Quantifying Dirac hydrogenic effects via complexity measures

The primary dynamical Dirac relativistic effects can only be seen in hydrogenic systems without the complications introduced by electron-electron interactions in many-electron systems. They are known to be the contraction-towards-the-origin of the electronic charge in hydrogenic systems and the nodal disapearance (because of the raising of all the non-relativistic minima) in the electron density of the excited states of these systems. In addition we point out the (largely ignored) gradient reduction of the charge density near and far the nucleus. In this work we quantify these effects by means of single (Fisher information) and composite (Fisher-Shannon complexity and plane, LMC complexity) information-theoretic measures. While the Fisher information measures the gradient content of the density, the (dimensionless) composite information-theoretic quantities grasp two-fold facets of the electronic distribution: The Fisher-Shannon complexity measures the combined balance of the gradient content and the total extent of the electronic charge, and the LMC complexity quantifies the disequilibrium jointly with the spreading of the density in the configuration space. Opposite to other complexity notions (e.g., computational and algorithmic complexities), these two quantities describe intrinsic properties of the system because they do not depend on the context but they are functionals of the electron density. Moreover, they are closely related to the intuitive notion of complexity because they are minimum for the two extreme (or least complex) distributions of perfect order and maximum disorder.