The LIBE dataset presents a more challenging task due to its inclusion of spin-varying and charged species. Moreover, the dataset exhibits a wide range of molecular free energies which further add to the difficulty of learning energetics here. In pitting QTAIM/ML versus non-QTAIM models we note that our non-QTAIM models do directly describe spin and charge as one-hot encoded global features while the QTAIM/ML models add QTAIM features, including α spin, β spin, and spin density at each critical point, to further inform learning. Both models perform quite well with the top QTAIM/ML model yielding a reduced error on formation energies from 76.26 meV/Atom to 45.09 meV/Atom and an increased proportion of predicted energies within chemical accuracy to true labels (8.5% vs. 5.4%) versus its non-QTAIM equivalent (Table ). In addition, no discernible trends can be gleaned across pre- Here, there is no pronounced improvement in the learning curves between the two sets of models as QTAIM models have a slightly more aggressive learning curve -indicative of their ability to increase model generalizability at higher data regimes.