Cioslowski Jerzy, Buchowiecki Marcin
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany.
J Chem Phys. 2005 Feb 22;122(8):84102. doi: 10.1063/1.1846655.
In the harmonium atom, the collective occupancies {n(l)} of natural orbitals with different angular momenta l can be rigorously studied for those values of the confinement strength omega that lead to ground-state wave functions with correlation factors given by polynomials of kth order. Analysis of two such cases, with omega equal to 12 (k=1) and 110 (k=2), uncovers some interesting properties of {n(l)}, which turn out to be given by rational functions of pi(12) with simple coefficients. In particular, contrary to naive expectations, the collective occupancies for l>2 actually decrease upon strengthening of correlation. The explicit formulas for l-matrices and {n(l)} can be readily utilized in testing, calibration, and benchmarking of approximate implementations of the density matrix functional theory (DMFT).
在哈蒙尼姆原子中，对于那些导致基态波函数具有由k阶多项式给出的关联因子的禁闭强度ω值，可以严格研究具有不同角动量l的自然轨道的集体占据数{n(l)}。对两种这样的情况进行分析，其中ω等于12（k = 1）和110（k = 2），揭示了{n(l)}的一些有趣性质，结果发现它们由具有简单系数的π(12)的有理函数给出。特别地，与天真的预期相反，对于l>2，集体占据数实际上会随着关联的增强而减少。l矩阵和{n(l)}的显式公式可很容易地用于密度矩阵泛函理论（DMFT）近似实现的测试、校准和基准测试。
