Rigorous upper and lower bounds on the atomic spherically averaged electron density are found for all radial values in terms of the charge density at the nucleus, ρ(0), and the first few radial expectation values. Moment-theory methods and Chebyshev inequalities are used to obtain the bounds. This type of result can be employed to compare diverse information obtained by using different models, numerical approximations or experimental data. In order to study the goodness of the bounds, a computation in a Hartree-Fock framework is done. The accuracy of our simplest upper bound is similar to a previous one found by King [J. Chem. Phys. 78, 2459 (1983)] using very different methods and information. Other bounds, containing more information, clearly improve the aforementioned result. The same method allows one to obtain bounds on the derivative and primitive functions of the electron density as well as on the atomic charge.

• Received 27 January 1993

DOI:https://doi.org/10.1103/PhysRevA.48.4149