A study of the reduced density gradient s together with the density of s, g(s), for atoms across the periodic table (Li through Xe), following the work of Zupan et al. (Int. J. Quantum Chem. 1997, 61, 835), is presented. The results indicate that the reduced density gradient has maxima and minima related with the shell structure, and that these critical points are associated to the maxima in g(s). The behavior of the critical points in s, of the maxima in g(s) and of the average s calculated through g(s) across the rows and the columns of the periodic table is analyzed. © 2012 Wiley Periodicals, Inc.