MONOTONICITY PROPERTIES OF THE ATOMIC CHARGE-DENSITY FUNCTION

The present knowledge of the monotonicity properties of the sphericall y averaged electron density rho(r) and its derivatives, which comes mo stly from Roothan-Hartree-Fock calculations, is reviewed and extended to all Hartree-Fock ground-state atoms from hydrogen (Z = 1) to uraniu m (Z = 92). in looking for electron functions with universal (i.e., va lid in the whole periodic table) monotonicity properties, it is found that there exist positive values of or so that the function g(0)(r; al pha) = rho(r)/r(alpha) is convex, and g(1)(r; alpha) = -rho'(r)/r(alph a) is not only monotonically decreasing from the origin but also conve x. This is, however, not the case for the function g(2)(r; alpha) = rh o ''(r)/r(alpha). Additionally, the conditions which specify values fo r beta such that the function g(n)(r; beta) = (-1)(n) rho((n))(r)/r(be ta) is logarithmically convex are obtained and numerically calculated for n = 0, 1 in all neutral atoms below uranium. The last property is used to obtain inequalities of general validity involving three radial expectation values which generalize all the similar ones known to dat e, as well as other relationships among these quantities and the value s of the electron density and its derivatives at the nucleus. (C) 1996 John Wiley & Sons, Inc.