From Local Atomic Environments to Molecular Information Entropy.

The similarity of local atomic environments is an important concept in many machine learning techniques, which find applications in computational chemistry and material science. Here, we present and discuss a connection between the information entropy and the similarity matrix of a molecule. The resulting entropy can be used as a measure of the complexity of a molecule. Exemplarily, we introduce and evaluate two specific choices for defining the similarity: one is based on a SMILES representation of local substructures, and the other is based on the SOAP kernel. By tuning the sensitivity of the latter, we can achieve good agreement between the respective entropies. Finally, we consider the entropy of two molecules in a mixture. The gain of entropy due to the mixing can be used as a similarity measure of the molecules. We compare this measure to the average and best-match kernel. The results indicate a connection between the different approaches and demonstrate the usefulness and broad applicability of the similarity-based entropy approach.