The Kohn-Sham kinetic energy density as indicator of the electron localization: atomic shell structure

In this report, it is shown that the Kohn-Sham (KS) kinetic energy density (KED) contains the average local electrostatic potential (ALEP) and the average local ionization energy (ALIE); the shell structure in atomic systems is presented as one application of the KS-KED. By writing the KS-KED from the KS equations, this quantity was divided in three contributions: orbital, Coulomb, and exchange correlation. By studying several closed and open shell atoms, the shell structure was established by the maxima presented by the Coulomb contribution and the minima in the orbital contribution of the KS-KED. The exchange-correlation contribution to the KS-KED does not show maxima or minima, but this quantity shows bumps where the division between shells is expected. The results obtained in this work were compared with other shell structure indicators such as the electron localization function, the ALEP, the ALIE, and the radial distribution function. The most important result in this work is related to the fact that even when the ALEP and the ALIE functions were built with different arguments to each other, they are contained in the KS-KED. In this way, the KS-KED shows its importance to reveal the electron localization in atomic systems.