ATOMIC-CHARGE CONVEXITY AND THE ELECTRON-DENSITY AT THE NUCLEUS

The convexity of the spherically averaged electron density (r) of neutral atoms with Z 54 is numerically studied in a Hartree-Fock framework. It is found that (r) is convex for Z=1, 2, 7 15, and 33 44, while for the rest of the atoms it presents a small nonconvex region. Second, rigorous relationships between the values of the single-particle density and its first derivative at the origin and the radial expectation values rk for a convex (r) are derived. These conditions are valid for any many-body system whose spherically averaged single-particle density is convex. Finally, for atomic systems, these determinantal conditions together with the electron-nucleus cusp condition are used to obtain novel upper and lower bounds to (0) by means of two or more expectation values. The quality of the new lower bounds is better than that of the corresponding ones known up to now. In particular, the convexity bound (1/6)(r-2 2/ r-1) to (0) improves by a factor of 4/3 the accuracy of the corresponding bound obtained from the property of monotonic decrease of (r). © 1990 The American Physical Society.