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

TL;DR

ELECTRAFI is a novel, highly efficient differentiable model that predicts periodic charge densities in crystalline materials using an analytical Fourier transform approach, significantly speeding up DFT calculations.

Contribution

We introduce ELECTRAFI, a fast, end-to-end differentiable model that constructs anisotropic Gaussians and analytically evaluates plane-wave coefficients for periodic charge densities.

Findings

ELECTRAFI matches or exceeds state-of-the-art accuracy.

It is up to 633 times faster than competing methods.

Using ELECTRAFI reduces DFT compute costs by up to 20%.

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.