Shannon entropies and logarithmic mean excitation energies from cusp- and asymptotic-constrained model densities - art. no. 022509

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 ion ization potential of the system, a strong similarity is observed between th is model entropy and the entropy obtained from correlated wave functions pr oviding 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 beh avior 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 momen tum space entropies as a function of a parameter are shown to be linearly r elated for these models. The expression for the entropy, derived from a den sity model that obeys the asymptotic behavior, is shown to be almost identi cal in nature to the general expression for entropy emanating in the stoppi ng power formalism.