. Larson, M. Kuno, F.-M. Tao, J. Chem. Phys. 112 (2000) 8830. [16] H. Arstila, K. Laasonen, A. Laaksonen, J. Chem. Phys. 108 (1998) 1031. [17] S. Re, Y. Osamura, K. Morokuma, J. Phys. Chem. A 103 (1999) 3535. [18] A.R. Bandy, J.C. Ianni, J. Phys. Chem. A 102 (1998) 6533. [19] L. Kurdi, E. Kochanski, Chem. Phys. Lett. 158 (1989) 111. [20] I. Kusaka, S.-G. Wang, J.H. Seinfeld, J. Chem. Phys. 108 (1998) 6829. [21] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [22] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petterson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B.G. Johnson, W. Chen, M.W. Wong, J.L. Andres, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian, Inc., Pittsburgh, PA, 1998. [23] A.D. Beck, J. Chem. Phys. 98 (1993) 5648. [24] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671. [25] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [26] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [27] G. Kresse, J. Hafner, J. Phys. Condens. Matter 6 (1994) 8245.
Theoretical study of hydrated sulfuric acid: clusters and periodic modeling C. Arrouvela,b, V. Viossatb, C. Minota,* a
Laboratoire de Chimie The´orique, UMR 7616 UPCM/CNRS, boıˆte 137, Universite´ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France b Laboratoire des Syste`mes Interfaciaux a` l’Echelle Nanome´trique, UMR 7142, Universite´ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France Received 6 October 2004; revised 15 December 2004; accepted 16 December 2004
Abstract This study was supported by DFT calculations analyses clusters and periodic systems describing the first hydration of the sulfuric acid. We are interested in the relative stability of the ionic and neutral forms. Several factors, like the number of water molecules and the topology of the hydrate, monitor the proton transfer from the acid molecule to water. q 2005 Elsevier B.V. All rights reserved. Keywords: Weakly hydrated sulfuric acid; SAD; SAT; NMR; DFT-B3LYP; DFT-GGA; Transfer of protons; Cluster models; Periodic models
1. Introduction Sulfuric acid is a strong acid at the limit of superacidity [1]. It is an important product for industry and environment. Its production is very large. The demand reached 18.2 million tons in 1997 [2]; it is mainly used to make fertilizers; in chemistry it is used in acidic catalysis [3]. The human activity plays a key role in the increase the acidification of the ecosystem such as emission from industry (via some industrial processes, energetic combustion) from fossil combustion (coal, fuel). In nature, H2SO4 can appear under aerosol of acidic stratospheric clouds [4]. H2SO4 can also be produced from natural reaction: volcano ejects SO2 that is oxidized under solar ray to SO3, which reacts with H2O and forms H2SO4. A biologic activity from bacterium (Thiobacillus) under anaerobic environment produces also H2SO4 [5]. There, crystal structures exist due to very low temperatures and the high acidity of SAD and SAT are primordial factor in this chemistry. The clouds contribute to the ozone disappearing in Antarctic [6]. The acid rains that have corrosive effects originate from the chemistry in stratospheric clouds. It acidifies the lakes and ground; * Corresponding author. Tel.: C33 1 44 27 25 05; fax: C33 1 44 27 41 17. E-mail address: [email protected] (C. Minot). 0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2004.12.032
this concerns the corrosion of buildings including for example the Athens Acropolis and the Rome coliseum [7]. The knowledge of the existing structures of the hydrates is a first necessary step to study the reactivity of the sulfuric acid. According to the number of water molecules per H2SO4 (we call here r the ratio nH2O/nH2SO4) and to the topology, the relative stability of the neutral structure and of the ion pairs is different. Successive Brønsted acidities induce one or two proton transfers. The conjugated bases Z are HOSOK 3 or SO4 while the protonated water could be C C H3O or H5 O2 . The acid cloud stoichiometry has been characterized by Mahe [8]: (H2O)0–0.2 H2SO4. In the phase diagrams, several structures in sulfuric acid clouds were presented. The sulfuric acid molecules exist as hydrates in vapor phase. The number of isolated molecules (monomers) is small relative to the total number of acid molecules [9]. The monomeric species is supposed to be neutral [10] whereas the hydrate forms should be made of ion pairs. The solid phases are ionic, except for the anhydrous one. For the dehydrate form, two protons are transferred from H2SO4 to the H2O molecules. X-ray data provide the geometry of the crystals: anhydrous [11], monohydrated [12], dihydrated [13] and tetrahydrated [14] sulfuric acid. Many calculations on (H2SO4)(H2O)n have been published using MP2 [15], BLYP [16], B3LYP [15,17,18] or
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SCF-MO-LCGO [19] methods. Kurdi et al. [19] have done first calculations on the monohydrated sulfuric acid. They conclude the gas form is neutral, which agrees with experiments [10]. The study by Larson et al. [15] is focused on the formation of sulfuric acid up to the trihydrated from SO3 and (H2O)1–4. Arstila et al. [16] have done calculations on sulfuric acid up to the trihydrated but their results do not clearly exhibit the proton transfer phenomenon. Bandy et al. [18] and Re et al. [17] have more explicitly investigated the proton transfer performing systematic studies. Bandy and Ianni [18] have considered the hydration of a single H2SO4 molecule with B3LYP/6-311GCC** and concluded that the ionic species became more stable than the neutral one when the number n of H2O was 5 or more. Re et al.’s results [17] are based on the B3LYP/D95** and the B3LYP/ D95CC** basis set. The neutral form is more stable up to nZ3. The energy difference between the two species is not very large especially for nZ3 and depends on the quality of the basis set. However, the difference is small and depends on the basis set; the difference is larger and more meaningful for nO4. Clusters restricted to the hydration of a single H2SO4 molecule are too small to be representative of the experimental media. In order to explain the binary systems, we need to consider at least dimers of H2SO4 and insert water in between. In comparison to the studies on the monomeric species, no systematic study has been done on with two molecules of H2SO4. Bandy and Ianni [18] have calculated [H2SO4(H2O)3]2 and they have found that this cluster is neutral. Another study by Kusaka et al. [20] has been done on highly hydrated sulfuric acid ((H2SO4)1–3, (H2O)100–300) using a Monte Carlo simulation [20]. They have found different conformations (ionic and neutral), which are close in free energy. Among them, the dissociation is not observed on small clusters. The environment plays a key role for the nucleation. The dissociation of sulfuric acid molecules is favored with the addition of water molecules. For the dimer of sulfuric acid, they have found that the dissociation occurs when the number of water molecules is high (240H2O) and when there is no water molecule between the dimer. In this paper, we considered weakly hydrated sulfuric acid for different stoichiometries from the monohydrated to the tetrahydrated sulfuric acid. We investigate the difference of acidity between gas phase and solid phase using DFT calculations, focusing on the comparison between the stability of the ionic and the neutral complexes. We also determine the nature of protonated water generated by the proton transfer in the hydrates: H3OC or H5 OC 2 . Our calculations have been carried out for clusters, (H2SO4)1–2 (H 2O) 1–4 , and periodic systems, H 2SO4 (H2 O) 2 and H2SO4(H2O)4. Clusters represent the gas phase and periodic systems represent the solid phase. For periodic systems, we have considered the dihydrated sulfuric acid (SAD) and the tetrahydrated sulfuric acid (SAT) using Vienna Ab initio Simulation Package (VASP)
[21]. In this work, the initial structure used to construct the crystal structures is taken from the X-ray values of the sulfuric acid [14].
2. Calculation methods 2.1. Cluster calculations To calculate the clusters we have used the Gaussian 98 code [22]. We have chosen B3LYP [23] functional because this functional gives good results for the water clusters. The 6-31G** basis set is sufficient to compare ionic pairs and neutral forms of cluster conformers and allows to compute larger clusters. However, we have also used the D95CC** basis set to test the effect of the size of the basis set and to compare our results with those obtained by Re et al. [17]. We have also used this basis set for the most stable structures for (H2SO4)2(H2O)2 and (H2SO4)2(H2O)4. The calculations by Re et al. with Zero-Point Vibration do not change the relative stability between each configuration. Therefore, we do not have calculated the ZPC for our models. 2.2. Periodic calculations To calculate the periodic systems we used VASP [21]. We have chosen the Density Functional Hamiltonian (DFT) using the Generalised Gradient Approximation (GGA) and the Perdew–Wang formalism [24,25]. Ultrasoft pseudopotentials were used [26,27] together with plane wave basis sets. The cutoff energy is 396 eV. The integrations in the Brillouin Zone are performed on a grid of 4!4!4 Monkhorst–Pack special k-points. To build the sulfuric acid tetrahydrated (rZ4, with r the number of H2O molecules per H2SO4 molecule), we have taken crystallographic values [14]. The space group is 1 c. The initial cell contains 38 atoms (2H2SO4 and P42 8H2O) repeated in x, y, and z direction. The structure is ˚ and cZ6.349 A ˚ , V exp.Z quadratic (aZbZ7.484 A ˚ 3). 355.61 A The cell for the sulfuric acid dihydrated that has been determined by X-ray diffraction [13] (space group C2/c) is too large, consisting of 156 atoms (12H2SO4 and 24H2O) and we decided to reduce the amount of calculation. Therefore, we have used a simplified model; we have derived a reasonable structure from that of the tetrahydrated C one by replacing each H5 OC 2 ion by H3O . The SAT structure obtained is smaller than the experimental one, the number SAD units per cell being decreased by a factor 4. We have optimized the resulting structure. For the SAD and the SAT, we have also constructed the neutral forms from the optimized ionic structures by back-transferring protons from the hydronium to the acid and we have run the optimization again.
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Table 1 Relative energies of the neutral and ionic form of (H2SO4)(H2O)2–4 Basis sets [H2SO4, (H2O)2] rZ2 (H2SO4), (H2O)2 C ðHSOK 4 Þ, ðH5 O2 Þ [H2SO4, (H2O)3] rZ3 (H2SO4), (H2O)2, (H2O) C ðHSOK 4 Þ, ðH7 O3 Þ [H2SO4, (H2O)4] rZ4 (H2SO4), (H2O)2, (H2O)2 C ðHSOK 4 Þ, (H2O)2, (H2O) (H3O ) a
6-31G** E (kcal/mol)
D95** E (kcal/mol)
D95CC** E (kcal/mol)
0.00 C6.77a
0.00 /(H2SO4), (H2O)2
0.00 /(H2SO4), (H2O)2
1.29 0.00
0.98 0.00 (C0.35 [17])
0.00 1.04 (0.46 [17])
2.88 0.00
1.60 [17] 0.00
0.90 [17] 0.00
Saddle point.
3. Results 3.1. Cluster models, monomers Table 1 presents our results for the hydration of a single H 2SO4 molecule (monomer) by two to four water molecules. Energy differences associated to the variations of conformation are weak. Several structures are very close C in energy. For example, for ðHSOK 4 Þ, ðH7 O3 Þ, we have found two structures with different OH conformation (in HSOK 4 ); one is lower energy by K0.35 kcal/mol with the D95** basis set and becomes higher by 0.58 kcal/mol using the D95CC** basis set. Results are essentially the same than found in Ref. [17] and thus validate using 6-31G** basis set. The optimization of the ionic structure for two water molecules led to a saddle point or to the neutral species. Those for four molecules led unambiguously to ionic forms of lower energy. The case of three water molecules is intermediate. The 6-31G** basis set provides this trend correctly. In one limit case (rZ3), the result is opposite to that obtained using the D95CC** basis set, however, the difference in energy is extremely small. The use of the D95** basis set would be similarly insufficient. Using the smallest basis set, the ionic species is that of lowest energy. The stabilization of the ionic trihydrated species is favored when a H2O–H3OC–H2O sequence is formed. The hydronium
ion is stabilized by two adjacent H2O molecules. This species is attached by three hydrogen bonds to three oxygen atoms of HSOK 4 (see Fig. 1a). The neutral structure implies the same total number of hydrogen bonds; however, one H2O has left the sequence of three water molecules to bind exclusively to the acid. Then the hydronium ion is not enough stabilized and the structure remains neutral. The topology of the hydrate seems to require sequences of three water molecules to allow the formation of H3OC. The stability of the different structures increases when the number of hydrogen bonds is higher especially between the water molecule and the acid. However, the total number of hydrogen bonds is not enough to explain the stability between the ionic form and the neutral form. The sequence of three H2O seems to facilitate the proton transfer. For rZ4, the ionic form is unambiguously the more stable form. The energy difference between the neutral form and the ionic form is higher (2.88 eV with 6-31G** basis set). The ionic cluster gets a sequence of 3H2O and 1H3OC. The H3OC ion is solvated by the three water molecules. 3.2. Cluster models, dimers Considering dimeric clusters (two H2SO4 molecules) leads to the appearance of the ionic form at lower stoichiometry. It is indeed possible to optimize a stable ionic form for a ratio C (H2O/H2SO4) rZ1, ðHSOK 4 Þ2 ðH3 O Þ2 (Fig. 2) whereas it was
Fig. 1. (a) Ionic form of H2SO4, (H2O)3; (b) neutral form.
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Fig. 2. Stability between the neutral and the ionic form of (H2SO4)2(H2O)2.
impossible for the monomeric species, (H2SO4)(H2O). This ionic form is, however, not the most stable one and the neutral species still has a lower energy. The neutral pair is stable by 1.16 kcal/mol using the 6-31G** basis set and by 0.75 kcal/ mol using the D95CC** basis set. For rZ2, ((H2SO4)2(H2O)4—Fig. 3a), the structure of lowest energy is the ionic pair where H3OC is stabilized by an adjacent H2O molecule. When neutral water molecules are initially between the two sulfuric acid molecules (neutral forms) the system spontaneously evolves to the ionic form during the optimization process. For the monomers, rZ2 the ionic structure did not correspond to an energy minimum. A neutral from with four independent water molecules, two bridging the two acid molecules and two bound to one acid molecule (Fig. 3b) is a metastable structure, 8.72 kcal/mol compared to the ionic one. C The ½ðHSOK 4 ÞðH3 O –H2 OÞ2 structure is stabilized by three hydrogen bonds. The moiety (H3OC–H2O) clearly C differs from a H5 OC would bridge 2 species where H symmetrically two OH2 molecules. 3.3. Crystalline hydrates First, we will first comment the result for rZ4 (SAT, sulfuric acid tetrahydrated) since it corresponds to existing crystallographic data [14].
3.3.1. Sulfuric acid tetrahydrated, rZ4 The ionic structure corresponds to the complete deprotonation of the sulfuric acid The SAT structure contains C 4ðSO2K 4 C 2H5 O2 Þ ions per unit cell. The optimized cell ˚ (exp. 7.484 A ˚ ), parameters (Fig. 4) are: aZbZ7.40 A ˚ ˚ cZ6.17 A (6.349 A). Fig. 5 shows a symmetric H5 OC 2 structure, at variance with the results obtained in cluster calculations. The neutral structure is not stable: we have back2K transferred the proton from the H5 OC 2 ions to SO4 creating neutral species. During the optimization, this structure returned to the ionic form. The transfer of half of them creating HOSOK 3 ions also led back to the fully ionic structure. 3.3.2. Sulfuric acid dihydrated, rZ2 As explained in Section 2.2, we have built a sulfuric acid dihydrated structure (SAD) starting from a tetrahydrated one containing 26 atoms by removing one H2O per H5 OC 2. The structure contains hydronium ions, H3OC. Under optimization, the structure (Fig. 6) remained fully ionic K (SO2K 4 and not HOSO3 anions). The optimized parameters ˚, of the orthorhombic structure (Fig. 6) are aZ6.40 A C ˚ ˚ bZ6.52 A and cZ6.93 A. Each H3O ion is surrounded C 2K by 3SO2K ions. We also 4 and each SO4 ion by 6H3O imposed a proton transfer to generate a neutral complex
Fig. 3. (a) Ionic form of (H2SO4)2(H2O)4 with 6-31G** basis set, (b) neutral form of (H2SO4)2(H2O)4 with 6-31G** basis set.
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C Fig. 4. 2!2!2 cell of 2SO2K 4 , 4H5 O2 . * Dark gray balls, oxygen atoms; light gray balls, sulfur atoms; white balls, hydrogen atoms.
(Fig. 7) and, as for the SAT structure, the optimization led back to the ionic structure.
4. Discussion and conclusion Hydration of a single acid molecule leads to ionic structures from rR3 in agreement with Re et al.’s [17]. The first acidity of H2SO4 is only involved. H3OC and HOSOK 3 2K are formed, never H5 OC 2 and SO4 . The hydration of dimer (H2SO4)2 always leads to ionic forms. Again, the first acidity of H2SO4 is only involved. Symmetric H5 OC 2 ions
Fig. 5. Surrounding of H5 OC 2 in the SAT structure.
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Fig. 6. Structure of the ionic form of a SAD.
are not generated even though the hydronium ions are solvated. The dissociation is easier for larger systems increasing the number of water molecules [20] or even increasing the number of sulfuric acid molecules. The dissociation is easier when pairs of acid molecules are considered. For the cluster with 2H2SO4, the neutral structure is more stable for 2H2O (rZ1) while it is the ionic for 2H2O (rZ2). The H5 OC 2 is a solvated hydronium species
Fig. 7. Structure of the neutral form of a SAD.
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and not a symmetrical structure. We can also note that there are different systems close in energy. In the crystal structures the ionic forms are always more stable than the neutral ones. The acid dissociation is always complete (second acidity). The cooperative effects are present since there is an alternation of ions of opposite charge (inducing a favorable Madelung field). The SAD crystal structure (rZ2) is ionic despite the lack of solvation of H3OC species. This was not the case for the molecule H2SO4, 2H2O but was already observed for the dimer 2H2SO4, 4H2O. The hydronium in these structures is stabilized by several sulfate ions. In the SAT crystal, HC is solvated by 2H2O molecules and forms a symmetrical H5 OC 2 species. The proton transfer then depends both on r and on the structure (isolated molecules, dimers or extended system). An isolated sulfuric acid molecule needs at least a ratio of three water molecules whereas the dimer needs a ratio of 2. The increase of cluster models shows that the better structures have insertion of water molecules between sulfuric acid molecules. The periodic systems are always zwitterionic. For rZ2 and 4, the neutral form cannot be stabilized.
Acknowledgements This work has been accomplished in the framework of the GDRs ‘re´ activite´ de surface de la glace dans l’environnement naturel et en danger’ and ‘Dynamique Mole´culaire Quantique Applique´e a` la catalyse’. Authors also are grateful to IDRIS and CCR centers for computational facilities.
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