Shannon-information entropy sum as a correlation measure in atomic systems

The interpretation of the entropy sum as a correlation measure is demonstrated for isoelectronic series via an analytical expression that models the asymptotic behavior of the electronic charge density in position space and the cusp behavior in momentum space. We also develop an expression for the entropy sum in neutral atoms with an explicit dependence on the ionization energy and the atomic number. The results obtained from these relations are in qualitative agreement with the behavior observed from ab initio calculations. A connection between the entropy sum and the correlation energy is obtained for the weakly inhomogeneous electron gas and demonstrated via calculations for the helium isoelectronic series.