Machine learning-aided first-principles calculations of redox potentials

We present a method combining first-principles calculations and machine learning to predict the redox potentials of half-cell reactions on the absolute scale. By applying machine learning force fields for thermodynamic integration from the oxidized to the reduced state, we achieve efficient statistical sampling over a broad phase space. Furthermore, through thermodynamic integration from machine learning force fields to potentials of semi-local functionals, and from semi-local functionals to hybrid functionals using Δ-machine learning, we refine the free energy with high precision step-by-step. Utilizing a hybrid functional that includes 25% exact exchange (PBE0), this method predicts the redox potentials of the three redox couples, Fe 3+ /Fe 2+ , Cu 2+ /Cu + , and Ag 2+ /Ag + , to be 0.92, 0.26, and 1.99 V, respectively. These predictions are in good agreement with the best experimental estimates (0.77, 0.15, 1.98 V). This work demonstrates that machine-learned surrogate models provide a flexible framework for refining the accuracy of free energy from coarse approximation methods to precise electronic structure calculations, while also facilitating sufficient statistical sampling.