Scaling Density Functional Theory with Gaussian Splatting

2026-09-25

AI Summary

This study addresses the inherent trade-off between computational accuracy and efficiency in conventional density functional theory (DFT) arising from fixed basis sets. We propose GS-DFT, a novel framework that parameterizes molecular orbitals as three-dimensional Gaussian clouds, introducing the first quantum-mechanical adaptation of 3D Gaussian splatting. By employing gradient descent to jointly optimize the positions, shapes, and coefficients of Gaussian basis functions for energy minimization, and by incorporating adaptive density fitting alongside a differentiable orthogonalization solver to ensure numerical stability, this approach achieves large-basis-set accuracy with significantly fewer parameters. The method successfully simulates systems comprising up to 2,742 atoms while substantially reducing memory overhead, thereby establishing an efficient new paradigm for large-scale first-principles computations.

Abstract

Density functional theory (DFT) strikes a practical balance between accuracy and computational cost in many problems of computational chemistry and materials science. However, many DFT calculations are limited by fixed atom-centered basis sets, which dictate how accuracy and cost scale with system size. We propose Gaussian Splatting for Density Functional Theory (GS-DFT), which represents molecular orbitals as a cloud of Gaussians whose positions, shapes, and mixing coefficients are optimized jointly by gradient descent to minimize the energy without training data. Conceptually, GS-DFT is 3D Gaussian splatting with the renderer replaced by quantum mechanics. We introduce two key solver components: adaptive density fitting with screening for efficient evaluation of two-electron integrals, and a regularized differentiable orthogonalization of the molecular orbitals. Empirically, the optimized basis reaches the accuracy of the largest conventional basis sets with a fraction of the parameters, converging systematically in energy, density, and nuclear forces. At equal parameter count, it captures the stretched-bond and anion physics that fixed bases only recover with specialized basis augmentation. The resulting solver exhibits quadratic peak memory scaling in the cloud size, allowing us to simulate systems of up to 2,742 atoms (10,406 electrons) without any modifications at triple-zeta scale using a single four-GPU node.

Problem

• Density Functional Theory
• Basis Sets
• Scalability
• Molecular Orbitals
• Computational Cost

Innovation

• Gaussian Splatting
• Density Functional Theory
• Differentiable Orthogonalization
• Adaptive Density Fitting
• Gradient Descent Optimization