Machine-Learning Energy Gaps of Porphyrins with Molecular Graph Representations

Molecular functionalization of porphyrins opens countless new opportunities in tailoring their physicochemical properties for light-harvesting applications. However, the immense materials space spanned by a vast number of substituent ligands and chelating metal ions prohibits high-throughput screening of combinatorial libraries. In this work, machine-learning algorithms equipped with the domain knowledge of chemical graph theory were employed for predicting the energy gaps of >12 000 porphyrins from the Computational Materials Repository. Among a variety of graph-based molecular descriptors, the electrotopological-state index, which encodes electronic and topological structure information, captures the energy gaps of porphyrins with a prediction RMSE < 0.06 eV. Importantly, feature sensitivity analysis suggests that the carbon structural motif in methine bridges connected to the anchor group predominantly influences the energy gaps of porphyrins, consistent with the spatial distribution of their frontier molecular orbitals from quantum-chemical calculations.