发表机构
Mila - Quebec AI Institute; Université de Montréal; Princeton University; ETH Zurich; Institut Courtois（米拉-魁北克人工智能研究所; 蒙特利尔大学; 普林斯顿大学; 苏黎世联邦理工学院; 库尔图瓦研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出GS-DFT，用高斯云团表示分子轨道并通过梯度下降优化，以少量参数达到大基组精度，可模拟2742原子系统。
AI 中文摘要
密度泛函理论（DFT）在计算化学和材料科学的许多问题中，在精度和计算成本之间取得了实际的平衡。然而，许多DFT计算受限于固定的原子中心基组，这些基组决定了精度和成本如何随系统规模变化。我们提出了用于密度泛函理论的高斯溅射（GS-DFT），该方法将分子轨道表示为高斯函数的云团，其位置、形状和混合系数通过梯度下降联合优化以最小化能量，无需训练数据。从概念上讲，GS-DFT是3D高斯溅射，但将渲染器替换为量子力学。我们引入了两个关键的求解器组件：用于高效评估双电子积分的带筛选的自适应密度拟合，以及分子轨道的正则化可微正交化。实验上，优化后的基组以一小部分参数达到了最大常规基组的精度，并在能量、密度和核力方面系统收敛。在相同参数数量下，它捕捉了固定基组仅通过专门基组增强才能恢复的拉伸键和阴离子物理。所得求解器在云团大小上表现出二次峰值内存缩放，使我们能够使用单个四GPU节点，在无需任何修改的情况下，以三zeta尺度模拟多达2,742个原子（10,406个电子）的系统。
英文摘要
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.
Comments45 pages, 6 figures, 18 tables
