Density functional study of atoms spatially confined inside a hard sphere

TL;DR

This paper develops a density functional approach to study atoms confined inside a hard spherical cavity, achieving accurate results for ground and excited states using a pseudospectral method and various correlation functionals.

Contribution

It introduces a simple, accurate density functional scheme for atomic systems confined in a spherical cavity, including ground and excited states, with comparison to literature results.

Findings

Accurate eigenvalues and eigenfunctions obtained for confined atoms.

Good agreement with existing literature for energy levels and densities.

Analysis of different correlation functionals' performance.

Abstract

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.