Cioslowski Jerzy, Pernal Katarzyna
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
J Chem Phys. 2006 Aug 14;125(6):64106. doi: 10.1063/1.2222361.
At the strong-correlation limit, electronic states of the three-electron harmonium atom are described by asymptotically exact wave functions given by products of distinct Slater determinants and a common Gaussian factor that involves interelectron distances and the center-of-mass position. The Slater determinants specify the angular dependence and the permutational symmetry of the wave functions. As the confinement strength becomes infinitesimally small, the states of different spin multiplicities become degenerate, their limiting energy reflecting harmonic vibrations of the electrons about their equilibrium positions. The corresponding electron densities are given by products of angular factors and a Gaussian function centered at the radius proportional to the interelectron distance at equilibrium. Thanks to the availability of both the energy and the electron density, the strong-correlation limit of the three-electron harmonium is well suited for testing of density functionals.
在强关联极限下，三电子谐振子原子的电子态由渐近精确波函数描述，这些波函数由不同斯莱特行列式的乘积和一个涉及电子间距离与质心位置的共同高斯因子给出。斯莱特行列式确定了波函数的角向依赖性和置换对称性。当限制强度变得无限小时，不同自旋多重性的态变得简并，其极限能量反映了电子围绕其平衡位置的简谐振动。相应的电子密度由角向因子的乘积和一个以与平衡时电子间距离成正比的半径为中心的高斯函数给出。由于能量和电子密度都可用，三电子谐振子的强关联极限非常适合用于检验密度泛函。
