We investigate the electronic structure of quasi-two-dimensional square qua
ntum dots by using the spin-density functional theory. In the weak interact
ing regime, we identify shell fillings due to Hund's rule and calculate the
electron-number-dependent addition energies of the dots. To understand the
interplay between the kinetic energy and Coulomb energy we examine the gro
und-state spin and charge configurations by varying size of the dot. We est
imate the existence of the Wigner-molecule-like state at a critical mean di
stance parameter r(s)similar to 6a(B)(*).