On the non-convexity of charge densities in atoms and ions

For neutral atoms with the number of electrons N less than or equal to 103 and singly charged cations and anions with N less than or equal to 54, the second derivative rho "(r) of the spherically averaged one-particle density rho(r) is studied within the Hartree-Fock framework. In all the three seri es of neutrals, cations and anions, rho "(r) displays one or more pairs of local extrema, whose number never decreases when the nuclear charge Z and/o r the number of electrons N increase. The existence of one or two non-conve xity regions of r is observed for some species, where rho "(r) is negative. The location and width of non-convexity regions are examined, and their de pendence on Z and N is discussed, as well as the properties of the other lo cal extrema in rho "(r). (C) 2000 Elsevier Science B.V. All rights reserved .