The "simple" measure of complexity of Shiner, Davison and Landsberg (SDL) and
the "statistical" one, according to Lopez-Ruiz, Mancini and Calbet (LMC), are
compared in atoms as functions of the atomic number Z. Shell effects i.e. local
minima at the closed shells atoms are observed, as well as certain qualitative
trends of SDL and LMC measueres of complexity. If we impose the condition that
SDL and LMC behave similarly as functions of Z, then we can conclude that
complexity increases with Z and for atoms the strength of disorder is zero and
order is four.Comment: 14 pages, 2 figures, revised version, accepted for publiaction in
Physics Letters
Shannon information entropies in position and momentum spaces and their sum are calculated as functions of Z (2 ≤ Z ≤ 54) in atoms. Roothaan-Hartree-Fock electron wave functions are used.The universal property S = a + b ln Z is verified. In addition, we calculate the Kullback-Leibler relative entropy, the Jensen-Shannon divergence, Onicescu's information energy and a complexity measure recently proposed. Shell effects at closed shells atoms are observed. The complexity measure shows local minima at the closed shells atoms indicating that for the above atoms complexity decreases with respect to neighboring atoms. It is seen that complexity fluctuates around an average value, indicating that the atom cannot grow in complexity as Z increases. Onicescu's information energy is correlated with the ionization potential. Kullback distance and Jensen-Shannon distance are employed to compare Roothaan-Hartree-Fock density distributions with other densities of previous works.
The net Fisher information measure I T , defined as the product of position and momentum Fisher information measures I r and I k and derived from the non-relativistic Hartree-Fock wave functions for atoms with Z = 1−102, is found to correlate well with the inverse of the experimental ionization potential. Strong direct correlations of I T are also reported for the static dipole polarizability of atoms with Z = 1 − 88. The complexity measure, defined as the ratio of the net Onicescu information measure E T and I T , exhibits clearly marked regions corresponding to the periodicity of the atomic shell structure. The reported correlations highlight the need for using the net information measures in addition to either the position or momentum space analogues. With reference to the correlation of the experimental properties considered here, the net Fisher information measure is found to be superior than the net Shannon information entropy.
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