Confined helium atom low-lying S states analyzed through correlated Hylleraas wave functions and the Kohn-Sham model

Abstract

Calculation including the electron correlation effects is reported for the ground 1 1S and lowest triplet 1 3S state energies of the confined helium atom placed at the center of an impenetrable spherical box. While the adopted wave-functional treatment involves optimization of three nonlinear parameters and 10, 20, and 40 linear coefficients contained in wave functions expressed in a generalized Hylleraas basis set that explicitly incorporates the interelectronic distance r12, via a Slater-type exponent and through polynomial terms entering the expansion, the Kohn-Sham model employed here uses the Perdew and Wang exchange-correlation functional in its spin-polarized version within the local-density approximation (LDA) with and without the self-interaction correction. All these calculations predict a systematic increase in the singlet-triplet energy splitting toward the high confinement regime, i.e., when the box radius is reduced. By using the variational results as benchmark, it is found that the LDA underestimates the singlet-triplet energy splitting, whereas the self-interaction correction overestimates such a quantity.

Compression effects in helium-like atoms constrained by hard spherical walls

“…As mentioned in two previous reports co-authored by one of us [29,30], the variational description of confined systems becomes increasingly difficult when use is made of wave function expansions of even moderate order, especially for small confinement box radii (typically for values of R c near the ionization radius for each atom), leading to an energy convergence that proceeds very slowly and may involve a careful adjustment of parameters along the optimization procedure. In the present investigation the confined atomic species H − was found to be particulary challenging to describe variationally due to its highly diffuse character.…”

“…In the analysis of confined hydrogen, helium and lithium, within an effective two-electron atomic Hamiltonian, Patil and Varshni [27] have used a screening model derived from the electronic energy behavior between two limiting situations: from extreme confinement (box radius → 0) to the free atom regime (box radius → ∞), whereas by using a two-parameter variational ansatz with some degree of correlation, Banerjee et al [28] have reported calculations for the ground and three low-lying excited states of confined helium. Variational studies of confined helium ground state including correlation effects have been reported [29], and also where the ground and lowest triplet states for the same atom under compression are analyzed by means of a variational approach via a correlated basis and a Kohn-Sham model within the local density approximation [30].…”

Electron correlation energy in confined two-electron systems

“…We have also employed a B-spline approach in order to evaluate the performance of the zero order spherical Bessel representation. B-spline calculations were carried out using a modified HF code [16] with the choice of 100-term B-spline set of order K = 9. A preset finite radius of 7 confinement R on an exponential type knot sequence [17] with the initial interval as 10 -4 was employed.…”

“…This work follows from the pioneering work of Gimarc [13], who investigated the correlation energy of the confined, two-electron atom using a three-term, explicitly correlated wavefunction to calculate the non-relativistic energy and a double-zeta wavefunction [14] to calculate the Hartree-Fock energy. Recent work using explicitly correlated wavefunctions to calculate accurate ground state energies [15][16][17][18] and accurate unrestricted Hartree-Fock calculations provided an opportunity to perform a detailed study confined two-electron systems.…”

Linear and nonlinear absorption coefficients of spherical two-electron quantum dot

“…The Coulomb interaction between electrons effects considerably the physical properties of such structures and must be considered in calculations [29]. Therefore, various properties of the confined helium and helium-like ions have been investigated by many researchers [30][31][32][33][34][35][36][37][38]. In the work of Ndengué and Motapon [31] was computed the energy levels of the ground and a few excited states of helium and helium-like ions confined in a finite potential well by using configuration interaction method.…”