Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blink

2026-01-27

AI Summary

This work proposes a novel, efficient, and accurate method for predicting charge densities in periodic crystals to accelerate density functional theory (DFT) calculations. By constructing anisotropic Gaussian functions in real space and leveraging their analytical Fourier transforms together with the Poisson summation formula, the approach directly generates fully periodic charge densities without resorting to grid sampling, Ewald-like summations over periodic images, or spherical harmonic expansions. For the first time, it integrates local Gaussian representations with analytically computed plane-wave coefficients into an end-to-end differentiable architecture, enabling millisecond-scale reconstruction. The method achieves state-of-the-art or better accuracy across multiple periodic benchmarks while accelerating inference by up to 633×. When employed for DFT initialization, it reduces total computational cost by approximately 20%.

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Abstract

We introduce ELECTRAFI, a fast, end-to-end differentiable model for predicting periodic charge densities in crystalline materials. ELECTRAFI constructs anisotropic Gaussians in real space and exploits their closed-form Fourier transforms to analytically evaluate plane-wave coefficients via the Poisson summation formula. This formulation delegates non-local and periodic behavior to analytic transforms, enabling reconstruction of the full periodic charge density with a single inverse FFT. By avoiding explicit real-space grid probing, periodic image summation, and spherical harmonic expansions, ELECTRAFI matches or exceeds state-of-the-art accuracy across periodic benchmarks while being up to $633 \times$ faster than the strongest competing method, reconstructing crystal charge densities in a fraction of a second. When used to initialize DFT calculations, ELECTRAFI reduces total DFT compute cost by up to ~20%, whereas slower charge density models negate savings due to high inference times. Our results show that accuracy and inference cost jointly determine end-to-end DFT speedups, and motivate our focus on efficiency.

Problem

• periodic charge density
• crystalline materials
• density functional theory
• computational efficiency
• electronic structure

Innovation

• ELECTRAFI
• periodic charge density
• anisotropic Gaussians
• Fourier transform
• density functional theory