Atomic shell structure based on inhomogeneity measures of the electron density

A measure of electron density inhomogeneity is proposed based on the distance of function values to the average value within a chosen region. The choice of the examined regions follows the approach of restricted space partitioning with fixed inhomogeneity as the restriction. The integration of electron density over the regions of the partitioning yields discrete distribution of charges, which is analyzed. The resulting functionals depend on the particular definition of distance. Two possibilities are selected for the distance definition, and the functionals are applied to examine the shell structure of the atoms Li to Xe.