# PyT\({}_{\mathbf{1,x}}\)TFSI Ionic Liquids (x = 1-8): A Computational Chemistry Study
## 1 Introduction  
Ionic liquids are a very wide class of materials with extremely varied properties and highly diversified potential ranges of application [1; 2]. Their use as solvents in battery electrolytes was proposed in the early 2000s and has so far been demonstrated for an extremely large number of ionic couples (e.g., pyrrolidinium, pyridinium, ammonium, imidazolium cations couples with hexafluorophosphate, bis-trifluoromethyl sulphonyl imide, trifluoromethyl sulphonate, and any other anions) [3; 4; 5]. Methyl-alkyl pyrrolidinium-based (PyrT\({}_{1,\mathbf{x}}\)) bis-trifluoromethyl sulphonyl imide (TFSI) ionic liquids have found in particular successful applications in many different novel aprotic battery formulations thank to their (a) large electrochemical stability, (b) facile synthesis, (c) extended thermal stability, and (d) good transport properties [6; 7; 8; 9; 10; 11]. The ability of PyrT\({}_{1,\mathbf{x}}\)TFSI ionic liquids to dissolve lithium and sodium salts [6; 7; 8] in particular allows researchers to obtain concentrated electrolytes suitable for real applications in Li-ion and Na-ion batteries with superior performance in terms of thermal stability [9; 10] and hazard mitigation [11]. Overall, the development of a new electrolyte formulation for any aprotic battery chemistry requires a complex compromise to balance different functional properties such as electrochemical stability, transport, viscosity, thermal stability,chemical stability, or stability of the metal ion coordination shells [12; 13]. Thus, knowledge of the physicochemical properties, such as ion pair structure, dissociation energies, and oxidation/reduction potentials, is fundamental to drive the screening and selection of innovative solvents [13].  
In this study, the analysis of the physicochemical properties of a homologous series of pyrrolidinium-based ionic liquids with general formula Pyr1,xTFSI (x = 1-8) have been tackled by first principles calculations based on the density functional theory using the Gaussian09 suite [14; 15; 16]. The molecular structures of isolated ions and ion pairs have been predicted by electronic structure calculations at B3 LYP [14; 15] level of theory in vacuum or in simulated solvents. Thermodynamic properties have been calculated to evaluate the ion pairs dissociation and oxidation/reduction stability.  
In the literature, the structure and physicochemical properties of Pyr1,xTFSI ionic liquids have been studies widely by many authors (see, as an example, [PERSON] and coworkers [15; 16], [PERSON] and coworkers [4; 7; 17], and us [9; 10]). These ionic molecules self-organize in the liquid phase in meso-domains where ionic and amphiphilic molecular fragments are clustered. This structural organization leads to the facile mobility of small size ions like Li+ [10; 17] and the easy dissociation of alkaline metal salts in a wide concentration range [6; 7]. Experimentally, the electrochemical stability and transport properties of many Pyr1,xTFSI ionic liquids have been reported [3; 7; 8; 10; 17] but a rational analysis of the impact of the size of the methyl-pyrrolidinium alkyl chain has not been reported so far The study presented here is the first systematic computational analysis of Pyr1,xTFSI (x = 1-8) molecules with a specific focus on the impact of the length of the alkyl chain on the overall physicochemical properties of the ion pair.