Information theoretic measures of Hookium using generalized pseudo-spectral technique within density functional theory

Atomic systems subjected to external confinement exhibit a range of intriguing physical properties. In this work, we employ a well-established work-function-based Kohn-Sham density functional theory (DFT) within a generalized pseudospectral (GPS) method to determine the energy eigenvalues and eigenfunctions of Hookium (a two-electron system bound by a harmonic potential). We consider the two cases, viz. (i) Hookium and (ii) Hookium under the influence of a spherical cavity confinement. Two correlation energy functionals like Wigner and Lee-Yang-Parr (LYP) are considered to include explicit correlation energy in the calculation. Furthermore, we provide a comprehensive analysis of the quantum information-theoretic aspects of confined systems by examining the position-space Shannon and Fisher entropies.