Information Entropy, Information Distances and Complexity in Atoms

Abstract

Shannon information entropies in position and momentum spaces and their sum are calculated as functions of Z (Z=2-54) in atoms. Roothaan-Hartree-Fock electron wave functions are used. The universal property S=a+b lnZ 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.

Major revision, accepted for publication in the Journal of Chemical Physics

References in corpus (14)

• A Statistical Measure of Complexity
• The role of ionization electrons in direct dark matter detection
• Universal property of the information entropy in atoms, nuclei and atomic clusters
• Direct dark matter search by observing electrons produced in neutralino-nucleus collisions
• A link of information entropy and kinetic energy for quantum many-body systems
• Wootters' distance revisited: a new distinguishability criterium
• Application of information entropy to nuclei
• The dependence of information entropy of uniform Fermi systems on correlations and thermal effects
• Information entropy as a measure of the quality of a nuclear density distribution
• Evaluation of cluster expansions and correlated one-body properties of nuclei
• The ionization of H, He and Ne atoms using neutrinos or antineutrinos at keV energies
• Electron Spectra in the Ionization of Atoms by Neutrinos
• Universal trend of the information entropy of a fermion in a mean field
• Quantum-Information Content of Fractional Occupation Probabilities in Nuclei

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