The role of cations in the interactions between anionic N-heterocycles and SO2

Our study shows that cation plays a more important role in the interactions between anionic N-heterocycles and SO2 than in the NHC-CO2 case. The adducts of NHC, SO2 and cation often exhibit multiple stable configurations with close energies rather than the only reported “CO2-sandwiched” planar NHC-CO2-cation structure. The structural diversity makes the models omitting cation inappropriate for predicting the SO2 capture products, which also leads to less clear trends of the cation effects than those observed in the CO2 case. The detailed cation effects are discussed in the text.

. Since the two acid gases, CO 2 and SO 2 , have a number of similarities in structure and property, we naturally wonder whether the interactions between SO 2 and NHC-cation systems simply follow the same story line? Nevertheless, in a recent simulation research, Ai group reported that for alkyl phosphonium tetrazolide-based ([P nnnm ][Tetz]) ILs, compared with the binding between the anion ([Tetz] − ) and SO 2 , the binding strength of the anion-cation pair with SO 2 decreased sharply by about 58 kJ mol −1 and resulted in reduced SO 2 absorption capacity 23 , which was also observed in the studies of Wang group and Wang group using different ILs 8,24 . In their calculations, SO 2 did not insert in between the anion and cation pair like CO 2 did. Actually, SO 2 rarely breaks the ion pair 8,15,[23][24][25][26][27] . Still for simplicity, calculations of SO 2 interacting with ILs were routinely carried out in the absence of cation since the cation effects are assumed to be negligible 5,7,9,10,12,28 . To date, whether cation promotes or restrains the binding between NHC and SO 2 has not yet been clarified. Additionally, there are also evident differences in the geometric and electronic structures between SO 2 and CO 2 , such as bond angle (118.7° for SO 2 vs. 180.0° for CO 2 ) and polarity (dipole 2.03 Debye for SO 2 vs. 0.00 for CO 2 ). How these differences are reflected in the interactions between the two gases (SO 2 and CO 2 ) and NHC-cation complexes calls for a systematic study.
Here, we tried to elucidate the cation effects on the interactions between NHCs and SO 2 by employing the density functional theory (DFT)-based calculations. In order to avoid the interference of complicated steric effects often found in ILs and to focus on the nature of the interactions, our systems were designed to consist of a number of representative conjugated anionic NHCs ( Fig. 1) and simple cations (alkali and alkaline earth metals). We first explored the reaction potential energy surface (PES) of pyrrolide, one of the simplest anionic NHCs, with SO 2 and Li + . From the PES, we identified multiple stable configurations of the pyrrolide-Li + -SO 2 complex with nearly equal energies. After checking other NHC-cation-SO 2 complexes, we found that multiple stable configurations are a common feature but the energy disparity among configurations is highly dependent on both the cation and anionic NHC. Due to the structural diversity of the complexes, we discovered that the lone pair orbital energy of NHCs is no longer a good descriptor to quantify their interactions with cation and SO 2 , unlike in the CO 2 case. Finally, we concluded aspects about the cation effects and their influence on designing NHC-based ILs and porous materials for SO 2 capture.

Results and Discussion
We chose a series of commonly seen conjugated NHC anions (single-ringed structures pyrrolide 1, imidazolide 2, 1,2,3-triazolide 3 and tetrazolide 4 and double-ringed structures indolide 5, benzene imidazolide 6 and benzene 1,2,3-triazolide 7). We studied their interactions with SO 2 and simple monovalent (Li + , Na + , K + , Rb + , Cs + ) and bivalent cations (Be 2+ , Mg 2+ , Ca 2+ , Sr 2+ ). SO 2 absorption and desorption. The reaction was explored by scanning the distance between the N atom (NHC) and the S atom (SO 2 ), which is an efficient and approximate way to explore the reaction energetics and identify key intermediates. The scans were done in two ways. The first started with SO 2 being far away (> 4.5 Å) from the NHC-cation complex and the N-S distance was gradually shortened until 1.5 Å. The second started with a NHC-SO 2 -cation complex analogous to the NHC-CO 2 -cation stable configuration (details see structure e′ in Fig. 2) and the N-S distance was gradually elongated to over 4.5 Å. The scans were supposed to give information about absorption and desorption of SO 2 , respectively.
Li + and pyrrolide 1 were used as the NHC-cation pair to help illustrate the processes (Fig. 2). The two scans of SO 2 resulted into two distinct energy profiles. When SO 2 is far away from 1 and Li + , the NHC and cation form an adduct a (Fig. 2a) featuring a (η 5 -NHC)Li type of binding (the binding energy is −682.2 kJ mol −1 ). The structure clearly differs from the planar complex composed of neutral NHC and Li + reported in our previous work 22 (their interconversions were described in details in ESI Fig. S1).
As SO 2 approaches the complex, it pushes the Li atom over the N atom with one O atom and the Li-N bond is nearly perpendicular to the ring plane (Φ LiNCH = −94.9°, Fig. 2b). Energy of the system keeps dropping until the N-S distance shrinks to 2.82 Å, where a stable structure c (Fig. 2c) is found. In structure c, the Li atom moves towards the ring plane (Φ LiNCH = −40.8°) and the O-Li-N interaction (bond lengths are 1.83 Å and 1.93 Å, respectively) drags SO 2 closer to the ring plane (the shortest S-C distance is 2.37 Å). Through a couple of key intermediates at the N-S distance of around 2.7-2.2 Å (Fig. 2d), SO 2 moves beyond the far end of the N atom in the ring but still stays above the ring plane. Then the S atom only interacts with the N atom rather than with the pyrrole ring as in previous configurations. The Li atom is pushed aside but the O-Li-N interaction remains (bond lengths are 1.83 Å and 1.95 Å, respectively). When the N-S distance is 2.14 Å, intermediate structure d (Fig. 2d) relaxes into a similar but more stable configuration e (Fig. 2e). Further decrease of the N-S distance leads to dramatic energy rise and no more stable configuration appears. Thus the whole absorption scan generates two stable structures (Fig. 2c,e) and does not produce the configuration with SO 2 inserted in between the N(NHC)-Li bond like in the CO 2 case 22 .
Nevertheless, this may be an artifact of constrained optimization (i.e. scans). The expected configuration e′ ( Fig. 2e′) with SO 2 bidentating to the Li + atom through its two O atoms was set as the initial guess structure for the desorption scan. Indeed it is stable at the N-S distance of 1.78 Å. Unlike CO 2 , SO 2 and the pyrrole ring are not coplanar and both the O atoms stick out of the ring plane. Thus, Li at one terminal of the complex is out of the pyrrole ring plane as well. Furthermore, a smaller N-S distance leads to substantial energy rise ( Fig. 2 dotted line). Then, from configuration e′, the desorption scan (elongation of the N-S distance) was carried out. As the N-S distances increases, Li + moves towards N of NHC and SO 2 detaches from the ring. The complex position switching process is best represented by an intermediate structure d′ (Fig. 2d′) which features the ring-leaving SO 2 above the ring-approaching Li atom. These position changes again results into the stable structure c at the N-S distance of 2.82 Å. After that, the desorption and absorption energetics overlap.
From the two scans, three nearly degenerate (ΔE < 2 kJ mol −1 ) stable structures c, e and e′ are identified and all exhibit strong interaction with SO 2 (binding energy of about −140 kJ mol −1 ). The great structural variation in the three configurations reflect complex NHC-cation-SO 2 interactions. Transformations between either two configurations were achieved through the IRC method and are found to require a relatively low barrier (< 40 kJ mol −1 , transition states shown as the top inset in Fig. 2), indicating that the SO 2 absorption product is multimorphic and flexible to interconvert among different configurations. Still, c may be the most populated structure as it is the first stable configuration formed during absorption. This supports the observation that SO 2 does not break the anion-cation pair 8,15,[23][24][25][26][27] . More importantly, it shows that both cation and anion (NHC) interact with SO 2 considerably, as the Li atom is dragged out of the pyrrole plane and the shortest S-C distance is only 2.37 Å.
In comparison, only planar structures with CO 2 sandwiched in the middle of the NHC-cation pair have been reported 22 . After we scanned the reaction between pyrrolide 1 and CO 2 in the presence of Li + , two metastable structures were obtained (ESI Fig. S2), which can be converted into the well-known planar product NHC-CO 2 -Li exothermically by 75.2 kJ mol −1 after overcoming a small (less than 10 kJ mol −1 ) energy barrier. It demonstrates that, compared with SO 2 , the multiple stable configurations of NHC-CO 2 -Li cannot coexist since the in-plane CO 2 -sandwiched configurations are much more stable and other less stable configurations can easily transform into it 22,29 .
Furthermore, NBO and NRT analyses of the pyrrolide-Li + -SO 2 complex were carried out to explore the nature of the interactions. The leading NRT structures are displayed in Fig. 3b and all major Lewis resonance structures and their abundances are shown in Fig. S3 (see ESI). For structure e′, like the interactions between anionic NHCs and CO 2 in the presence of Li +22 , pyrrolide donates its lone pair to SO 2 to form a N-S σ single bond (Fig. 3a). The similar chemical bonding occurs in the case of structure c, whose σ bond is between the C and S atoms, while there is no S-pyrrole covalent bonding in the case of structure e. Thus in e, three electron lone pairs with two on N and one on S constitute the frontier NBO orbitals. Further bond order analyses confirmed that there is just a N/C-S σ single bond (NBO bond orders are 0.86 and 0.32 for e′ and c, respectively), rather than the π bond observed in the CO 2 case 22 .
For multiple-site anions, e.g. 1,2,3-triazolide (3), SO 2 can interact with two unequal N sites (labelled as 1 and 2 in Fig. 1) to produce two stable structures in the presence of Li + (ESI Fig. S4b). Interestingly, these two absorption products can also interconvert to each other through a moderate barrier (about 50 kJ mol −1 ) via two pathways, whose differences only lie in the way of SO 2 's movement, while Li always bidentately binds to two N atoms (Fig. 4). Route 1 is called migration, as the Li atom in 3′ moves from N1 to N2 while SO 2 is gradually pushed from N2 to N3. Route 2 is called swapping, as Li and SO 2 switch their positions. During the transition, the Li atom stays in the NHC plane (Φ LiNNN = 175.2°), while SO 2 moves from N2 to N1 by going over one side of the NHC plane. It is noteworthy that although the same structure 3 is produced by these two different pathways, SO 2 actually interacts with different N atoms (N3 in route 1 and N1 in route 2). Different substitution groups on the two carbon atoms should be able to make the pathways more distinct. From the scan calculations of other NHC-Li + -SO 2 systems, it can be clearly seen that multiple stable configurations are a common feature (ESI Fig. S4). Yet the energy disparity among the configurations may vary substantially. To get a more complete picture of the relative stability of the configurations, other variables such as the cation species including its charge need to be considered. Moreover, to make sure there was no significant stable structures omitted by the constrained scan calculations, we performed configuration search utilizing a Monte-Carlo method implemented in the Molclus program 30 .
Stable configurations. Again, pyrrolide 1 was taken as an example to illustrate the factors influencing the relative stability of multiple stable configurations. The three leading stable configurations of the 1-Li + -SO 2 system are relabelled as 1S-Li-1 (e), 1S-Li-2 (e′) and 1S-Li-3 (c) in the top panel of Fig. 5, which have all been obtained by the scans. In contrast, for the 1-cation-CO 2 systems (ESI Fig. S5a), the classical CO 2 -sandwiched in-plane  structure is always the most stable configuration and the disparity in energy among configurations are much bigger than that in the 1-cation-SO 2 systems.
For the 1-Na + -SO 2 system, four states with close energies and substantial structural variations have been identified. The first configuration (1S-Na-1) is the most stable one and is similar to 1S-Li-3, featuring the "expected" SO 2 -sandwiched structure. Only the second structure (1S-Na-2) has no close resemblance in the 1-Li + -SO 2 system and it differs from the first one by bending the Na end over SO 2 , approaching the pyrrole ring. However, for bigger alkali metals like K + and Rb + , the energy disparity among configurations rises (over 25 kJ mol −1 ) quickly. The most stable configurations both mimic 1S-Na-2 but with the cation even closer to the ring, which reflects the increasing importance of the cation-π stabilization as a function of the rising cation size. Alkaline earth metals like Mg 2+ and Ca 2+ help produce more stable configurations, as the cations also favor the position over the pyrrole ring (e.g. 1S-Mg-2 and 1S-Ca-2). Nevertheless, the most stable ones (e.g. 1S-Mg-1 and 1S-Ca-1), analogue to 1S-Li-2, feature the SO 2 -π interaction rather than the cation-π interaction.
For multiple-site NHCs (e.g. 3, ESI Fig. S5b) more stable configurations with close energies appear. This is natural because the cation and SO 2 can both interact strongly with different N atoms. For NHCs with fused rings (e.g. 6, ESI Fig. S5c), as the second ring also can stabilize the cation or SO 2 , more stable structures also tend to form. In general, SO 2 does not succeed in breaking the N-Li bond, which is consistent with the previous observations 8,15,[23][24][25][26][27] .
Multiple-configuration mixture instead of the only SO 2 -sandwiched structure may be the true products. This may help us understand the measured spectra better. Benzene imidazolide, a well-studied anionic NHC 7 , serves as a good example. Five stable configurations were predicted when it interacts with SO 2 and Li + (ESI Figs S4e and S5c). Their diverse S-O bond vibration frequencies are listed in Table 1  When using NHC-functionalized ionic liquids to capture SO 2 , the presence of a new IR band right below 1000 cm −1 (948 cm −1 in most reports) is an evidence that SO 2 is absorbed through chemical interaction, while the presence of other two new bands at about 1324 cm −1 and 1143 cm −1 implies physical interaction 6,7,10,14,28,31,32 , which is in good agreement with our findings. Therefore, new IR bands near 1000-1300 cm −1 after the reaction can indicate whether the SO 2 absorption product is a mixture of multiple configurations or just the previously focused "sandwiched" structure.
Li + -assisted NHC-SO 2 interaction. In Fig. 6, we present the SO 2 binding energy change between the [NHC-Li + ] complexes and the NHCs. Overall, the introduction of Li + cation does not exhibit obvious influences (usually |ΔBE| < 20 kJ mol −1 ). Notably, for single-ringed 1-3 and double-ringed 5, the presence of Li + even has a slight to moderate suppressing effect, agreeing with the previous reports 8, 23,24 . It is also crucial to highlight that   with the increasing number of nitrogen atoms in both single-ringed and double-ringed structure, the difference in NHC-SO 2 binding energy with or without Li + decreases gradually. Although cation affects the structural properties of the NHC-SO 2 adducts substantially, it only has a slight influence on the binding energies.
Other metal cation-assisted NHC-SO 2 interactions. NHC-SO 2 interactions with other alkali and alkaline earth metals were also investigated. Most monovalent cations, i.e., alkali metal ions have very limited (weakening) effects on the interaction of NHC-SO 2 complex, while all the bindings are enhanced by divalent cations, especially by the small ones like Be 2+ and Mg 2+ (|BE| > 100 kJ mol −1 , Fig. 7 and ESI Fig. S6), whose smaller size and higher charge are critical.
Correlation between structure and binding energy. From the above analysis we know there is a big variation in the most stable configurations of NHC-cation-SO 2 ( Fig. 5 and ESI Figs S4-5). Particularly, among some of the most stable configurations, the N atoms are not necessarily the only interacting site and the NHC ring sometimes interact with the cation and SO 2 as a whole. Thus, a simple descriptor such as NBO nitrogen lone pair orbital energy, used in the case of CO 2 22 , fails to correctly describe the binding energy, and so does the NBO charge unsurprisingly (ESI Fig. S7). In other words, there still lacks a simple and accurate descriptor to link the reactivity of NHC-cation and SO 2 .
Comparison between cation-assisted NHC-SO 2 and NHC-CO 2 interactions. In the previously studied NHC-cation-CO 2 system 22 , only the planar NHC-cation was identified as the most stable configuration (e.g. ESI, Fig. S1a, pyrrolide-Li + (1 + Li), Φ LiNCH = 1.0°). However, this simple and uniform picture is now found to be incomplete: the most stable configuration of the NHC-cation pair is NHC-dependent. For example, for pyrrolide and 1,2,3-triazolide, their most stable complexes with Li + assume very different geometries (ESI Fig. S1). The planar 1 + Li is only meta-stable and the (η 5 -NHC)Li configuration is more stable by 45 kJ mol −1 , while for 3(1,2,3-triazolide) + Li, the order of configuration stability is reversed (ESI Fig. S1 and the accompanying text). Yet the most stable configuration of the final NHC-cation-CO 2 product remains planar (ESI Fig. S5a). Thus, the cation effect should also be NHC-dependent. Moreover, although the whole observation applies to Be 2+ , more study is definitely needed to map out the detailed relationship between other cations and NHCs.
When the cation effects in both anion-CO 2 and anion-SO 2 systems are re-evaluated (ESI Fig. S8) using the newly-identified most stable NHC-cation configurations, different results are obtained. Unlike the previous study 22 , the introduction of Li + cation does not strengthen the binding between CO 2 and pyrrolide but causes a weak inhibiting effect (0 < ΔBE < 25 kJ mol −1 , the weakening effect is weaker than in the SO 2 case). The further study of the interactions between pyrrolide-CO 2 and other alkali and alkaline earth metals reveals that monovalent cations and even divalent cations also have limited weakening effects on the interactions (ESI Fig. S9). This is because the most stable pyrrolide-cation pair configuration has the cation hoving over the NHC ring while the most stable configuration of the final pyrrolide/imidazolide-cation-CO 2 complexes assume planar structure (ESI Fig. S5a vs. Fig. S1). The shift of the cation's position costs about more than 50 kJ mol −1 , rendering the cation a weakening rather than an enhancing role. For other NHCs like imidazolide, the cation effect is more complex and is cation dependent (ESI Fig. S9), which is also a result of the energy difference between the configurations the NHC-cation pair assumes before and after interacting with CO 2 .
Similarly, for NHC-SO 2 systems, the cation effects are also cation dependent. Monovalent cations usually have small weakening effect and divalent cations mostly show enhancing effect. In contrast to the CO 2 case, the NHC-cation-SO 2 complex can assume multiple non-planar forms (particularly for divalent cations, as they prefer to bind to multiple sites in the ring) and the cation's position over the ring can be more or less kept (Fig. S5b) after the SO 2 attachment, which reduces the weakening effect of cation substantially. As a result, all bindings of the NHC-SO 2 complexes are enhanced by divalent cations.

Conclusions
The cation effects on the interactions between anionic N-containing heterocycles (NHCs) and SO 2 have been carefully examined using DFT calculations. Cation, along with NHC, makes SO 2 binding much more complex than its CO 2 counterpart. Particularly, multiple stable configurations with close energies may coexist and their interconversion are possible at ambient conditions, which is crucial to properly understand the SO 2 capture products. This structural diversity makes the relationship between the structures of NHCs and their reactivity with SO 2 much less clear than those observed in the CO 2 case.
However, monovalent cations (Li + , Na + , K + , Rb + , Cs + ) and big divalent cations (Ca 2+ and Sr 2+ ) usually show very limited influences on the binding energy between SO 2 and NHC, either weakening or strengthening the binding by less than 20 kJ mol −1 . Only for pyrrolide and imidazolide, their bindings with SO 2 are weakened by Li + by over 25 kJ mol −1 . Small bivalent cations like Be 2+ and Mg 2+ promote the binding by over 100 kJ mol −1 , which indicates the electrostatic nature in NHC-M 2+ -SO 2 interaction.
In summary, the products of SO 2 capture using materials consisting of cation-anion pairs are possibly mixture of multiple stable structural isomers, which should be considered when designing new SO 2 capture materials.

Computational Methods
The Gaussian 09 package 33 was chosen to conduct all the calculations. Geometry optimizations were carried out unrestrained at the model chemistry of B3LYP 34 /6-311 ++ G(d, p) 35 (SDD 36 for the third to fifth period elements), which has shown appreciable performance over a wide range of NHCs 5,7,8,10,12,24,28 . Frequency analyses with the same model chemistry followed the structure optimization to identify energy minimum.
The binding energy between SO 2 and NHCs is defined in the following equation: where -E sorbent SO 2 , E sorbent and E SO 2 stand for the electronic energies of the complex, the pure sorbent, and SO 2 , respectively. To help understand the NHC-cation-SO 2 interactions, constrained optimizations were performed by scanning the N-S distance (d N-S ) at 0.05 Å intervals and all the transformations between two stable configurations were achieved using the Intrinsic Reaction Coordinate (IRC) method. The same methods were used for natural resonance theory (NRT) [37][38][39] , natural bond orbital (NBO) and NBO charge calculations, all in the NBO 6 program 40,41 . In addition, the Molclus program was utilized to search for the multifarious stable configurations of the NHC-cation-SO 2 complexes 30 .