Computational and Theoretical Chemistry 966 (2011) 225–231

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Computational and Theoretical Chemistry

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On the stabilization of the sulfate dianion by sulfur dioxide in the gas phase.Theoretical studies on structure and stability of SnO2n+2 anions, n = 1–4

Justin Chan, Friedrich Grein ⇑Department of Chemistry, University of New Brunswick, PO Box 4400, Fredericton, NB, Canada E3B5A3

a r t i c l e i n f o a b s t r a c t

Article history:Received 21 December 2010Received in revised form 22 February 2011Accepted 2 March 2011Available online 5 March 2011

Keywords:Dianion stabilizationSulfate dianionStabilization with SO2

Electron detachment energiesDensity functional studies

2210-271X/$ - see front matter � 2011 Elsevier B.V.doi:10.1016/j.comptc.2011.03.005

⇑ Corresponding author. Tel.: +1 506 453 4776; faxE-mail address: fritz@unb.ca (F. Grein).

The stabilization with respect to electron detachment of the sulfate dianion SO2�4 in gas phase by addition

of SO2 molecules is being studied. Geometries of SO2�4 (SO2)n and SO1�

4 (SO)n for n = 1–3 have been opti-mized using the B3PW91 method. The energies of the smaller clusters have been recalculated at the CCSDand CCSD(T) level based on the B3PW91 geometry. In the gas phase the sulfate monoanion is more stablethan the dianion, the latter having an adiabatic electron detachment energy of �1.57 eV. However, withthe addition of two SO2 molecules the dianion becomes more stable by 0.38 eV (CCSD energies). The ver-tical electron detachment energy, while negative for the lone sulfate dianion (�1.26 eV), turns positivewith the addition of a single SO2 molecule (0.64 eV). Chemically bonded monoanions S2O1�

6 and S3O1�8 ,

as well as dianions S2O2�6 , S3O2�

8 and S4O2�10 , have been identified.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

In the gas phase, the sulfate dianion SO2�4 , like other di- and

polyanions (e.g. carbonate dianion CO2�3 , phosphate trianion

PO3�4 ), is not stable with respect to the loss of an electron. However,

such polyanions are stabilized in solution and in solids.Quantum chemical studies by Stefanovich et al. [1] found that

the vertical electron detachment energy (VDE) of CO2�3 changes

from �3.4 eV in the gas phase to +9.9 eV in water. For the sulfatedianion SO2�

4 , the change goes from �1.6 eV in the gas phase to+9.6 eV in water (a positive sign implies the dianion to be morestable than the monoanion).

It is of interest to ask for the smallest number of solvent mole-cules to stabilize a dianion. By electrospray mass spectrometry,Blades and Kebarle [2] obtained hydrated sulfate clustersSO2�

4 (H2O)n, hydrated dithionate clusters S2O2�6 (H2O)n, and hy-

drated peroxydisulfate clusters S2O2�8 (H2O)n in the gas phase. By

collision induced dissociation, SO2�4 (H2O)n clusters with n = 3 and

higher were found. For n smaller than 3, HSO�4 and OH� were de-tected, but not SO1�

4 . On the other hand, S2O2�6 (H2O)n and

S2O2�8 (H2O)n could be reduced to n = 0, indicating that S2O2�

6 andS2O2�

8 are stable in the gas phase. The results for SO2�4 (H2O)n were

confirmed by Wang et al. [3,4] using photoelectron spectroscopy.In theoretical studies performed by the Wang group [3] (DFT/B3LYP) on SO2�

4 (H2O)n and SO1�4 (H2O)n with n = 1–6, negative adia-

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: +1 506 453 4981.

batic electron detachment energies (ADE) (unstable dianionic clus-ters) were obtained for n = 1 and n = 2, but positive ones startingwith n = 3. For n = 3, the ADE was calculated as 0.32 eV, comparedwith an experimental value of 0.4 ± 0.2 eV. The calculated ADE’sfrom n = 3 to n = 6 were found to lie within the error bars of theexperimental values.

Photoelectron spectra of oxalate dianion clusters C2O2�4 (H2O)n

in the gas phase have also been investigated [5]. The smallestobservable cluster was again n = 3, with an experimental ADE of0.0 eV, and a VDE of 0.50 eV. In calculations up to n = 6, VDE forn = 3 was found to be 0.48 eV, in excellent agreement with theexperimental value. The value for the highest calculated cluster,n = 6, was 1.75 eV vs. 1.84 eV experimental. All calculated VDE’swere found to lie within 0.1 eV of the experimental values.

While the stabilization of dianions by water has been relativelywell studied, dianions can also be stabilized by other solvents. In aprevious paper by this group [6], the stabilization of the carbonatedianion by the addition of sulfur dioxide molecules was studied. Itwas found that the dianionic complexes CO2�

3 (SO2)n are less stablethan the corresponding monoionic ones for n = 0–2, but turn morestable starting with n = 3. The ADE changes from �0.39 eV to+0.20 eV between n = 2 and n = 3. The VDE becomes positive al-ready at n = 2, with a value of 1.35 eV.

In the present paper, the stabilization of the sulfate dianion bysulfur dioxide will be investigated. Geometries of the clustersSO1�

4 (SO2)n and SO2�4 (SO2)n are to be optimized by DFT methods.

Single point calculations are to be performed at the CCSD andCCDS(T) level. These studies predict that the sulfate dianion (withS–O–S bonding) requires a minimum of two sulfur dioxide

Table 1Comparison of bond distances R (Å), angles a (deg), and relative energies (eV) at theB3PW91/6-311+G(3df) (DFT) and CCSD(T)/6-311+G(d) (CC) level for SO�4 at varyingsymmetries.

Method Symmetry R (S–O1)

R (S–O2)

a (O1–S–O2)

a (O1–S–O3)

a (O2–S–O4)

RelativeE

DFT C2v 1.449 1.509 111.6 114.0 95.1 0.00C3v 1.446 1.487 112.9 112.9 105.9 0.08D2d 1.475 1.475 108.1 112.2 112.2 0.15

CC C2v 1.470 1.538 111.7 114.2 94.1 0.00C3v 1.468 1.513 112.9 112.9 105.8 0.13D2d 1.502 1.502 112.3 111.5 111.5 0.10

Table 2Calculated B3PW91/6-31+G(d) total energies of SO1�

4 ðSO2Þn and SO2�4 ðSO2Þn , E(�1)

and E(�2), in atomic units. Binding energies DE(�1) and DE(�2) in eV. Energies forthe most stable species of each n are printed in bold face. For structure labels seeFig. 1. The energy of SO2 is �548.488222 a.u.

Struct. E(�1) DE(�1) E(�2) DE(�2)

0 �698.899002 – �698.840050 –Ia �1247.419421 0.88 �1247.411047 2.25

226 J. Chan, F. Grein / Computational and Theoretical Chemistry 966 (2011) 225–231

molecules to be adiabatically stabilized in the gas phase, while ver-tical stabilization requires only one SO2.

2. Methods

DFT geometry optimizations on SO1�4 (SO2)n and SO2�

4 (SO2)n, forn = 0–3, were performed with the Gaussian03 programs [7], usingthe B3PW91 functional [8,9] with the 6-31+G(d) basis set. Thestructures yielding the lowest energies for a given n were reoptim-ized with the higher basis set 6-311+G(3df).

Fig. 1 summarizes the starting structures of SO1�4 (SO2)n and

SO2�4 (SO2)n. They are labeled Ia, IIa, IIb, IIc, IIIa, etc., where the ro-

man numerals indicate the number of added SO2 groups, while theletters differentiate between the various structures for a given n.Structures that require the breaking of an S–O bond have beenomitted, in light of the high bond dissociation energy of SO2

(128 kcal/mol, 5.55 eV). One to four SO2’s can be O–S bonded tothe SO4 oxygens (primary SO2’s). Clusters having only primarySO2’s are Ia, IIb, IIIc. IIb and IIIc may have C2 or C3 symmetry,respectively. SO2 groups attached to a previously added SO2 canbe S–S or O–S bound. Both possibilities have been taken into ac-count. Clusters that have O–S bonds in addition to the primarybonds (IIa, IIIa, IIIb) cannot have any symmetry. For clusters withS–S bonds Cs symmetry is possible. The same starting structureswere used for monoanionic and dianionic clusters. Structures fit-ting these basic types will be shown in the forthcoming figures.

Single point calculations for n = 0, 1 and 2 were performed or at-tempted using the coupled cluster method with single, double(CCSD) and noniterative triple excitations (CCSD(T)) and the 6-311+G(d) basis set, at the B3PW91/6-311+G(3df) optimized geom-etries. Due to limitations in computer resources, CCSD(T) values forn = 2 could not be obtained.

IIa �1795.909347 0.92 �1795.945430 3.51IIb �1795.922884 1.29 �1795.947899 3.58IIc – – �1795.933248 3.18IIIa �2344.408975 1.23 �2344.462326 4.29IIIb �2344.409126 1.24 �2344.469797 4.49IIIc �2344.423194 1.62 �2344.469951 4.50IIId �2344.407890 1.20 �2344.465987 4.39IIIe �2344.374321 0.29 �2344.458762 4.19

Table 3Calculated B3PW91/6-311+G(3df) energies E(�1), E(�2) (atomic units) of the moststable isomers of SO1

4 � ðSO2Þn and SO2�4 ðSO2Þn . Binding energies DE(�1), DE(�2) in

eV. The energy of SO2 is �548.602792 a.u.

3. Results

3.1. SO2�4 and SO1�

4

The geometry of SO2�4 was optimized at the B3PW91/6-

311+G(3df) level, to result in a Td structure with a bond length of1.495 Å. This result is backed by a number of sources. Anderson[10] determined a tetrahedral arrangement with bond lengths of1.49 Å, while Zheng et al. [11] calculated bond lengths of 1.503 Åusing the MP2/6-311+G(2df) level of theory. Morton et al. [12]found by ESR measurements that the monoanionic SO1�

4 could have

Fig. 1. Labelling of structures for SO4 ðSO2Þ1�n and SO4ðSO2Þ2�n .

a symmetry no higher than C2v. Using photoelectron spectroscopy,Wang et al. [13] ruled out C3v and D2d symmetries for SO1�

4 . In Table1, B3PW91/6-311+G(3df) and CCSD(T)/6-311+G(d) optimizedgeometries and energies are listed for SO�4 at C2v, C3v, and D2d sym-metries. As expected, the C2v structure is the most stable as calcu-lated by each method. From the DFT calculations, C3v is seen to bethe second most stable symmetry, whereas coupled cluster calcu-lations show it to be the least stable of the three symmetries. In

Struct. E(�1) DE(�1) E(�2) DE(�2)

0 �699.088909 – �699.024501 –Ia �1247.729952 1.04 �1247.709931 2.25IIb �1796.346138 1.41 �1796.360029 3.54IIIc �2344.959152 1.68 �2344.994853 4.41

Table 4Adiabatic (ADE) and vertical (VDE) electron detachment energies (eV) for SO2�

4 (SO2)n,with n = 0–3, obtained by B3PW91/6-311+G(3df) and single-point CCSD/6-311+G(d)and CCSD(T)/6-311+G(d) calculations, based on the B3PW91/6-311+G(3df) optimizedgeometries.

Cluster B3PW91 CCSD CCSD(T)

ADEa VDE ADE VDE ADE VDE

SO1�=2�4

�1.77 �1.51 �1.57 �1.26 �1.61 �1.41

SO4ðSO2Þ1�=2�1

�0.52 0.40 �0.28 0.64 �0.30 0.50

SO4ðSO2Þ1�=2�2

0.40 1.59 0.38 1.95 – –

SO4ðSO2Þ1�=2�3

0.98 2.26 – – – –

a Adjusted for zero-point energy differences.

0(-2) Ia(-2) IIa(-2)

IIb(-2) IIc(-2) IIIa(-2)

Fig. 2. Optimized structures of the dianionic clusters SO4ðSO2Þ2�n .

J. Chan, F. Grein / Computational and Theoretical Chemistry 966 (2011) 225–231 227

either case, the C2v structure is more stable than the next higher-energy structure by at least 0.08 eV. Using geometries obtainedat the B3LYP/TZVP+level, Wang et al. [13] calculated the single-point energies of the C2v, C3v, and D2d structures at the CCSD(T)/6-311+G(d) level, finding that C3v and D2d were 0.12 eV and0.25 eV higher in energy, respectively, than C2v. McKee [14], Zhenget al. [11] and Zama et al. [15] calculated the geometry of SO1�

4 invarious symmetries, all finding the C2v structure to have the lowestenergy.

3.2. Binding and stabilization energies of clusters

In Table 2, the B3PW91/6-31+G(d) energies of the SO�4 (SO2)n

and SO2�4 (SO2)n clusters are given for the structures listed in

Fig. 1. Energies for the most stable species of each n are printedin bold face.

The lowest-energy structures of the monoanions and dianionshave the added SO2 molecules coordinated with different O atomsof SO4, as represented by the structures Ia, IIb and IIIc. Table 2 alsocontains the binding energies DE(�1) and DE(�2) for each cluster,calculated with the 6-31+G(d) basis set. They are defined in Eqs. (1)and (2).

DEð�1Þ ¼ �E½SO1�4 ðSO2Þn� þ E½SO1�

4 � þ nE½SO2Þ�; ð1Þ

DEð�2Þ ¼ �E½SO2�4 ðSO2Þn� þ E½SO2�

4 � þ nE½SO2Þ�; ð2Þ

where the E’s are the total energies as calculated. DE(�1) increasesfrom 0.88 (n = 1) to 1.62 eV (n = 3), and DE(�2) from 2.25 to4.50 eV.

Table 3 lists the total energies and binding energies of the moststable structures, calculated using the higher-level basis set 6-311+G(3df). At this level of theory, the monoanionic bindingenergies increase from 1.04 eV to 1.68 eV, whereas the dianionicones increase from 2.25 eV at to 4.41 eV.

Table 4 gives the adiabatic and vertical electron detachmentenergies (or ionization potentials), obtained at the B3PW91/6-311+G(3df) level and in single-point calculations at the CCSD (forn = 0, 1 and 2) and CCSD(T) (for n = 0 and 1) level with the6-311+G(d) basis set. These detachment energies are defined as

ADE ¼ E0½SO1�4 ðSO2Þn� � E0½SO2�

4 ðSO2Þn�; ð3Þ

using the calculated energies E0 of the lowest-energy structures ofthe mono- and dianions. The vertical electron detachment energyis defined as

IIIb(-2) IIIc(-2)

IIId(-2) IIIe(-2)

Fig. 2 (continued)

228 J. Chan, F. Grein / Computational and Theoretical Chemistry 966 (2011) 225–231

VDE ¼ Evert½SO1�4 ðSO2Þn� � E0½SO2�

4 ðSO2Þn�; ð4Þ

where the energy of the anionic cluster SO1�4 (SO2)n is calculated at

the optimized geometry of the lowest-energy dianion SO2�4 (SO2)n

for the given n. As defined, ADE and VDE are negative if the dianionis less stable than the monoanion, and positive otherwise. ADEenergies from DFT calculations have been corrected for differencesin zero-point energies. All corrections lie within 0.02 eV.

It is seen that ADE is negative for n = 0 and 1. However, ADE val-ues become positive with the second addition. From one additionto two, the ADE (DFT value) changes from �0.52 eV to +0.40 eV,indicating the dianion to stabilize. CCSD and CCSD(T) results, asfar as available, are in reasonable agreement with the B3PW91 val-ues. It is gratifying to see the ADE values from CCSD switch sign ingoing from n = 1 to n = 2, being �0.28 eV at n = 1 and 0.38 eV at n= 2, confirming the stabilization of the dianion at this level. As withB3PW91, the VDE obtained from CCSD turns positive after only oneSO2 addition.

3.3. Geometries of dianionic and monoanionic clusters

Figs. 2 and 3 show the optimized structures of Table 2 for dian-ionic SO4ðSO2Þ2�n and monoanionic SO4ðSO2Þ1�n , respectively. In the

following, a distinction will be made between structures that havecovalent bonds only, and such that have in addition to covalentbonds one or more weak bonds, of van der Waals type.

Dithionate, S2O2�6 , has a Cs structure, with an O–S distance of

1.885 Å between SO2�4 and SO2. For S3O2�

8 the structure IIb, O2S–O–S(O2)–O–SO2, with C2 symmetry, is the most stable one. Optimiza-tion of cyclic species was attempted, but all ended in IIb. IIa, whichis only about 0.1 eV higher in energy than IIb, has the structure O3S–O–S(O)–O–SO2 (C1). The most stable isomer of S4O2�

10 (IIIc) has a pad-dlewheel structure with C3 symmetry. This type of structure wasalso seen for CO2�

3 (SO2)3 [6]. IIIa, IIIb and IIId have energies closeto that of IIIc. All are covalently bonded. Interestingly, the structureIIIe has a very long S–S bond (2.945 Å) between attached SO2’s. TheS–O bond length for SO2�

4 binding to one SO2 is 1.7–1.9 Å (Ia, IIa, IIc),but it becomes about 2.0 Å when binding to two SO2’s (IIb), andabout 2.2 Å when binding to three SO2’s (IIIc). In the dianionic series,no S–O bonds longer than 2.3 Å are seen.

In summary, addition of nSO2 to SO2�4 results in covalently

bonded dianions having structures O3S–O–SO2 (Ia, Cs) for n = 1,O3S–O–S(O)–O–SO2 (IIa, C1) and O2S–O–S(O2)–O–SO2 (IIb, C2) forn = 2, O3S–O–S(O)–O–S(O)–O–SO2 (IIIa, C1), O2S–O–S(O)–O–S(O2)–O–SO2 (IIIb, C1), the paddlewheel structure OS(OSO2)3 (IIIc,C3), and the branched structure OS–O–S–(O–SO2)2 (IIId, C1) for

0(-1) Ia(-1) IIa(-1)

IIb(-1) IIc(-1) IIIa(-1)

Fig. 3. Optimized structures of the monoanionic clusters SO4ðSO2Þ1�n .

J. Chan, F. Grein / Computational and Theoretical Chemistry 966 (2011) 225–231 229

n = 3. The remaining dianionic isomers encountered in the calcula-tions have S–S bonds between added SO2 molecules (IIc and IIIe),with very large S–S distances ranging from 2.7 to 2.9 Å.

Considering the case of the monoanions (Fig. 3 and Table 2),S2O1�

6 is most stable as O3S–O–SO2, having no symmetry. Any at-tempt to impose Cs symmetry resulted in higher energy species.McKee’s [14] most stable structure (structure a in Fig. 1, Table 8of Ref. 14), also of type O3S–O–SO2 but with Cs symmetry, is1.11 eV higher in energy, as calculated here with B3PW91/6-311+G(3df). For S3O1�

8 , obtained by addition of two SO2 to SO1�4 ,

the most stable structure is IIb, O2S–O–SO3� � �SO2, the dots indicat-ing a very weak bond with a distance of 2.63 Å between O2S–O–SO3 and SO2. The other isomer, O3S–O–S(O)–O–SO2, as representedby IIa, is 0.37 eV higher in energy, although it is covalently bonded.The most stable isomer of S4O1�

10 is IIIc, represented by weak bondsbetween O3S–O–SO2 and 2 SO2’s. IIIa and IIIb both have one longbond between O2S–O–S(O)–O–SO3 and SO2, whereas IIId is abranched S3O8 with a long bond to SO2. Finally, structure IIIe hasan S–S bond of 2.31 Å, not as long the S–S bond in the correspond-ing dianion.

Chemically bonded monoanions having covalent bonds with S–O distances of less than 2 Å are O3S–O–SO2 (Ia), C1) for n = 1 andO3S–O–S(O)–O–SO2 (IIa, C1) for n = 2. All structures with three

SO2’s added to SO1�4 have at least one long S–O bond, usually

around 2.7 Å.

4. Discussion

According to the data in Table 4, two SO2 molecules are requiredto adiabatically stabilize the SO2�

4 dianion in the gas phase, whileonly one is required to vertically stabilize it. According to the liter-ature, three H2O molecules are required to adiabatically stabilizethe sulfate dianion, while two are required to vertically stabilizeit [3]. The corresponding numbers for the stabilization of carbonateby SO2 molecules are three for adiabiatic and two for vertical sta-bilization [6].

Binding energies calculated with DFT for SO4ðSO2Þ2�n are2.25 eV, 3.54 eV, and 4.41 eV for n = 1–3, respectively. The moststable structures for the dianionic clusters have the SO2 moleculesattached to the SO2�

4 center, rather than having chain-like arrange-ments of SO2 molecules. This type of bonding facilitates the dis-semination of the excess negative charge of the dianion to theneighbouring SO2’s. As an example, the Mulliken charge on SO4

changes from �2 to �1.33 electrons due the addition of one SO2

molecule (structure Ia), whereas the natural charge changes from�2 to �1.58. With the addition of SO2 molecules to the sulfate

IIIb(-1) IIIc(-1)

IIId(-1) IIIe(-1)

Fig. 3 (continued)

230 J. Chan, F. Grein / Computational and Theoretical Chemistry 966 (2011) 225–231

dianion, the O–S bond length increases from 1.885 Å for one addi-tion (Ia), to 2.067 Å for two additions (IIb), and to 2.216 Å for threeadditions (IIIc).

The binding energy found at n = 3, being 4.38 eV for the dian-ionic cluster and 1.68 eV for the monoanionic one, may be com-pared with the solvation energy of SO2�

4 and SO1�4 dissolved in

SO2. Using the PCM model (dielectric constant e(SO2) = 15.4) thesolvation energy is calculated as 9.1 eV for SO2�

4 and 2.4 eV forSO1�

4 . Accordingly, at n = 3, 48% of the n =1 solvation energy ofthe dianion SO2�

4 , and 70% of the monoanion SO1�4 was obtained.

According to McKee [14], dithionate, S2O2�6 , is most stable as

O3S–SO3, having D3d symmetry. The well known dithionic acidH2S2O6 and halogen salts like Na2S2O6 also have S–S linkages.B3PW91/6-311+G(3df) calculations show that (O3S–O–SO2)2� (Ia,Cs symmetry) is only 0.04 eV higher in energy than (O3S–SO3)2�

in D3d symmetry. Including zero-point energies, this differenceshrinks to 0.02 eV. The only other structure shown by McKee[14] for S2O2�

6 has C2h symmetry with a peroxy bond (O2S–O–O–SO2), which lies at much higher energy.

McKee [14] also found that S–S bonded S2O2�6 is 9.1 kcal/mol or

0.39 eV higher in energy than the most stable S–O–S bondedmonoanion (which is less stable than our monoanion Ia). DFT cal-culations at the B3PW91/6-311+G(3df) level performed in thepresent work show that the S–S bonded dianion S2O2�

6 is 0.22 eVhigher in energy than the S–S bonded monoanion S2O1�

6 , both keptat D3d symmetry. Single point CCSD calculations at the optimizedDFT geometries, however, place the S–S bonded dianion 0.03 eVbelow the S–S bonded monoanion. It is therefore possible thatthe S–S bonded dianion is not only vertically, but also adiabaticallystable, in agreement with the observation of S2O2�

6 in the gas phaseby Blades and Kebarle [2].

In this paper, the stability of the dianion with respect to loss ofan electron has been considered. In addition, the stability withrespect to dissociation into monoanions should also be taken intoaccount [16]. According to our DFT calculations, S2O2�

6 with anO–S–O linkage is less stable than 2SO1�

3 by 1.44 eV, but more stablethan SO1�

4 + SO1�2 by 0.50 eV. Furthermore, the lowest energy iso-

mer of S3O2�8 is less stable than 2SO1�

3 + SO2 by 0.15 eV, while the

J. Chan, F. Grein / Computational and Theoretical Chemistry 966 (2011) 225–231 231

stability turns around with the addition of three SO2’s, as S4O2�10 is

more stable than 2SO1�3 + 2SO2 by 0.72 eV.

5. Concluding remarks

It has been shown by DFT and CCSD methods that the sulfatedianion SO2�

4 is stabilized in the gas phase by bonding to at leasttwo SO2 molecules. For n = 2, the energy of the dianionic cluster[SO2�

4 (SO2)n]2� is 0.27 eV (CCSD(T) value) lower than that of themonoanionic [SO4(SO2)n]1�. The vertical electron detachment en-ergy is positive already for n = 1, with a CCSD(T) value of 0.50 eV.S2O2�

6 with S–S linkage appears to be slightly more stable thanthe corresponding monoanion. This isomer has been observed inthe gas phase by Blades and Kebarle [2]. Chemically bonded dia-nions S2O2�

6 , S3O2�8 and S4O2�

10 , as well as monoanions S2O1�6 and

S3O1�8 (but no S4O1�

10 ) have been predicted.We are confident that it will be possible to experimentally ver-

ify the stabilization of the sulfate dianion by the addition of twoSO2 molecules, in a manner analogous to experiments showingthe stabilization of the sulfate dianion by water molecules. Inci-dentally, reactions of sulfates with SO2, recently carried out inDr. Passmore’s labs in this Department, gave evidence of S–O–Sbonded S2O2�

6 , having a Raman spectrum in good agreement withour calculated results [17]. There is also some indication of S3O2�

8

units looking similar to the optimized structures shown in thispaper.

A manuscript on the geometries and properties of SnO2n+2

monoanions and dianions, as well on corresponding acids anddisodium salts, is in preparation. Work on the stabilization of thecarbonate and sulfate dianions in the gas phase by CO2 is inprogress.

Acknowledgments

Financial support by NSERC-Canada in the form of a DiscoveryGrant is gratefully acknowledged. Thanks to Dr. Pablo J. Bruna foruseful comments, and to Dr. Jack Passmore as well as Sonya Burrill

for their interest and help in these studies. Provision of computertime by the ACEnet computer network has been essential to thiswork.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.comptc.2011.03.005.

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