Next, we used HDBSCAN to cluster the molecules based on proximity, as shown in Figure ). HDBSCAN takes as input the reduced dimension data from UMAP and outputs a number for each datapoint. It is a soft clustering, not creating distinct categories but instead giving molecules a rating between 0 and 1 (or -1 for no cluster, as approximately 1/3 of the molecules were unable to be clustered) and 100 distinct clusters were created manually from these ratings. We used a minimum cluster size of 10 and the leaf cluster selection method. We can see that HDBSCAN effectively clusters molecules in space, with most molecules in close proximity included in the same cluster. Some of the clusters themselves are spread out across space, such as the purple cluster that includes many molecules along the edge of the global space. Note that this is a dataset-agnostic clustering, as the clustering algorithm only sees molecular information and no labelled data. More details about the HDBSCAN algorithm can be found in their paper and website. A natural question is whether each cluster as defined by HDBSCAN has a particular error associated with it. For example, it seems that xTB-sTDA does a relatively good job for the red cluster, but over-predicts energies for molecules in light blue, purple, and orange clusters. In contrast, the dark green and red clusters seem to have low errors. Although HDBSCAN is a soft clustering, we can categorize molecules into 100 distinct clusters based on the number assigned to them, as well as 2 additional clusters (1 each for unclustered molecules and for outliers). Figure quantifies the mean errors for S 1 and T 1 energies for each cluster.