A notable example comes from Guan et al., where the authors combined machine-learned representation from molecular structures with QM descriptors to create a fused reactivity representation. Using this approach, they implemented a QM-augmented graph neural network (QM-GNN) using the Weisfeiler-Lehman network (WLN) as the GNN architecture to predict reaction regioselectivity for 3,003 electrophilic aromatic substitution reactions. They computed and utilized Hirshfeld partial charges, nucleophilic and electrophilic Fukui indices, and NMR shielding constants as atom descriptors, along with bond orders and bond lengths as bond descriptors. Since calculating QM descriptors for each new molecule would not be amenable to high-throughput inference, they also developed a multitask constrained D-MPNN model to quickly predict QM descriptors on the fly. Their findings demonstrated that incorporating QM descriptors can improve the ML model performance in terms of accuracy and reduce the need for extensive training data, although the benefits of QM descriptors diminish as more training data are used. In particular, replacing QM-calculated descriptors with ML-predicted ones (termed ml-QM-GNN in their work) maintained high performance and outperformed the baseline GNN model, especially in models trained on smaller datasets, showcasing the advantages of using hybrid representations to potentially achieve improved model performance with limited data. However, subsequent studies suggest that the effectiveness of including QM descriptors varies with specific tasks. Stuyver and Coley further explored the performance, generalizability, and explainability of ml-QM-GNN in predicting regioselectivity for substitution reactions and predicting activation energy for competing E2/S N 2 reactions in the gas-phase. Their results indicated that this approach could outperform purely structure-based GNNs in datalimited regimes, making it appealing for tasks with limited experimental data availability.