Density functional study of atoms spatially confined inside a hard sphere

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, 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 hard spherical box within the rubric of KS density functional theory.

Confined H$$^-$$ ion within a density functional framework

“…These outcomes are almost identical with HF results obtained by using B-spline approach employing the zeroth-order spherical Bessel function [19]. In this context, note that an analogous agreement with HF calculation [81] is also observed in the case of He-isoelectronic series and Li, Be atoms for which similar calculation has been done by the authors and it will be published soon [82]. Apart from that, the X-only values are also compared by invoking a combined quantum genetic algorithm (QGA) and RHF method [6].…”

“…). It has been found earlier that the influence of confinement seems to be more pronounced on valence orbitals leading to the rearrangement of atomic states at strong confinement regime [10,82]. Once we move from free to confinement limit, multiple crossovers between states occur, and the above order gets dissolved.…”

Shell-confined atom and plasma: incidental degeneracy, metallic character and information entropy

“…Thus in essence, it combines the simplicity of direct finite-difference or finite element method, with the fast convergence of finite basis set approaches. Over the time, it has been successfully used to estimate various bound-state properties of several central potentials including energy and other properties in CHA and confined many-electron atom [24,25,29,[62][63][64][65][66],…”

The confined helium atom: An information–theoretic approach

“…Gimarc [20] used the same method but employing 5 different trial wave functions, one of which produced results similar to the HF calculations, and two of them explicitly included electronic correlation. Subsequent to Gimarc, different methods have been developed, for example, Hartree-Fock [21], Roothaan-Hartree-Fock [22], Configuration Interaction [23], time independent perturbation theory [24], linear and non-linear variational method [24][25][26][27][28][29][30][31][32][33][34][35], Lagrange mesh method [36], B-splines [37], variational quantum Monte Carlo [38,39] and density functional theory [40][41][42]. Most of these studies have been devoted to the total energy calculations, correlation energy due to the radial and angular contribution of trial wave functions [31,32], polarizability, critical cage radius and so forth, as a function of the confining radius.…”