Restricted and unrestricted Hartree-Fock approaches for addition   spectrum and Hund's rule of spherical quantum dots in a magnetic field
  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, the charging energy and the total spin expected values have been calculated, and we have verified the validity of the quantum dot energy shell structure as well as the Hund rule for electronic occupation at zero magnetic field. For 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 with LS-coupling scheme for low electronic occupation numbers. We focus only on ground state properties and consider quantum dots populated up to forty electrons, constructed by GaAs or InSb semiconductors. 
C. F. Destefani, J. D. M. Vianna, G. E. Marques