## 3 Results and Discussion
### TDDFT Results  
In this section, we will compare the results of the TD-DFT calculations, as described in the computational section. In Figure 3, we show the correlation between the calculated wavelength of the maximum of the absorption CT band of the model cluster and the experimental values reported in Tables 1 and 3. First we note that by using a double-\(\zeta\) and or a triple-\(\zeta\) basis set, namely the 6-31+G(d,p) and the aug-cc-pVTZ with the CAM-B3 LYP functional, the calculated absorption spectra change very  
Figure 1: Optimized geometries in CH\({}_{2}\)Cl\({}_{2}\) of: (**a**) MVI\({}_{2}\); (**b**) MVBr\({}_{2}\); (**c**) MTMVI\({}_{2}\); (**d**) MV(PF\({}_{6}\))\({}_{2}\). Graphics produced with VMD [35]. Figure 2: Geometrical parameters of the energy minimized structures vs. the dielectric constants of the solvent (vacuum, \(n\)-hexane, dichloromethane, acetone). (**a**) Average distance between each pyridinium nitrogen and the closest anion’s center of mass and (**b**) dihedral angle between the two pyridinium rings. (black circles): MV(PF\({}_{6}\))\({}_{2}\); (red squares): MVBr\({}_{2}\); (green triangles): MTMVI\({}_{2}\); (blue rhombi): MVI\({}_{2}\). little, as we can appreciate by inspecting the corresponding columns in Table 3. Therefore, all the remaining calculations were run using the smaller basis set of double-\(\zeta\) quality which strongly reduces the computational burden. Concerning the functionals used, we note that the correlation itself is always rather good, with relatively high correlation coefficients R\({}^{2}\) for all levels of theory used. Nevertheless, some of the functionals strongly overestimate the slope of the correlation, namely PBE0, while others underestimate it, for example, LC-\(\omega\)HPBE. Also CAM-B3 LYP and \(\omega\)B97-XD do not perform particularly well. In contrast, M06-2X gives calculated values of \(\lambda_{\text{max}}\) in very good agreement with the experimental values. Not only the correlation is good, but also the slope of the fitting line is close to unity and the mean absolute error (MAE) is significantly smaller than for the other cases. The calculated results, at the M06-2X level, appear to be only systematically shifted to lower values, compared to experiments, by a roughly constant value. The result obtained at the M06-2X(PCM)/6-31+G(d,p)//B3 LYP-D3(PCM)/6-31G+(d,p), represent, therefore, the ones in better agreement with experiments among the protocols tested. At the same time, this is a relatively cheap protocol from a computational point of view. The predicting power of the protocol is extremely high if we consider that we are concerned with intermolecular CT bands between anions and cations, therefore noncovalently bound donors and acceptors. Moreover, the experimental  
Figure 3: Correlation between calculated (\(\lambda_{\text{calc}}\)) and experimental (\(\lambda_{\text{expt}}\)) maximum wavelength absorption of the most red-shifted band of the model systems corresponding to the experimental values of Tables 1 and 3 at three different levels of theory, TD-DFT(PCM)/6-31+G(d,p). See Table 3 for complete data. Solvent reaction field is included in the TD-DFT calculation (either CH\({}_{2}\)Cl\({}_{2}\) or acetone).