Jensen–Shannon divergence in conjugate spaces: The entropy excess of atomic systems and sets with respect to their constituents

The disorder of a composite system or of a set of different systems is always higher than the mere sum of the internal disorder of its constituents. One of the most widely used functionals employed for measuring the randomness of a single distribution is the Shannon entropy, from which the increase of disorder within the composite system with respect to those of the constituents is quantified by means of the Jensen–Shannon Divergence (JSD). In this work two different applications of the JSD in the study of the information content of atomic electron densities are carried out: (i) finding the contribution for a given atom of its composing subshells to the total atomic information; (ii) and similarly for selected sets of atoms, such as periods and groups throughout the Periodic Table as well as isoelectronic series. In both cases, the analysis is performed in the two conjugate position and momentum spaces, and the results are interpreted according to physically relevant quantities such as the ionization potential.