Self-interaction-free density-functional theoretical study of the electronic structure of spherical and vertical quantum dots

We study the electronic structure and shell-filling effects of both spherical and vertical quantum dots by means of the density functional theory (DFT) with optimized effective potential (OEP) and self-interaction-correction (SIC) recently developed. The OEP/SIC procedure allows the elimination of the spurious self-interaction energy and the construction of accurate single-particle local potential with proper long-range Coulombic behavior. The OEP/SIC equations are discretized and solved accurately and efficiently by the generalized pseudospectral (GPS) method. The highest occupied orbital energy of N-electron quantum dots provides a direct measure of the electron affinity or chemical potential. We apply the OEP/SIC method to the study of the capacitive energy of N-electron spherical dots fur N up to 70. The results show the shell and subshell structure pattern and the electron filling pattern follows closely the Hund's rule. We also consider the effect of including the vertical dimension in the quantum dot study. We perform a detailed study of the shell-filling effect and the angular and radial density distributions of vertical quantum dots. The calculated capacitive energy spectrum is in good agreement with the recent experimental results, providing physical insights regarding the origin of electron shells and the role of electron-electron interaction in quantum dots.