First and Second Reductions in an Aprotic Solvent: Comparing Computational and Experimental One-electron Reduction Potentials for 345 Quinones

Using reference reduction potentials of quinones recently measured relative to the saturated calomel electrode (SCE) in N,N-dimethylformamide (DMF), we benchmark absolute one-electron reduction potentials computed for 345 Q/Q●− and 265 Q●−/Q2− reactions using adiabatic electron affinities computed with density functional theory and solvation energies computed with three continuum solvation models; IEF-PCM, COSMO, and SM12. Regression analyses indicate a strong linear correlation between experimental and absolute computed Q/Q●− reduction potentials with Pearson's correlation coefficient r between 0.95-0.96 and mean absolute error (MAE) relative to the linear fit between 83.29-89.51 mV for different solvation methods when the slope of the regression is constrained to one. The same analysis for Q●−/Q2− gave a linear regression with r between 0.74-0.90 and MAE between 95.87-144.53 mV, respectively. The y-intercept values obtained from the linear regressions are in good agreement with the range of absolute reduction potentials reported in the literature for the SCE but reveal several sources of systematic error. The y-intercepts from Q●−/Q2− calculations are lower than those of Q/Q●− by around 400 mV for PCM and SM12 and 200 mV for COSMO. Systematic errors also arise between molecules having different ring sizes (benzoquinones, naphthoquinones, and anthraquinones) and different substituents (titratable vs. non-titratable). SCF convergence issues were found to be a source of random error that were slightly reduced by directly optimizing the solute structure in the continuum solvent reaction field. While SM12 MAEs were lower than those of PCM and COSMO for Q/Q●−, SM12 had larger errors for Q●−/Q2− pointing to a limitation when describing multiply charged anions in DMF. Together, the results highlight the advantage of---and further need for---testing computational methods using a large experimental data set that is not skewed (e.g., having more titratable than non-titrable substituents on different parent groups or vice versa) to help further distinguish between sources of random and systematic errors in the calculations.