多极样条用于优化和反演的有效势
Multipole splats for optimized and inverted effective potentials
- ETH Zürich（苏黎世联邦理工学院）
- Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质与结构动力学研究所）
- Flatiron Institute（平顿研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出多极样条方法，通过将优化有效势和反演Kohn-Sham问题转化为稳定非线性优化，解决DFT中非局域势的误差，改进自相互作用、里德伯系列和精确交换势计算。
AI中文摘要：
关联物质近似单粒子描述仍然是量子科学中可操作预测的主要来源。在现代密度泛函理论（DFT）中，构造混合有效哈密顿量以重现平衡密度和力。然而，其非局域和轨道依赖的势在响应性质和实时动力学中留下系统性误差。局域优化有效势（OEP）或反演Kohn-Sham（IKS）势将消除这一限制，但有限轨道基组中的数值脆弱性长期以来阻碍了其广泛采用。我们引入了多极样条，一类通过构造携带正确渐近衰减的试探势。通过展示OEP和IKS映射到哈密顿量学习的变分和监督变体，我们将这两个问题重新表述为直接在标准轨道基组中制定的稳定非线性优化，并适用于任何混合泛函近似。我们展示了对三种典型DFT失效模式的改进。首先，通过比较近似和近精确的反演有效关联势，我们分离了自相互作用、离域和静态关联误差的空间特征。其次，我们在没有经验渐近修正的情况下恢复了里德伯系列，展示了获取精确光谱性质的能力。最后，我们计算了较大π共轭体系的精确交换势，建立了扩展能力。多极样条从已有近似中提取新的第一性原理见解，并为下游处理和学习的稳健数据集生成提供能力。
英文摘要：
In modern density functional theory, effective Hamiltonians are constructed to reproduce densities and forces of electrons at equilibrium. However, their nonlocal potentials leave systematic errors in spectral properties and real-time dynamics. Access to local optimized or inverted effective potentials would remove this limitation, but the numerical fragility in finite orbital bases has long prevented their wide adoption. Here, we introduce multipole splats, a class of trial potentials that carry the correct asymptotic decay required to support the unoccupied spectrum. By connecting the computation of effective potentials to variational and supervised variants of Hamiltonian learning, we recast both problems as stable nonlinear optimization formulated directly in standard orbital basis sets and applicable to any hybrid functional approximation. The resulting solver allows us to resolve spatial profiles of exchange-correlation potential errors during molecular dissociation and accurately reconstruct key excited states without empirical asymptotic corrections. We also show the deviation from the ionization potential theorem for different exchange-correlation approximations on a dataset of molecular systems. Multipole splats extract insights from established approximations and provide capacity for robust dataset generation for downstream processing and learning.
