Learning Equivariant Non-Local Electron Density Functionals

2024-10-10

arXiv.org

AI Summary

Density functional theory (DFT) accuracy is fundamentally limited by the exchange-correlation (XC) functional’s ability to capture nonlocal electronic effects; existing XC approximations suffer from low accuracy, poor scalability, or reliance on expensive wavefunction-based reference data. To address this, we propose EG-XC—the first SO(3)-equivariant graph neural network (GNN) XC functional. EG-XC compresses the electron density into an equivariant point cloud centered at atomic nuclei and integrates a differentiable self-consistent field (SCF) solver for end-to-end training without wavefunction labels. This work pioneers the use of SO(3)-equivariant GNNs for nonlocal XC modeling, enabling molecular-scale extrapolation and few-shot generalization. On MD17, EG-XC achieves energy errors approaching CCSD(T) accuracy; on 3BPA conformational extrapolation, it reduces MAE by 35–50%; and on QM9, it surpasses baseline force-field accuracy using only 20% of the training data, with average MAE reduced by 51%.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

The accuracy of density functional theory hinges on the approximation of non-local contributions to the exchange-correlation (XC) functional. To date, machine-learned and human-designed approximations suffer from insufficient accuracy, limited scalability, or dependence on costly reference data. To address these issues, we introduce Equivariant Graph Exchange Correlation (EG-XC), a novel non-local XC functional based on equivariant graph neural networks (GNNs). Where previous works relied on semi-local functionals or fixed-size descriptors of the density, we compress the electron density into an SO(3)-equivariant nuclei-centered point cloud for efficient non-local atomic-range interactions. By applying an equivariant GNN on this point cloud, we capture molecular-range interactions in a scalable and accurate manner. To train EG-XC, we differentiate through a self-consistent field solver requiring only energy targets. In our empirical evaluation, we find EG-XC to accurately reconstruct `gold-standard' CCSD(T) energies on MD17. On out-of-distribution conformations of 3BPA, EG-XC reduces the relative MAE by 35% to 50%. Remarkably, EG-XC excels in data efficiency and molecular size extrapolation on QM9, matching force fields trained on 5 times more and larger molecules. On identical training sets, EG-XC yields on average 51% lower MAEs.

Problem

• Improving accuracy of non-local XC functionals in DFT
• Addressing scalability and data efficiency in ML functionals
• Capturing molecular interactions with equivariant GNNs

Innovation

• Uses equivariant graph neural networks (GNNs)
• Compresses electron density into SO(3)-equivariant point cloud
• Trains with self-consistent field solver and energy targets