Learning the Electronic Hamiltonian of Large Atomic Structures

TL;DR

This paper introduces a local equivariant graph neural network that accurately predicts the electronic Hamiltonian of large, complex atomic structures, enabling efficient analysis of realistic materials with thousands of atoms.

Contribution

It presents a novel GNN architecture capable of learning the electronic Hamiltonian for large, disordered systems, surpassing previous methods limited to smaller or idealized structures.

Findings

Achieved less than 0.53% error in eigenvalue spectra for systems with up to 3,000 atoms.

Predicted the electronic Hamiltonian with high accuracy for complex, realistic materials.

Enabled scalable electronic property predictions for large, disordered systems.

Abstract

Graph neural networks (GNNs) have shown promise in learning the ground-state electronic properties of materials, subverting ab initio density functional theory (DFT) calculations when the underlying lattices can be represented as small and/or repeatable unit cells (i.e., molecules and periodic crystals). Realistic systems are, however, non-ideal and generally characterized by higher structural complexity. As such, they require large (10+ Angstroms) unit cells and thousands of atoms to be accurately described. At these scales, DFT becomes computationally prohibitive, making GNNs especially attractive. In this work, we present a strictly local equivariant GNN capable of learning the electronic Hamiltonian (H) of realistically extended materials. It incorporates an augmented partitioning approach that enables training on arbitrarily large structures while preserving local atomic environments beyond boundaries. We demonstrate its capabilities by predicting the electronic Hamiltonian of various systems with up to 3,000 nodes (atoms), 500,000+ edges, ~28 million orbital interactions (nonzero entries of H), and $\leq$0.53% error in the eigenvalue spectra. Our work expands the applicability of current electronic property prediction methods to some of the most challenging cases encountered in computational materials science, namely systems with disorder, interfaces, and defects.