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Mutual information is introduced as an electron correlation measure and examined for isoelectronic series and neutral atoms. We show that it possesses the required characteristics of a correlation measure and is superior to the behavior of the radial correlation coefficient in the neon series. A local mutual information, and related local quantities, are used to examine the local contributions to Fermi correlation, and to demonstrate and to interpret the intimate relationship between correlation and localization. [ABSTRACT FROM AUTHOR]

The phenomenon of electron correlation in atomic systems is examined and compared from the statistical, information theoretic, and energetic perspectives. Local correlation measures, based on the correlation coefficient, information entropies, and idempotency measure, are compared to the correlation energy density. Analysis of these local measures reveals that the chemically significant valence region is responsible for the behavior of their respective global measures in contrast to the correlation energy density which has large contributions to the correlation energy from both the core and valence regions. These results emphasize the difference in the mechanisms inherent in the different perspectives, the similarity between the statistical, information entropic, and idempotency views, and provides further evidence for the use of information theoretic based quantities in studies of electron correlation. [ABSTRACT FROM AUTHOR]

The one-electron Shannon information entropy sum is reformulated in terms of a single entropic quantity dependent on a one-electron phase space quasiprobability density. This entropy is shown to form an upper bound for the entropy of the one-electron Wigner distribution. Two-electron entropies in position and momentum space, and their sum, are introduced, discussed, calculated, and compared to their one-electron counterparts for neutral atoms. The effect of electron correlation on the two-electron entropies is examined for the helium isoelectronic series. A lower bound for the two-electron entropy sum is developed for systems with an even number of electrons. Calculations illustrate that this bound may also be used for systems with an odd number of electrons. This two-electron entropy sum is then recast in terms of a two-electron phase space quasiprobability density. We show that the original Bialynicki-Birula and Mycielski information inequality for the N-electron wave function may also be formulated in terms of an N-electron phase space density. Upper bounds for the two-electron entropies in terms of the one-electron entropies are reported and verified with numerical calculations. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Relationships between the Jaynes and Shannon information entropies, both of which are related to the correlation energy, are given and the physical implications are explored. Evidence is provided from a study of the Be and Ne isoelectronic sequences that the Shannon entropy is more sensitive to the effects of the nuclear charge than is the Jaynes entropy. It is shown that the Jaynes entropy may be considered as the difference between the mean orbital Shannon entropy per electron and the mean orbital Shannon entropy of one electron. These mean orbital entropies display the same functional behavior as the total Shannon entropy throughout the isoelectronic sequence. We demonstrate that the Jaynes entropy may be considered as the sum of the Kullback-Leibler distance entropies occurring between natural spin orbital densities and a reference point whose occupation number is one. The large Z asymptotic behavior of the Jaynes and Shannon entropies is discussed. From a study of a Ne isonuclear sequence, it is shown that both Shannon and Jaynes entropies increase with the number of electrons, illustrating that these quantities are sensitive to the amount of electronic interactions present in the system. Relationships for the changes in the Shannon and Jaynes entropies with respect to the number of electrons for an isonuclear sequence are obtained, which depend on the electron affinity, first and second ionization potentials, and the hardness and chemical potential of the system. [ABSTRACT FROM AUTHOR]

Numerical evidence for the monotonicity of the isotropic atomic form factor, F(k), is presented. It is shown that the structural features of F(k) can be considerably enhanced by taking its Laplacian, ∇2F(k). Roots and extrema of this function can be assigned to different atomic shells. Linear relationships between the position of the roots and extrema and the atomic number Z are found for the neutral atoms with Z≤92. [ABSTRACT FROM AUTHOR]

The Laplacian of the spherically averaged momentum density, ∇2Π(p), is computed from nonrelativistic self-consistent-field wave functions for the neutral atoms from hydrogen to uranium, and the singly positive ions, from helium to barium and lutetium to radium. In particular, the topography of ∇2Π(p) reveals that there are seven distinct types of behavior for the studied atomic and ionic cases, based on the number of zeros and extrema present and the value of ∇2Π(p) at the origin. Shell structure within ∇2Π(p) is shown to be exhibited by the zeros that occur as ∇2Π(p) crosses from negative values to positive values. These zeros have been found to be the topographical feature most intimately related to the radii predicted by the Bohr theory of an atom. At most four shells per atom or ion are revealed based on this criterion. [ABSTRACT FROM AUTHOR]

The Laplacian of the spherically averaged charge density ∇2ρ(r) has been computed from nonrelativistic SCF wave functions for the neutral atoms from hydrogen to uranium, and the singly positive ions, from helium to barium and lutetium to radium, in order to examine the shell structure. ∇2ρ(r) exhibits a number of extremal points and zeros with the absolute value of the function becoming smaller at each successive extremal point. The zeros, in particular the odd numbered zeros, are shown to exhibit good correlation with the Bohr theory of an atom while the extremal points correlate to a lesser extent. At most five shells are seen in the studied atomic cases based on the fact that the odd numbered zeros are the topological feature of ∇2ρ(r) most indicative of a shell. [ABSTRACT FROM AUTHOR]

Integrations of the charge density between the critical points of ∇2ρ(r) show that these points are not suitable as definitions of atomic shell boundaries. A comparison with the corresponding scheme based on D(r) favors the latter. Minima in D(r) and corresponding shell populations are tabulated for 55≤Z≤92. [ABSTRACT FROM AUTHOR]