Comparison of the utility of the shape function and electron density for predicting periodic properties: Atomic ionization potentials

Using data from atomic Hartree-Fock calculations, we examine whether it is easier to predict the ionization potential of a system using its shape function or using its electron density. A simple linear combination of two moments of the shape function capably predicts the periodic trends in the ionization potential, while a similar expansion in terms of the electron density does not. While it is known that the shape function determines all the properties of an electronic system, this suggests that the shape function is actually more useful than the electron density for predicting periodic properties, where the dependence of the electron density on the number of electrons only obscures the essential phenomenon. We present a theoretical argument as to why this might be true. Generalizing our results, one suspects the shape function will be more useful than the electron density when examining molecules' chemical properties.