Predicting Redox Potentials With Rowan

why it matters; insensitivity to theoretical precision; our workflow; applications

The redox potential is a quantity which measures how difficult it is to add or remove electrons from a molecule. This is pretty important in synthetic organic chemistry: single-electron chemistry has become the cornerstone of a lot of new synthetic methods (photoredox, electrochemistry, odd-electron Ni/Cu chemistry, etc), and understanding the redox potential of different species can be critical in predicting whether a reaction will work well or fail miserably.

There are broad trends to redox potentials, as shown below. Negative voltages indicate reduction (adding electrons), while positive voltages indicate oxidation (removing electrons). But redox potentials are quite sensitive to substitution effects, so unless your precise compound has been studied before it’s helpful to measure or compute the value.

Figure 2 from Nicewicz et al, Synlett, 2016 (link).

People have been interested in computing redox potentials for a while. Since redox processes involve a change in overall charge, like pKa, they’re difficult to compute with extreme accuracy—implicit solvent methods are notoriously inaccurate at predicting free energies of solvation for charged species. Hagen Neugebauer and co-workers benchmarked redox potential calculations in 2020 and found that a standard DFT method, B97-D3/def2-QZVPP, predicted redox potentials for organic molecules with a mean absolute error of 0.27 V. Moving to the (expensive) double-hybrid functional PWPB95-D4 only reduced the error to 0.22 V, and switching to xTB, a fast semi-empirical method, only increased the error to 0.30 V.

The low sensitivity of these errors to the quality of the underlying theory may be frustrating for theorists, but it’s great news for us pragmatists here at Rowan—since errors from solvent makes it impossible to get perfectly accurate results, why not get pretty good results extremely fast? Accordingly, we’ve developed a rapid redox potential prediction workflow: we use GFN2-xTB, speed things up by skipping the Hessian calculation (assuming that the change in vibrational modes between the reduced and oxidized species is small), and use the new CPCM-X method from Grimme and co-workers to get better free energies of solvation.

Our final results are pretty much the same as Neugebauer et al report—we get an MAE of 0.32 V on the OROP benchmark set after excluding a few values that don’t start from a neutral species or aren’t in acetonitrile:

To counterbalance the slightly increased error, our method is extremely fast—the median calculation in OROP takes 1.1 seconds on my laptop! This allows redox potentials to be calculated basically instantly through Rowan’s web interface. We’ve made a video demonstrating this, shown here (Youtube link):

We hope that this method can be useful for organic chemists everywhere—happy computing!