Computational study of halogen-halogen interactions in polyhalide ionic liquids

Recent years have seen many specific applications of polyhalide ionic liquids (ILs) such as oxidizing solvents for metals and alloys, immersion fluids for optical mineralogy, and electrolyte components for dye-sensitized solar cells. In this work, interhalogen interactions in a set of polyhalide ILs composed of polyhalide anions, [X3]−, [X5]−, and [X7]− (X = I or Br), with two typical cations, tetramethylammonium [NMe4]+ and 1,3-dimethylimidazolium [DMIM]+, were thoroughly studied from a computational point of view. In addition, a halogen-bonded supramolecular anion, [C6F13-I∙∙∙I∙∙∙I-C6F13]−, was also taken into account for comparison. Unlike those in bare polyhalide ions, halogen-halogen interactions in ionic pairs for the investigated ILs are somewhat asymmetric caused by the interactions between the cations and the anions. In general, there are two classes of interhalogen bonds in ionic pairs: one class with longer X∙∙∙X distances and smaller bond energies can be recognized as strong halogen bonds, while the other with shorter distances and much larger bond energies exhibits a significantly enhanced strength.


Introduction
Room temperature ionic liquids (ILs) are completely composed of ions with melting points below 100 °C [1][2][3]. These non-volatile liquids have several unique properties, such as excellent thermal stability, high ionic conductivity, and low combustibility, which are being explored as environmentally benign solvents [4][5][6][7]. In addition, ILs have also been described as "designer solvents" with characteristics that can be tuned to meet specific requirements for a particular application [8,9].
ILs can be roughly divided into three categories: (i) aprotic ILs, the most frequently used ILs so far; (ii) protic ILs that are formed by the simple proton transfer from a Brønsted acid to a Brønsted base [10][11][12]; and (iii) solvate ILs, the equimolar mixtures of alkali metal salts and oligoethers [13]. Over the past few years, polyhalide ILs consisting of polyhalide anions in their structure have attracted increasing research interest and can be recognized as an important subclass of ILs [14,15]. A common synthesis route of these ILs is the addition of elemental chlorine, bromine, or iodine to halide IL precursors.
Polyhalide ILs have been used as selective halogenation reagents in organic synthesis for a long time. Bortolini et al. previously studied several trihalide ILs composed of trihalide anions ([I 3 ] − , [IBr 2 ] − , [ICl 2 ] − ) and imidazolium cations with different alkyl chain lengths as reagent-solvents for stereoselective iodination of alkenes and alkynes. High yields and steroselectivities of the reactions were observed when using these "green" alternative media [16]. Of particular attention is that many other specific applications of such ILs were also reported in recent years. For example, a series of polyhalide ILs, which are comprised of trihalides (like  [17]. These environmentally benign fluids not only have high refractive indices but also reduce health risk. Subsequently, the group of Kloo prepared some trihalide ILs containing trihalide ions ([Br 3 ] − , [IBr 2 ] − , [I 2 Br] − ) and imidazolium cations with different lengths of alkyl chains, which were used as electrolyte components for dye-sensitized solar cells [18]. They found high efficiency and long-term stability achieved by these ILs-based electrolytes. More recently, a number of trihalide ILs consisting of trihalides (like [I 3 ] − , [Br 3 ] − , [IBr 2 ] − , [I 2 Br] − ) and a variety of cations, e.g., imidazolium, ammonium, phosphonium, and pyridinium, were synthesized and applied as oxidizing agents for dissolving various metals and alloys under mild conditions [19,20]. These trihalide ILs provided a safe dissolution method for metals and alloys, because the whole dissolution process can proceed without the production of any gases.
Polyhalide ions have been extensively investigated during the last decades due to their interesting structures and vast applications. The most well-studied polyhalides are the simplest trihalide anions ([X 3 ] − , X = Cl, Br, I), in which the bonding was characterized as a three-center, four-electron (3c-4e) σ bond through topological analysis of either experimental or theoretical electron density [21]. Furthermore, recent X-ray adsorption spectroscopy experiments have unraveled that the degree of charge transfer in solid-state I 2 Cl − and I 2 Br − materials is comparable to that detected in coordination complexes, and X•••X contacts in these systems thus should have substantial covalent contributions [22]. However, halogen-halogen interactions in polyhalide ILs, especially those in higher polyhalide ILs, have received far less attention to date. Giver that polyhalide ILs have shown great potential in diverse fields of chemistry, it is certainly necessary to study the properties of interhalogen interactions in these ILs from a computational viewpoint.
In this work, a series of polyhalide ILs composed of trihalide ([I 3 [23]. For the first time, the features of interhalogen interactions in polyhalide ILs and their discrepancies versus classical halogen bonds were examined.

Computational methods
All the geometries of isolated ions and ionic pairs for the investigated ILs were fully optimized without any symmetry constraints via the hybrid functional B3LYP including empirical dispersion correction term (DFT-D3) [24][25][26], which has been widely used for studying Scheme 1 Chemical structures of polyhalide anions under study (X = I or Br) molecular interactions in a large number of ILs [27,28]. The aug-cc-pvdz-PP basis set [29], which uses pseudopotentials to describe the core electrons, was employed for the heaviest I atom (28 core electrons), while for the remaining atoms Dunning's correlation-consistent basis set, aug-cc-pvdz [30], was applied. Frequency calculations were carried out at the same level of theory for all the optimized geometries to affirm that they are real minima on the potential energy surface. All of these calculations were performed by means of the Gaussian 09/16 suite of programs [31,32].
Many possible binding sites for polyhalide anions around the cations were initially taken into consideration, and the most stable configurations of ionic pairs were then employed for analyses. The interaction energy of ionic pairs was computed via the following equation: where E (ionic pair) is the electronic energy of the ionic pair, and E (cation) and E (anion) are the energies of the optimized cation and anion, respectively. All the interaction energies were corrected by the basis set superposition error (BSSE) using the counterpoise method of Boys and Bernardi [33].

Geometrical properties of polyhalide ions in ionic pairs for the investigated ILs
The optimized structures of ionic pairs containing polyiodide anions ([I 3  with the difference between the two I•••I distances being of about 0.04 Å. Furthermore, this anion tends to bent in ionic pairs (θ ≈ 169°), which can be ascribed to the interactions between this anion and the cations. Notably, upon the formation of ionic pair complexes, one I•••I distance elongates and simultaneously the other shortens, leading to a comparable Bare pentaiodide ion can be considered as the adduct of two Lewis acidic I 2 molecules with a Lewis basic iodide anion. As a matter of fact, the two interacting I•••I distances (r 1 and r 2 ) are computed much longer than other two distances (r 3 and r 4 ) in this anion that has a V-shaped structure. Similarly, when complexed with the cations, the pentaiodide anion becomes asymmetric, in view of the two I 3 units exhibiting different I•••I distances and interaction angles. Furthermore, owing to the I atoms in I 5 − involved into HB interactions with the cations, this anion undergoes an obvious bent, producing two almost perpendicular I 3 units (θ 3 ≈ 90° . In P configuration of bare heptaiodine ion, r 1 , r 2 , and r 3 are identical (about 3.21 Å) accompanied by equivalent r 4 , r 5 , and r 6 (ca. 2.86 Å), and θ 1 , θ 2 , and θ 3 are close to 180° while θ 4 , θ 5 , and θ 6 amount to 101.8°. Evidently, this configuration can be seen as the adduct of three I 2 molecules with a single iodide anion. As a result of three I 2 molecules establishing iodine-iodine contacts with I − , the interacting I•••I distances in I 7 − (r 1 , r 2 , r 3 ) appear to be approximately 0.03 Å longer than those in I 5 − (r 1 and r 2 ). In contrast, in the L configuration, three kinds of interatomic distances (r 1 /r 2 , r 3 /r 4 , r 5 /r 6 ) and two different triiodide angles (θ 1 /θ 3 /θ 5 , θ 2 /θ 4 ) were detected, which can be viewed as the I 2  can be classified into two groups: the shorter ones with the interatomic distances less than 3.0 Å and the longer ones having the distances within the 3.160-3.238 Å range.
As can be deduced from Table 2, polybromide ions and mixed ones exhibit similar geometric properties as Here, it is worth mentioning that different polyhalide anions affect the interaction energies of ionic pair complexes to a less degree with the largest gap amounting to only about 4 kcal/mol. Although higher polyhalides have a more diffuse charge, more HB interactions can be formed between these larger anions and the cations.

Bond energies for interhalogen bonds in ionic pairs under investigation
To measure the strength of interhalogen bonds in the studied complexes, the bond energies were computed herein. As mentioned above, there are two types of I•••I bonds in polyiodide ionic pairs: (i) the interacting ones including r 1 /r 2 in I 3 − and I 5 − , r 1 /r 2 /r 3 in I 7 − -P, and r 1 /r 2 /r 3 /r 4 in I 7 − -L and (ii) the terminal ones like r 3 /r 4 in I 5 − , r 4 /r 5 /r 6 in I 7 − -P, and r 5 /r 6 in I 7 − -L. Therefore, two sets of bond energies (BE 1 and BE 2 ) were determined as follows, taking I 5 − as an example: (2) The calculated bond energies for interhalogen contacts in the investigated complexes are summarized in Tables 3  and 4. As can be seen, in the complexes of I 5 − , the bond energies for the terminal iodine-iodine bonds (r 3 and r 4 ) are estimated almost two times of those for the interacting ones (r 1 and r 2 ), which indicates that the former bonds are much stronger than the latter ones. Similarly, considerably larger bond energies are predicted for the terminal I•••I contacts (r 1 , r 2 , r 3 ) with respect to the interacting ones (r 4 , r 5 , r 6 ) in the systems involving I 7 − -P. However, compared with those in complexes of I 5 − , the bond energies for the interacting contacts in these systems appear to be somewhat smaller. As far as the complexes of I 7 − -L are concerned, the bond energies for I•••I bonds increase in the order r 1 /r 2 < r 3 /r 4 < r 5 /r 6 . These energetic results are in good agreement with the trends observed in the I•••I distances.
In general, iodine-iodine interactions in polyiodide ionic pairs can be categorized into two groups: one group, which possesses longer interatomic distances and thus smaller bond energies (from 12.81 kcal/mol to 21.07 kcal/ mol), can be considered as strong halogen bonds, while the other exhibits a markedly increased strength due to shorter distances and much larger bond energies (34.47 kcal/mol ~ 41.67 kcal/mol). Similarly, two classes of interhalogen interactions were also detected in the complexes of polybromide anions and mixed ones based on the distances and bond energies.

Implications for the application of polyhalide ILs
As stated above, polyhalide ions have been the target of a number of research works. The most well-studied polyhalides are the simplest trihalide anions, and the bonding in these anions can be described as a delocalized 3c-4e bond [34,35]. Particularly, as revealed by previous K-edge X-ray adsorption spectroscopy experiments, charge transfer is extremely large in some trihalide systems, comparable to that observed in coordination complexes. Consequently, X•••X bonds in these systems should be partially covalent, analogous to coordination bonds [22]. However, interhalogen interactions in polyhalide ILs remain largely unexploited, although these ILs have shown potential applications in many scientific fields. Incorporating polyhalide ions into the IL structure could combine the properties of these ions (such as strong oxidizing power and high reactivity) and the advantages of ILs (like negligible vapor pressure and highly tunable character). Cation-anion interactions and intermolecular forces in ILs were intensively studied from both theoretical and experimental viewpoints, since these intrinsic interactions are directly related to the physicochemical properties of ILs. However, the interactions within anions or cations of ILs have drawn much less attention to date, possibly due to their absence in most cases. As a matter of fact, such intramolecular interactions play a fundamental role in certain specific characteristics of ILs. Wang et al. previously reported an interesting method for decreasing the viscosity variation in CO 2 capture process by amino-functionalized ILs through the formation of intramolecular HBs [36]. When it comes to polyhalide ILs, many of their applications are indeed based on the properties of polyhalide anions in which multiple halogen-halogen interactions are presented. For instance, trihalide ILs can be used as Table 2 Geometric data for bare polybromide ions and mixed ones and ionic pairs containing these anions a a Distances in angstroms, and angles in degrees. The structures of ionic pairs of mixed polyhalide anions with [NMe 4 ] + are given in Fig. S1. The definitions of r and θ are shown in Scheme 1 oxidizing solvents for metals and alloys, mainly arising from the strong oxidizing character of trihalides [19,20,37]. Therefore, a detailed understanding of interhalogen bonds in polyhalide ILs should be of particular importance for realizing the potential of these ILs. According to our calculations on ionic pair complexes for a series of polyhalide ILs, all the defined angles become smaller in ionic pairs compared with those in isolated ions. Namely, the geometry of polyhalide anions tends to bent when complexed with the cations, on account of the formation of HBs between these anions and the cations. Notably, in higher polyhalide systems, halogenhalogen bonds can be divided into two catalogues according to interatomic distances: the longer ones belonging to strong halogen bonds and the shorter ones showing a significantly amplified strength.
Owing to the delocalized bonding in polyhalides, polyhalide ILs possess much lower viscosity with respect to traditional halide ILs, attractive as solvents or components of electrolytes. Furthermore, higher halogen concentrations in these ILs may also be beneficial for dyesensitized solar cells, in which the iodide/triiodide redox couple was generally used [38]. All in all, polyhalide ILs not only show the properties of polyhalides but also have the favorable characteristics of ILs, and two different types of halogen-halogen interactions were characterized in higher polyhalide ILs, which will inspire the applications of these ILs in a wider chemical community.

Conclusions
In the present work, interhalogen bonds in a series of polyhalide ILs, which are comprised of trihalides ([I 3    Compared with those in bare polyhalide ions, halogenhalogen interactions in ionic pairs for the ILs under study become somewhat asymmetric induced by the cation-anion interactions. The interaction energies for the complexes under study remain somewhat unchanged, because higher polyhalides not only have a more diffuse charge but also can form more HB interactions with the cations. Notably, the shorter X•••X bonds always possess much larger values of bond energies, approaching covalent bonds, while smaller values are estimated for the longer ones, close to those of the complexes of SI 3 − . Therefore, interhalogen interactions in ionic pairs can be divided into two groups: one group with longer interatomic distances can be recognized as strong halogen bonds, while the other with shorter distances has a considerably enhanced strength.
The results and conclusions reported in this work can provide helpful guidance for applying polyhalide ILs in diverse scientific fields.

Supplementary information
The online version contains supplementary material available at https:// doi. org/ 10. 1007/ s11224-021-01838-3. Data availability Data can be obtained from the corresponding authors through email.