Cioslowski Jerzy
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany.
J Chem Phys. 2015 Mar 21;142(11):114104. doi: 10.1063/1.4914171.
Explicit asymptotic expressions are derived for the reduced one-electron density matrices (the 1-matrices) of strongly correlated two- and three-electron harmonium atoms in the ground and first excited states. These expressions, which are valid at the limit of small confinement strength ω, yield electron densities and kinetic energies in agreement with the published values. In addition, they reveal the ω(5/6) asymptotic scaling of the exchange components of the electron-electron repulsion energies that differs from the ω(2/3) scaling of their Coulomb and correlation counterparts. The natural orbitals of the totally symmetric ground state of the two-electron harmonium atom are found to possess collective occupancies that follow a mixed power/Gaussian dependence on the angular momentum in variance with the simple power-law prediction of Hill's asymptotics. Providing rigorous constraints on energies as functionals of 1-matrices, these results are expected to facilitate development of approximate implementations of the density matrix functional theory and ensure their proper description of strongly correlated systems.
推导了处于基态和第一激发态的强关联两电子和三电子谐振子原子的约化单电子密度矩阵（1 - 矩阵）的显式渐近表达式。这些表达式在小限制强度ω的极限下有效，得出的电子密度和动能与已发表的值一致。此外，它们揭示了电子 - 电子排斥能交换分量的ω(5/6)渐近标度，这与它们的库仑和关联对应分量的ω(2/3)标度不同。发现两电子谐振子原子全对称基态的自然轨道具有集体占据情况，其对角动量的依赖遵循幂次/高斯混合关系，这与希尔渐近的简单幂律预测不同。这些结果为作为1 - 矩阵泛函的能量提供了严格约束，有望促进密度矩阵泛函理论近似实现的发展，并确保对强关联系统的恰当描述。
