## 3 Results and Discussion  
### Geometry  
As mentioned in the Materials and Methods Section, while experimental systems consist of dialkylviologens with relatively long alkyl chains (C\({}_{8}\) and C\({}_{10}\)), the model systems used in the calculations are the simpler methylviologens (C\({}_{1}\)). This structural difference is expected not to affect the comparison between calculated and experimental results since the optical properties of the viologen salts are not influenced by the length of the alkyl chain. In fact, recent experiments concerning the electrochemistry and UV-Vis properties of several alkyl and polyfluoroalkyl viologens revealed that the CV (Cyclic voltammetry) potentials and spectral properties are not affected by the chain length (though they are affected by the type of chain, alkyl vs. polyfluoroalkyl) [3]. Moreover, as we will see below, none of the relevant orbitals involved in the electronic transitions are localized on the methyl group of the model systems, but only on the bipyridinium core and anions, see also [34]. On the other hand, the weak electron-donor effect of the alkyl chain can be well-modelled by a simple methyl group. We first discuss the geometry of the model systems and its dependence on the solvent reaction field. In Table 2 we report some relevant structural parameters, that is the average X-N distance (with respect to the closest nitrogen) in the neutral cluster MVX\({}_{2}\), where MV represents a model viologen, and MTMV is a model 2,2',6,6'-tetramethyl methylviologen, and the anion X (Br\({}^{-}\), I\({}^{-}\) or P for PF\({}_{6}\)-), and the dihedral angle between the two aromatic rings of the cation. The optimized structures in CH\({}_{2}\)Cl\({}_{2}\) for the four model systems are shown in Figure 1. Finally, in Figure 2 we graphically show the trend of the geometrical parameters of Table 2 as a function of the dielectric constant of the solvent. First we note that, qualitatively, the structure in CH\({}_{2}\)Cl\({}_{2}\) of the neutral cluster MVBr\({}_{2}\), in Figure 1b, is quite different from the other ones. For the bromide case, each anion is approximately sitting on top of the pyridinium ring and the two pyridinium rings are strongly twisted (\(\varphi\sim\) 70\({}^{\circ}\)). The other systems, instead, feature the anion closer to the nitrogen and the twist of the two pyridinium units is smaller, see Table 2. The structure of the iodide viologen salt is qualitatively rather similar to the structure of iodide methylviologen in the solid state [36] since the anion is close to the positive nitrogen and to the ortho carbons of the pyridinium ring. However, the bipyrinium is planar in the solid state. The similarity with the solid state structure is much less for the bromide salt, both concerning the position of the anion as well as for the twist angle between the pyridinium units [36]. The geometry also appears to be influenced by the inclusion of a solvent reaction field in the optimization run. As expected for charged systems, the presence of a solvent decreases the strength of the electrostatic interaction compared to the gas phase. The effect is the largest for the bromide salt, with bromide being the hardest anion considered, and almost negligible for the PF\({}_{6}\) case, since the charge density is largely reduced in the hexafluorophosphate anion. Therefore the inclusion of the solvent in the optimization of the geometry is strongly recommended, and, especially for relatively low polar solvents, it makes a significant effect on the geometry, compared to vacuum. The effect, being a nonspecific reaction field only dependent on the dielectric constant (and geometric details of the cavity) levels off for dielectric constants larger than about 10 a result which is consistent with the dielectric response in the simpler Onsager model [37] of a dipole in a spherical cavity, which is \(2(\varepsilon-1)/(2\varepsilon+1)\)