Extended Hückel tight-binding approach to electronic excitations

Machine learned Hückel theory: Interfacing physics and deep neural networks

The Hückel Hamiltonian is an incredibly simple tight-binding model known for its ability to capture qualitative physics phenomena arising from electron interactions in molecules and materials. Part of its simplicity arises from using only two types of empirically fit physics-motivated parameters: the first describes the orbital energies on each atom and the second describes electronic interactions and bonding between atoms. By replacing these empirical parameters with machine-learned dynamic values, we vastly increase the accuracy of the extended Hückel model. The dynamic values are generated with a deep neural network, which is trained to reproduce orbital energies and densities derived from density functional theory. The resulting model retains interpretability, while the deep neural network parameterization is smooth and accurate and reproduces insightful features of the original empirical parameterization. Overall, this work shows the promise of utilizing machine learning to formulate simple, accurate, and dynamically parameterized physics models.

Development of Multimodal Machine Learning Potentials: Toward a Physics-Aware Artificial Intelligence

Machine learning interatomic potentials (MLIPs) are widely used for describing molecular energy and continue bridging the speed and accuracy gap between quantum mechanical (QM) and classical approaches like force fields. In this Account, we focus on the out-of-the-box approaches to developing transferable MLIPs for diverse chemical tasks. First, we introduce the "Accurate Neural Network engine for Molecular Energies," ANAKIN-ME, method (or ANI for short). The ANI model utilizes Justin Smith Symmetry Functions (JSSFs) and realizes training for vast data sets. The training data set of several orders of magnitude larger than before has become the key factor of the knowledge transferability and flexibility of MLIPs. As the quantity, quality, and types of interactions included in the training data set will dictate the accuracy of MLIPs, the task of proper data selection and model training could be assisted with advanced methods like active learning (AL), transfer learning (TL), and multitask learning (MTL).Next, we describe the AIMNet "Atoms-in-Molecules Network" that was inspired by the quantum theory of atoms in molecules. The AIMNet architecture lifts multiple limitations in MLIPs. It encodes long-range interactions and learnable representations of chemical elements. We also discuss the AIMNet-ME model that expands the applicability domain of AIMNet from neutral molecules toward open-shell systems. The AIMNet-ME encompasses a dependence of the potential on molecular charge and spin. It brings ML and physical models one step closer, ensuring the correct molecular energy behavior over the total molecular charge.We finally describe perhaps the simplest possible physics-aware model, which combines ML and the extended Hückel method. In ML-EHM, "Hierarchically Interacting Particle Neural Network," HIP-NN generates the set of a molecule- and environment-dependent Hamiltonian elements α_μμ and K^‡. As a test example, we show how in contrast to traditional Hückel theory, ML-EHM correctly describes orbital crossing with bond rotations. Hence it learns the underlying physics, highlighting that the inclusion of proper physical constraints and symmetries could significantly improve ML model generalization.