Electronic properties of several states of the five- and six-electron harmonium atoms are obtained from large-scale calculations employing explicitly correlated basis functions. The high accuracy of the computed energies (including their components), natural spinorbitals, and their occupation numbers makes them suitable for testing, calibration, and benchmarking of approximate formalisms of quantum chemistry and solid state physics. In the case of the five-electron species, the availability of the new data for a wide range of the confinement strengths ω allows for confirmation and generalization of the previously reached conclusions concerning the performance of the presently known approximations for the electron-electron repulsion energy in terms of the 1-matrix that are at heart of the density matrix functional theory (DMFT). On the other hand, the properties of the three low-lying states of the six-electron harmonium atom, computed at ω = 500 and ω = 1000, uncover deficiencies of the 1-matrix functionals not revealed by previous studies. In general, the previously published assessment of the present implementations of DMFT being of poor accuracy is found to hold. Extending the present work to harmonically confined systems with even more electrons is most likely counterproductive as the steep increase in computational cost required to maintain sufficient accuracy of the calculated properties is not expected to be matched by the benefits of additional information gathered from the resulting benchmarks.

中文翻译：

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五电子和六电子的谐原子：高度精确的电子性质及其在约一矩阵功能的基准测试中的应用

通过使用显式相关的基函数的大规模计算，可以获得五电子和六电子谐原子的几种状态的电子性质。计算出的能量（包括其成分），自然自旋轨道及其占据数的高精度使它们适合于量子化学和固态物理学的近似形式主义的测试，校准和基准测试。在五电子物种的情况下，可获得广泛的约束强度ω的新数据允许对先前得出的结论进行确认和归纳，这些结论涉及密度矩阵泛函理论（DMFT）的核心，即关于1电子矩阵的电子-电子排斥能的当前近似值的性能。另一方面，在ω = 500和ω时计算出的六电子谐原子的三个低态态的性质= 1000，发现先前研究未发现的1-矩阵功能的缺陷。通常，发现保留了先前发布的对DMFT的当前实现的评估，该评估的准确性较差。将目前的工作扩展到具有更多电子的谐波约束系统中最有可能适得其反，因为维持计算出的特性的足够准确性所需的计算成本的急剧增加预计不会与从所得基准中收集到的额外信息的好处相匹配。