# PyT\({}_{\mathbf{1,x}}\)TFSI Ionic Liquids (x = 1-8): A Computational Chemistry Study
## 2 Materials and Methods  
The density functional theory (DFT) was adopted to calculate molecular properties of ions and ion pairs and to make thermodynamic predictions following the same approach validated by us in [18]. A B3 LYP functional [19] was adopted within the 6-31++g(d,p) basis set [20] in the final calculations. The choice of the B3 LYP functional has been done to follow the same computational approach illustrated by [PERSON] [21] and considering [18]. In this last study, we estimated the mean accuracy of various density functionals (either purely DFT or hybrid) compared to post-Hartree Fock (post-HF) methods. Apparently, post-HF methods, like MP2, are still too computational expensive to deal with large molecules with few tenths of atoms, thus B3 LYP is still an optimal compromise to achieve reasonable accuracy on energetics. Based on our previous method validation, the computational accuracy has been evaluated in approximately 8 kJ mol\({}^{-1}\). In all calculations, we incorporated solvation effects by employing a self-consistent reaction field in continuum solvation model C-PCM [22; 23]. As model solvents, we used tetrahydrofuran (dielectric constant \(\varepsilon\) = 7.42) to mimic the low dielectric constant of Pyr1,xTFSI pure ionic liquids [24; 25]. Simulating ion pairs requires a careful screening of the multiple possible configurations. Here, four ion pairs configurations were pre-evaluated for each molecular system to identify the most stable one. The computational protocol follows this procedure: (a) cations and ions are optimized individually in vacuum and in simulated solvent using the level of theory discussed above; (b) four different starting structures for each ion pair are identified using the SECIL code [21] that generates automatically and \"mindlessly\" a preset number of pair configurations; (c) these preliminary configurations are relaxed to local minima using the Hartree-Fock 6-31 g(d,p) method and the simulated solvent; (d) for each ion-pair, the configuration with the minimal total energy was selected. All molecular structures were relaxed to their minima: frequency calculations were performed to check that the minima all have real vibrational frequencies. The basis set superimposition error (BSSE) correction37 has been evaluated at the same level of theory for all ion pairs. All calculations have been carried out by using the Gaussian09 package [14]. The cartesian atomic position of all the optimized structures of ion pairs are reported in the Supplementary Material (Tables S1-S8). Molecular sizes have been calculated by evaluating the volume inside a contour of 0.001 electrons Bohr\({}^{-3}\) density. Ion pair Gibbs energy of dissociation energies in ions, i.e., \(\Delta_{\text{diss}}G^{\circ}{}_{298K}\), were obtained from the total energies by the simple equation:  
\[\Delta_{\text{diss}}G^{\circ}_{298K}\ =\ \left[G^{\circ}_{298K}(\textit{ cation})+G^{\circ}_{298K}(\textit{ anion})\right]-G^{\circ}_{298K}(\textit{ion pair}).\]  
Ionization energies (E\({}_{\text{ion}}\)) of anions were obtained in vacuum from the energy of each ions and the corresponding neutral molecule (open shell, doublet spin state) with one missing electron. The Franck-Condon approximation was assumed (vertical transitions), and thus, the energies of the neutral radicals were calculated from the nonrelaxed geometry of the corresponding anions following the method described by [PERSON] and coworkers [26; 27]. A similar approach has been adopted for the ionization energies of ion pairs as well as for the electron affinities (EA) of cations and neutral ion pairs. EA and E\({}_{\text{ion}}\) were converted to approximate oxidation and reduction potentials vs. Li\({}^{+}\)/Li, accordingly to what was suggested by [PERSON] and coworkers [12; 28]. In particular, to convert the EA and E\({}_{\text{ion}}\), in units of eV, to a relative potential in reference to the Li\({}^{+}\)/Li redox couple, a constant value (k) was subtracted from the calculated absolute potential.