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The authors present GS-DFT, an ab initio framework that replaces rigid, atom-centered basis sets in density functional theory with molecular orbitals parameterized as dynamic 3D Gaussian clouds optimized directly via gradient descent. To make this variational optimization tractable, the method couples regularized differentiable orbital orthogonalization with adaptive density fitting and screening for two-electron integrals. The resulting solver matches the accuracy of the largest conventional basis sets at a fraction of the parameter count, exhibiting quadratic peak memory scaling that enables triple-zeta simulation of 2,742 atoms (10,406 electrons) on a single four-GPU node.
Replacing rigid quantum chemistry basis sets with freely optimizable 3D Gaussian clouds slashes parameter counts and scales triple-zeta DFT to over 2,700 atoms on just four GPUs.
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.
