硬球内原子空间禁闭的密度泛函研究
Density functional study of atoms spatially confined inside a hard sphere
摘要：
一个原子被放置在一个有限尺寸的腔中，提供了许多有趣的特性，因此一直是当前研究的一个重要课题。本文提出了一种密度泛函方法来研究球形封闭腔中多电子原子的基态和激发态。径向Kohn-Sham（KS）方程已通过调用物理激励的基于功函数的交换势，它提供了近Hartree-Fock质量的结果求解。通过满足Dirichlet边界条件的广义伪谱方法（GPS）得到精确的数值特征函数和特征值。两个相关泛函，\emph{viz.,}（i）简单的，参数化的本地Wigner型，和（ii）梯度和拉普拉斯相关的非本地Lee-Yang-Parr（LYP）泛函被用来分析电子相关效应。对He等电子系列（$Z=2-4$）以及Li和Be原子的基态进行了初步探索。还报道了He原子的几种低激发态激发态。这些与现有的文献结果进行比较-这提供了很好的协议。还提供了径向密度以及期望值。相关能量泛函的性能进行了批判性的讨论。从本质上讲，这提出了一个简单的，准确的计划，研究原子系统内的\emph{hard}球形盒内的标题KS密度泛函理论。
英文摘要：
An atom placed inside a cavity of finite dimension offers many interesting features, and thus has been a topic of great current activity. This work proposes a density functional approach to pursue both ground and excited states of a multi-electron atom under a spherically impenetrable enclosure. The radial Kohn-Sham (KS) equation has been solved by invoking a physically motivated work-function-based exchange potential, which offers near-Hartree-Fock-quality results. Accurate numerical eigenfunctions and eigenvalues are obtained through a generalized pseudospectral method (GPS) fulfilling the Dirichlet boundary condition. Two correlation functionals, \emph{viz.,} (i) simple, parametrized local Wigner-type, and (ii) gradient- and Laplacian-dependent non-local Lee-Yang-Parr (LYP) functionals are adopted to analyze the electron correlation effects. Preliminary exploratory results are offered for ground states of He-isoelectronic series ($Z=2-4$), as well as Li and Be atom. Several low-lying singly excited states of He atom are also reported. These are compared with available literature results -- which offers excellent agreement. Radial densities as well as expectation values are also provided. The performance of correlation energy functionals are discussed critically. In essence, this presents a simple, accurate scheme for studying atomic systems inside a \emph{hard} spherical box within the rubric of KS density functional theory.
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