Department of Chemistry, Technion, Haifa 32000, Israel.
J Chem Phys. 2012 Apr 14;136(14):144112. doi: 10.1063/1.3702632.
Atomic orbitals with a common principal quantum number are degenerate, as in the hydrogen atom, in the absence of interelectronic repulsion. Due to the virial theorem, electrons in such orbitals experience equal nuclear attractions. Comparing states of several-electron atoms that differ by the occupation of orbitals with a common principal quantum number, such as 1s(2) 2s vs. 1s(2) 2p, we find that although the difference in energies, ΔE, is due to the interelectronic repulsion term in the Hamiltonian, the difference between the interelectronic repulsions, ΔC, makes a smaller contribution to ΔE than the corresponding difference between the nuclear attractions, ΔL. Analysis of spectroscopic data for atomic isoelectronic sequences allows an extensive investigation of these issues. In the low nuclear charge range of pertinent isoelectronic sequences, i.e., for neutral atoms and mildly positively charged ions, it is found that ΔC actually reverses its sign. About 96% of the nuclear attraction difference between the 6p (2)P and the 6s (2)S states of the Cs atom is cancelled by the corresponding interelectronic repulsion difference. From the monotonic increase of ΔE with Z it follows (via the Hellmann-Feynman theorem) that ΔL > 0. Upon increasing the nuclear charge along an atomic isoelectronic sequence with a single electron outside a closed shell from Z(c), the critical charge below which the outmost electron is not bound, to infinity, the ratio ΔC/ΔL increases monotonically from lim(Z→Z(c)(+))ΔC/ΔL=-1 to lim(Z→∞)ΔC/ΔL=1. These results should allow for a more nuanced discussion than is usually encountered of the crude electronic structure of many-electron atoms and the structure of the periodic table.
具有相同主量子数的原子轨道在没有电子间排斥作用时是简并的,如氢原子。由于维里定理,处于这种轨道中的电子受到相等的核吸引力。比较具有相同主量子数的轨道占据情况不同的多电子原子的状态,例如 1s(2)2s 与 1s(2)2p,我们发现,尽管能量差ΔE 是由于哈密顿量中的电子间排斥项引起的,但电子间排斥的差异ΔC 对ΔE 的贡献比核吸引力的差异ΔL 小。对原子等电子序列的光谱数据的分析允许对这些问题进行广泛的研究。在相关等电子序列的低核电荷范围,即中性原子和轻度正离子中,发现ΔC 实际上改变了符号。铯原子的 6p(2)P 和 6s(2)S 态之间的核吸引力差异的 96%左右被相应的电子间排斥差异抵消。由于ΔE 随 Z 的单调增加(通过赫尔曼-费曼定理)可知ΔL>0。沿着具有一个单电子在闭壳层之外的原子等电子序列从 Z(c)到无穷大增加核电荷时,最外层电子不再束缚的临界电荷,ΔC/ΔL 的比值从 lim(Z→Z(c)(+))ΔC/ΔL=-1 单调增加到 lim(Z→∞)ΔC/ΔL=1。这些结果应该允许比通常遇到的多电子原子的粗糙电子结构和元素周期表的结构更细致的讨论。