Free-basis-set method to describe the helium atom confined by a spherical box with finite and infinite potentials

Abstract

The finite difference method based on a non-regular mesh is used to solve Hartree-Fock and Kohn-Sham equations for the helium atom confined by finite and infinite potentials. The reliability of this approach is shown when this is contrasted with the Roothaan's approach, which depends on a basis set and therefore its exponents must be optimized for each confinement imposed over the helium atom. The comparison between our numerical approach and the Roothaan's approach was done by using total and orbitals energies from the Hartree-Fock method where there are several sources of comparison. By the side of the Kohn-Sham method there are a few published results and consequently the results reported here can be used as benchmark for future comparisons. The electron density, through the Shannon's entropy, was also used for the comparison between our approach and other reports. This entropy shows that the helium atom confined by an infinite potential can be described almost with any approach, Hartree-Fock or Kohn-Sham give almost same results. This conclusion cannot be applied for finite potential since Hartree-Fock and Kohn-Sham methods present large differences between themselves. This study represents the first step to develop a numerical code free of basis sets to obtain the electronic structure of many-electron atoms.

Coulomb correlation and information entropies in confined helium-like atoms

“…The study of quantum systems in information theory context already has a series of published works, for instance, analyses involving the one-dimensional systems [13][14][15][16][17] and confined hydrogen atom [18][19][20][21][22][23]. Studies on the free or confined helium-like atoms also have received attention in the informational context [24][25][26][27][28][29][30][31][32][33].…”

Electron density analysis of two-electron systems confined by prolate spheroids with hard walls

“…We have mentioned one example where the electronic structure of atoms is altered by hard confinement. Several examples of these systems exist [11][12][13][14][15]. Confinement imposed by soft walls is another important model potential for studying the electronic structure of confined atoms and molecules, although this confinement is not considered in this article [16][17][18][19][20][21][22][23].…”

“…Total energy for the hydrogen molecule confined by a prolate spheroidal box with hard walls. The values obtained from this approach (EHF) are compared with values obtained by Batael et al[13] (E). All quantities are in Hartrees.…”

Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength

“…Understanding the electronic properties of atoms under high-pressure conditions remains a formidable task for both theory and measurement alike. For the theorist, the description of atoms under confinement has been largely limited to simple semi-analytic models [1][2][3][4][5][6][7][8][9][10][11], which though interesting and useful, are only capable of providing essentially qualitative descriptions. For the experimentalist, there is problem of reaching significant pressures without the sample environment preventing easy access to the embedded material.…”