Abstract
Jensen–Shannon divergence is used to quantify the discrepancy between the Hartree–Fock pair density and the product of its marginals for different N-electron systems, enclosing neutral atoms (with nuclear charge Z=N) and singly-charged ions (N = Z pm 1). This divergence measure is applied to determine the interelectronic correlation in atomic systems. A thorough study was carried out, by considering (i) both position and momentum conjugated spaces, and (ii) systems with a nuclear charge as far as Z = 103. The correlation among electrons was measured by comparing, for an arbitrary system, the double-variable electron-pair density with the product of the respective one-particle densities. A detailed analysis throughout the Periodic Table highlights the relevance not only of weightiness for the systems considered, but also of their shell structure. Besides, comparative computations between two-electron densities of different atomic systems (neutrals, cations, anions) quantify their dissimilarities, patently governed by shell-filling patterns throughout the Periodic Table.
Highlights
The two-electron density Γ (r1, r2) is the probability density of any two electrons that are located at radii r1 and r2, respectively, and is a convenient starting point to study the spatial interaction between two electrons in an explicit manner [1]
Jensen–Shannon divergence (JSD) is applied to quantify the interelectronic correlation in atomic systems
The absence of correlation translates into the extreme allowed value JSD = 0, Page 13 of 16 763 (a)
Summary
The two-electron density Γ (r1, r2) is the probability density of any two electrons that are located at radii r1 and r2, respectively, and is a convenient starting point to study the spatial interaction between two electrons in an explicit manner [1]. The concepts of uncertainty, randomness, disorder and delocalization are basic ingredients in the study, within an information-theoretic framework, of relevant structural properties for many different probability distributions appearing as descriptors of several chemical and physical systems and processes The relevancy of these concepts has motivated new studies that pursue quantification, giving rise to a variety of density functionals, such as Shannon entropy [22], Fisher information [23], disequilibrium [24], complexity [25], and many others. Its non-negativity arises from the convex character of the Shannon entropy functional This comparative measure has found deep applications in statistics and many other fields, including entanglement characterization [38], analysis of symbolic sequences or series, and in particular in the study of segmentation of DNA sequences [39]. Conclusions and open problems or future work are briefly described in the last section
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