How to accurately predict electronic properties of a Columbic system with the electron density obtained from experiments such as X-ray crystallography is still an unresolved problem. The information-theoretic approach recently developed in the framework of density functional reactivity theory is one of the efforts to address the issue. In this work, using 27 atoms and 41 molecules as illustrative examples, we present a study to demonstrate that one is able to satisfactorily describe such electronic properties as the total energy and its components with information-theoretic quantities like Shannon entropy, Fisher information, Ghosh-Berkowitz-Parr entropy, and Onicescu information energy. Closely related to the earlier attempt of expanding density functionals using simple homogeneous functionals, this work not only confirms Nagy's proof that Shannon entropy alone should contain all the information needed to adequately describe an electronic system but also provides a feasible pathway to map the relationship between the experimentally available electron density and various electronic properties for Columbic systems such as atoms and molecules. Extensions to other electronic properties are straightforward.