Theoretical Study of Formic Acid− Sulfur Dioxide Dimers

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Theoretical Study of Formic Acid-Sulfur Dioxide Dimers John W. Keller,* Bronwyn L. Harrod, and Sifat A. Chowdhury Department of Chemistry and Biochemistry, UniVersity of Alaska Fairbanks, 900 Yukon DriVe, Fairbanks, Alaska 99775-6160, United States ReceiVed: August 12, 2010; ReVised Manuscript ReceiVed: October 24, 2010

We report the first theoretical study of noncovalent and covalent interactions in formic acid (FA)-SO2 complexes. Using ab initio and DFT model chemistries, five stable noncovalent complexes were identified, as well as a covalent adduct, formic sulfurous anhydride HOSO2CHO. syn-FA is predicted to form two nonplanar bidentate complexes with SO2: the more stable one contains a normal hydrogen bond donated by OH, and the less stable one contains a blue-shifted hydrogen bond donated by CH. Both are stabilized by charge transfer from FA to SO2. anti-FA forms three planar complexes of nearly equal energy containing OH-to-SO2 hydrogen bonds. Formic sulfurous anhydride forms via an endothermic concerted cycloaddition. Natural bond orbital analysis showed that the bidentate SO2-FA complexes are stabilized by n f π* donation from FA to SO2, and back-donation from SO2 n and π* orbitals into FA σOH* or σCH* orbitals. The bidentate formic acid-SO2 complex that contains an O-H · · · O hydrogen bond is more stable than the similar nitric acid-SO2 complex. The latter contains a stronger hydrogen bond but shows no OfS charge transfer interaction. 1. Introduction SO2 is a trace component in the atmosphere formed by erupting volcanoes, burning sulfur-containing fossil fuels, and industrial processes. In sufficient quantities, SO2 is toxic and hazardous to plants and animals. However, there is recent evidence that SO2 is also formed in vivo in low concentrations, where it functions as a mediator of biological function.1 The biochemical reactions of SO2 related to toxicity or metabolic processing, as well as most chemical reactions, require initial formation of a noncovalent complex whose stability and orientation influence subsequent chemical events. Therefore, understanding and predicting SO2’s biological functions will require a thorough knowledge of various types of noncovalent interactions of the molecule. Although there have been many studies of monodentate SO2-small molecule dimers, and SO2-water clusters,2-4 very few, if any, complexes of SO2 with bifunctional or polyfunctional ligands, such as might be found in a protein, have been studied from a theoretical or structural point of view. This is the aim of the present work, which focuses on a simple carboxylic acid as an SO2 ligand. Qualitative prediction of the geometry of a given SO2-ligand complex is difficult due to SO2’s bent shape, rich endowment with lone pair and π-electrons, and strong polarity. More than 40 noncovalent, nonmetal, neutral SO2 complexes have been studied experimentally and/or theoretically, and display a wide assortment of interactive forces and geometries. SO2 dimers can be categorized as either hydrogen-bonded or non-hydrogenbonded. Hydrogen bonding ligands include HF,5,6 HCl,7 HO2 radical,8 HNO3, HNO2,9 and several SO2 · nH2O (n ) 2-4) clusters.4 Weak Brønsted acids do not hydrogen bond, but instead utilize charge transfer when complexed with SO2, including monomeric water,4,10-13 methanol,14,15 and HCN.16-19 Chloroform and SO2 form a blue-shifted O · · · H-C hydrogen bond.20,21 Lewis bases interact by transfer of lone pair electrons to the electropositive S atom; these include acetonitrile,22 * Corresponding author. E-mail: [email protected]. Phone: 907-4746042. Fax: 907-474-5640.

pyridine,23 dimethyl ether,24 and ammonia.25 Finally, π-electronrich molecules, such as CO2,26 OCS,27 CS2,28 SO2 itself,29-31 N2O,32,33 and acetylene,34,35 donate π-electrons to S. Most SO2 complexes with small ligands contain only one pair of interacting atoms or bonds; i.e., they are monodentate. On the other hand, a large ligand molecule with multiple functional groups, such as a protein, might be able to form a cyclic bidentate complex with SO2 that takes advantage of its electronegative O and electropositive S atoms. Only HO2 radical is solidly in this category, forming a three-atom bridge across one S-O bond.8 Methanol interacts with SO2 mainly by n-electron donation as in water dimer; however, there is also cyclic character contributed by weak back-bonding to the C and H atoms of the CH3 group.15 Also, bidentate SO2 complexes potentially could be formed by nitric, carboxylic, or other acids capable of donating both a hydrogen bond and electrons from a carbonyl O lone pair. Nitric acid-SO2 complexes have been studied experimentally and theoretically, but none of the other types has been until the present study of the formic acid ligand. The overall goal of this study was to assess the relative roles of hydrogen bonding and donor-acceptor interactions between SO2 and formic acid, and compare these to the same interactions in other known SO2 and formic acid complexes. In addition to probing the underlying interaction mechanisms, these calculations provide models for neutral complexes of SO2 with naturally occurring carboxylic acids such as aspartic and glutamic acid side chains, or related functional groups in proteins. 2. Computational Methods Gaussian 0336 and Gaussian 0937 were used in this work. Geometry optimizations were carried out using MP2 ab initio (frozen core approximation) and B3LYP38,39 and PBE1PBE40 hybrid DFT methods. The latter methods performed well in a benchmark study of noncovalent complexes.41 In the present study, the Dunning correlation consistent basis sets aug-ccpVDZ (130 basis functions) to aug-cc-pVTZ (326) were used.42 Geometry optimizations used a tight convergence criterion; frequency analysis showed zero imaginary vibrational frequen-

10.1021/jp1076214  2010 American Chemical Society Published on Web 11/30/2010

Formic Acid-Sulfur Dioxide Dimers

J. Phys. Chem. A, Vol. 114, No. 50, 2010 13183 TABLE 1: Binding Energies and Enthalpies (kcal mol-1) of Formic Acid-SO2 Complexesa complex d

C1 C2d C3e C4e C5e FSAd

∆Eelectb

∆Eoc

∆H (298 K)

-5.83 -4.53 -4.36 (-0.112) -3.99 (0.252) -4.22 (0.028) 7.65

-4.81 -3.64 -3.42 (0.462) -3.26 (0.753) -3.47 (0.550) 9.20

-4.45 -3.18 -2.99 (1.08) -2.59 (1.47) -2.84 (1.23) 8.56

a Computed at the MP2/aug-cc-pVTZ level on the counterpoisecorrected (C1-C5) or standard (FSA) PES. b For C1-C5, ∆Eelect ) Ecomplex,CP - (EFA + ESO2); for FSA, ∆Eelect ) EFSA - (EFA + ESO2). c ∆Eo ) ∆Eelect + ∆ZPE (unscaled, CP-corrected PES for C1-C5, or standard PES for FSA). d syn-FA standard state. e anti-FA standard state (syn-FA standard state).

Figure 1. Calculated minimum energy structures of SO2-formic acid (FA) dimers and monomers (FSA, formic sulfurous anhydride). C1, C2, and FSA are nonplanar. C3, C4, C5, and formic acid are planar.

cies for stable complexes; the reported transition state showed a single imaginary frequency corresponding to the reaction coordinate. In the latter case, forward and reverse IRC calculations showed smooth conversion into product and reactants. For several MP2 and DFT model chemistries, geometry optimization on the counterpoise corrected potential energy surface was carried out, that is, using the counterpoise keyword in Gaussian.43 Results from density functional theory calculations are reported in the Supporting Information. Natural bond orbital (NBO) parameters were determined using NBO 3.1 within the Gaussian program.44 Computational results were visualized using GaussView v 3.0, ORTEP-3 v 2.02,45 and WebMO v 10 software. 3. Results and Discussion Geometries and Energies. We found five stable, noncovalent complexes (C1-C5) on the SO2-formic acid potential energy surface (PES), plus the related covalent adduct formic sulfurous anhydride (FSA) (Figure 1). The binding energies of C1-C5 on the counterpoise (CP) corrected PES, and FSA on the standard PES, are shown in Table 1 and Figure 2. The data in Table 1 are based on the MP2/aug-cc-pVTZ model chemistry, which was the highest level correlated ab initio theory used in this study. Results from several other methods including B3LYP, PBE1PBE, CCSD(T), and G4MP2 are shown in Figure S1 and Tables S1-S4 in the Supporting Information which includes optimizations on both the standard and CP-corrected surfaces. Basis set superposition errors calculated on the CP-corrected surfaces ranged from 2.275 kcal/mol (MP2/6-311++G(d,p)) to 0.139 kcal/mol (B3LYP/aug-cc-pVTZ, Table S4). All model chemistries identified the same geometric minima; however, C4 and C5 occupy very shallow minima, and in these cases several model chemistries failed to converge or produced an imaginary frequency.

Figure 2. Electronic energy changes (kcal/mol) for formation of SO2-formic acid complexes and formic sulfurous anhydride (FSA), and for syn-anti isomerization of formic acid, computed at the MP2/ aug-cc-pVTZ level on the counterpoise-corrected potential energy surface for C1-C5.

Formic acid exists in two conformations: the more stable syn conformer, which has the O-H bond on the same side of the carbonyl oxygen and which benefits from a favorable electrostatic interaction between the partially positive O-H and the partially negative carbonyl O;46 and the anti conformer, which has the O-H bond poised on the opposite side of the carbonyl oxygen. The experimental ∆Eanti-syn is 3.9 kcal/mol,46 while theoretical values for ∆Eo range from 3.8 to 4.3 kcal/mol (Table S1). Both formic acid conformers can form complexes with SO2 (Figures 1 and 2). syn-Formic acid interacts with SO2 to form nonplanar bidentate complexes C1 and C2. FSA is derived from C1 by S-O bond formation and transfer of the formic acid OH hydrogen to SO2. anti-Formic acid interacts with SO2 to form planar monodentate complexes C3, C4, and C5. No stable bidentate complexes containing anti-formic acid, or monodentate complexes containing syn-formic acid, were located using either manual or automated methods to construct optimization input structures. Although anti-FA forms stable complexes with SO2, when ∆Eanti-syn values are included in the binding energy, the overall complexation equilibria become significantly less favorable than for C1 or C2. In general, a CP-corrected PES predicts a greater monomermonomer separation and a lower binding energy compared to a standard PES.43 In the case of complex C1 with the MP2/ aug-cc-pVTZ model chemistry, for example, on the standard and CP-corrected PES, the H · · · O distances were 1.962 and 2.011 Å, and the O · · · S distances were 2.848 and 2.889 Å,

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TABLE 2: SO2-syn-Formic Acid Complexesa R(O1 · · · Hn) R(S · · · O4) θ(O1 · · · Hn-Y) φ(O2-S-O1 · · · Hn) r(C-O3) 1.347c r(CdO4) 1.205 r(C-H2) 1.0925 r(O3-H1) 0.971

C1 (n ) 1)

C2 (n ) 2)

FSAb (n ) 1)

2.011 2.889 163 (Y ) O3) -76 1.336 (-11) 1.212 (+7) 1.0923 (-0.2) 0.9758 (+5)

2.529 2.846 115 (Y ) C) -87 1.339 (-8) 1.210 (+5) 1.0923 (-0.2) 0.971

0.986 1.765 136 (Y ) O3) -53 1.213 1.343 1.094 (+2) 1.858

a Selected intermolecular (R, Å) and intramolecular (r, Å) distances, angles (θ, deg), dihedral angles (φ, deg), and changes relative to monomer (in parentheses, ∆r in mÅ). MP2/aug-cc-pVTZ level on the counterpoise-corrected PES. Complete list in Table S7 in the Supporting Information. b No CP corrections made to PES. c Computed monomer quantity.

TABLE 3: SO2-anti-Formic Acid Complexesa R(O1 · · · H1) θ(O1 · · · H1-O3) r(C-O3) 1.354b r(CdO4) 1.199 r(C-H2) 1.0987 r(O3-H1) 0.966

C3

C4

C5

2.034 176 1.348 (-6) 1.202 (+3) 1.099 0.970 (+4)

1.996 179 1.349 (-5) 1.201 (+2) 1.099 0.969 (+3)

2.018 170 1.347 (-7) 1.201 (+2) 1.099 0.970 (+4)

The greatest change in intramolecular geometry upon formation of these complexes occurs with the formic acid ligand. The largest changes are in the C-O3 bond, which lengthens by 11 mÅ in C1 and by 8 mÅ in C2 compared to the syn-monomer. The same bond lengthens by 5-7 mÅ in forming C3, C4, or C5. Another significant geometric change accompanying complex formation is in the CdO bonds of C1 and C2, which lengthen upon complexation by 7 and 5 mÅ, respectively. Finally, the O-H bond lengthens by 5 mÅ in forming C1, whereas in C3-C5, which also form hydrogen bonds, this bond lengthens by 3-4 mÅ relative to the anti conformer of formic acid. Formic sulfurous anhydride (FSA) is the product of a formal π2 + π2 + σ2 cycloaddition of formic acid to SO2 via a sixcenter transition state derived from C1. The conformation of FSA that contains an internal hydrogen bond was optimized in this study, although there may be other non-hydrogen-bonded conformations. In the optimized FSA structure, the OH · · · O hydrogen bond distance is 1.858 Å and the O1-H1 · · · O3 angle is 139°. This is the shortest O · · · H approach in any of the complexes studied. FSA formation from the free monomers is endothermic by 7.56 kcal/mol at the MP2/aug-cc-pVTZ level of theory. FSA is formed from C1 in a single step via a TS 2.42 kcal/mol less stable than FSA.

a Selected intermolecular (R, Å) and intramolecular (r, Å) distances, angles (θ, deg), dihedral angles (φ, deg), and changes relative to monomer (in parentheses, ∆r in mÅ). MP2/aug-cc-pVTZ on the counterpoise-corrected PES. Complete list in Table S8 in the Supporting Information. b Computed monomer quantity.

respectively. The dimer binding energies were -6.79 and -5.83 kcal/mol, respectively (Tables 1 and S3). The CP correction term for C1 decreased from 2.28 kcal/mol using MP2/6311++G(d,p) (154 basis functions) to 0.929 kcal/mol using MP2/aug-cc-pVTZ (326 basis functions) (see Table S4 in the Supporting Information). Inter- and intramolecular geometries of the SO2-formic acid complexes are shown in Tables 2 and 3. The intermolecular interactions feature H-to-O distances that are less than the sum of O and H van der Waals radii, which are 1.46 and 1.42 Å, respectively.47 In the complexes that contain an OH · · · O hydrogen bond (C1, C3, C4, and C5), the intermolecular distances range from 2.00 to 2.03 Å, which are 0.85-0.88 Å closer than the sum of the radii. In C2, which contains a CH · · · O grouping, the O · · · H distance is 0.35 Å closer than the sum of radii. Bidentate complexes C1 and C2 also contain close O and S distances, which are 0.73 and 0.77 Å, respectively, less than the sum of the van der Waals radii of those atoms. These close intermolecular contacts allow significant orbital overlaps and donor-acceptor interactions between the two molecules, as discussed below. The intermolecular angles O · · · H-X vary with the type of complex. In the bidentate complex C1, where the O1 · · · H1-O3 atoms are constrained to a six-member ring, the O · · · H-O angle is 163° (Table 2). In C2, where the O1 · · · H2-C atoms are part of a five-membered ring, the angle is a rather acute 115°. In monodentate complexes C3-C5, the O1 · · · H1-O3 atoms are almost linear. In the nonplanar complexes, the formic acid carbonyl O lies above the SO2 plane, allowing its electrons to interact with orbitals on S. The nonplanar geometry is characterized by the O2-S-O1 · · · H1 torsion angle for C1, or the O2-S-O1 · · · H2 torsion angle for C2, which are -76° and -87°, respectively. Therefore, in these complexes SO2 leans toward formic acid.

Natural Bond Orbitals. Donor-acceptor interactions and charge separations in the two most stable SO2-formic acid complexes, C1 and C2, were analyzed using the natural bond orbital theory of Weinhold and Landis.48 Several NBOs on each monomer overlap across the intermolecular gap and contribute second-order stabilization energy to the complex. The interacting orbitals and interaction energies are plotted in Figures 3 and 4. The strongest interactions are observed in the most stable complex C1, and involve donation of electron density from orbitals on SO2 into the σ* orbital of the formic acid OH bond (Figure 3a). The donating orbitals, which overlap the proximate end of σ*OH, are the σ, π, and π*SO2,1 bonds of the in-plane S-O moiety. Figure 3b shows three modes of electron donation in the opposite direction: from the carbonyl O lone pair orbital of formic acid into the σ* and π*SO2,2 antibonds of the out-ofplane S-O moiety, and into the σ* NBO of the in-plane S-O moiety. In addition, within SO2 there is a strong intramolecular donor-acceptor interaction between π*SO2,2 and π*SO2,1 (not shown). Overlap of these orbitals at the S atom facilitates electron transfer from the CdO side to the OH side of the complex. The result is that in C1 net electron transfer from SO2 to formic acid is predicted to be virtually nil (0.0014 e). In C2, the secondary orbital interactions between SO2 and formic acid are weaker than those in C1. These mainly involve electron donation from the carbonyl O lone pair to antibonding NBOs on SO2 (Figure 4b). In the opposite direction, SO2 electrons are donated to the σ*CH of formic acid from two sources: a lone pair orbital on the SO2 O atom, and the inplane π*SO2 orbital, i.e., the same one that receives electron density from the formic acid carbonyl O. The formic acid-toSO2 donation predominates in C2, with a net electron transfer

Formic Acid-Sulfur Dioxide Dimers

Figure 3. NBO analysis of donor-acceptor interactions in complex C1 with (a) SO2 as donor and (b) formic acid as donor, with secondorder stabilization energies in parentheses. The three leading interactions between the NBOs of the complexes are shown (MP2/aug-cc-pVTZ model chemistry, counterpoise PES; 0.05 e/Å3 isosurface). The σ and π NBOs centered on SO2, and which lie in the plane of formic acid, are labeled “1”; those which are perpendicular are labeled “2”.

Figure 4. NBO analysis of donor-acceptor interactions in C2 with (a) SO2 as donor and (b) formic acid as donor, with second-order stabilization energies in parentheses. The two or three leading interactions between the NBOs of the complexes are shown (MP2/aug-ccpVTZ model chemistry, counterpoise PES; 0.05 e/Å3 isosurface).

of 0.0082 e. Thus, in both C1 and C2 the carbonyl oxygens donate to SO2; however, in C1 much of that electron density is back-donated to the σ*OH of formic acid. C1 has a more favorable overlap stereochemistry with the donating SO2 orbitals compared to σ*CH in C2. The latter forms a smaller bidentate ring and therefore has a more acute O · · · H-C angle. A consequence of these electron transfer differences is that C2 is more polar than C1 (2.325 D vs 1.454 D, Table S10). Vibrations. Calculated harmonic frequencies of the complexes C1-C5, along with the corresponding vibrations calcu-

J. Phys. Chem. A, Vol. 114, No. 50, 2010 13185 lated for the monomers, are shown in Table 4 and Table S9 in the Supporting Information. The overall pattern of frequency shifts relative to monomers is similar among the five complexes, with the exception of the C-H stretching mode, which is discussed below. All the intramolecular normal modes can be identified with the corresponding modes in the monomers due to the weak energetic and vibrational coupling between monomers in the complexes. MP2/aug-cc-pVTZ model chemistry predicts several blueshifted out-of-plane bending modes in the monomers. For example, in C3-C5, where the hydrogen bond is the only contact between monomers, out-of-plane OH bending frequencies are 125-137 cm-1 higher than in anti-formic acid. In C1 the same vibration is 74 cm-1 higher than that of syn-formic acid. The magnitudes of these shifts do not necessarily reflect the relative hydrogen bond strengths of the two complexes: the OH out-of-plane motion in syn-formic acid is already 148 cm-1 higher thanthat of anti-formic acid due to the attractive interaction of the OH bond with the carbonyl. The largest red shifts in intramolecular vibrations are predicted to be stretching of bonds directly involved in normal hydrogen bonds, especially formic acid O-H and CdO. The O-H bonds are lengthened and have lower bond orders compared to the monomers, due to electron donation by SO2 into the σ*OH NBO. Partial separation of H1 from O3 in formic acid indirectly affects the CdO bond because it invokes a more polar, carboxylate-like bonding pattern within the O-C-O moiety. This can be seen in the increased bond order and stretching frequency, as well as the shorter bond length, in the C-O3 bond. Blue-Shifted Hydrogen Bond Is Predicted for Complex C2. C2 contains an O · · · H-C interaction that is similar to those predicted for the syn-syn reversed formic acid dimer (FADr)49 and the syn-anti formic acid dimer.50 FADr contains a normal hydrogen bond donated by one OH moiety, and a blue-shifted hydrogen bond donated by the C-H group to the opposite carbonyl O. Table 5 shows a detailed comparison of C2, C1 and FADr. To facilitate comparison with C2, the FADr structure was reoptimized at the MP2/aug-cc-pVTZ level of theory on the standard PES; it was originally studied at the MP2/631+G(d) level of theory, which gives qualitatively similar results.49 FADr is about 5 kcal/mol more stable than C2, but is 5 kcal/mol less stable than the normal syn-syn formic acid dimer.51-53 Alagubin et al.54 have shown that blue-, red-, or no-shifted X-H bonds result from different effects on the X-H bond by the lone pair of an approaching heteroatom. These electrons can both donate into the σ*XH orbital, which lengthens and weakens it and red-shifts the bond stretch vibration, and they can also repel σXH electrons, which leads to rehybridization of the X-H bond and increased s-character at the X atom. The latter process shortens and strengthens the X-H bond and blueshifts the bond stretch vibration. In the present case, both C2 and the FADr donor C-H bond are predicted to have blueshifted stretching frequencies, although the shift is larger in FADr. However, the latter has a shorter CH · · · O distance (by 0.138 Å), and its 7-membered cyclic structure enjoys a more linear C-H · · · O angle (by 10.9°) (Table 5). NBO analysis predicts a stronger nfσ* donor-acceptor interaction (by 0.54 kcal/mol) in FADr compared to C2. The stronger O · · · H interaction in FADr compared to C2 leads to rehybridization of C to greater s-character, which in turn leads to more polarization of the C-H bond and greater partial positive charge q on H. The nondonating C-H bonds in FADr and C1 have

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TABLE 4: Stretching and Out-of-Plane Bending Harmonic Vibrations Computed for Monomers and SO2-Formic Acid (FA) Complexes and Frequency Shifts Relative to Monomers (Unscaled, cm-1)a mode

monomers (SO2, syn-FA)

C1

C2

O-H str C-H str CdO str C-H ip O-H ip SO2 unsym str C-O str SO2 sym str C-H oop O-H oop

3741 3124 1794 1409 1302 1305 1130 1099 1059 675

3644 (-97) 3126 (+2) 1772 (-22) 1422 (+11) 1339 (+37) 1303 (-2) 1173 (+43) 1113 (+14) 1070 (+11) 749 (+74)

3736 (-5) 3133 (+9) 1776 (-18) 1413 (+4) 1318 (+16) 1305 1149 (+19) 1109 (+10) 1075 (+16) 686 (+9)

a

monomer (anti-FA) 3809 3040 1830 1419 1274 1117 1035 527

C3

C4

C5

3728 (-81) 3037 (-3) 1821 (-9) 1424 (+5) 1318 (+44) 1298 (-7) 1143 (+26) 1101 (+2) 1044 (+9) 662 (+135)

3740 (-69) 3038 (-2) 1824 (-6) 1420 (+1) 1319 (+45) 1297 (-8) 1144 (+27) 1104 (+5) 1041 (+6) 652 (+125)

3731 (-78) 3036 (-4) 1822 (-8) 1420 (+1) 1321 (+47) 1301 (-4) 1147 (+30) 1103 (+4) 1041 (+6) 664 (+137)

MP2/aug-cc-pVTZ on the counterpoise-corrected PES. Complete list in Table S9 in the Supporting Information.

TABLE 5: Comparison of C-H Bonds in Formic Acid and Formic Acid Complexesa

a MP2/aug-cc-pVTZ level on the standard PES. b Angle formed by formic acid C-H bond with the donating O in the cyclic complex. c Sum of NBO 2nd-order stabilization energies of the three leading donor-acceptor interactions (kcal/mol).

similar properties to FA itself; therefore, the changes seen in the donating C-H bonds in FADr and C2 are due to juxtaposition of the opposing O and H atoms, and are not due to bonding changes elsewhere in the complexes. Comparing C1 and the SO2-Nitric Acid Complex. Wierzejewska and co-workers identified an SO2-nitric acid complex in mixtures of SO2 and nitric acid deposited in a solid Ar matrix.9 The infrared spectrum, and theoretical optimization at the MP2/ 6-31G(p) level, provided evidence for a nonplanar, hydrogenbonded heterodimer with a geometry and stability similar to the SO2-formic acid complex C1. However, the SO2-nitric acid complexation forces are weaker and rely entirely on the intermolecular O · · · HO hydrogen bond. Single-point calculations for SO2-nitric acid at the MP2/6311++G(2d,2p) level of theory gave a ∆Eelec value of -4.21 kcal/mol (-17.6 kJ/mol) including a counterpoise correction.9 At the same level of theory ∆Eelect for C1 is -4.58 kcal/mol. Optimizing both complexes with a larger basis set on the CPcorrected PES (MP2/aug-cc-pVTZ), ∆Eelect values for the nitric and formic acid complexes are -5.20 and -5.83 kcal/mol, respectively. In both model chemistries the geometries are similar; however, nitric acid forms a shorter O · · · HO hydrogen bond distance to SO2 (1.9347 vs 2.0114 Å in C1), and a considerably longer O · · · S distance (3.2806 vs 2.8895 Å in C1). These results indicate a stronger hydrogen bond and essentially no O-to-S electron donation in SO2-nitric acid compared to

C1. This notion is further supported by NBO analysis of the SO2-nitric acid complex which shows negligible nitric acidto-S interaction (Figure S2 in the Supporting Information). 4. Conclusions Five stable noncovalent complexes C1-C5 were optimized in the formic acid + SO2 system using ab initio correlated and density functional theory methods, and on both the standard and counterpoise-corrected potential energy surfaces. The most stable, C1, was predicted to be about 1.5 kcal/mol more stable than C2; both these contain formic acid in the more stable syn conformation. Complexes formed from SO2 and the anti conformation of formic acid, C3-C5, are the less stable due to the unfavorable HOsCdO interaction and the lack of a carbonyl O-S interaction. C1 and C2 are true bidentate complexes in that they contain two stabilizing interactions: charge transfer from carbonyl O to S, and back-donation from SO2 to antibonding orbitals localized on O-H or C-H. Back-donation in C1 is sufficient to almost nullify electron transfer between the two molecules. Back-donation in C2 is weak, resulting in a strong predicted dipole from formic acid to SO2. The various donor-acceptor interactions were quantified using natural bond orbital theory which showed that orbital overlap in the six-atom cyclic C1 complex is more favorable for donor-acceptor interactions than those in the five-atom cyclic C2 complex.

Formic Acid-Sulfur Dioxide Dimers While nitric acid does form a stable nonplanar complex with SO2 with a rather strong hydrogen bond, the complex is predicted to be less stable than the analogous SO2-formic acid complex C1. Therefore, nitric acid-SO2 is best characterized as a nonplanar monodentate complex. Considering the importance of O-to-S electron donation in these types of complexes, we predict that weaker carboxylic acids such as acetic or carbamic will form even stronger bidentate complexes with SO2 compared to formic acid. It can also be seen that, in a biological setting, the interaction energies of SO2 with groups at protein surfaces or enzyme active sites may be modulated by local modification of the group’s Brønsted acid and donor-acceptor properties. Acknowledgment. This research was supported in part by a grant of computer time from the University of Alaska Arctic Region Supercomputing Center, and grants from the University of Alaska Fairbanks Technology Advisory Board and the University of Alaska Foundation. Supporting Information Available: Additional tables and figures. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Li, L.; Moore, P. K. An Overview of the Biological Significance of Endogenous Gases: New Roles for Old Molecules. Biochem. Soc. Trans. 2007, 35, 1138–1141. (2) Hirabayashi, S.; Ito, F.; Yamada, K. M. T. Infrared Spectra of the (H2O)n-SO2 Complexes in Argon Matrices. J. Chem. Phys. 2006, 125, 034508. (3) Cukras, J.; Sadlej, J. On the Nature of the Interaction in Ternary Water-Sulfur Dioxide Complexes. Pol. J. Chem. 2008, 82, 675–685. (4) Steudel, R.; Steudel, Y. Sulfur Dioxide and Water: Structures and Energies of the Hydrated Species SO2-nH2O, HSO3-nH2O, SO3H-nH2O, and H2SO3-nH2O (N ) 0-8). Eur. J. Inorg. Chem. 2009, 2009, 1393– 1405. (5) Andrews, L.; Withnall, R.; Hunt, R. D. Infrared-Spectra of the O3-HF and SO2--HF Complexes in Solid Argon. J. Phys. Chem. 1988, 92, 78–81. (6) Tachikawa, H.; Abe, S.; Iyama, T. An Ab Initio Mo Study on the Structures and Electronic States of Hydrogen-Bonded O3-HF and SO2-HF Complexes. Inorg. Chem. 2001, 40, 1167–1171. (7) Ford, T. A. Ab Initio Molecular Orbital Calculations of the Structures and Vibrational Spectra of Some Molecular Complexes Containing Sulphur Dioxide. J. Mol. Struct. 2009, 924-926, 466–472. (8) Wang, B.; Hou, H. Theoretical Investigations on the SO2 + HO2 Reaction and the SO2-HO2 Radical Complex. Chem. Phys. Lett. 2005, 410, 235–241. (9) Wierzejewska, M.; Mielke, Z.; Wieczorek, R.; Latajka, Z. Infrared Matrix Isolation and Theoretical Studies of SO2 - HNO3 and SO2 - HONO Systems. Chem. Phys. 1998, 228, 17–29. (10) Matsumura, K.; Lovas, F. J.; Suenram, R. D. The Microwave Spectrum and Structure of the H2O--SO2 Complex. J. Chem. Phys. 1989, 91, 5887–5894. (11) Bishenden, E.; Donaldson, D. J. Ab Initio Study of SO2 + H2O. J. Phys. Chem. A 1998, 102, 4638–4642. (12) Yang, H.; Wright, N. J.; Gagnon, A. M.; Gerber, R. B.; FinlaysonPitts, B. J. An Upper Limit to the Concentration of an SO2 Complex at the Air-Water Interface at 298 K: Infrared Experiments and Ab Initio Calculations. Phys. Chem. Chem. Phys. 2002, 4, 1832–1838. (13) Cukras, J.; Sadlej, J. Structure and Energetics of Weakly Bound Water-Sulfur Dioxide Complexes. THEOCHEM 2007, 819, 41–51. (14) Sun, L.; Tan, X.-Q.; Oh, J. J.; Kuczkowski, R. L. The Microwave Spectrum and Structure of the Methanol-SO2 Complex. J. Chem. Phys. 1995, 103, 6440–6449. (15) Rayo´n, V. M.; Sordo, J. A. Methanol-Sulfur Dioxide Van Der Waals Complexes: A Theoretical Study. J. Chem. Phys. 1997, 107, 7912–7920. (16) Goodwin, E. J.; Legon, A. C. The Rotational Spectrum and Molecular Geometry of an Antihydrogen-Bonded Dimer of Sulfur Dioxide and Hydrogen Cyanide. J. Chem. Phys. 1986, 85, 6828–6836. (17) Chattopadhyay, S.; Plummer, P. L. M. Ab Initio Studies on the Dimer of Sulfur Dioxide and Hydrogen Cyanide. J. Chem. Phys. 1990, 93, 4187–4191.

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