Analysis of correlation and ionization from pair distributions in many-electron systems

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 $$Z=N$$ Z = N ) and singly-charged ions ($$N = Z \pm 1$$ N = Z ± 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 $$Z = 103$$ 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.

Mutual Information in Conjugate Spaces for Neutral Atoms and Ions

“…A recent study of the authors [ 61 ] have considered the Jensen–Shannon divergence ( ) as a comparative measure with similar purposes to those presented here. In that case, the measure employed is a symmetrized version of , thus loosing the ‘directed character’ which makes an appropriate measure of mutual information, in the sense that it takes the uncorrelated distribution as the reference/a priori one.…”