Katriel Jacob, Roy Sudip, Springborg Michael
Physical and Theoretical Chemistry, University of Saarland, Germany.
J Chem Phys. 2005 Sep 8;123(10):104104. doi: 10.1063/1.2033747.
The correlation energies of the helium isoelectronic sequence (IS) and of Hooke's IS are very similar and are both weakly increasing upon increasing the nuclear charge/force constant, respectively. However, their separation into radial and angular correlations shows interesting differences. First, for intermediate (and high) values of the force constant radial correlation in Hooke's IS is surprisingly low. Second, both systems exhibit a decrease in the relative contribution of radial versus angular correlation upon strengthening the one-body attractive potential; however, unlike the helium IS, in Hooke's IS the radial correlation energy increases in absolute value upon strengthening the attractive one-body potential. The contribution of radial correlation to the Coulomb hole is examined and the asymptotic behavior at both strong and weak attractive potentials is considered. Radial correlation in Hooke's IS is found to constitute about 9.3% of the total correlation energy when the spring constant approaches the limit k-->infinity, but 100% of the total correlation energy for k-->0. Our results highlight both the similarities and the differences between the helium and Hooke's ISs.
氦等电子序列（IS）和胡克等电子序列的相关能非常相似，并且分别随着核电荷/力常数的增加而微弱增加。然而，它们分解为径向和角向相关性时显示出有趣的差异。首先，对于中等（和高）力常数，胡克等电子序列中的径向相关性出奇地低。其次，在增强单体吸引势时，两个系统中径向与角向相关性的相对贡献都减小；然而，与氦等电子序列不同，在胡克等电子序列中，增强吸引性单体势时，径向相关能的绝对值增加。研究了径向相关性对库仑空穴的贡献，并考虑了强吸引势和弱吸引势下的渐近行为。当弹簧常数趋近于极限k→∞时，发现胡克等电子序列中的径向相关性约占总相关能的9.3%，但当k→0时占总相关能的100%。我们的结果突出了氦等电子序列和胡克等电子序列之间的异同。
