Shannon entropy along hydrogen isoelectronic sequence using Numerov method

Shannon entropy (SE) for hydrogen isoelectronic sequence is calculated through numerical simulation. Fast and accurate Numerov method is applied for the computation of the wavefunctions used for the evaluation of Shannon entropy. The reliability of this approach is verified by the excellent comparison with the available literature results. It is observed that Shannon entropy values diminish with an increment in atomic number (Z). Additionally, previously unexplored Shannon entropy behaviour for a variety of higher excited orbitals is investigated. It is found that Shannon entropy exhibits an interesting behavior of increasing and decreasing nature with principal quantum number n and orbital quantum number l, respectively. Benchmark values for Shannon information entropy are established for the ground and excited states as a signature of localization and delocalization of electron density. This will further contribute to the diagnostics of spectroscopic data and atomic system complexity.