3.1 Geometric Analysis
3.1.1 Structures of Isolated Cation and Anion
One of the distinctive features of ionic liquids containing the imidazolium [EMI]+ cation, bis(trifluorosulfonyl) imide [TFSI]− and bis(fluorosulfonyl) imide [FSI]− anions is the fact that the charge delocalization and/or the asymmetry of these ions generally determines the unusual properties these ionic liquids. The fact that those large ions are non-rigid which can adopt different conformations is another key feature of these ionic liquids. It is, therefore, worth analysing and revising the conformational behaviour of such constituent ions corresponding to those ionic liquids. To better understand the interaction between [EMI]+ cation and [FSI]− anion, the structures of the most stable geometry of the isolated [FSI]− anion was analysed and revised first. The structures of the fully optimized [EMI]+ cation has already been discussed in our previous reports [32]. Vibrational frequencies of all the optimized structures have also been calculated to ensure that the optimized structure represents the true minimum. The absence of imaginary vibrational frequency confirms that the optimized geometry represents the stable structure. The atomic numbering scheme employed in the present work is shown in Fig. 2. The structures of the fully optimized [FSI]− anion and [EMI]+ cation are shown in Fig. 3. Selected structural parameters for [FSI]− anion are compiled in Tables 1.
The [FSI]− anion gives two minimum energy structures: one with trans-symmetry where the F-atoms are on opposite sides of the O-S-N-S dihedral angle, and another one with cis-symmetry where the F-atoms are on the same side of the O-S-N-S dihedral (see Fig. 3). On the basis of ω97X-D functional and in the presence polarizable dielectric continuum medium, we found that the conformers with the O-S-N-S dihedral angles − 35.58° (trans-[FSI]−) and − 45.90° (cis-[FSI]−) give the global and local minima, respectively, with the SCF energy difference of 4.3 kJ mol− 1. Similarly, previous studies conducted on the same [FSI]− anion showed that the [FSI]− anion could exist as the cis-[FSI]− or trans-[FSI]− conformers which are located either at the cis or trans position with respect to the F-S-N-S-F skeleton [33]. Experimentally, the cis-[FSI]− anion conformer was observed in crystals of [M]+[FSI]− (M+ = Li+, K+, C6H6‚ Ag+) [34]. The trans-[FSI]− anion conformer was observed in crystals of [M]+[FSI]− (M+ = Cs+, CHCl3‚ Ph3C+, Ph3PH+, and (CH3)3Pb+) [35, 36]. Two stable conformers of anti-[FSI]− and cis-[FSI]- have also been identified by Hartree-Fock (HF) calculations [37], MP2- level calculations [38], MD simulation [39], DFT calculations and Raman spectroscopy [40]. Our calculated results for the S-N-S-F dihedral angles are 66.3˚ for the cis conformer and 76.5˚ for the trans conformer. The ωB97X-D functional approach which includes dispersion interactions is generally regarded as the most excellent alternative to deal with ionic liquids containing imidazolium based systems where the effect of dispersion interactions leads to ring stacking interactions and delicate intermolecular interactions like H-bonding [41].
Table 1
Structural parameters of the cis-[FSI]− and trans-[FSI]− conformers in the gas and in dielectric continuum using ωb97xd functional.
|
Trans-[FSI]
|
|
Cis-[FSI]
|
|
|
ωB97X-D/DGDZVP
|
ωB97X-D/DGDZVP
|
ωB97X-D/DGDZVP
|
ωB97X-D/DGDZVP
|
Bond
length (A)
|
gas
|
Solvent
|
Gas
|
solvent
|
S-N
|
1.59407
|
1.59436
|
1.59280
|
1.59278
|
S-O
|
1.44275
|
1.44582
|
1.44402
|
1.44407
|
S-F
|
1.64143
|
1.63431
|
1.64456
|
1.63736
|
Bond angle(deg)
|
|
|
|
|
F-S-O
|
103.49000
|
103.85342
|
103.54547
|
104.36272
|
F-S-N
|
102.61468
|
102.57116
|
102.85583
|
102.64415
|
O-S-N
|
116.18928
|
115.79915
|
116.44396
|
116.51174
|
Dihedral angle(deg)
|
|
|
|
|
F-S-N-S
|
76.11848
|
76.45744
|
63.96540
|
66.36446
|
O-S-N-S
|
-36.19447
|
-35.58000
|
-48.48105
|
-45.89868
|
E(Hartree)
|
-1351.52037376
|
-1351.59497617
|
-1351.51865795
|
-1351.59333838
|
3.1.2 Structures of Isolated Ion pair Conformers
The transport properties of ionic liquids such as viscosity and diffusion coefficients are controlled by the intermolecular interaction among the ions, and the nature of this intermolecular interaction, in turn, is governed by the type of the specific molecular conformation adopted by each ion. Both experimental and theoretical studies have shown that the anions and cations that constitute ionic liquids could exhibit the same conformational landscape in the liquid phase as the ones calculated by making use of ab initio (DFT) methods for the isolated ions [42]. In the liquid state, the ions do have enough freedom to adopt the conformations dictated by their internal structure and may also have enough freedom to interconvert among different conformations. The close inspection of the [FSI]− anion and [EMI]+ cation which can adopt different conformational states could shed some light into a better understanding of the nature of intermolecular interactions in 1-ethyl-3-methylimidazolium bis(fluoromethylsulfonyl)imide ([EMI][FSI]) ionic liquid. To find the most stable geometry and the molecular interactions of [EMI][FSI] ion pairs, geometry optimization of each ion pair conformer was done on isolated ion pair with ωB97X-D/DGDZVP level of theory and basis set. Electrostatic interactions of the ion pair with surrounding ions were effectively accounted for by introducing apparent dielectric constant (acetonitrile) for the ionic liquid environment. The results of selected parameters for interionic bond lengths, angles, dihedral angle in different ion pair conformations are compiled in Table 2. For convenience, the atomic numbering scheme employed in the present work is displayed in Fig. 1. A total of six optimized different minimum energy were obtained for [EMI][FSI] ion pair that could be connected via the most acidic proton (H1) of the cation or via the other protons of the methyl and ethyl group hydrogen’s of the cation (see Fig. 4). Vibrational frequencies of all the optimized structures have also been calculated to ensure that the optimized structure represents the true minimum.
Table 2
Bond distance, bond angle and dihedral angles of between [EMI]+ cation and [FSI]− anion in dielectric continuum using ωB97x-D/ DGDZVP level of theory and basis set.
Acceptor – Donor
|
C1
|
C2
|
C3
|
C4
|
C5
|
C6
|
Bond length
(Å)
|
|
|
|
|
|
C1-H1
|
1.07725
|
1.0780400
|
1.0785800
|
1.0772200
|
1.0802500
|
1.0780100
|
C1-H1--O1
|
2.73614
|
2.9015400
|
2.8343600
|
2.7770500
|
2.2554100
|
2.9170200
|
C5-H8--O1
|
2.85678
|
2.8318300
|
2.9662200
|
2.8709300
|
2.4190900
|
2.8173500
|
C5-H8—O2
|
-
|
-
|
-
|
-
|
2.6102100
|
-
|
C2-H2—O2
|
2.50633
|
2.5108300
|
2.5110800
|
2.4960500
|
2.7637600
|
2.5633700
|
C6-H9—O2
|
-
|
-
|
-
|
-
|
2.6155300
|
-
|
C5-H8--F1
|
-
|
-
|
2.8868200
|
-
|
-
|
-
|
C5-H8--F3
|
-
|
-
|
2.7379200
|
-
|
-
|
-
|
C1-H1--N1
|
3.31033
|
3.4415100
|
2.4694700
|
3.2980500
|
3.8058200
|
3.3626100
|
C6-H9--N1
|
2.77450
|
-
|
2.7365900
|
2.8163600
|
-
|
-
|
Bond angle
(Deg)
|
|
|
|
|
|
<C1-H1---O1
|
98.84145
|
92.5937500
|
92.5632200
|
98.7495700
|
142.3496600
|
94.3120200
|
<C5-H8---O1
|
104.15898
|
102.3672500
|
94.0405800
|
105.7652600
|
149.4774300
|
105.0089700
|
< C5-H8—O2
|
|
|
|
149.4774300
|
-
|
<C2-H2---O2
|
135.28604
|
138.0078600
|
143.4563400
|
137.3390900
|
-
|
134.6842400
|
< C6-H9—O2
|
|
|
|
124.2583500
|
-
|
<C1-H1---N1
|
65.89927
|
62.8324100
|
115.3648900
|
65.0406000
|
124.9747300
|
63.1374400
|
<C6-H9----N1
|
130.15767
|
-
|
124.4734100
|
128.3002500
|
|
-
|
Dihedral angle
(Deg)
|
|
|
|
|
|
<N2–C1–H1–O1
|
-64.51571
|
-63.4812800
|
65.0589200
|
-65.0274300
|
21.5993700
|
-63.1281600
|
<N1–C1–H1–O1
|
113.48378
|
115.1537600
|
-113.2586000
|
112.8972700
|
-157.2667900
|
115.4729400
|
Dipolment (µ)
|
16.0866000
|
16.4032000
|
19.3222000
|
16.6407000
|
19.2968000
|
17.1168000
|
E (Hartree)
|
-1696.141775
|
-1696.1418525
|
-1696.1417945
|
-1696.1434792
|
-1696.1413133
|
-1696.1435412
|
There has been prior reported studies about the geometries of the [EMI][FSI] complex at the MP2/cc-pVTZ//MP2/6-311G** level calculations by Tsuzuki et al. [43] and co-workers. In those studies, the nonplanar staggered [EMI] + cation, in combination with the trans and/or cis forms of [FSI]− anion were used for the geometry optimizations of the [EMI][FSI] complex. However, no indications were made on the conformational preference of the [EMI]+ cation (as either non-planar staggered [EMI]+ and/or planar cis-[EMI]+ cation), and thus there were missing details on the optimized geometry of minimum energy structures [23]. In our study, all possible combinations of planar cis-[EMI]+ -- cis-[FSI]−, planar cis-[EMI]+ -- trans-[FSI]−, non-planar staggered-[EMI]+ -- cis-[FSI]− and non-planar staggered-[EMI]+ -- trans-[FSI]− interactions were analysed. As presented in Fig. 4, a total of six minimum energy different stable ion pair conformers (C1 − C6) were obtained. The energetic difference relative to the lowest energy ion pair conformer ranges from 0.163 to 4.64 kJ/mol (Table 2). According to our results, the C6 (Fig. 4) ion pair conformer was found to be the lowest energy conformer. From our closer inspection of the C6 ion pair conformer, we found that the C6 ion pair conformer constitutes the nonplanar staggered [EMI]+ - cis [FSI]− ion pair configuration with the [FSI]− anion on top position. The second, third, fourth, fifth and sixth lowest energy conformations predicted were respectively, nonplanar staggered-[EMI]+ (anti) – cis-[FSI]− (C2), nonplanar staggered-[EMI]+ (syn) – cis-[FSI]− (C3), planar cis-[EMI]+ -- cis-[FSI]− (C1), nonplanar staggered-[EMI]+ (syn) – trans-[FSI]− (C5). The [FSI]− anion, in all of the C1 – C6 states, was found to be on top position with respect to the imidazolium rings. For the [EMI][TFSI] ion pair conformers, however, both in plane and out-of-plane configurations were possible [31]. The [FSI]− anion adopts a cis conformation for C1 C2 and C3 for the C − S−S − C dihedral angle, whereas a trans conformation for the [FSI]− anion was predicted for C4, C5 and C6 ion pair conformers. The [FSI]− anion in the two most stable ion pair conformers adopted the trans configuration. The values of the dihedral angles N1–C1–H1–O1 for all of the C1-C6 ion pair conformers are in the range of 112.9° − 115.5° indicating that the [FSI]− anion is on top position with respect to the imidazolium rings.
For imidazolium based ILs, weak H bonds are usually formed with C1–H1 group of the cation as the primary H-bond donor unit [44] in imidazolium-based ILs, the presence of a hydrogen bond between the C1-H1 unit of the imidazolium ring and the oxygen atom of the [TFSI]− anion was reported [21, 45, 46]. Delicate intermolecular forces such as H-bonds and π-type interactions that simultaneously occur in [EMI][FSI] based ionic liquids are worth mentioning. Despite the absence of conclusive and universally accepted definition of H-bond, H-bonding is still a key area of debate on the properties of ionic liquids. The strength of H-bond can be related to the donor–acceptor distance and angle as a first estimate [47–49]. This, of course, also depends on the nature of atoms involved and the angle between them. Figure 5 shows possible H-bond interactions sites of [EMI]+ cation with the [TFSI]− anion. Generally, H-bond distance of less than 250 pm is considered to be a very strong H-bond, H-bond distance between 250 pm and 265 pm is considered as a strong or moderately strong H-bond, and a H-bond distance greater than 280 pm is considered very weak. On the basis of a distance criteria, the [EMI][FSI] complex shows distances of rather weak hydrogen bonds.(see Table 2). The values of the distances of Cl−H1---O1 for the ion pair conformers C1, C2, C4, C5 and C6, respectively, are 2.78 Å, 2.90 Å, 2.83 Å, 2.78 Å, 2.26 Å and 2.92 Å, indicating that only the C5 ion pair conformer is within the accepted criteria of the C1 − H1---Ol primary H-bonds. The C5 ion pair conformer exhibits bifurcated C − H—O1 inter ion interactions through the primary C1 − H1 (2.26 Å) and terminal methyl group C5 − H8 cation H-bonds (2.42 Å) (see Fig. 4). Terminal methylene H-bond interactions through C2 − H2—O2 were observed for the C1(2.50 Å), C2(2.51 Å), C3(2.51 Å) and C6(2.56 Å) ion pair conformers. From Table 2, it can be seen that the structures of the [EMI]+ cation rings show very little changes for the distance of C1 − H1 except for C5 ion pair conformer (1.08 Å) which indicates that only the C5 conformer has C1 − H1---Ol primary H-bond interaction. On the basis of geometric criteria given in Table 2, there are no C − H—F interactions observed for the [EMI][FSI] single ion pair conformers. The presence of the out-of-plane interactions between the [EMI]+ and [FSI]− ions ties in well with the higher interaction of the [FSI]− anions with alkyl group hydrogens. The presence of out-of-plane conformers could also be tied to the interaction of the anion with π clouds of the [EMI]+ ring, which is further discussed in section 3.3 from the natural orbital analysis of the conformers. In [EMI]+ cation, the aromatic ring is π-acidic due to the presence of a positive charge in the N1-C1-N2 ring, which consequently leads to the presence of [FSI]− anion donor [EMI]+ π-acceptor type interactions.
3.2 Interaction Energies of Isolated Ion Pair Conformers.
The intermolecular interactions between the anions and cations of ionic liquids are the most important factors that dictate the transport properties of such liquids. Despite extensive studies on the magnitude of interaction energy between ions, and its influence on the structure and physical properties of ionic liquids, however, little has been known on its magnitude and dependence on the ions [23]. Ab initio molecular orbital calculation methods are a method of choice for the investigation of intermolecular interaction energies. So far as large basis set is used, and electron correlation is properly implemented, ab initio calculations could provide accurate values of interaction energies [49–51]. Aiming at investigating the molecular interactions and the occurrence of H-bonding in [EMI][FSI] ion pairs, the interaction energy of the different ion pair conformations were calculated using ωB97x-D/DGDZVP level of theory and basis set in the presence of acetonitrile as a solvent, and the results are shown in Fig. 6. The interaction energy between the cation and the anion of the ILs was calculated according to the following expression (Eq. 1):
$$\text{E}\left(\frac{\text{k}\text{J}}{\text{m}\text{o}\text{l}}\right)= \text{E}\left(\text{I}\text{P}\right) -(\text{E}\left(\text{c}\text{a}\text{t}\text{i}\text{o}\text{n}\right) + \text{E}\left(\text{a}\text{n}\text{i}\text{o}\text{n}\right))$$
1
Where E(IP) is the energy of the ion pair, and E(cation) and E(anion) are the energy of the cation and anion, respectively.
The correlations between interaction and relative conformer energies of the different [EMI][FSI] conformers are shown in Fig. 6. The C4 ion pair conformer has the maximum and C5 conformer has the minimum absolute interaction energy. Comparison between interaction and relative conformer energies reveals that there are very important revelations among the ordering of calculated relative and interaction energy values. According to Fig. 6, the values of the relative optimized energies among the six conformers changes in the following order: C6 > C4 > C2 > C3 > C1 > C5 whereas the absolute interaction energies change in the order: C4 > C1 > C6 > C2 > C3 > C5. The absolute values of the interaction energies of the conformers C1, C4 and C6 respectively, are 44.011, -44.186 and − 40.466 (kJ/mol) which are higher than those of C2 (40.332 kJ/mol) C3(40.180 kJ/mol), and C5 (-34.616 kJ/mol). The relative energy of the C6 ion pair conformer is lower than that of the ion pair conformers of C4 by 0.163 kJ/mol) (see Table 2). On the other hand, the absolute interaction energy of C4 (44.186 kJ/mol) conformer is greater than the absolute interaction energy of the C6 (40.466 kJ/mol) conformer. The question why the C6 ion pair (global minimum) conformer has less absolute interaction energy than C4 (local minimum) is likely to be raised. Ludwig and co-workers have shown that agreement with experimental data could only be obtained by choosing conformers which hold higher absolute interaction energies than the global minimum. Thus, the sole importance of the global minimum structure for the condensed phase is highly questionable [52]. Apparently from the results in Fig. 6, for the ion pair [EMI][FSI], the absolute value of the interaction energies is lower than the normal hydrogen bond energies (50 kJ/mol), which indicates that there exist very weak electrostatic interaction between the [EMI]+ cations and [FSI]− anions. The weaker attraction between the [EMI]+ and [FSI]− ions suggests as one contributor to the larger value of diffusion coefficients of the ions The smaller viscosity of the [EMI][FSI] compared to [EMI][TFSI] based ionic liquids originates from its relatively smaller value of the interaction energy. Similar conclusions were drawn by Tsuzuki et al [43] and co-workers for the [FSI]− complex with [EMI]+ by ab initio molecular orbital methods.
Further to our analysis of the ion pair conformers, we also stress the importance of H-bonding between the C1-H1 of the [EMI]+ ring and [FSI]− anion. The values of the interaction energies are not well reflected in the geometry of the H-bond (donor-acceptor distance and angle) indicating that the H-bond is not the only interaction. For example, the absolute value of the interaction energy has the lowest value for the C5 ion pair conformer which has the strongest and more linear C1-H1--O1 interaction (see Table 2). On the other hand, the value of this interaction energy is the highest for C4 conformer, while this conformer has the weakest and nonlinear C1-H1--O1 primary H-bond interaction, indicating that the [FSI]− anion interaction with C1-H1 proton of the [EMI]+ ring does have little influence on the interaction of the conformers. Tsuzuki et al [54] have drawn similar conclusions because they obtained small angle (lacking directionality) in energetically stable conformers than the ones in linear arrangements.
From our geometry optimizations, we found ion pairs that display a wide range of H-bond length and angles. The C1 (2.506Å, 135.29˚), C4 (2.496Å, 137.34˚) and C6 (2.563Å, 134.68˚) ion pair conformers exhibit secondary H-bond interaction with the methylene hydrogen atoms (C2-H2—O2). The C3 ion pair conformer exhibits a strong C1-H1—N1 (2.469Å, 115.37˚) interaction while all other ion pair conformers do not exhibit this kind of interaction. The C5 ion pair conformer has shorter and stronger primary H-bond interaction with the C1-H1 hydrogen of the [EMI]+ cation while it has the lowest value of absolute interaction energy. On the other hand, C1, C4 and C6 ion pair conformers have weaker primary H-bond interaction with C1-H1 of the [EMI]+ cation but yet stronger and more linear secondary H-bond interaction with the methylene hydrogen (C2-H2) of the [EMI]+ cation, and have higher values of absolute interaction energy. Prior reported studies argued that the interaction between the C1-H1 hydrogen atom of [EMI]+ cation was not a H-bond like interaction and the distance from the nearest hydrogen atom was not the main factor determining the size of the attraction [23]. In those reports, it has been shown that the nature of the interaction between the C1-H1 hydrogen atom of [EMI]+ cation and a range of anions was considerably different from that of conventional hydrogen bonds and this interaction did not show any dependence on orientation for these authors have found that small angles (lacking directionality) in energetically more stable conformers than in the ones with linear arrangement [23]. When imidazolium cations are associated with large anionic groups, like [FSI]− anion, there exist varying levels of H-bond strength and interaction, and additionally, the [FSI]− anion takes preferential on-top distributions above and below imidazolium rings, leading to π-type interactions. The delicate interplay of H-bond and π-type interactions in [EMI][FSI] ionic species depends on the particular [EMI][FSI] ion pair conformer, and in general, weak interaction energies have been observed [54]. However, an individual [EMI][FSI] ion pair may undertake multiple interactions within the liquid environment, increasing the overall energy contribution from H-bonds.
3.3 The Stabilization Energies of Isolated Ion Pair Conformers.
The mode of intermolecular interactions between the [EMI]+ cations and larger anions such as [TFSI]− and [FSI]− is the subject of continuing scientific debate and discussions. Some authors believe that the ions in ionic liquids are held together by H-bonding, while others believe that the role of the H-bond is minor compared with the role of electrostatic interactions. The natural bond orbital population analysis (NBO) carried out on DFT optimized [EMI][FSI] ion pair structures gives unique feature of analysing the electron density, which thereby allows the analysis of intermolecular donor-acceptor orbital interactions. Therefore, we carried out NBO analysis of the different [EMI][FSI] ion pair conformers. This analysis, which has been proven to provide reliable (in a chemical sense) information regarding the change in charge densities of donor and acceptor ions, is also less method dependent [55]. The H-bond strength of the \({n}_{Y }\to\)\({\sigma }_{X-H}^{*}\) donor-acceptor follows the same trend with NBO stabilization energies (\({E}_{n\to \sigma *}^{2}\)) expressed by Eq. 2 [56]. For each donor NBO(i) and acceptor NBO(j) orbitals, the stabilization energy E(2) associated with delocalization of electron pair from donor orbital (i) to acceptor orbital (j) and is defined as:
$$\text{E}\left(2\right) = {Δ \text{E}}_{\text{i}\text{j}}= \frac{{\text{q}}_{\text{i}}\text{F}{(\text{i},\text{j})}^{2}}{{{\epsilon }}_{\text{i}} -{{\epsilon }}_{\text{j}} }$$
2
Where qi is the donor orbital occupancy, εi and εj are the diagonal elements (orbital energies) and F(i,j) is the interaction element between donor and acceptor orbitals and is known as diagonal NBO Fock matrix element. The value of the stabilization energy (E(2) (kcal/mol)) is obtained from second order perturbation theory [91]. When electrons are shared via the lone pairs of oxygen and nitrogen atom to the σ-type and π-type anti-bonding orbital of the C–H, C = C and N–C bonds (Ylp\(\to\)σ*C–H, Ylp\(\to {\pi }\)*C=C, Ylp\(\to {\pi }\)*C–N), where Y = N, O; this is equivalent to transferring electron density from the lone pair of N and/or O atoms into the σ*C–H, \({\pi }\)*C=C and/or \({\pi }\)*C–N orbitals. The magnitude of cation – anion interaction can be related to the charge transfer component of E(2)n\(\to\)σ*, E(2)n\(\to {\pi }\)*C=C and/or E(2)n\(\to\)π*C−N, which is proportional to the amount of electron density (qi) donated from the filled donor lone-pair orbital into the empty σ* and/or π* antibonding orbital, moderated by the energy difference between these two fragment orbitals (Δε), and thus the NBO analysis on the DFT optimized structure allows the analysis of intermolecular donor–acceptor orbitals interactions [56].
Early studies on NBO analysis on ionic liquids have been limited to various alkyl-imidazolium derivatives with simple poly/mono-atomic anions [24, 56]. However, there have not been any prior reported studies on the detailed NBO analysis of alkyl-imidazolium derivatives with bis(fluoromethylsulfonyl)imide [FSI] ion pair conformers that have multiple interactions sites for the anion. In this article, we are reporting how stabilization energy obtained from NBO analysis of different ion pair conformers of [EMI][FSI] helps to get the details of orbital interactions between the empty σ*C–H, \({\pi }\)*C=C and \({\pi }\)*C–N fragment orbitals (FO) of the [EMI][FSI] ion pair complex at ωB97X-D level using the DGDZVP basis set and the presence of dielectric continuum medium, and the results are compiled in Tables S1-S6. Past reports [23, 54–56] have shown that imidazolium based ion pairs with weakly H-bond acceptor anions such as [BF4]− and [PF6]− have E(2)n\(\to\)σ* = 50–60 kJ/mol while those with strongly H-bond acceptor anions such as Cl− and [NO3]− have E(2)n\(\to\)σ* = 110–180 kJ/mol. H-bond interaction is not a binary on–off phenomenon but occurs in a graduated scale which makes quantifying and demarking H-bonding difficult. Generally, weak H-bonds have E(2)n\(\to\)σ* < 30 kJ/mol and strong hydrogen bonds have E(2)n\(\to\)σ* > 150 kJ/mol [44] and those lying between these extremes are moderate hydrogen bonds. A more robust level of knowledge is required to relate the E(2)n\(\to\)σ* parameter with respect hydrogen bonds in ionic liquids containing the [EMI]+ cation and large more diffuse anions such as [FSI]−. It requires the close inspection and analysis of a large range of ionic liquid ion pair conformers, geometric influences and the impact of multiple concomitant hydrogen bonds that need to be better understood.
From the Tables S1-S6, we observed, in general that, for [EMI][FSI] ion pair conformers, charge transfer occurs mainly from the lone pairs of oxygen and nitrogen atom to the σ-type anti-bonding orbital of the C–H, and to the π-type anti-bonding orbitals of N-C and C = C bonds. This is evident from the values of the stabilization energy (E(2)) associated with each electron delocalization from the donor to acceptor orbitals. The [FSI]− anion transfers charge to [EMI]+ cation, and this extra electron density is distributed over the N1, N3 and C4/5-H centres. There is a rough correlation between the amount of charge transferred and the relative value of the stabilization energy: the greater the values of the stabilisation energy, the more stable an ion pair, and the more charge is transferred. Apparently, from the above results, it is noticeable that, for the [EMI][FSI] ion pair conformers, the values of the stabilization energy E(2) are generally small (E(2)n\(\to\)σ* < 2 kcal/mol) for the individual E(2)n\(\to\)σ*, E(2)n\(\to {\pi }\)*C=C and/or E(2)n\(\to\)π*N−C interactions. The [EMI]+ cation and [FSI]− anions tend to form multiple σ* and \({\pi }\)* interactions, but reducing the strength of the individual contributions from a potential (linear) maximum. The relative contribution from each of these is not easily resolved via the association energy which includes the ionic as well as a combined H-bond contribution.
The shorter the C1–H1---O H-bond distance, the larger the charge transfer, and the larger the corresponding stabilization energy E(2) associated with electron delocalization from donor to acceptor anti-bonding orbital. The ion pair conformer C5, for example, has the shortest C1–H1---O1 bond (2.26 Å) and more linear angle (142.35°), and thus relatively with greater value of second-order perturbation energy for O1\(\to\)σ*C1−H1 (E(2) = 1.37 kcal/ mol) among all ion pair conformers investigated. NBO analysis of [EMI][FSI] ion pair conformers also revealed that the lone pairs of oxygen and nitrogen atoms donate electrons to the σ-type (σ*C1−H1) and π-type anti-bonding orbital for π*N1−C1 and π*C4=C5 bonds. The occurrences of NBO interactions of n\(\to\)π*N1−C1 and n\(\to\)π*C4=C5 imply the existence of anion donor - π* interactions in these systems. The LP(1)F, LP(2)F and LP(1)F (donor NBO)\(\to\) BD*(2)C1-N1 (acceptor NBO) interaction shows the presence of weak N1 − C1---F anion donor - π* interactions for the C5 ion pair conformer. Furthermore, for the C5 conformer, the LP(1)O1, LP(3)O1 (donor NBO)\(\to\) BD*(2)C1-N1 (acceptor NBO) interaction shows the presence of weak N1 − C1---O anion donor - π* interactions. Similar types of weak N1 − C1---O anion donor - π* interactions have been observed for all other types C1-C5 conformers. A second type of weak C = C—O anion donor - π* interactions have also been observed for C2 and C6 ion pair conformers.
Further to our analyses of the ion pair conformers, the NBO method has also been employed to characterize the natural orbital coefficients and orbital hybridizations of the different conformers of the [EMI][FSI] ion pair. The main listing of NBOs, displaying occupancy, natural atomic hybrids, polarization coefficient, and spλ composition of the different conformers of the [EMI][FSI] ion pair for a selected set of NBOs are shown in Tables S7-11. For the ion pair conformer C5, which has relatively higher value of E(2) values for C1–H1---O interaction, the σ*C1−H1 NBO is formed from an sp0.34 hybrid (62.03% p-character) on carbon interacting with hydrogen (100.00%) s-character corresponding to linear combination of atomic orbitals 0.6097*C(p 1.64) − 0.7926*H (s) comprising larger polarization coefficient of H. The orbital interaction between lone pair orbitals LP(1)O1 and σ*(1)C1–H1 (E(2) = 1.37 kcal/mol) has sp1.63 hybrid orbital with s(75.44%) character and p(24.55%) character; and the orbital interaction between lone pair orbitals of LP(2)O1 and σ*(1)C1–H1 (E(2) = 1.15 kcal/mol) with s(0.01%) character and p(99.70%) character for LP(2)O1 orbital. Similarly, for the C2 ion pair conformer, the π*C4=C5 NBO is formed from an sp0.34 hybrid from carbon (C4) with p(99.87%) character and carbon (C5) with p(99.88%) character corresponding to the linear combination of the orbitals 0.7061*C(sp0.34) − 0.7081*C(sp0.34) with nearly equivalent polarization carbon atoms. The natural bond orbital (NBO) interactions of the different conformers C2 – C6 of [EMI][FSI] ion pairs are shown in Fig. 7.
Selected partial charges for the different ion pair conformers of [EMI][FSI] are also reported in Tables S7-11.Those hydrogen atoms that interact with the [FSI]− anion are more positive, and the associated carbon atoms are slightly more negative. NBO analyses for [EMI][FSI] ion pair conformers were performed to obtain the NBO charge distribution. For the C5 ion pair conformer, the NBO charge of H1 (0.25252) is more positive than that of other hydrogen atoms, while the NBO charges of O1(-0.97161) is more negative than that of other oxygen/fluorine atoms which are ascribed to the C1 ̶ H1—O1 H-bond interactions. Similarly, the anion donor π-type anti-bonding interaction between the most electronegative N1 and O1 atoms of the [FSI]− anion with the π*N1−C1 anti-bonding orbital of the [EMI]+ cation leads to more positive charges on C1 atoms of the C1(0.34293), C2(0.35193) and C5(0.35038) ion pair conformers. The greater the magnitude of the anion donor π*N1−C1 anti-bonding interaction, the higher the values of the positive charges on C1 atoms of the [EMI]+ cation.