发表机构
Technical University of Munich（慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对立方晶格上的Gausslet轨道，提出利用对称性、重排预计算和早期截断的高效算法，将电子排斥积分从1.25亿降至32万，并在2秒内完成计算，成功演示了氢原子和分子的基态求解。
AI 中文摘要
立方晶格上的Gausslet轨道，由Steven R. White在《J. Chem. Phys. 147, 244102 (2017)》中引入，代表了一种局域化、光滑且可系统细化的基组，具有电子排斥积分张量的“对角”近似性。本工作开发了用于使用这些Gausslet进行电子结构模拟所需的重叠积分（特别是动能、核和电子排斥积分，包括有无对角近似的两种情况）的高效算法。计算效率的提升依赖于利用平移、置换和八面体对称性，对嵌套求和进行重新排序和预计算，以及对小系数的早期截断。我们的算法将$5 \ imes 5 \ imes 5$网格上的电子排斥积分数量从$125^4 = 244140625$减少到$324275$（得益于对称性），并在笔记本电脑上以$10^{-5}$的截断容差评估剩余积分时，实现了不到2秒的墙钟运行时间。我们将所开发的方法应用于计算氢原子和氢分子的基态作为演示。
英文摘要
Gausslet orbitals on a cubic lattice, introduced in [Steven R. White, J. Chem. Phys. 147, 244102 (2017)], represent a localized, smooth, and systematically refineable basis set featuring a "diagonal" approximability of the electron repulsion integral tensor. The present work develops efficient algorithms for evaluating overlap integrals required for electronic-structure simulations using these Gausslets, specifically the kinetic, nuclear, and electron repulsion integrals (both with and without the diagonal approximation). Computational efficiency improvements rest on the exploitation of translation, permutation, and octahedral symmetries, a reordering and precomputation of nested sums, as well as an early truncation of small coefficients. Our algorithms reduce the number of electron repulsion integrals on a $5 \times 5 \times 5$ grid from $125^4 = 244140625$ to $138187$ due to symmetries, and achieve a wall-clock runtime for evaluating the remaining integrals with a truncation tolerance of $10^{-5}$ in under 1 second on a laptop computer. We apply the developed methodology to compute the ground state of the hydrogen atom and molecule as a demonstration.
Comments14 pages, 6 figures
