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 density functional theory (DFT) calculations. Typically, these validations involve benchmarking data sets. Currently, such data sets are usually assembled in an unprincipled manner, suffering from uncontrolled chemical bias, and limiting the transferability of benchmarking results to a 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 data set and design a chemical reaction space around this initial data set 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 reaction space is explored, enabling the identification of challenging regions, i.e., regions with large DFT functional divergence, for which representative reactions are subsequently acquired as additional training points. Remarkably, it turns out that the function mapping the molecular structure to functional divergence is readily learnable; convergence is reached upon the acquisition of fewer than 100 reactions. With our final updated model, a more challenging─and arguably more representative─pericyclic benchmarking data set is curated, and we demonstrate that the functional performance has changed significantly compared to the original BH9 subset.