原子中的复杂性：一种新的分析密度方法
Complexity in atoms: an approach with a new analytical density
摘要：
在这项工作中，计算复杂性的原子系统被认为是。为了揭示相对论效应导致的统计量随原子序数的增加而增加的现象，最近在[A. Borgoo，F. De Proft，P. Geerlings，K.D. Sen，Chem. Phys. Lett.，444（2007）186]，提出了一种新的描述中性原子的解析密度。这个密度是受Tietz势模型的启发。该密度的参数由归一化条件和能量的变分计算确定，能量是密度的函数。密度在原点是非奇异的，并且其特定形式被选择为适合来自非相对论性Hartree-Fock计算的结果。能量泛函的主要成分是非相对论性动能、核-电子吸引能和电子排斥的经典项。对动能和Weizsacker项的相对论修正也被考虑在内。狄拉克和相关项被证明是不太重要的比其他条款，他们已被丢弃在这项研究中。当用该模型导出的解析密度在位置空间中计算复杂性的统计测度时，还发现复杂性的大小随原子序数的增加而增加的趋势。
英文摘要：
In this work, the calculation of complexity on atomic systems is considered. In order to unveil the increasing of this statistical magnitude with the atomic number due to the relativistic effects, recently reported in [A. Borgoo, F. De Proft, P. Geerlings, K.D. Sen, Chem. Phys. Lett., 444 (2007) 186], a new analytical density to describe neutral atoms is proposed. This density is inspired in the Tietz potential model. The parameters of this density are determined from the normalization condition and from a variational calculation of the energy, which is a functional of the density. The density is non-singular at the origin and its specific form is selected so as to fit the results coming from non-relativistic Hartree-Fock calculations. The main ingredients of the energy functional are the non-relativistic kinetic energy, the nuclear-electron attraction energy and the classical term of the electron repulsion. The relativistic correction to the kinetic energy and the Weizsacker term are also taken into account. The Dirac and the correlation terms are shown to be less important than the other terms and they have been discarded in this study. When the statistical measure of complexity is calculated in position space with the analytical density derived from this model, the increasing trend of this magnitude as the atomic number increases is also found.
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