发表机构
Donostia International Physics Center (DIPC); Kimika Fakultatea, Euskal Herriko Unibertsitatea (EHU); Ikerbasque Foundation for Science; Institute for Advanced Chemistry of Catalonia (IQAC), CSIC（多诺西亚国际物理中心; 巴斯克大学化学学院; 伊克尔巴斯科科学基金会; 加泰罗尼亚高级化学研究所，西班牙国家科学研究委员会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于拓扑模糊Voronoi晶胞的多中心数值积分方案，用于高效计算内库对密度及其矩，在烷烃和S22数据集上验证了高精度与可靠性，支持电子关联和色散研究。
AI 中文摘要
内库对密度为电子关联提供了洞察，但在扩展系统中的常规分析受限于数值积分的成本以及解析方法对高斯基函数的限制。我们提出了一种高效的多中心积分方案，用于内库密度及其矩的计算。通过采用拓扑模糊Voronoi晶胞形式，我们围绕原子间位移矢量划分内库空间，将求积点集中在标准单中心网格难以解析的次级密度极大值附近。对线性烷烃的基准测试显示，随着分子尺寸的增加，收敛性得到改善，在电子-电子排斥能中实现了低于0.02%的相对误差，且所需求积点少于单中心方法。这种划分还使得全局双电子性质能够分解为与短程和长程电子对分离相关的空间贡献。将多中心网格与核密度估计相结合，可以在大电子间距离处重建平滑的径向内库分布，而无需传统表面积分所需的密集角度网格。在S22数据集上的验证支持了该方法在不同分子系统中的可靠性。这些进展促进了多原子系统中的内库分析以及对电子关联和色散相互作用的研究。
英文摘要
Intracule pair densities provide insight into electron correlation, but their routine analysis in extended systems is limited by the cost of numerical integration and the restriction of analytical methods to Gaussian basis functions. We present an efficient multicenter integration scheme for intracule densities and their moments. By adapting the topological fuzzy Voronoi cell formalism, we partition intracule space around interatomic displacement vectors, concentrating quadrature points near secondary density maxima that standard single-center grids poorly resolve. Benchmarks on linear alkanes show improved convergence with increasing molecular size, achieving relative errors below 0.02% in electron-electron repulsion energies with fewer quadrature points than single-center methods. The partitioning also enables the decomposition of global two-electron properties into spatial contributions associated with short- and long-range electron-pair separations. Coupling the multicenter grid with kernel density estimation reconstructs smooth radial intracule distributions at large interelectronic distances without the dense angular grids required by conventional surface integration. Validation on the S22 dataset supports the reliability of the method across diverse molecular systems. These developments facilitate intracule analysis in polyatomic systems and the investigation of electron correlation and dispersion interactions.
