Restricted and unrestricted Hartree–Fock approaches applied to spherical quantum dots in a magnetic field

Abstract

ABSTRACT:The Roothaan and Pople-Nesbet approaches for real atoms are adapted to quantum dots in the presence of a magnetic field. Single-particle Gaussian basis sets are constructed, for each dot radius, under the condition of maximum overlap with the exact functions. The chemical potential, charging energy, and total spin expected values are calculated, and we have verified the validity of the quantum dot energy shell structure as well as Hund's rule for electronic occupation at zero magnetic field. At finite field, we have observed the violation of Hund's rule and studied the influence of magnetic field on the closed and open energy shell configurations. We have also compared the present results with those obtained within the LS-coupling scheme for low electronic occupation numbers. We focus only on ground-state properties and consider quantum dots populated up to 40 electrons, constructed by GaAs or InSb nanocrystals.

Analytical solutions for Yukawa potential applied to atomic systems embedded in debye plasmas

“…Two‐electron confined systems have been studied by some authors: Ludeña and Gregory 17 performed configuration interaction calculations by considering a spherical box and an atomic basis set formed by appropriated Gaussian functions; Destefani et al 18 studied three‐dimensional quantum dots defined by a spherical potential; Bielinska‐Waz et al 19 have analysed two‐electron quantum dots under a spherically symmetric quadratic confinement potential; Rivelino and Vianna 20 have proposed a configuration interaction method to investigate many‐electron systems in cavities and applied their method to study confined He atom.…”