Spin-density functional approach to N-electron quantum dots within the Matlab pde-tool

The ground-state electronic structures of N-electron quantum dots have been studied by using the spin-density functional method. The calculations are performed in real space using a developed program based on the Matlab pde-tool. Within the program, the recently proposed analytic representation of the exchange–correlation energy functional of Attaccalite et al. is used instead of the most used form of Tanatar and Ceperley. To compare with experimental results and theoretical studies, the addition energy spectra of quantum dots defined by harmonic and anisotropic confinements are examined. The calculations show that when the harmonic confining potential is weak enough the peak in addition energy spectra at N=2 can be firstly disappeared. For geometrical deformed circular quantum dots, the standard shell structure with N=2,6,12,… is continually destroyed, but the slightly distorting does not change the shell-filling order of electrons.