  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.
