Abstract
The discrepancy among one-electron and two-electron densities for diverse N-electron atomss, enclosing neutral systems (with nuclear charge ) and charge-one ions (), is quantified by means of mutual information, I, and Quantum Similarity Index, , in the conjugate spaces position/momentum. These differences can be interpreted as a measure of the electron correlation of the system. The analysis is carried out by considering systems with a nuclear charge up to and singly charged ions (cations and anions) as far as . The interelectronic correlation, for any given system, is quantified through the comparison of its double-variable electron pair density and the product of the respective one-particle densities. An in-depth study along the Periodic Table reveals the importance, far beyond the weight of the systems considered, of their shell structure.
Highlights
Π(~p1, ~p2 ) and the respective one-electron functions γ(~p1 ) and γ(~p2 ). This means that, in both spaces, determining electron correlation is equivalent to measuring differences between the electron pair distribution in a given space and the product of one-electron distributions in the same space
Those differences have been studied in the past, by considering the so-called ’mutual information’ (I) between the respective pairs of variables in each conjugate space for some specific atomic systems
The differences between the monoelectronic and the electron pair densities can be interpreted as a measure of the electron correlation of the system
Summary
The description of main physical and chemical properties of those systems can be achieved in terms of entropic spreading measures of the electron distribution [24,25], which quantify, for instance, uncertainty, randomness, disorder and localization These concepts have induced the birth of a diversity of density functionals: Shannon entropy [26], Fisher information [24, 27] and complexity [28] among others. S (which provides a first quantitative notion of the spreading for a given distribution), the mutual information I (interpreted in terms of the Kullback–Leibler divergence) and the Quantum Similarity Index QSI (which constitutes a measure of the ’overlap’ among distributions on their domain) are employed In this analysis, neutral atoms and their singly charged ions are considered.
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