Near homogeneous variation of potentials in large systems and the electronic structure of molecular quantum dots

It is shown from Kohn-Sham (KS) density-functional theory that in a large molecular system, the Coulomb potential, molecular electrostatic potential, and KS effective potential may exhibit an approximately homogeneous variation in space, in response to a small change of the electron number. The homogeneous variation of potentials underlies the constant interaction (CI) model of quantum dots (QDs) and is related to the delocalization and invariance of KS orbitals, the identical shift of KS levels, and a natural definition of the QD capacitance. Calculation results of a fullerene C60 and a single-walled carbon nanotube are presented. Although the homogeneity of the potential variation is not perfect, it seems to lead to fairly good approximation of the CI model to the addition energy spectra of these systems.