Improving the reliability of, and confidence in, DFT functional benchmarking through active learning

Validating the performance of exchange-correlation functionals is vital to ensure the reliability of DFT calculations. Typically, these validations involve benchmarking datasets. Currently, such datasets are typically assembled in an unprincipled manner, suffering from uncontrolled chemical bias, and limiting the transferability of benchmarking results to broader chemical space. In this work, a data-efficient solution, based on active learning, is explored to address this issue. Focusing -- as a proof of principle -- on pericyclic reactions, we start from the BH9 benchmarking dataset, and design a chemical space around this initial dataset by combinatorially combining reaction templates and substituents. Next, a surrogate model is trained to predict the standard deviation of the activation energies computed across a selection of 20 distinct DFT functionals. With this model, the designed chemical space is explored, enabling the identification of challenging regions, for which representative reactions are subsequently acquired. Remarkably, it turns out that the function mapping molecular structure to DFT functional divergence is readily learnable; convergence is reached upon the acquisition of less than 100 reactions. With our final model, a more challenging -- and arguably more representative -- pericyclic benchmarking dataset is curated, and we demonstrate that the functional performance has changed significantly compared to the original BH9 subset.