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

TL;DR

This paper investigates the confined negative Hydrogen ion using a density functional approach, achieving near Hartree-Fock accuracy and analyzing electron correlation effects through various functionals and information measures.

Contribution

It introduces a new density functional strategy to study confined H$^-$ ions, including energy and information measures, with results matching literature and insights into correlation effects.

Findings

Exchange-only results are of near Hartree-Fock quality.

Correlation effects diminish with increased confinement strength.

Energy and information measures are effectively estimated using the new functional approach.

Abstract

Ground and excited states of a confined negative Hydrogen ion has been pursued under Kohn-Sham density functional approach by invoking a physically motivated work-function-based exchange potential. The exchange-only results are of near Hartree-Fock quality. Local parameterised Wigner-type, and gradient- and Laplacian-dependent non-local Lee-Yang-Parr functionals are chosen to investigate the electron correlation effects. Eigenfunctions and eigenvalues are extracted by using a generalized pseudospectral method obeying Dirichlet boundary condition. Energy values are reported for 1s$^{2}$ ($^{1}$S), 1s2s ($^{3,1}$S) and 1s2p ($^{3,1}$P) states. Performance of the correlation functionals in the context of confinement is examined critically. The present results are in excellent agreement with available literature. Additionally, Shannon entropy and Onicescu energy are offered for ground and low lying singly excited 1s2s ($^{3}$S) and 1s2p ($^{3}$P) states. The influence of electron correlation is more predominant in the weaker confinement limit and it decays with an increase in confinement strength. In essence, energy and some information measures are estimated using a newly formulated density functional strategy.