发表机构
University of California, Irvine（加州大学尔湾分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对高斯基哈密顿量提出参考密度哈特利筛选方法，结合低秩单粒子校正，可大幅降低直接哈特利误差，避免虚假HF坍缩，在减少基组函数数的同时保持高精度。
AI 中文摘要
高斯基（Gausslet）是少数能将四索引电子-电子相互作用替换为精确二索引积分对角近似（IDA）的电子结构基组之一。然而，在多电子原子核附近，核吸引势与核心电子的哈特利场各自数值很大且会大幅抵消；将前者作为完整有限基组矩阵处理、后者用IDA处理会导致不可避免的不平衡。我们提出参考密度哈特利筛选：精确表示选定参考密度的哈特利场，仅对其附近的密度涨落应用IDA。对氦（He）、氖（Ne）、氟原子（F）、氟分子（F₂）及铬分子（Cr₂）的测试显示，直接哈特利误差大幅降低，包括将拟合的中性原子场转移至分子的情况。对于Cr₂，原子核心筛选可避免未筛选的q=5和q=7哈密顿量出现的虚假哈特里-福克（HF）坍缩，而无筛选的有限参考匹配则无法做到；筛选不改变交换项与残余关联项。因此我们还提出低秩单粒子校正，利用精确的常规高斯基组哈特利-福克计算匹配占据空间的交换信息或完整占据福克向量。在F₂和Cr₂中，X_HF可将有限参考能量与占据福克向量重现至数值精度，且轨道微扰后选定态会恢复。对于Cr₂，经校正的q=5基组所用函数数仅为q=7对照组的四分之一，同时保持亚毫Hartree（sub-mHa）的平均场精度。筛选为直接场提供了物理层面的改进，而特定态校正则恢复了高斯基组平均场参考的剩余精度。
英文摘要
Gausslets are among the few electronic-structure bases that permit the four-index electron--electron interaction to be replaced by an accurate two-index integral diagonal approximation (IDA). Near a many-electron nucleus, however, the nuclear attraction and core-electron Hartree field are individually large and substantially cancel. Treating the first as a full finite-basis matrix while treating the second with IDA leaves an avoidable imbalance. We introduce reference-density Hartree screening: the Hartree field of a chosen reference density is represented accurately, and IDA is applied only to density fluctuations about it. Tests on He, Ne, atomic F, F$_2$, and Cr$_2$ show large reductions in direct Hartree errors, including transfer of fitted neutral-atom fields to molecules. For Cr$_2$, atomic-core screening prevents the spurious HF collapse found with the unscreened $q=5$ and $q=7$ Hamiltonians, whereas finite-reference matching without screening does not. Screening leaves exchange and residual correlation unchanged. We therefore also introduce a low-rank one-particle correction that uses an accurate conventional Gaussian-basis Hartree--Fock calculation to match either occupied-space exchange information or the complete occupied Fock vectors. In F$_2$ and Cr$_2$, $X_{\rm HF}$ reproduces the finite-reference energy and occupied Fock vectors to numerical precision and the selected states return after orbital perturbations. For Cr$_2$, the corrected $q=5$ basis uses one quarter as many functions as the $q=7$ control while retaining sub-mHa mean-field accuracy. Screening provides the physical improvement to the direct field; the state-specific correction then restores the remaining accuracy of the Gaussian-basis mean-field reference.
Comments11 pages, 1 figure, 4 tables
