In a new study, published in Proceedings of the National Academy of Sciences, researchers from Los Alamos National Laboratory have proposed incorporating more of the mathematics of quantum mechanics into the structure of the machine learning predictions. Using the specific positions of atoms within a molecule, the machine learning model predicts an effective Hamiltonian matrix, which describes the various possible electronic states along with their associated energies. Compared to traditional quantum chemistry simulations, the machine learning-based approach makes predictions at a much-reduced computational cost. It enables quantitatively precise predictions regarding material properties, allows interpretable insight into the nature of chemical bonding between atoms, and can be used to predict other complex phenomena, such as how the system will respond to perturbations, such as light-matter interactions. The method also provides greatly improved accuracy relative to traditional machine learning models, and demonstrates success in transferability, i.e., the ability of the model to make predictions that go well beyond the data that formed the basis of its training.