Theoretical determination of half-wave potentials for phenanthroline-, bipyridine-, acetylacetonate-, and...

We report a protocol for the evaluation of theoretical half-wave potential (E_1/2) using a set of 22 mixed chelate copper (II) complexes containing 1,10-phenanthroline and 2,2'-bipyridine derivatives as primary ligands, and acetylacetonate or glycinate as secondary ligands (formally from the Casiopeínas® family) for which accurate experimental values were determined in a 2/5 mixture of ethanol/water. We have calibrated the BP86, PBE, PBE0, B3LYP, M06-2X, and ω-B97XD functionals, using the Los Alamos LANL2DZ and Stuttgart-Köln SDDAll effective core potentials for the Cu and Fe atoms and the 6-311+G* basis set for the C, H, O, and N atoms. To address the solvent effects, we have saturated the first solvation shell with up to 9 water molecules for the explicit model and compared it with the Continuum Like-Polarizable Continuum Model (CPCM) implicit solvent scheme. We found that the PBE/LANL2DZ-6-311+G* protocol (with the CPCM implicit solvent scheme with an effective dielectric constant ε = 64.9121 for the 2/5 mixture of ethanol/water) yields the overall best performance. The theoretical values are compared with experimental data, three of which are reported here for the first time. We find good correlations between the theoretical and experimental E_1/2 values for the 2,2'-bipyridine derivatives (R² = 0.987, MAE = 86 mV) and 1,10-phenanthroline derivatives (R² = 0.802, MAE = 58.4 mV). The correlation trends have been explained in terms of the copper atom's ability to be reduced in the presence of the ligands. The Gibbs free energy differences at 298 K obtained for the redox reactions show that the more flexible secondary ligands (acetylacetonate) lead to larger entropic contributions which, as expected, increase the average MAE values as compared with the more rigid ligands (glycine). The present protocol yields lower MAEs as compared with previous approaches for similar mixed and flexible Cu(II) complexes.