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

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.