Transferable E(3) equivariant parameterization for Hamiltonian of molecules and solids

Abstract

Using the message-passing mechanism in machine learning (ML) instead of self-consistent iterations to directly build the mapping from structures to electronic Hamiltonian matrices will greatly improve the efficiency of density functional theory (DFT) calculations. In this work, we proposed a general analytic Hamiltonian representation in an E(3) equivariant framework, which can fit the ab initio Hamiltonian of molecules and solids by a complete data-driven method and are equivariant under rotation, space inversion, and time reversal operations. Our model reached state-of-the-art precision in the benchmark test and accurately predicted the electronic Hamiltonian matrices and related properties of various periodic and aperiodic systems, showing high transferability and generalization ability. This framework provides a general transferable model that can be used to accelerate the electronic structure calculations on different large systems with the same network weights trained on small structures.

arXiv comment33 pages, 6 figures

References in corpus (32)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties
• On representing chemical environments
• Bandgap Engineering of Strained Monolayer and Bilayer MoS2
• SchNet - a deep learning architecture for molecules and materials
• E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials
• On the Convergence of Adam and Beyond
• Crossover of Three-Dimensional Topological Insulator of Bi2Se3 to the Two-Dimensional Limit
• PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges
• Atomistic Line Graph Neural Network for Improved Materials Property Predictions
• Topological insulators in twisted transition metal dichalcogenide homobilayers
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
• SIESTA: recent developments and applications
• Spin Polarization and Transport of Surface States in the Topological Insulators Bi2Se3 and Bi2Te3 from First Principles
• Ultraflat bands and shear solitons in Moiré patterns of twisted bilayer transition metal dichalcogenides
• GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations
• Magic in twisted transition metal dichalcogenide bilayers
• SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects
• FCHL revisited: faster and more accurate quantum machine learning
• Alchemical and structural distribution based representation for improved QML
• Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
• Deep-Learning Density Functional Theory Hamiltonian for Efficient ab initio Electronic-Structure Calculation
• High-throughput Density Functional Perturbation Theory and Machine Learning Predictions of Infrared, Piezoelectric and Dielectric Responses
• Unified Graph Neural Network Force-field for the Periodic Table
• Electronic, optical and transport properties of van der Waals Transition-metal Dichalcogenides Heterostructures: A First-principle Study
• Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties
• Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models
• GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles
• Spin-Orbit Coupling in an f-electron Tight-Binding Model
• SE(3)-equivariant prediction of molecular wavefunctions and electronic densities
• Electronic structure study of screw dislocation core energetics in Aluminum and core energetics informed forces in a dislocation aggregate
• Importance of van der Waals interactions for ab initio studies of topological insulators

Cited by in corpus (13)

• AI-driven inverse design of materials: Past, present and future
• Universal materials model of deep-learning density functional theory Hamiltonian
• Universal Machine Learning Kohn-Sham Hamiltonian for Materials
• Recent Advances in Unconventional Ferroelectrics and Multiferroics
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• Exploring the design space of machine-learning models for quantum chemistry with a fully differentiable framework
• General time-reversal equivariant neural network potential for magnetic materials
• Equivariant neural network for Green's functions of molecules and materials
• Materials discovery acceleration by using condition generative methodology
• Equivariant Electronic Hamiltonian Prediction with Many-Body Message Passing
• Revealing Higher-Order Topological Bulk-boundary Correspondence in Bismuth Crystal with Spin-helical Hinge State Loop and Proximity Superconductivity
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Accelerated Discovery of Topological Conductors for Nanoscale Interconnects