Shannon entropies and logarithmic mean excitation energies from cusp- and asymptotic-constrained model densities

A model correctly describing the asymptotic behavior of the charge density is used to derive an expression for the Shannon entropy in terms of the ionization potential of the system. A strong similarity is observed between this model entropy and the entropy obtained from correlated wave functions providing evidence that it is the asymptotic regions that are responsible for the behavior of the entropy. We also show via a model entropy that the behavior of the momentum space Shannon entropy is due to a correct description of the cusp behavior at the nucleus. The changes in the position and momentum space entropies as a function of a parameter are shown to be linearly related for these models. The expression for the entropy, derived from a density model that obeys the asymptotic behavior, is shown to be almost identical in nature to the general expression for entropy emanating in the stopping power formalism.