Analysis of Momentum Density Shifts in Carbon-Like Ions Using Kullback-Leibler Divergence

, Riam

doi:10.25673/123561

Proceedings of International Conference on Applied Innovation in IT · 2026/03/31 · Vol. 14 · Issue 1 · pp. 209–219

Analysis of Momentum Density Shifts in Carbon-Like Ions Using Kullback-Leibler Divergence

Riam Amer Ahmed and Wissam Ahmed Ameen

📄 Download PDF DOI: 10.25673/123561

Abstract

Roothaan-Hartree-Fock method was utilized to examine momentum density shifts in each of the shells of the carbon atom. The analysis is further expanded to include some carbon-like ions: N^(+1),O^(+2) and F^(+3) in the ground state. The shift in the momentum density of adjacent ions within the isoelectronic series was analysed using the Kullback–Leibler divergence as an information-theoretic tool. They were found to have four distinct zones (two favouring the preceding ion in the isoelectronic sequence (lower nuclear charge) at low and high momenta and two favouring the succeeding ion in the isoelectronic sequence (higher nuclear charge) at intermediate and relatively high momenta). It was observed that the values of the Kullback-Leibler divergence of the identified momentum zones decrease in a systematic way with the nuclear charge, indicating an increasing similarity of the momentum-density distributions of the compared distributions. The shared momentum domain (core zone) is an overlapping grey zone, which typically escalated with ionisation. This alteration in the size of zoning is compatible with the principle of conservation of probability, when the density decreases in one zone and increases in another. The expectation values of various momentum moments were computed to optimize the interpretation of the momentum density shifts that were found using KL divergence.

Keywords

Roothaan-Hartree-Fock (RHF) Momentum Density Shift KL-Divergence Momentum Space.

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