Gaussian clouds speed up quantum chemistry simulations to thousands of atoms
Scaling Density Functional Theory with Gaussian Splatting
Machine Learning
Summary
Calculating the properties of molecules and materials accurately usually takes a lot of computer work because traditional methods rely on fixed mathematical building blocks centered on atoms. This paper introduces a new technique where shapes called Gaussians float freely and change to better describe molecules, optimizing themselves using quantum mechanics rules. This approach reaches high accuracy with fewer parameters and scales well to very large systems, allowing simulations of thousands of atoms on a standard GPU setup. The method also better captures tricky cases like stretched bonds and charged molecules that older methods struggle with.
What this means in practice
- •For computational chemists: Run large-scale molecular simulations with improved efficiency and accuracy for systems up to thousands of atoms on modest hardware.
- •For materials modeling teams: Conduct detailed materials property predictions capturing complex electronic effects without needing very large fixed basis sets.
Authors
Andrés Guzmán-Cordero, Cindy Zhang, Majdi Hassan, Marta Skreta, Kirill Neklyudov, Matija Medvidović
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.