  A novel quantum similarity measure (QSM) is constructed based on concepts
from information theory. In an application of QSM to atoms, the new QSM and its
corresponding quantum similarity index (QSI) are evaluated throughout the
periodic table, using the atomic electron densities and shape functions
calculated in the Hartree-Fock approximation. The periodicity of Mendeleev's
table is regained for the first time through the evaluation of a QSM.
Evaluation of the information theory based QSI demonstrates, however, that the
patterns of periodicity are lost due to the renormalization of the QSM,
yielding chemically less appealing results for the QSI. A comparison of the
information content of a given atom on top of a group with the information
content of the elements in the subsequent rows reveals another periodicity
pattern. Relativistic effects on the electronic density functions of atoms are
investigated. Their importance is quantified in a QSI study by comparing for
each atom, the density functions evaluated in the Hartree-Fock and Dirac-Fock
approximations. The smooth decreasing of the relevant QSI along the periodic
table illustrates in a quantitative way the increase of relativistic
corrections with the nuclear charge.
