The Fisher–Shannon and LMC shape complexities and the Shannon–disequilibrium, Fisher–Shannon and Fisher–disequilibrium information planes, which consist of two localization–delocalization factors, are computed in both position and momentum spaces for the one-particle densities of 90 selected molecules of various chemical types, at the CISD/6-311++G(3df,2p) level of theory. We found that while the two measures of complexity show general trends only, the localization–delocalization planes clearly exhibit chemically significant patterns. Several molecular properties (energy, ionization potential, total dipole moment, hardness, electrophilicity) are analyzed and used to interpret and understand the chemical nature of the composite information–theoretic measures above mentioned. Our results show that these measures detect not only randomness or localization but also pattern and organization.

The spreading of the quantum-mechanical probability distribution density of $D$ -dimensional hydrogenic orbitals is quantitatively determined by means of the local information-theoretic quantity of Fisher in both position and momentum spaces. The Fisher information is found in closed form in terms of the quantum numbers of the orbital.

The Fisher divergence (FD) and Jensen–Shannon divergence (JSD) are used in this work with the aim of providing quantitative measures of the discrepancies between two arbitrary $D$ -dimensional distribution functions, the FD being of local character and the JSD of global one. In doing so, the concepts of Fisher information and Shannon entropy associated to a distribution are the essential quantities for building up these comparative functionals. This kind of relative measures are here applied to the study of the one-particle densities in both conjugated spaces (position and momentum) of neutral atoms, discussing the results as compared to those provided by other previous functional measures. It is clearly shown how these divergences provide relevant information on the atomic shell structure, up to a level which depends on the considered space and measure.