domain: chim phys sde

text:
What quantum chemical simulations tell us about the infrared spectra, structure and interionic interactions of a bulk ionic liquid anions. Both structural and spectroscopic analyses allow the contacts to be interpreted as hydrogen bonds of approximately equal strength. The enthalpies of these liquid-state H-bonds, estimated with the use of empirical correlations, amount to 1.2-1.5 kcal mol À1 , while the analogous estimates obtained for the gas-phase charged species [Emim][BF 4 ] 2

À and [Emim] 2 [BF 4 ] + increase to 3.6-3.9 kcal mol À1 .

Ionic liquids (ILs), organic salts with low melting points, have reached practically all areas of science and industry. Their useful properties, and possibilities for their tuning on the basis of near limitless available combinations of ionic components of ILs, is the main reason for this wide spread. [START_REF] Philippi | Targeted modifications of ionic and intermolecular interactions[END_REF] At the same time, the sheer number of possible variations of both cations and anions constituting ILs requires structure-property relationships for tailoring their properties. A thorough understanding of how the properties of an IL arise from its structure is impossible without knowledge of the supramolecular architecture of the IL and the forces acting between its elements. Infrared (IR) spectroscopy is one of the most popular experimental methods used to establish the abovementioned features. [START_REF] Paschoal | Vibrational Spectroscopy of Ionic Liquids[END_REF] To derive structural information from IR spectra, input is required from quantum chemical calculations at computational levels that match the experimental resolution and accuracy. The latter condition is achievable in most cases of gas-phase studies, but it is very problematic for the condensed state. [START_REF] Katsyuba | Is there a simple way to reliable simulations of infrared spectra of organic compounds?[END_REF] In particular, IR spectra of bulk ILs differ dramatically from the spectra of their isolated cationic and/or anionic components. 4 Molecular dynamics (MD) simulations of both molecular [START_REF] Praprotnik | Temperature Dependence of Water Vibrational Spectrum: A Molecular Dynamics Simulation Study[END_REF][START_REF] Stare | Hydrogen Bond Dynamics of Histamine Monocation in Aqueous Solution: Car-Parrinello Molecular Dynamics and Vibrational Spectroscopy Study[END_REF] and ionic liquids, [START_REF] Thomas | Computing vibrational spectra from ab initio molecular dynamics[END_REF] allow the liquid-state IR spectra to be obtained via Fourier transform of the velocity autocorrelation function in the MD trajectory. However, the most rigorous ab initio MD [START_REF] Stare | Hydrogen Bond Dynamics of Histamine Monocation in Aqueous Solution: Car-Parrinello Molecular Dynamics and Vibrational Spectroscopy Study[END_REF][START_REF] Thomas | Computing vibrational spectra from ab initio molecular dynamics[END_REF] approach involves a huge amount of computer resources while the accuracy of the theoretical spectra obtained on the grounds of classical molecular mechanical treatment of the liquid strongly depends on the quality of the applied empirical force fields. [START_REF] Katsyuba | Revisiting Conformations of Methyl Lactate in Water and Methanol[END_REF] Recently, we presented an efficient approach to an accurate, fully quantum-mechanical (QM) modeling of IR spectra of condensed-phase systems. [START_REF] Katsyuba | Fast and Accurate Quantum Chemical Modeling of Infrared Spectra of Condensed-Phase Systems[END_REF] An automated cluster generation algorithm was applied to construct an ensemble of explicitly solvated molecular clusters that were re-optimized at a reasonable but efficient level of Density Functional Theory (DFT). The DFT simulated IR spectrum of the system matches the corresponding condensed-phase IR experiment better than the theoretical spectrum of the isolated molecule compared to the gas-phase IR spectrum. More details can be found in Section 2.

Our approach was successfully tested on hydrogen-bonded molecular liquids, such as methanol [START_REF] Katsyuba | Fast and Accurate Quantum Chemical Modeling of Infrared Spectra of Condensed-Phase Systems[END_REF] and ethanol, [START_REF] Katsyuba | Computer-aided Simulation of Infrared Spectra of Ethanol Conformations in Gas, Liquid and in CCl 4 Solution[END_REF] and aqueous and methanolic solutions of methyl lactate. [START_REF] Katsyuba | Revisiting Conformations of Methyl Lactate in Water and Methanol[END_REF] It has been suggested that vibrational modes and dipole moment derivatives are mainly influenced by their immediate local surroundings, and the inclusion of the first solvation shell is sufficient to simulate liquid-phase IR spectra with similar

Introduction

and IR intensities were calculated analytically. This highly efficient method has been shown [START_REF] Katsyuba | Fast Quantum Chemical Simulations of Infrared Spectra of Organic Compounds with the B97-3c Composite Method[END_REF] to perform well for IR spectra computations in the harmonic approximation, being only slightly inferior to B3LYP -one of the best performing DFT methods for the calculation of vibrational frequencies and IR intensities of organic molecules. [START_REF] Katsyuba | Is there a simple way to reliable simulations of infrared spectra of organic compounds?[END_REF][START_REF] Zvereva | Ab Initio and DFT Predictions of Infrared Intensities and Raman Activities[END_REF] For better agreement with the experimental anharmonic frequencies, the computed harmonic frequencies with n 4 1100 cm À1 were scaled by 0.979. [START_REF] Katsyuba | Computer-aided Simulation of Infrared Spectra of Ethanol Conformations in Gas, Liquid and in CCl 4 Solution[END_REF] The collective vibrations of clusters ([Emim][BF 4 ]) n involve species at the external surface of a cluster, which have no analogs in the case of the bulk IL. In order to minimize these finite cluster size effects, we separated the vibrations of the central ion pair [Emim][BF 4 ] from the vibrations of the surrounding ions by increasing the atomic masses of the latter species to 400 amu, and thus shifting their vibrations to the low-frequency region (these separated spectra are represented in Fig. 3 and Tables 234). For comparison with experimental spectra, the computed absolute intensities (km mol À1 ) were plotted against computed frequencies, with a Lorentzian broadening (fwhm = 15 cm À1 ). All DFT calculations were carried out using the Turbomole-7.5.1 program package. 17 The [Emim] + cation can adopt not only the nonplanar conformation shown in Fig. 1A, but also a planar form with the ethyl moiety eclipsing the C2-H bond. The nonplanar conformer, which is known to dominate both in the isolated cation and in the liquid [Emim][BF 4 ], [START_REF] Umebayashi | Evidence of Conformational Equilibrium of 1-Ethyl-3-methylimidazolium in its Ionic Liquid Salts: Raman Spectroscopic Study and Quantum Chemical Calculations[END_REF] was used as the starting structure of the ion pair (Fig. 1A) for the generation of clusters ([Emim][BF 4 ]) n . No conversion from the nonplanar to the planar conformer was obtained during the process of the cluster growth (see Section 2), and thus, the relative abundance of the [Emim] + conformers within the clusters did not coincide with the real IL, where the planar cations were still detected by Raman spectroscopy. [START_REF] Umebayashi | Evidence of Conformational Equilibrium of 1-Ethyl-3-methylimidazolium in its Ionic Liquid Salts: Raman Spectroscopic Study and Quantum Chemical Calculations[END_REF] Nevertheless, this structural deviation of our models from the experiment is of minor importance for the cluster simulations of IR spectra, since the mid-IR spectrum of the IL is practically insensitive to the cation conformation. [START_REF] Heimer | Vibrational Spectra of Imidazolium Tetrafluoroborate Ionic Liquids[END_REF][START_REF] Katsyuba | Application of Density Functional Theory and Vibrational Spectroscopy toward the Rational Design of Ionic Liquids[END_REF] Variation of the number (n) of ion pairs in the clusters ([Emim][BF 4 ]) n demonstrates that formation of the first solvation shell of the [Emim] + cation is accomplished at n = 8 (Fig. 1A). The protons of the solvated cation in this cluster form short contacts (less than the sum of the corresponding van der Waals radii) with six [BF 4 ] À anions (Table 1). The seventh anion resides on top of the [Emim] + ring, while the bottom position is occupied by another cation (Fig. 2).

This geometry reasonably well matches characteristics of the liquid [Emim][BF 4 ] obtained from the 1 H, [START_REF] Heimer | Vibrational Spectra of Imidazolium Tetrafluoroborate Ionic Liquids[END_REF] F-HOESY NMR experiment, [START_REF] Lingscheid | Heteronuclear NOE spectroscopy of Ionic Liquids[END_REF] indicating strong contacts of all the cation protons with the anions (Table 1). It is also worth noting that the positions of the anions forming short contacts with the protons of the [Emim] + ring (Fig. S2, ESI †) closely resemble those found in crystals of [Emim][BF 4 ] and revealed by the accuracy as for individual molecules in a vacuum. In this work, we apply this protocol to prototypic room-temperature IL 1-ethyl-3-methyl-imidazolium tetrafluoroborate [Emim][BF 4 ], where apart from hydrogen bonds (HBs), long-range Coulomb interactions are present. The purpose of our study is two-fold: (i) to improve our understanding of the factors influencing the IR spectra of condensed-phase systems in general, and (ii) to gain new knowledge about how these factors are reflected in the IR spectra of ILs, to search for spectroscopic markers of various structural subunits in the bulk IL, and to assess the strength of HBs functioning therein.

Computations

The IL was approximated by a representative ensemble of molecular clusters. In these clusters, solvation shells around the ''solute'' are formed by interaction with explicit ''solvent'' molecules. Both the ''solute'' and ''solvent'' species were represented by ion pairs consisting of cation [Emim] + and anion [BF 4 ] À (Fig. 1). Clusters were generated by the Quantum Cluster Growth (QCG) algorithm 11 which, in short, adds solvent molecules around the solute at energetically favorable positions using an intermolecular force field docking algorithm (xTB-IFF). [START_REF] Grimme | A general intermolecular force field based on tight-binding quantum chemical calculations[END_REF] The cluster generation step is followed by MD simulations in which equilibrated snapshots from the trajectory are fully geometry optimized at the robust and fast semiempirical GFN2-xTB [START_REF] Bannwarth | GFN 2Àx TB -An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions[END_REF] level, forming an ensemble of lowenergy clusters. To simulate the liquid [Emim][BF 4 ] clusters, 4 to 8 ion pairs were taken into account. The cluster of lowest free energy (i.e., including thermostatistical corrections) was used as the starting point for the calculation of the IR spectra of the liquid. It should be noted that a comparison of the IR spectra calculated for clusters that are populated by more than 20% has shown that the difference between the spectrum of the lowest-energy cluster and all other clusters from the final ensemble is practically negligible (Fig. S1,ESI †).

For a more accurate treatment of explicit solvent effects, the GFN2-xTB generated clusters were re-optimized with the B97-3c composite DFT method, [START_REF] Brandenburg | B97-3c: A revised low-cost variant of the B97-D density functional method[END_REF] and harmonic vibrational frequencies analysis of the corresponding data-files from the Cambridge Structural Database. [START_REF] Zvereva | A Simple Physical Model for The Simultaneous Rationalisation of Melting Points and Heat Capacities of Ionic Liquids[END_REF]

IR spectra of ([Emim][BF 4 ]

) n clusters, isolated [Emim] + and [BF 4 ] À ions, and their various associations B97-3c computations of vibrational frequencies of the isolated ionic constituents of [Emim][BF 4 ] are in reasonably good agreement with the corresponding gas-phase experiment, 4 providing practically the same quality of the spectra simulations as more time-demanding B3LYP/6-31+G(d,p) calculations (Table S1, ESI †). This suggests that B97-3c represents an adequate level of DFT approximation for simulation of the IR spectra of the IL under study.

Indeed, the IR spectrum simulated for cluster ([Emim][BF 4 ]) 8 (Fig. 3b) quite well matches the corresponding experimental spectrum of the bulk [Emim][BF 4 ] liquid in the lower-frequency part (500-900 cm À1 ) of the fingerprint region. Absorption saturation by the intense broad bands of stretching vibrations of the [BF 4 ] À anion, n str (BF 4 ), in the bulk IR spectrum, prevents the simulation vs. experiment comparison of the IR intensities in the region B1000-1100 cm À1 . Nevertheless, the positions of n str (BF 4 ) bands, known from attenuated total reflectance IR spectra [START_REF] Yamada | Infrared Spectroscopy in the Middle Frequency Range for Various Imidazolium Ionic Liquids -Common Spectroscopic Characteristics of Vibrational Modes with In-Plane + C(2)-H and + C(4,5)-H Bending Motions and Peak Splitting Behavior Due to Local Symmetry Breaking of Vibrational Modes of the Tetrafluoroborate Anion[END_REF][START_REF] Shalygin | Interactions of CO 2 with the homologous series of C n MIMBF 4 ionic liquids studied in situ ATR-FTIR spectroscopy: spectral characteristics, thermodynamic parameters and their correlation[END_REF] ] is also clearly seen from visual comparison of Fig. 3A andB.

It should be noted that the accurate comparison of our harmonic computations with the experiment is hampered by contamination of the region 4B1100 cm À1 by combination bands and overtones. [START_REF] Fournier | Comparison of the local binding motifs in the imidazolium-based ionic liquids[END_REF] These manifestations of anharmonism are most pronounced in the region of CH stretching vibrations, n str (CH), critical for assessing hydrogen bonds (HBs) in the IL, which have become a topic of vigorous discussion (e.g. ref. 26-28). Deuteration of [Emim] + at the C2 position allows the isolation of the band of n str (C2D) from the Fermi resonance and other strong anharmonic effects, and its use as a convenient IR spectroscopic marker of HBs and other intermolecular interactions functioning in bulk IL and various gas-phase associations of the [Emim-d] + cation. 4,[START_REF] Fournier | Comparison of the local binding motifs in the imidazolium-based ionic liquids[END_REF] Our computations of the isolated cation perfectly reproduce the corresponding experimental value of n str (C2D), while a small red shift of this band in the experimental IR spectrum of bulk liquid [Emim-d][BF 4 ] 20 relative to the gas-phase spectrum 4 of [Emim-d] + is qualitatively reproduced by the calculations of cluster ([Emim-d][BF 4 ]) 8 (Table 3). The qualitatively incorrect blue shift of n str (C2D) in the simulated spectra of the ([Emim-d][BF 4 ]) n species (n = 4-7) relative to the spectrum of [Emim-d] + (Table 3) indicates that these models of bulk IL are oversimplified.

The above comparative analysis of n str (C2D), as well as the fingerprint region (Fig. 3) in the spectrum simulated for an isolated ion pair, i.e. the simplest model of IL broadly used for interpretation of bulk IR spectra, and the spectrum computed for the ion pair solvated by the first solvation shell of other ion pairs, clearly demonstrates much better quality of the latter. This theoretical spectrum of the cluster ([Emim][BF 4 ]) 8 matches the bulk IR experiment at least no worse than the simulated spectra of isolated

[Emim] + , [BF 4 ] À , [Emim-d][BF 4 ] 2
À and [Emim-d] 2 [BF 4 ] + species match the corresponding gas-phase experiment 4 (Tables S1-S3 (ESI †), respectively). This strongly suggests that, similar to the case of molecular liquids/ solutions, 8-10 the IR spectrum of the bulk IL is determined mainly by interaction of a minimal neutral entity, an ion pair, with its immediate surroundings, while the role of farther ions is minor, in spite of long-range Coulomb forces acting in such a medium. d]Br relative to the spectra of the melts. [START_REF] Grondin | Revisited Vibrational Assignments of Imidazolium-Based Ionic Liquids[END_REF] Furthermore, even in the case of H-bonded pairs forming a ''classical'' two-center HB isolated in an innocent solvent or gas, the shift can be zero or even negative. [START_REF] Iogansen | Direct Proportionality of the Hydrogen Bonding Energy and the Intensification of the Stretching n(XH) Vibration in Infrared Spectra[END_REF] In contrast, strengthening of the n str (XH) IR band is one of the well-accepted criteria of HB formation. [START_REF] Arunan | Definition of the Hydrogen Bond (IUPAC Recommendations[END_REF] There exists a correlational equation [START_REF] Iogansen | Direct Proportionality of the Hydrogen Bonding Energy and the Intensification of the Stretching n(XH) Vibration in Infrared Spectra[END_REF] linking HB enthalpy, ÀDH HB , and intensity of n str (XH):

Hydrogen bonding in bulk [

ÀDH HB [kcal mol À1 ] = 0.29 DI 1/2 [km mol À1 ] (1)
here, DI 1/2 = I 1/2 À I 0 1/2 , where I is the IR intensity for the localized, uncoupled stretching vibration n str (XH) of the X-H group participating in the HB as compared to the noninteracting group (I 0 ). Equation ( 1) is applicable to 1 : 1 H-bonded complexes, in particular formed by CH moieties, [START_REF] Iogansen | Direct Proportionality of the Hydrogen Bonding Energy and the Intensification of the Stretching n(XH) Vibration in Infrared Spectra[END_REF] in which the ÀDH HB values are lower than 15 kcal mol À1 . [START_REF] Tupikina | Estimations of FHÁ Á ÁX hydrogen bond energies from IR intensities: Iogansens's rule revisited[END_REF] Its applicability to CHÁ Á Á[PF 6 ] À 29 and CHÁ Á Á[OAc] À 30 HBs in ILs has been demonstrated on a limited number of examples.

To apply eqn (1) to our systems, the IR intensities have been calculated for isotope-isolated vibrations of the various associations of [Emim] + with [BF 4 ] À species (I) and the bare [Emim] + cation (I 0 ). For example, in the case of the C2HÁ Á Á[BF 4 ] À HB all hydrogen atoms except for the (C2)H atom of the imidazolium ring were substituted by deuterium atoms. Such an approach results in n str (CH) and the ÀDH HB values collected in Table 4. [START_REF] Katsyuba | Application of Density Functional Theory and Vibrational Spectroscopy toward the Rational Design of Ionic Liquids[END_REF] and frequencies computed for various models scaled with 0.979 (the computed IR intensities in km mol À1 are given in parentheses) , representing an ion pair solvated by the first solvation shell comprising seven cations and seven anions. This strongly suggests that, similar to the case of molecular liquids/ solutions, the impact of the remaining part of the surrounding medium on the IR spectrum of the solvated species is rather moderate. In other words, the influence of the electric field of the ions behind the first solvation shell of a solute on its dipole moment derivatives and force constants is quite moderate. This knowledge not only improves our understanding of solute-solvent interactions, but also allows minimization of the computational costs of quantum chemical simulations of the IR spectra of bulk ILs. Good match of the simulated and experimental spectra suggests a close structural correspondence of the actual IL and model cluster ([Emim][BF 4 ]) 8 . Geometries of the latter cluster and, most probably, of actual IL closely resemble the solid-state structure of [Emim][BF 4 ] and are characterized by short contacts of all CH moieties of the imidazolium ring with [BF 4 ] À anions. Both structural and spectroscopic analyses allow the contacts to be interpreted as H-bonds of approximately equal strength. The combined action of the HBs and other condensed-state forces induces quite moderate red shifts of the IR bands of stretching vibrations of the CH moieties, and ca. 5-fold increase of their intensity relative to the case of an isolated [Emim] + cation. Enthalpies of the liquid-state CHÁ Á Á[BF 4 ] À HBs, estimated on the basis of quantitative characteristics of this intensification with the use of empirical correlations, amount to 1.2-1.5 kcal mol À1 , while the enthalpies are more than doubled in the negatively and positively charged gas-phase associations of ionic components of the IL. This disparity, already marked in the case of another IL, [C 2 OHmim][OAc], [START_REF] Katsyuba | Quantification of Conventional and Non-conventional Charge-Assisted Hydrogen Bonds in the Condensed and Gas Phases[END_REF] suggests that an analysis of the role of H-bonding in ILs based solely on ''gasphase'' computations can lead to the misinterpretation of the data. Reliable simulations of both the gas-phase, and the liquidstate IR spectra within the framework of our cluster approach deliver confidence in reliability of modeling of other properties of the actual systems in both states. The quantitative analysis described herein should facilitate further studies on the role of hydrogen bonding in ILs and ultimately it could aid the rational design of ILs with specific physical and chemical properties.

Inspection of

[Emim-d] + (gas-phase experiment) 2362 [Emim-d] + 2362 (9.3) [Emim-d][BF 4 ] 2 À (gas-phase experiment) B2310 [Emim-d][BF 4 ] 2 À 2299 (143) [Emim-d] 2 [BF 4 ] + (gas-phase experiment) B2350 [Emim-d] 2 [BF 4 ] + 2343 (244) Bulk IL (experiment) 2358 ([Emim-d][BF 4 ]

Conflicts of interest

There are no conflicts of interest to declare.

  Sergey A. Katsyuba* a and Elena E. Zvereva* ab The recently developed efficient protocol to explicit quantum mechanical modeling of the structure and IR spectra of liquids and solutions [Katsyuba et al., J. Phys. Chem. B, 2020, 124, 6664-6670] is applied to ionic liquid 1-ethyl-3-methyl-imidazolium tetrafluoroborate [Emim][BF 4 ], and its C2-deuterated analog [Emim-d][BF 4 ]. It is shown that the solvation strongly modifies the frequencies and IR intensities of both cationic and anionic components of the ionic liquids. The main features of the bulk spectra are reproduced by the simulations for cluster ([Emim][BF 4 ]) 8 , representing an ion pair solvated by the first solvation shell. The geometry of the cluster closely resembles the solid-state structure of the actual ionic liquid and is characterized by short contacts of all CH moieties of the imidazolium ring with [BF 4 ] À

3. Results and discussion 3 . 1 .

 31 Structure of ([Emim][BF 4 ]) n clusters.

Fig. 1

 1 Fig. 1 The B97-3c optimized geometries of the [Emim][BF 4 ] ion pair (A) and ([Emim][BF 4 ]) 8 cluster (B). Hydrogen atoms in the cluster are omitted for clarity. The atom numbering scheme is given for the imidazolium ring.

Fig. 2

 2 Fig. 2 The closest surrounding of the solvated [Emim] + cation in the B97-3c optimized cluster ([Emim][BF 4 ]) 8 shown in Fig. 1 (B). Hydrogen atoms are omitted for clarity.

Fig. 3

 3 Fig. 3 Comparison of the experimental IR spectrum of liquid [Emim][BF 4 ] 20 with B97-3c simulated IR spectra of ion pair [Emim][BF 4 ] (A), and of cluster ([Emim][BF 4 ]) 8 (B). The spectra are normalized so that the maximum experimental intensity is equal to unity, and the calculated and experimental intensities of the bands around 850 cm À1 coincide with each other.

  of liquid [Emim][BF 4 ], are reproduced by our simulations for cluster ([Emim][BF 4 ]) 8 reasonably well, in contrast to the computations of ion pair [Emim][BF 4 ] (Table 2). Much better quality of the spectra simulated for the cluster ([Emim][BF 4 ]) 8 than for ion pair [Emim][BF 4

Table 1

 1 Computed and experimental characteristics of HÁ Á ÁF short contacts in [Emim][BF 4 ]

	Emim][BF 4 ] IL, and the gas-

+

, as well as a similarly small red shift reported for the gas-phase cationic cluster [Emim-d] 2 [BF 4 ] + (Table

3

), were interpreted

4

as an indication of very weak or even absent H-bonding in both cases. Nonetheless, as discussed in ref.

29

, stretching frequencies of the CH groups

  Table 4 clearly demonstrates all signatures of HBs for [Emim][BF 4 ] 2 À and [Emim] 2 [BF 4 ]

+ species: (i) red shift and (ii) intensification of n str (C2H) and n str (C4H), (iii) lengthening

Table 2

 2 Experimental frequencies (cm

	Bulk IL (experiment)	1016	B1025/1033	1046
	Ion pair [Emim][BF 4 ]	972	992	1167
	([Emim][BF 4 ]) 8	997	1027	1097

À1

) of stretching vibrations of the [BF 4 ] À anion in bulk liquid [Emim][BF 4 ],

[START_REF] Yamada | Infrared Spectroscopy in the Middle Frequency Range for Various Imidazolium Ionic Liquids -Common Spectroscopic Characteristics of Vibrational Modes with In-Plane + C(2)-H and + C(4,5)-H Bending Motions and Peak Splitting Behavior Due to Local Symmetry Breaking of Vibrational Modes of the Tetrafluoroborate Anion[END_REF][START_REF] Shalygin | Interactions of CO 2 with the homologous series of C n MIMBF 4 ionic liquids studied in situ ATR-FTIR spectroscopy: spectral characteristics, thermodynamic parameters and their correlation[END_REF]

and frequencies computed for different models

Table 3

 3 Experimental frequencies (in cm À1 , bold) of stretching vibrations n

str (C2D) of [Emim-d] + in gas (isolated cation and [Emim-d][BF 4 ] 2 À anion), 4 and in bulk liquid [Emim-d][BF 4 ],

  the C2H and C4H bonds, and (iv) quite short HÁ Á ÁF contacts. ÀDH HB values, estimated for these ions with the use of Eqn.(1), vary between 3.6 and 3.9 kcal mol À1 . In the case of cluster ([Emim][BF 4 ]) 8 the signatures (i) and (iii) are absent. Nevertheless, short HÁ Á ÁF contacts, and ca. 5-fold increase of the IR intensity of n str (C2H) and n str (C5H) for ([Emim][BF 4 ]) 8 relative to [Emim] + suggests that C2H and C5H moieties of the imidazolium ring of ([Emim][BF 4 ]) 8 still form HBs, though less pronounced than in the case of [Emim][BF 4 ] 2 À and [Emim] 2 [BF 4 ] + species. The use of Eqn. (1) produces estimates of ÀDH HB , which amount to ca. 1.5 kcal mol À1 for C2H and ca. 1.2 kcal mol À1 for C5H. Thus, CH moieties of the imidazolium ring form HBs of moderate strength in all the studied species, and the almost negligible red shift of n str (C2D) relative to isolated [Emim] + does not indicate negligible H-bonding in the ([Emim][BF 4 ]) 8 cluster. The good match of the spectra simulated for this cluster to the experimental spectra of bulk IL (Section 3.2) strongly suggests that the above statement is also applicable to the bulk IL. The estimates of ÀDH HB for CH . . . [BF 4 ] À HBs in the cluster model of liquid [Emim][BF 4 ] (Table 4) are of the same order of magnitude as the analogous estimate of the enthalpy of C2HÁ Á Á[PF 6 ] À HB (2.1 kcal mol À1 ) 29 obtained for crystals of 1-(2 0 -hydroxylethyl)-3-methylimidazolium hexafluorophosphate ([C 2 OHmim][PF 6 ]). They are expectedly much smaller than the enthalpies of HBs formed by C2H and C5H moieties of the [C 2 OHmim] + cation with the much more HB-basic acetate anion [OAc] À (4.9 and 5.4 kcal mol À1 , respectively) in crystals of [C 2 OHmim][OAc]. 30 Nevertheless, both [Emim][BF 4 ] and [C 2 OHmim][OAc] bulk ILs have one common feature, namely, a rather moderate difference between the enthalpies of HBs formed by the C2H and C5H moieties of the imidazolium ring. This counterintuitive behavior of the C2H and C4H/C5H sites with the different acidity persists also in the case of the gas phase: the enthalpies of HBs C2HÁ Á Á[BF 4 ] À and C4HÁ Á Á[BF 4 ] À in isolated anion [Emim][BF 4 ] 2À differ by less than 10% (Table4).Another common specific of the above ''non-conventional'' charge-assisted HBs formed by CH moieties of the imidazolium ring is their significant strengthening in the gas phase relative to the bulk IL: cf. 3.9 or 3.7 kcal mol À1 in isolated [Emim][BF 4 ] 2 À or [Emim] 2 [BF 4 ] + ions, respectively, vs. 1.5 kcal mol À1 in ([Emim][BF 4 ]) 8 ; and 10.4 kcal mol À1 in the isolated [C 2 OHmim] [OAc] ion pair vs. 4.9 kcal mol À1 in the corresponding crystal. 30 4. Conclusions In this work, we applied an explicit solvation protocol for the quantum chemical simulation of the structure and IR spectra of bulk ILs [Emim][BF 4 ] and [Emim-d][BF 4 ]. We have shown that the solvation strongly modifies the frequencies and IR intensities of both cationic and anionic components of the ILs. The main features of the bulk spectrum are reproduced by the spectrum simulated for cluster ([Emim][BF 4 ]) 8

	) 4	2389 (13.8)
	([Emim-d][BF 4 ]) 5	2379 (14.8)
	([Emim-d][BF 4 ]) 6	2368 (39.1)
	([Emim-d][BF 4 ]) 7	2375 (22.3)
	([Emim-d][BF 4 ]) 8	2361 (40.6)

of

Table 4

 4 Geometric and spectroscopic parameters computed for [Emim] + and its various associations. Frequencies (in cm À1 ) of isotopically isolated stretching vibrations n str (C2H), and the IR intensities in km mol À1 (in parentheses); interatomic distances r(C2H) and r(HÁ Á ÁF), in Å; enthalpy of HB CHÁ Á Á[BF 4 ] À , ÀDH HB (kcal mol À1 ) according to eqn(1). The same parameters for C4H and C5H are given in italics n str (C2H) a r(C2H) r(HÁ Á ÁF). The sum of van der Waals radii E 2.6 Å. ÀDH HB Scaled with 0.979. b Computed for C4H. c Computed for C5H.

	[Emim] +	3174 (17) 1.074
		3176 (9) b 1.074 b
	3177 (9) c 1.074 c À 3075 (306) 1.080 1.961 [Emim][BF 4 ] 2 3180 1.078 b 2.039 b	3.9 3.6 b
		(239) b
	[Emim] 2 [BF 4 ] + 3143 (283) 1.076 2.111	3.7
	([Emim][BF 4 ]) 8 3175 (88) 1.072 2.150 3178 (52) c 1.073 c 2.159 c	1.5 1.2 c
	a

Acknowledgements

The authors are grateful to Prof. S. Grimme for permission to use program QCG 11 and computational facilities of Mulliken Center for Theoretical Chemistry (Institut fu ¨r Physikalische und Theoretische Chemie der Universita ¨t Bonn). Useful advice from Prof. P. M. Tolstoy, and Dr E. Y. Tupikina is gratefully acknowledged (SAK).