## 3 Results and Discussion
### Computational Results  
The vibration frequencies and infrared intensities of the lowest energy configuration of the EMI and TfO ions calculated at the B3 LYP/6-31G** level are reported in Table S1 of the Supplementing Information. These results are in good agreement with previous investigations on the same ions [32]. Recently, it has been shown that a good agreement between the calculated and the experimental infrared spectrum of the protic ionic liquid DEMA-TfO can be obtained by exploiting DFT calculations on the ionic couple with the \(\omega\)B97X-D functional, including empirical dispersion corrections and the presence of a polar solvent (dimethylformamide, \(\epsilon_{\mathrm{r}}\) = 37.22) [49]. Here, we want to investigate whether this better agreement is visible also in the case of the presently investigated non-protic IL. Figure 5 reports the optimized geometry of the lowest energy configuration of the EMI-TfO couple with the \(\omega\)B97X-D functional, considering the presence of a polar solvent. The TfO anion resides above the plane of the imidazolium cation, pointing the O atoms towards the C2 atom of EMI (C atom directly linked to the two N atoms of the imidazolium ion). The calculated distance between the H atom (H2) attached to C2 and the closest O (O1) atom of the anion is 2.23 A, a value very close to the value of 2.24 A reported for the solid phase of EMI-TfO, as obtained by X-ray diffraction experiments [51]. The calculated angle formed by the C2, H2 and O1 atoms is 136.6\({}^{\circ}\), a value slightly lower than the  
Figure 4: Dependence of the frequency of the vibration mode centered at 1031 cm\({}^{-1}\) at 0.1 GPa from the applied pressure. experimental value of 149\({}^{\circ}\), which, however, was reported for the solid phase of EMI-TFO [51]. It must be noted that the most evident change induced by considering the presence of a solvent in the DFT calculations is enlargement of the distance between anion and cation in similar ionic couples containing TFO [49], and, indeed, this approach allows to correctly evaluate the H2-O1 distance. After optimization of the geometry, the frequencies and intensities of the infrared vibration for the EMI-TFO couple were calculated (see Table S1 of the Supplementing Information). The derived absorbance is compared in Figure 6 with the experimental absorption spectrum at 110 and 330 K and with the calculated absorbance for the single, isolated ions in vacuum. In all cases, no scaling factors for the vibration frequencies were considered. Comparing the performances of the single ion and ionic couple calculations, one can observe in Figure 6 that the latter can properly account in the fir range for the two bands between 200 and 220 cm\({}^{-1}\), the band around 240 cm\({}^{-1}\), the three bands, visible at low temperatures, between 300 and 360 cm\({}^{-1}\) and the band at 440 cm\({}^{-1}\). In addition, the frequency position of the intense band experimentally detected around 520 cm\({}^{-1}\) is better predicted by the ion couple model. Moreover, in the mid-infrared  
Figure 5: Lowest energy configuration of the EMI–TFO ionic couple, obtained by DFT calculations employing the \(\omega\)B97X-D functional (including empirical dispersion corrections) and the 6-31G\({}^{**}\) basis set. The numbers are the distances of selected atoms, expressed in Å.  
Figure 6: Comparison of the experimental absorbance spectra of EMI–TFO at 110 and 330 K (top part of the panels) with the calculations (bottom part of the panels). For the isolated TFO ion, a frequency scaling factor of 0.97 was used. The panel (**a,b**) reports the far- (mid-) infrared range. range, this last model is able to predict the position and number of bands between 550 and 1100 cm\({}^{-1}\). Above such wavenumbers, the strong SO stretching vibrations seems to be concentrated in too narrow a frequency range and, finally, the CH bending modes are shifted to higher frequencies compared to the experiments.