Benchmark Study of Electrochemical Redox Potentials Calculated with Semiempirical and DFT Methods

The calculation of redox potentials by semiempirical quantum mechanical (SQM) approaches is evaluated with a focus on the recently developed GFN<i>n</i>-xTB methods. The assessment is based on a data set comprising 313 experimental redox potentials of small to medium-sized organic and organometallic molecules in various solvents. This compilation is termed as ROP313 (reduction and oxidation potentials 313) and divided for analysis purposes into the organic subset OROP and the organometallic subset OMROP. Corresponding data for a few common density functional theory (DFT) functionals employing extended AO basis sets and small basis-set DFT composite schemes are computed for comparison. Continuum solvation models are used to calculate the important solvation free energy contribution. The results for ROP313 show that the GFN<i>n</i>-xTB methods provide a robust, efficient, and generally applicable workflow for the routine calculation of redox potentials. The GFN<i>n</i>-xTB methods outperform the PM<i>x</i> competitor for the OROP subset (mean absolute deviation from the experiment, MAD_GFN2-xTB = 0.30 V, MAD_GFN1-xTB = 0.31 V, PM6-D3H4 = 0.61 V, PM7 = 0.60 V), almost reaching low-cost DFT quality (MAD_B97-3c = 0.25 V) at drastically reduced computational cost (2-3 orders of magnitude). All SQM methods perform considerably worse for the OMROP subset. Here, the GFN2-xTB still yields semiquantitative results slightly better and more robustly than with the PM<i>x</i> methods (MAD_GFN2-xTB = 0.74 V, PM6-D3H4 = 0.78 V, PM7 = 0.82 V). The proposed workflow enables large-scale quantum chemical computations of organic and, to a lesser extent, organometallic molecule redox potentials on common laptop computers in seconds to minutes of computation time enabling, e.g., screening of extended compound libraries.