Spreading measures of information-extremizer distributions: applications to atomic electron densities in position and momentum spaces

The problem of finding the information-extremizer distribution with a set of given constraints (partial information) has a relevant role from both physical and chemical points of view, specially when working within a density functional theory framework. Beyond the variance, there exist different measures of information susceptible of being extremized, such as the Fisher information and the Shannon and Tsallis entropies. Each one possesses its own properties which make their use more or less convenient according to the systems and/or the process we are dealing with. In this work, we analyze the main information measures of the electron densities of neutral atoms throughout the periodic table, in the two conjugated position and momentum spaces. It is shown how these measures display shell-filling patterns, within a level which depends on the information measure and the space considered. Additionally, the values of all these measures for the solution of various atomic information extremization problems (MaxEnt, MaxTent, MinInf), using radial expectation values as constraints, are analytically obtained, numerically evaluated and also interpreted and discussed in terms of physical characteristics of the atomic systems, such as periodicity and shell structure.