A density functional theory insight towards the rational design of ionic liquids for SO 2 capture †

A systematic density functional theory (DFT) analysis has been carried out to obtain information at the molecular level on the key parameters related to efficient SO2 capture by ionic liquids (ILs). A set of 55 ILs, for which high gas solubility is expected, has been selected. SO2 solubility of ILs was firstly predicted based on the COSMO-RS (Conductor-like Screening Model for Real Solvents) method, which provides a good prediction of gas solubility data in ILs without prior experimental knowledge of the compounds’ features. Then, interactions between SO2 and ILs were deeply analyzed through DFT simulations. This work provides valuable information about required factors at the molecular level to provide high SO2 solubility in ILs, which is crucial for further implementation of these materials in the future. In our opinion, systematic research on ILs for SO2 capture increases our knowledge about those factors which could be controlled at the molecular level, providing an approach for the rational design of task-specific ILs.


Introduction
Air pollution is attracting increasing attention throughout the world. Among the main air pollutants, sulfur dioxide (SO 2 ), which is mainly emitted through the combustion of fossil based fuels, is causing serious harm to the environment and human health. 1,2 At the same time, SO 2 is a useful source of many intermediates in chemical synthesis. 3 As a matter of fact, there is general interest in the design and improvement of methods for SO 2 capture. Although several methods have been developed for this purpose, all of them have several drawbacks. For instance, an effective method based on flue gas desulfurization (FGD) needs a large amount of water and subsequent treatment of the consequent waste, in order to prevent excessive amounts of calcium sulphate that lead to secondary pollution in the environment. Other methods, such as amine scrubbing, are affected by solvent loss and degradation due to the low volatility and stability of amine solutions. 2,4,5 In recent years, ionic liquids (ILs) have demonstrated their effectiveness for acid-gas removal from flue gas such as SO 2 2,3,5-9 and CO 2 . [8][9][10][11][12][13][14] In addition, ILs contain unique properties, including good thermal and chemical stability, non-flammability and most distinctly they have almost null vapor pressure. All these features have been proved to be useful in chemical processes to replace volatile organic compounds. Nonetheless, the major advantage of ILs is the possibility to design task-specific solvents through the adequate cation-anion combinations, which requires a deep understanding of the structure-property relationship. 9,15 There is a large collection of compounds (approximately about B10 6 when considering only ''pure'' ILs), and thus, system approaches on the ability of ILs for acid gas capture are useful in the selection of ILs for SO 2 storage. Unfortunately, the larger number of ILs hinders systematic experimental studies on a huge number of ILs, due to the economical and temporal cost as well as limited experimental resources. Having mentioned the cost of experimental difficulties and cost hurdles associated with broad screening of ILs for acid-gas removal, density functional theory (DFT) simulations have proven their ability to provide valuable indications and guide to the experimentalists. As a matter of fact, DFT is a suitable tool for the analysis of the interactions between ILs and gas molecules at the nanoscopic level, which allow a deeper knowledge of the structure-property relationship. Most of the reported DFT studies only consider CO 2 . 7,12,13,16,17 Though, some researches leading with SO 2 capture have been reported. 7,17 There are few recent studies that address utilization of ILs for gas capture at the molecular level, especially SO 2 capture. Damas et al. have shown a systematic study of acid-and sour-gas mitigation alternatives (SO 2 , CO 2 and H 2 S) by using ILs through DFT simulations, which mainly focuses on imidazolium cation based ILs. 17 In this presented work, we broadened the study that was conducted by Damas et al. by including other cations such as piridinium or cholinium cations in combination with anions such as bis(trifluorosulfonyl)imide, triflate, or tetrafluoroborate as shown in Table 1 and Fig. 1.
In our opinion, the analysis of those ILs with high efficiency for SO 2 capture through DFT tools should be a good starting point to shed some light on the main molecular factors related with efficient SO 2 capture. Unfortunately, experimental studies dealing with SO 2 capture by ILs are still scarce and reduced to a small number of selected ionic liquids. A key parameter in the selection of an ionic liquid for SO 2 capture is gas solubility. It is well known that gas solubility in ILs can be predicted based on the COSMO-RS (Conductor-like Screening Model for Real Solvents) method. 18 The COSMO-RS predicts thermodynamics properties of solvents on the basis of uni-molecular quantum chemical calculations for the individual molecules, which provides a good Table 1 The selected family of ionic liquids studied in this work along with their estimated Henry's Law constants of SO 2 (K H ) at 303 K predicted using the COSMO-RS method prediction of gas solubility data in ILs without prior experimental knowledge on the compound's properties. 14 Thus, COSMO-RS is able to carry out fast screening on a huge number of ionic liquids, reducing the number of candidates for experimental studies, which also reduces try-and-error attempts and economical and temporal cost. Consequently, the COSMO-RS method was firstly used to carry out a quick screening on a big matrix of ILs. Then, an in-depth study of those ILs, which are expected to provide high SO 2 solubility according to the COSMO-RS method, from a molecular point of view was done using DFT tools. The combination  The [C + A] GAS model was employed in this work, which is based on two main steps: (i) quantum chemical optimization for the molecular involved species and (ii) COSMO-RS statistical calculations. Firstly, the isolated ions and SO 2 were optimized at the B3LYP/ 6-311+G(d,p) level using Gaussian 09 (Revision D.01) package, 19 which was also instructed to provide the COSMO files. For these structures, COSMO files were calculated at the BVP86/TZVP/DGA1 theoretical level and used as input in the COSMOthermX program 18 to estimate Henry's law constants. The COSMO-RS model parameterization used for all calculations was BPTZVPC21-0111.
In this work, Henry's law constants (K H ) for SO 2 were selected as a measure of absorbing capability. Henry's constants are directly calculated by COSMOthermX code. The details of theory of COSMO-RS can be found in the original work of Klamt et al. 18 Briefly, Henry's law constants can be defined as the ratio between the liquid phase concentration of SO 2 and its partial vapour pressure in the gas phase: where P i and x i are the partial vapour pressure of a compound i (SO 2 in our study) in the gas phase and its molar fraction in the liquid. g N i is the activity coefficient of the compound at infinite dilution, and P S i is the saturated pure compound vapor pressure of the gas. Those parameters are directly provided by the COSMOthermX code.

DFT simulations
Systems composed by one isolated molecule (i.e. isolated ions and SO 2 ) up to the system composed by both ions and SO 2 were optimized. Optimized minima were checked through their vibrational frequencies. For those simulations wherein two or more molecules are present, different starting points were employed in order to study different relative dispositions, focusing our attention on the disposition of minimal energy. All these calculations were carried out using a B3LYP-D2 functional. B3LYP 20 has been selected since it has been proven to show appreciable performance over a previously studied wide range of systems, 21 while dispersion corrections (D2) are adequate since we dealt with systems with dispersive interactions such as hydrogen bonds. 22 In addition, other works dealing with the performance of dispersion corrected functionals to study ionic liquid concluded that dispersion correction could significantly decrease mean absolute deviations for binding energies up to 10.0 kJ mol À1 or lower in comparison with the MP2 method. 23 All atomic elements, except iodine, were described with the standard Pople basis set 6-311+G(d,p). For iodine, a small core Stuttgart-Dresden-Bonn effective core potential was used (SDB-cc-pVTZ). 24 Interaction energies (BE) related with SO 2 capture were computed as the energy difference between the complex and the sum of the energy of each component. For example, BE for ILÁ Á ÁSO 2 was calculated as: Binding energies were also estimated by considering the IL as a whole (BE 0 ), i.e., the binding energy due to the interaction between the IL and the gas molecule: where E IL-SO 2 , E cat , E ani , E IL and E SO 2 stand for the energies of ILÁ Á ÁSO 2 , cation, anion, IL and SO 2 , respectively. For those systems composed of two or more molecules, computed energies were corrected according to the counterpoise method to avoid basis set supper position error (BSSE). 25 It has been shown that there is a specific charge transfer interaction between SO 2 and the ions. 26 There are different methods to calculate charge distributions, such as the Mulliken method, 27 whose basis set dependence is well known. 28 ChelpG scheme 29 has demonstrated its suitability for ILs. 12,30 Thus, atomic charges were also computed according to both ChelpG and Mulliken schemes. Intermolecular interactions where analyzed in the framework of Bader's theory (Atoms in Molecules, AIM). 31 In this context, intermolecular interactions are characterized through critical points (CP). Although four kind of critical points were obtained, we focused on bond critical points (BCP), which raises the criteria for considering the presence of intermolecular interactions. 31 AIM analysis was carried out with the MultiWFN code. 32 All the above-mentioned calculations were carried out with Gaussian 09 (Revision D.01) package. 19

Results and discussion
3.1. COSMO-RS analysis: selection of the optimal IL family As said, the first step in our study was the selection of an optimal family of ILs with high SO 2 solubility. The SO 2 absorption capacities were evaluated in terms of Henry's law constants (K H ) predicted according to the COSMO-RS method. COSMO-RS is a predictive method for thermodynamic equilibrium of fluids, which uses a statistical thermodynamic approach based on the results of uni-molecular quantum chemical calculations. The efficiency of COSMO-RS to predict the solubility behaviour of different solutes in ILs was evaluated by comparing both the experimental and computed (according to the COSMO-RS method) Henry's constants. 14,18,33,34 Although some publications have reported that COSMO-RS systematically overestimates the Henry's constants, it provides a reasonable linear fit between the calculated and experimental values. 14,34 In this work, COSMO-RS approach has been used to perform a fast screening on SO 2 solubility in ILs. Although several properties, such as s-surfaces, screening charge density, s-profiles, and histograms of screening charge can be computed with COSMO-RS, we have focused on Henry's law constants for SO 2 as a measure of absorbing capability. For this, K H (at 303 K) was estimated for a matrix of C7600 ILs formed through a combination of cations based on imidazoluim, piperidinium, choline, ammonium cations paired with anions such as halogens, phosphates, tetrafluoroborate, dicyanamide or bis(trifluorosulfonyl)imide (see Table S1, ESI †). In addition to low Henry's law constants, only those ILs with an adequate viscosity profile for industrial applications as suitable ILs for SO 2 capture were considered. Thus, a set of 55 ILs (see Table 1 and Fig. 1) was selected for a deeper DFT analysis. Table 1 and Fig. 2 gather the computed Henry's law constants of the selected ionic liquids. All selected ILs yield K H within the range of 2.5 Â 10 5 to 6.5 Â 10 5 Pascal at 303 K. These values are smaller (which means higher solubility) than those reported by González-Miquel et al. (of around 30 Â 10 5 Pascal-60 Â 10 5 Pascal) for CO 2 absorption. 35 Then, high efficiency for SO 2 capture can be expected for selected ILs. Note that most of the selected ILs are based on cations such as imidazolium, pyridinium or piperazinium and anions such as [BF 4 ] À , [PF 6 ] À , [NTf 2 ] À triflate or halides. Then, the combination of these anions would be adequate to design ILs for SO 2 capture with high efficiencies.

DFT analysis
As a first approximation, SO 2 capture at the molecule level could be related with the strength of the interactions between the ions and the SO 2 molecule. In this work, the interaction strength has been mainly analyzed based on binding energies (BE). Prior to analysis of SO 2 capture by selected ILs, ionÁ Á ÁSO 2 and ionic pairs were also briefly assessed. Such information could be useful to rationalize the behavior of ILÁ Á ÁSO 2 systems.
3.2.1. IonÁ Á ÁSO 2 systems. Fig. 3 shows computed binding energies (|BE|) for anionÁ Á ÁSO 2 interactions. In general, the selected cations provide similar |BE|, whose values lie between 31 ]) has been selected as its CO 2 capture performance has been demonstrated experimentally. 11 According to eqn (2), CO 2 capture by IL 22 yields |BE| 0 = 36.58 kJ mol À1 . This energy could be considered as a low limit, from which higher |BE| would be adequate to provide high SO 2 affinities. It has been proven that there is a charge transfer interaction between SO 2 and the anion motif of ILs. This charge transfer interaction is proportional to the anion basicity and plays an important role on the gas adsorption capacity. 26 Fig. 4 collects the charge transfers between the cation/anion and SO 2 molecule. For cation (anion)Á Á ÁSO 2 systems, the total charge over the SO 2 molecule takes positive (negatives) values, which means that charge is transferred from the SO 2 up to the cation (from the anion up to the SO 2 ). Broadly, charge populations according to the Mulliken scheme are smaller than those computed using the ChelpG model. According to ChelpG (Mulliken) atomic charges, charge transfer between cations and the SO 2 molecule is, on average, 0.05 (0.05) electrons. Thus, van der Waals interactions are one of the main contribution to the |BE| for cation-SO 2 systems, which is in concordance with lower |BE| values than anion-SO 2 systems. Now, the total charge over SO 2 molecule is 0.23(0.21) electrons for anion-SO 2 systems. These higher values are in concordance with greater anion appetency to interact with the SO 2 molecule due to a charge transfer interactions. Fig. 5 shows the relationship between binding energies and charge transfer of anion Á Á ÁSO 2 systems (a similar pattern has not been found for cationÁ Á ÁSO 2 systems), which follows a linear behavior for most anions. Fig. 6 gathers computed |BE| of the isolated ionic pair and the charge transfer (CT) between ions according to the ChelpG scheme. Most ILs yield |BE| between 318.99 kJ mol À1 (IL 21) and 492.70 kJ mol À1 (IL 20), while ILs 25, 29, 31, 33 and 35 provide the smallest values, around 173.09 kJ mol À1 . As known, the columbic attraction between opposite charges is the main force between both ions forming the ionic liquid. Even though, other intermolecular forces can also be present. Both the charge transfer and BE follow similar patterns (Fig. 6), i.e., the columbic interaction between both positive and negative charges is one of the main contributions to the binding energy. ILs with the smallest |BE|, i.e. IL 25, 29, 31, 33 and 35, are those wherein high charge transfer does not provide high binding energies, which points out that other interactions (such as hydrogen bonds) also represent an important contribution (intermolecular interactions between ions are below described for some ILs). ILs based on halide anions (45-55) show increasing CT with the halide electronegativity. Those effects are stronger from chloride to bromide halides. CTs and binding energies depend on both the cation and anion nature as well. For instance, those ILs based on imidazol cations and [NTF 2 ] À anions (except ILs 25 and 29) yield similar |BE| (C339.0 kJ mol À1 ).   (2)) of ILÁ Á ÁSO 2 systems, which has been decomposed as a sum of the ionic pair, cationÁ Á ÁSO 2 and anionÁ Á ÁSO 2 contributions. Thus, using the optimized ILÁ Á ÁSO 2 geometries, contributions from cationanion, cationÁ Á ÁSO 2 and anionÁ Á ÁSO 2 have been also calculated. BE energies were also estimated taking into account the ILs as a whole (eqn (2), |BE 0 |). All these quantities are also provided in Fig. 7. The largest contribution to the binding energy comes from the interaction between both ions. For an easier comparison, this contribution has been also represented in Fig. 6. For most ILs, the SO 2 molecule only induces a scarce weakening on the interaction between ions (lower |BE|). However, ILs with the lowest |BE| in the absence of SO 2 (ILs 25, 29, 31, 33 and 35, see Fig. 6) are those wherein the SO 2 molecule steers to a strengthening on the interaction between ions. This is due to the phenomena that the new arrangement between ions of SO 2 improves the interaction between both ions and their interactions with the gas molecule, which is described in detail below.

Ionic liquids.
Regarding ionÁ Á ÁSO 2 contributions, cationÁ Á ÁSO 2 one is, in general, much lower than anionÁ Á ÁSO 2 contributions. Even if, the behavior of both ionÁ Á ÁSO 2 contributions and its relationship with |BE| 0 depends on the analyzed IL. For instance, anionÁ Á ÁSO 2 contributions present similar values to |BE 0 | for ILs 1-6 (based on tetrafluoroborate anion) and 45-55 (based on halides), i.e., anionÁ Á ÁSO 2 interactions stand for the main contribution to the total binding energies of these IL-SO 2 systems. Hence, for those ILs based on [BF 4 ] À (1-6) and halide (45-55) anions, the SO 2 adsorption process is mainly governed by the anion. For ILs based on triflate, thiocianathe or dicyanamide (ILs 36-44), the sum of both ionÁ Á ÁSO 2 contribution yields similar values of |BE 0 |. In consequence, the SO 2 capture using ILs 36-44 would be guided by both ions. Based on average values, binding energies of cation/anion-SO 2 systems (Fig. 3) yield values C37.09 kJ mol À1 /72.37 kJ mol À1 . However, cation/anionÁ Á ÁSO 2 contributions to the binding energy (Fig. 7) are of around 13.94 kJ mol À1 /52.03 kJ mol À1 . For both ions, interaction energies reduce C21.9 kJ mol À1 due to the presence of the paired ion. Ions became less negative, since they transfer charge up to both the cation and SO 2 molecule. However, both ions strongly interact between them, hindering cation/ anionÁ Á ÁSO 2 interactions. Afresh, this general trend depends on the selected family. For example, for [BF 4 ] À /[Cl] À /[Br] À /[I] À anion |BE| = 55.45 kJ mol À1 /54.64 kJ mol À1 /50.07 kJ mol À1 / 51.83 kJ mol À1 , while anion-SO 2 contributions to the total |BE 0 | for ILs 1-6 (which are those based on tetrafluoroborate anion) are C69.28 kJ mol À1 , and C90.07 kJ mol À1 for those ILs based on halides (45-55). As seen above, anionÁ Á ÁSO 2 interactions are mainly ruled by the anionÁ Á ÁSO 2 . Both factors point out that the CT between both ions would increase anion basicity, as well as its interaction strength with the SO 2 molecule. Bearing in mind  Total charges over both ions and the SO 2 molecule are displayed in Fig. 8. The gas usually gets a negative charge, i.e., there is a charge transfer for the anion up to the SO 2 molecule. Charge populations over both ions for ILs in the absence of SO 2 are also included in Fig. 8. According to the ChelpG scheme, cationic charges slight vary due to the SO 2 molecule, while anionic charges suffer drastic lessening due to the charge transfer up to the SO 2 molecule.
In short, anionÁ Á ÁSO 2 interactions play an important role in SO 2 capture by ILs. When both ions are considered, anionÁ Á ÁSO 2 strengths will be affected by cation-anion interactions. We have defined the binding energies of IL-SO 2 systems (BE, according eqn (2)) as a function of the BE of ion-SO 2 systems (Section 3.2.1. and Fig. 3) and ionic pairs (Section 3.2.2. and Fig. 6): where BE IL-SO 2 , BE CAT-SO 2 , BE ANI-SO 2 , BE IL are the binding energies of the IL-SO 2 , cation-SO 2 , anion-SO 2 and anioncation systems, respectively, while a, b, c, x, y and z are adjustable parameters. Fig. 9a plots the results of a statistical analysis after expressing BE IL-SO 2 according to eqn (4). Fig. 9a gathers the data collected for the whole set of ILs. Most of them yield a linear behavior between BE IL-SO 2 estimated from the IL-SO 2 optimized systems (BE IL-SO 2 ,DFT ) and those ones after the fit of eqn (4) (BE IL-SO 2 ,Statistical ). Hence, the total binding energy of IL-SO 2 systems, which takes into account both anioncation and anion-SO 2 interactions, could be directly obtained through the optimization of ionÁ Á ÁSO 2 systems and ILs. The fit yields R 2 = 0.6772 and medium deviation (MD) = 3.20 kJ mol À1 , which could be considered an acceptable value despite the variety in the chemical structure of the selected ionic liquid.   not suffer important geometrical arrangements in the presence of the gas molecule. Note that the z parameter is close to one. As a result, we defined eqn (4) based only on BE ANI-SO 2 and BE IL . BE IL-SO 2 ,Statistical as follows: The fit was repeated despising ILs 20, 25, 29, 31, 33 and 35. As seen in Fig. 9b, there is a notable improvement in the fit performance with R 2 = 0.7887 and MD = 2.55 kJ mol À1 . It could be concluded that SO 2 capture by ILs is mainly governed by ILs, while interactions between ions are also an important parameters. Since BE between ions is much higher than anion-SO 2 ones, BE IL grants the most important contribution to BE IL-SO 2 ,Statistical . Then, for those ILs with similar BE IL , the efficiency in SO 2 capture will be ruled by the anion. In addition, eqn (5) allows estimating BE IL-SO 2 only through the optimization of anion-SO 2 and cationanion systems, which can be considered a useful insight into the rational design of ILs for SO 2 capture.
3.2.4. Representative ionic liquids for SO 2 capture. Up to now, properties for ILÁ Á ÁSO 2 interactions have been analyzed for the whole family of selected ILs based on binding energies. As seen, the SO 2 absorption capacity is often governed by anionÁ Á ÁSO 2 interactions, although cations have also an important role. Even though, cation-SO 2 contributions to the total |BE 0 | are always lower than cation-SO 2 binding energies, while this general trend was not found for anionÁ Á ÁSO 2 contributions. For instance, anionÁ Á ÁSO 2 contributions to the total |BE 0 | for ILs (1-4, which are based on imidazolium cations paired with tetrafluoroborate anion) are higher than binding energies for anion-[BF 4 ] À systems, while the opposite trend was noted for ILs 22-29 (also based on imidazol derived cations, but paired with the [NTf 2 ] À anion). In addition, a statistical analysis has shown that BE of IL-SO 2 systems mainly depends on anion-SO 2 and cation-anion interactions. The diversity in the nature of both ions forming the family of studied ILs hinders the search of structure-property relationships. Therefore the IL family has been divided into six sets (labelled as I-VII, see Fig. 2 and 7), wherein ILs within the same sets have similar features regarding the chemical structure of their ions. For each one, the most representative ILs have been selected, whose intermolecular interactions where analyzed within the context of the AIM theory to obtain some information on the SO 2 capture mechanism at the nanoscopic level.
Set  6 ] À anions have an effect of thermophysical properties such as viscosity or density. 30,36 ILs included in set I would provide similar SO 2 capture efficiency (based on K H and |BE 0 | values). As a matter of fact, several papers highlight the effect on macroscopical properties as a function of the selected ions elsewhere. 30,36,37 In order to discuss the effects on different ions at the molecular level, besides previously described parameters, the interaction mechanisms of [ 6 ] (IL 13) have been deeply analyzed as representative compounds of this set. Intermolecular interactions were localized and featured through the AIM theory (we have focused on electronic density values, r, for the main intermolecular interactions). Fig. 10 plots their optimized structures in the presence of the SO 2 molecule (optimized geometries for isolated ILs are not represented since the presence of SO 2 does not carry out important changes on the relative disposition between ions), whereas bond length and AIM features of intermolecular interactions are reported in Table 2. In the absence of the SO 2 molecule, several anioncation interactions are established. The main interactions are formed between F and H in position 2 of the imidazolium/ pyridinium ring, whose d (intermolecular distance) and r are C2.240 and 0.0140 a.u., respectively. In this sense, it is well known that the main interaction in imidazilium based ILs is carried out through the H atom in position 2. 17 The presence of the SO 2 molecule leads to an intermolecular distance elongation and electronic density decrease, in concordance with lower |BE| of ILs using their geometries in the presence of SO 2 . As seen below, this effect is also noted for almost all ILs under study. Anion-SO 2 interactions are mainly characterized by a BCP between F and S, labeled as d 6 , d 15 , d 24 and d 33 for ILs 2, 7, 8 and 13, respectively, whose r are 0.0273 a.u., 0.0189 a.u., 0.0135 a.u., 0.0092 a.u., respectively. Similar patterns are noted for anion-SO 2 contribution to the total binging energies (Fig. 7) (19) in the presence and absence of SO 2 are reported in Fig. 11. [EtNH 3 ][NO 3 ] (20) IL has been also selected to obtain some insight up to the behaviour of this IL. In the absence of the SO 2 molecule, the main interaction between imidazolim cation and the corresponding anion is carried out by a hydrogen bond between the O atom (anion) and H in position 2 of the imidazolium ring (labelled d 1 , d 8 and d 16 for ILs 14, 17 and 19 respectively). Again, the presence of the SO 2 molecule brings a diminution of the interaction between both ions. As seen in Fig. 7 for IL 17, contribution from anionÁ Á ÁSO 2 interaction to the |BE| is larger than cationÁ Á ÁSO 2 interaction, which agrees with larger r values for d 12 regarding to interaction between cation and SO 2 , i.e., d 13 and d 14 (similar behaviour can be drawn for ILs 14 and IL19). The SO 2 molecule interacts with the anion through an intermolecular bond between the S and one oxygen atom located in the anion.
[EtNH 3 ][NO 3 ] (20) presents the highest charge transfer and |BE| between ions in the absence of SO 2 (see Fig. 6). As seen in Fig. 11, there is a proton transfer between ions. In fact, the distance between [NO 3 ] À and H (d 23 ) is 1.045 Å, while the distance between N and H (d 24 ) is 1.595 Å. ChelpG charges have shown that such O has an atomic charge of À0.58 (larger than the À0.46 e À over the other O), while the positive charge over this H is 0.39 (charge over remaining H linked to N is of around 0.26 e À ).  Table 2 for a more detailed description on intermolecular interactions.
This effect is not observed in the presence of the SO 2 molecule. The adsorption of SO 2 by IL 20 is carried out by a strong interaction between SO 2 and the anion (d 25 ), while there are dual interactions between SO 2 and the cation (d 26 and d 27 , being the latter the weakness). Once more, a larger electronic density for d 35 (respect to d 26 ) agrees with the greater contribution from SO 2 Á Á Áinteraction to |BE 0 |.
ILs based on the [NTf 2 ] À anion (set III) are the largest group, whose K H C 3.4 Â 10 5 Pascal and |BE 0 | C 38.45 kJ mol À1 (despising ILs 25,29,31,33 and 35). For ILs 25, 29, 31, 33 and 35, |BE 0 | is much larger than sum of both ionÁ Á ÁSO 2 contributions. Furthermore, ILs 25, 29, 31, 33 and 35 are the only ones whose interactions between ions are strengthened in the presence of the SO 2 molecule (see Fig. 6). The SO 2 brings a rearrangement between ions which improves their mutual interaction and also their interactions with SO 2 . To obtain information about this fact, we have focused on IL [BMIm][NTf 2 ]. Optimized geometries as well as the main results from intermolecular interaction  (20). Main intermolecular interactions are also displayed. Atom colour code: C (gray), oxygen (red) sulphur (yellow), hydrogen (white), nitrogen (blue)and phosphorous (orange). See Table 3 for a more detailed description on intermolecular interactions.
analysis are collected in Fig. 12 and Table 4.
[BMIm][NTf 2 ] ILs yields five intermolecular interactions (d 1 -d 5 ) between both ions, wherein the one between the N (anion) and the H (cation) is position 2 is the strongest one. Although the same interactions between both ions are found in the presence of the SO 2 molecule, all of them suffer an elongation/decrease on intermolecular distances/electronic density values. SO 2 molecule is able to for two bonds with the anion, i.e., d 6 (SÁ Á ÁO) and d 7 (SÁ Á ÁF), being the latter much weaker than SÁ Á ÁO interaction. Further, two OÁ Á ÁH bonds (d 8 and d 9 ) are noted between SO 2 and cation molecules. Although SO 2 causes a weakening of the interaction between ions (based on electronic density values), it also allows the formation of a cage, with their corresponding cage critical points (CCP). Concretely, two cage critical points (represented as purple points along the yz view) are found, whose electronic density is 0.0027 a.u. and 0.0018 a.u. The presence of both CCP points out to a charge delocalization process between different motifs. Results described for this IL could be extrapolated to ILs 29, 31, 33 and 35, i.e., larger |BE 0 | values and stronger interaction between ions are due to the charge delocalization process. This charge delocalization brings an increase on inter ionic interaction (with respect to isolated IL), and |BE 0 | is higher than the sum of both ionÁ Á ÁSO 2 contributions. Although, CCPs are also found for other ILs, they own much lower electronic density values. ILs based on the triflate anion ([SO 3 CF 3 ] À ) are within set IV (IL [36][37][38][39][40]. Those ones also based on imidazolium cations (36)(37)(38)(39) provide K H C 4.22 Â 10 5 Pascal and |BE 0 | C 60.30 kJ mol À1 , which is due to the sum of both ionÁ Á ÁSO 2 contributions.
[BMPyr][SO 3 CF 3 ] (IL40) yields K H = 3.57 Â 10 5 Pascal and |BE 0 | = 51.97 kJ mol À1 , mainly due to the anionÁ Á ÁSO 2 contribution. Larger anionÁ Á ÁSO 2 contributions (Fig. 7) to the binding energy mimic the previously reported compound for ionÁ Á ÁSO 2 binding energies (Fig. 3). Fig. 13 and Table 5 gather optimized geometries and intermolecular  Table 4 for a more detailed description on intermolecular interactions.  (37). Results obtained for this IL could be extrapolated for the whole set IV. The main interaction between both ions takes places through O corresponding to the anion and H in position 2 located in the cation (d 1 ), whose r and distances are more affected by the SO 2 molecule, which causes its weakening. However, the remaining interactions are slightly affected by the gas molecule. Thus, binding energy for IL 37 is very similar to contribution from inter ionic interaction to the BE estimated for the IL 37Á Á ÁSO 2 system (see Fig. 6).   Table 5 for a more detailed description on intermolecular interactions.  Table 6 for a more detailed description on intermolecular interactions. IL41-SO 2 system (Fig. 7). The SO 2 molecule also interacts (through both hydrogen atoms) with the cation (d 6 Fig. 15, while the main structural parameter of intermolecular interactions along their electronic density values are collected in Table 7. As expected, the main interaction between both ions is a hydrogen bond between the halide and the H atom located in position 2 (d 1 or d 6 for IL 45 or 48/51, respectively), which is weakened in the presence of SO 2 molecule. For ILÁ Á ÁSO 2 systems, SÁ Á ÁX (X = Cl, Br or I) is the main interaction (labelled as d 3 or d 9 for IL 45 or 48/51, respectively), while two OÁ Á ÁH intermolecular bonds are also found between SO 2 and the cation. As seen in Table 6, electronic density for d 6 is much greater than those of cationÁ Á ÁSO 2 interactions in concordance with its larger contribution from [Cl] À Á Á ÁSO 2 interaction. The same behaviour is also noted for ILs 48 and 51.

Conclusions
This contribution reports a density functional theory (DFT) on several ILs, for which high SO 2 solubility is expected. This work  Table 7 for a more detailed description on intermolecular interactions. is divided into three parts: (i) we selected a set of ILs which should provide high efficiency for SO 2 capture. For this, a screening of a large number of ILs via the COSMO-RS method was done; (ii) binding energies between SO 2 and ILs were analyzed intensely through DFT simulations for a set of 55 ILs, which provided high efficiency in SO 2 capture according to the COSMO-RS method; (iii) intermolecular interaction for some representative ILs were deeply studied through the AIM theory aimed at obtaining some information on the SO 2 adsorption mechanism at the molecular level. The results evidenced the ability of the selected cations and anions to interact with the SO 2 molecule, which is stronger for anionÁ Á ÁSO 2 interactions. Thus, anionÁ Á ÁSO 2 interactions are ruled by a strong charge transfer from the anion to SO 2 molecule. For the ILsÁ Á ÁSO 2 system, the total binding energy (BE) has been decomposed in the contributions from the interactions between ions, anionÁ Á ÁSO 2 and cationÁ Á ÁSO 2 . The interaction between both ions always provided the largest contribution to the total binding energy. Then, the binding energy related with SO 2 capture by ILs was also calculated considering the ILs as a whole (BE 0 ). A value of around 36.58 kJ mol À1 (for CO 2 capture by [EMIM][NTf 2 ] IL, which was taken as a pivotal reference for comparison purposes) as a low limit; all ILs yield larger binding energies. Most of them provide values of around 45.0 kJ mol À1 . Therefore, all of them would provide high SO 2 capture efficiency. Through the comparison between ionÁ Á ÁSO 2 contributions and BE 0 , we could obtain some information on what ions mainly govern the SO 2 capture within the ILs. In most cases, SO 2 capture would be mainly ruled out by the anion or by both ions. Even if the SO 2 capture mechanism at the molecule level depends on each ILs, some common features as found for related ions. Even though, a statistical analysis of binding energies of IL-SO 2 systems as a function of ion-SO 2 and cation-anion ones brings to light that SO 2 adsorption by ILs at the molecular level is mainly ruled by anion-SO 2 interaction and cationanion as well. Thus, qualitative trends on SO 2 capture by ILs can be obtained only based on the study of anion-SO 2 and isolated ILs systems. Systematic research on ILs for SO 2 capture allow increase of our knowledge about those factors which could be controlled at the molecular level, allowing an approach up to the rational design of task-specific ILs for future applied studies.