Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
J Chem Phys. 2018 Apr 14;148(14):144107. doi: 10.1063/1.5021419.
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.
采用显式相关基函数的大规模计算得到了五电子和六电子谐振子原子的若干态的电子性质。计算出的能量（包括其分量）、自然自旋轨道及其占据数的高精度使它们适用于测试、校准和基准量子化学和固态物理的近似形式。在五电子的情况下，新数据的可用性范围广泛的限制强度 ω 允许确认和推广先前关于电子-电子排斥能的现有近似值的性能的结论，这些结论是密度矩阵泛函理论 (DMFT) 的核心的 1 矩阵。另一方面，在 ω = 500 和 ω = 1000 下计算的六电子谐振子原子的三个低能态的性质揭示了先前研究未揭示的 1 矩阵泛函的缺陷。一般来说，先前发表的关于 DMFT 的现有实现精度较差的评估被认为是正确的。将目前的工作扩展到具有更多电子的谐和限制系统很可能适得其反，因为计算成本的急剧增加，以保持计算性质的足够精度，预计不会与从基准测试中收集到的额外信息的收益相匹配。
