Introduction

Room-temperature ionic liquids (RTILs) have gained a wide variety of attentions and applications in recent years [1]. They are salts with a bulky and asymmetric organic cation, which inhibits an ordered crystalline structure to form, and have low melting points (melting points below 100 °C). RTILs posses very low vapor pressure and are nonflammable, which provide an environmentally friendly alternative to organic solvents [2–5]. They have great potential applications in CO2 removal process due to its stability and non-volatile nature [6, 7]. Their electrochemical and thermal stability also make them a potential replacement of existing electrolytes for high efficiency electrochemical devices [8, 9].

Hexafluorophosphate ([PF6]−) based RTILs are a class of most widely used RTILs in many fields. However, [PF6]− anion is hydrolytic unstable at high temperature: HF is produced following the reaction between [PF6]− anion and water. By introducing hydrophobic pentafluoroethyl groups to replace some fluorine atoms, Ignat’ev and his co-workers [10] synthesized a new RTIL anion: tris(pentafluoroethyl)-trifluorophosphate ([FAP]−). Due to its unique properties, it shows promising applications in many fields since its birth. [FAP]− based RTILs are hydrolytic stable, and are the most hydrophobic of all RTILs which have been synthesized: their water uptakes are more than 10 times less in comparison with the [PF6]− based RTILs [10]. Together with their negligible vapor pressures, [FAP]− based RTILs were proposed as an ideal extraction solvents in separation processes, especially in the sampling of large volumes of aqueous solutions [11]. Indeed, [FAP]− based RTILs show much higher selectivity and capacity at infinite dilution than the generally used organic solvents [12]. Due to their hydrolytic stability and low viscosity, they are also very promising in tribological applications: tribological tests showed very low friction coefficient while [FAP]− based RTILs were used as neat lubricant [13, 14], and the anti-friction and anti-wear performance of the base oil were substantially improved when [FAP]− based RTILs were used as an additives [15, 16]. They have a very broad electrochemical window, which offers perspectives for increasing the maximum voltage in supercapacitor applications or other electrochemical devices [17]. Computational screening predicted [FAP]− based RTILs should increase the solubility of CO2 compared to a wide range of conventional anions, and it was confirmed experimentally: [FAP]− based RTILs can absorb more than 70 % more CO2 relative to PF\(_{6}^{-}\) based RTILs [18–20].

All these interesting physicochemical properties of [FAP]− based RTILs, which in turn are governed by the interactions prevailing between their cations and anions [21–23], make [FAP]− based RTILs a class of very attractive ionic liquids. The growing interests in [FAP]− based RTILs require better understanding of the mechanism behind all these interesting physical properties. Recently Althuluth et al. [24] studied the gas solubilities in [Emim]+[FAP]− using Peng-Robinson Equation of State. As far as we know no other theoretical studies about [FAP]− based RTILs were reported. In this work, the molecular interactions between the cation [Emim]+ and the anion [FAP]− was investigated using density functional theory.

Quantum mechanical method

Calculations were performed at Density Functional Theory (DFT) level with the hybrid functional B3LYP, which incorporates Becke’s three-parameter exchange functional [25] and the Lee, Yang, and Parr correlation functional [26] using the Gaussian 09 program [27]. The 6-31+G(d, p) basis sets [28] implemented in the Gaussian program were used. The geometries of ion pairs were fully optimized at the B3LYP/6-31+G(d, p) level, and the basis set superposition error (BSSE) [29] was corrected for all interaction calculations using the counterpoise method [30, 31]. Zero-point energies (ZPE) were also corrected for all optimized structures, and frequencies were calculated to ensure that no imaginary components existed. Natural bond orbital (NBO) [32] and atoms in molecules (AIM) [33, 34] analyses were carried out by programs implemented in the Gaussian 09 and Firefly QC package [35] to study the interactions between ion pairs. Vibrational frequencies were assigned by visualizing displacements of atoms around their equilibrium positions and through Potential Energy Distribution (PED) analysis.

Experimental

Chemical

1-Ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate (CAS# 377739-43-0) was purchased from EMD Chemicals and used without further purification.

Infrared and raman spectroscopy

The IR spectrum was collected from 400 to 4000 cm−1 on an attenuated total reflection (ATR) module with a Nicolet Model 360 FTIR at 2 cm−1 nominal resolution. The number of reflections at the diamond crystal surface is “1”, and the penetration depth of the system is approximately one-fifth of the wavelength. For the measurement, a droplet of the IL was placed on the ATR crystal under dry nitrogen flow.

Results and discussion

Geometric analysis

Both computational and experimental works [36, 37] showed that the ethyl group bound to the imidazolium ring in [Emim]+ ion is able to rotate to yield different conformers, and there exist two stable [Emim]+ structures: a planar C s structure and a non-planar C1 structure (Fig. 1). Umebayashi et al. reported the presence of both conformers in RTIL [Emim]+[PF6]− at a population of 3:2 [37], and our calculations showed the C1 structure is slightly favored (2.3 kJ/mol) than C s structure.

Fig. 1
figure 1

[Emim]+ cation conformers optimized at the B3LYP/6-31+G∗∗ level. (a): C s planar structure. (b): C1 non-planar structure. The non-planar structure is slightly more stable than planar structure by 2.3 kJ/mol

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In another side, [FAP]− is reported as a mixture of two isomers: a meridional structure with C s symmetry and a facial structure with C3 symmetry (Fig. 2). Our calculations showed that meridional isomer is 7.1 kJ/mol more stable than facial isomer. The meridional isomer is preferably generated in the synthesis reaction but both isomers’ coexistence were observed by NMR spectroscopy at a ratio of 85:15 (meridional:facial) [10].

Fig. 2
figure 2

[FAP]− anion conformers optimized at the B3LYP/6-31+G** level. (a): C3 facial structure. (b): C s meridional structure. The meridional structure is more stable than facial structure by 7.1 kJ/mol

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Due to these small energy difference, it is certainly expected that both of the conformers from cation and anion exist in RTIL [Emim]+[FAP]−. Both meridional and facial isomer of [FAP]− anion were placed around planar and non-planar conformer of [Emim]+ cation in various positions to begin geometric optimizations. Four most stable structures of [Emim]+[FAP]− ion pair were located during optimization calculations, and they are shown in Fig. 3. These stable geometries were confirmed to be local minima on the potential energy surface through vibrational frequency analysis (no imaginary components). Their energies (E), along with zero-point vibrational energy corrections, are listed in Table 1.

Fig. 3
figure 3

Optimized stable [Emim]+[FAP]− ion pair structures. Relative energy in kJ/mol. [FAP]− is facial in structures (a) and (b), and meridional in structures (c) and (d); [Emim]+ is planar conformer in structure (d), and non-planar in structures (a), (b), and (c)

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Table 1 Energiesa, energies with ZPE corrections, interaction energiesa, Natural Energy Decompositon Analysis (NEDA), and dispersion interactions for different [Emim]+[FAP]− conformations
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Among the four stable structures (shown in Fig. 3), the only structure in which [Emim]+ takes the C s planar conformer is structure (d) and it is least stable. Structure (a) and (b) consist of facial [FAP]− structure and structure (c) and (d) consist of meridional [FAP]− structure. The energy difference between structures (a) and (c) is almost negligible (1.3 kJ/mol), which means the isomer structure of [FAP]− ion is not crucial for the stabilization.

AIM analysis

AIM analysis [38] was carried out to identify the interactions between [Emim]+ cation and [FAP]− anion. In AIM analysis, critical points are identified as the points where all components of the gradient of electron density vanish. They are classified by the number and sign of eigenvalues from the Hessian matrix of molecular electron density at the point. A bond critical point is a critical point with three non-zero eigenvalues and exactly one of them is negative. An electron density at the bond critical point in the range of 0.002-0.035 has been proposed as a criterion to confirm and characterize existence of a hydrogen bond [33, 34].

For the most stable [Emim]+[FAP]− structures (a) and (c) (Fig. 3), eight and seven inter-ionic bond critical points were identified respectively by AIM analysis and electron densities at these located bond critical points were shown in Figs. 4 and 5. The electron densities at these points are all in range of 0.002-0.023, which confirm the existence of hydrogen bondings. For both structures (a) and (c), the strongest hydrogen bondings exist between the F atoms of [FAP]− and H atom which bonded to C(2) of [Emim]+ (atomic numbering refers to Figs. 6 and 7). Structures (a) and (c) are much more stable than structures (b) and (d) (Fig. 3) because of short distances between [FAP]− anion and C(2)-H of [Emim]+ cation.

Fig. 4
figure 4

[Emim]+⋯[FAP]− inter-ionic hydrogen bonding for structure (a). Critical bond points are marked by green points, and electron densities at inter-ionic critical bond points are shown aside

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Fig. 5
figure 5

[Emim]+⋯[FAP]− inter-ionic hydrogen bonding for structure (c). Critical bond points are marked by green points, and electron densities at inter-ionic critical bond points are shown aside

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Fig. 6
figure 6

(a): Atom numbering scheme of most stable [Emim]+[FAP]− ion pair conformation with facial [FAP]− structure. (b) Corresponding difference electron density (Δ ρ=ρ ion pair−ρ cation−ρ anion) map. Purple region is where Δ ρ>0 and turquoise region is where Δ ρ<0

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Fig. 7
figure 7

(a): Atom numbering scheme of most stable [Emim]+[FAP]− ion pair conformation with meridional [FAP]− structure. (b) Corresponding difference electron density (Δ ρ=ρ ion pair−ρ cation−ρ anion) map. Purple region is where Δ ρ>0 and turquoise region is where Δ ρ<0

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Inter-ionic interactions induce the electron density reorganization between cations and anions. The reorganization can be presented by plotting the difference in electron density (Δ ρ=ρ i o n p a i r −ρ cation−ρ anion) map. The difference electron density maps for the most stable [Emim]+ [FAP]− conformations were plotted in Figs. 6 and 7. The purple region shows where electron density is enhanced, and the turquoise region is where electron density is depleted. Note that bonds in the region where electron density is enhanced are strengthened, and bonds in the region where electron density is depleted are weakened. It is important to note that all inter-ionic critical bond points are situated in the purple region where electron density increases.

Interaction energies

Interaction energies were calculated as the difference between the energies of the cation-anion pair and the sum of the energies of the sole cation and anion species,

$$E(\text{int})=E(\text{[Emim]}^{+}\text{[FAP]}^{-}) -E(\text{[Emim]}^{+})-E(\text{[FAP]}^{-})$$

The counterpoise approach [30] was applied to correct basis-set superposition error (BSSE) [29] and results are shown in Table 1. Comparing to the reported interactions for [Emim]+[PF6]− ion pairs which are around 364 kJ/mol [39] (329 kJ/mol at our calculation level, as Table 1 shown), interactions for [Emim]+[FAP]− ion pairs (around 280 kJ/mol) are much weaker. The weakened interactions are proposed to be important for ILs: they possibly enable more free volume in ILs and result in an enhanced CO2 capture ability [40].

To investigate the origin of this interaction decrease, Natural Energy Decomposition Analysis (NEDA) [32, 41, 42] were carried out. NEDA identifies interactions into three components: electrical component, core component, and charge transfer component. Electrical component represents the classical-like Coulombic interactions, core component represents repulsions at the equilibrium position which is inside van der Waals contact, and charge transfer represents delocalization interactions between subunits:

$$\varDelta E=E(\text{Electrical}) + E(\text{Core}) + E(\text{Charge Transfer}) $$

The NEDA results for most stable [Emim]+[FAP]− conformers are shown in Table 1. As an ionic liquid, it was expected that the electrical components are the largest individual contributors to the total interactions between cation and anion. The charge transfer was shown clearly as another very important component.

Comparing the NEDA results between optimized [Emim]+[PF6]− ion pair and [Emim]+[FAP]− ion paris (Table 1), it suggests that the decrease in interaction energies from [Emim]+[PF6]− to [Emim]+[FAP]− are mainly due to the electrical component. This is reasonable since the distance between cation and anion increases from [Emim]+[PF6]− ion pairs to [Emim]+[FAP]− ion pairs due to bulky [FAP]− ion.

Another interaction component which should be investigated is the dispersion term, which is important but not included in DFT calculations. To estimate the dispersion interactions between [Emim]+ cation and [FAP]− anion, the interactions were recalculated at RHF and MP2 levels respectively, and their difference were calculated as dispersion interactions (Table 1). It was shown that comparing to charge transfer or electrical term, dispersion interaction is much weaker for [Emim]+[FAP]− IL. DFT theory, despite the fact of missing dispersion term, is usually quite successful in predicting accurate structure and vibrational spectra of ILs.

Vibrational spectra and spectral assignments

Harmonic vibrations for most stable [Emim]+[FAP]− ion pairs were calculated at B3LYP/6-31+G** level and scaled by a factor of 0.964 [43] to compared to experimental Raman and infrared spectra (Fig. 8). The correlation diagram between calculated frequencies and experimental frequencies shows a correlation coeffcient 0.9998 (Fig. 9).

Fig. 8
figure 8

Raman and IR spectra of [Emim]+[FAP]−. Range from 400 cm−1 to 3500 cm−1

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Fig. 9
figure 9

Correlation diagram for the experimental vibrational spectrum of [Emim]+[FAP]− versus calculated frequencies at B3LYP/6-31+G(d,p) level with a scaling factor of 0.964. The correlation coefficient is 0.9996 for IR and 0.9998 for Raman

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Vibrational peaks were assigned (Table 2) by visualizing displacements of atoms around their equilibrium positions and through Potential Energy Distribution analysis. The most strong peak in the Raman spectrum is located at 748 cm−1. This band is assigned to a ring H-C=C-H symmetric out-of-plane bending. The band region between 2700 and 3200 cm−1 is the CH stretching region. Although it was pointed out that the origin of this CH vibrations profile is very complicated [44], they are potential spectroscopic probes for the inter-ionic interactions [45].

Table 2 Vibrational assignments of experimental and computed IR and Raman spectra of [Emim]+[FAP]−.a,b,c The calculated spectra were corrected using scaling factor of 0.964 at B3LYP/6-31+G(d, p) level
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Conclusion

In summary, two stable ion pair conformers were predicted using DFT among several other possibilities for the Ionic liquid [Emim]+[FAP]−. [Emim]+ cation adopts a non-planar orientation and the [FAP]− anion adopts both facial and meridional structures in the most stable conformation. Atoms-in-molecules (AIM) analysis indicated the existence of several inter-ionic hydrogen bonds in the ion pair. Interaction energy calculations indicate that [Emim]+[FAP]− has weaker inter-ionic interactions compared to the [Emim]+[PF6]− ion pair. Further, Natural Energy Decomposition Analysis (NEDA) calculations conclude that the decrease in the interaction energy is mainly due to the electrical component, which include both the electrostatic (ES) and polarization (POL) contributions. Assignments of the experimental and computed IR and Raman spectra were done by visualizing displacement of atoms around their equilibrium positions and through Potential Energy Distribution (PED) analysis.