We report a systematic investigation of the far- and mid-infrared spectra of ionic liquids (ILs) containing the bis(fluorosulfonyl)imide (FSI) anion, both in the liquid state at room temperature and in solid phases at low temperatures. We extended to lower frequencies a previous study, and we observed four additional vibration bands below 500 cm-1, attributable to FSI. Moreover, DFT calculations of vibration frequencies were performed using three combinations of theory and basis set: (1) B3LYP/6-31G∗∗, (2) B3LYP/6-311 + G(3df) and (3) PBE0/6-31G∗∗. Model 1, largely used in the previous literature concerning ILs, shows the poorest performances; model 2, which generally gives a good agreement with the experiments, misses the vibration frequencies by ∼40 cm-1 in the range 650-900 cm-1 where one finds the largest spectral differences between cis- and trans-FSI; model 3 gives the best agreement with the experiments and, moreover, is much less time consuming than model 2. The comparison with calculations suggests that the band centered around 1217 cm-1 is a good marker of the occurrence of the cis-FSI conformer. Finally, the bands located around 730 and 750 cm-1 are attributable to cis- and trans- conformer of FSI, respectively. © 2015 Elsevier B.V.