Shannon entropy and Fisher information for endohedral confined one-and two-electron atoms

In this work, we study the Shannon entropy and Fisher information of the H, He, Li+, and Be2+ atoms confined by a C-60 cavity. The fullerene cavity is described by three model potentials: the square well (SW), Woods-Saxon (WS), and the Gaussian model (GM). We solved the time-independent Schrodinger and Hartree-Fock equations by means of a numerical method. We find that the C-60 endohedral cavity modifies the ground- and excited-states of the hydrogen atom where the largest effect is given for the 2s state leading to an increase of similar to 2.5% of the Shannon entropy. The Fisher information results for the excited-states are highly sensitive to the presence of the C-60 cavity where the largest increase is reported for the 5s state with 50%. For the two-electron atoms, we find slight changes on the ground-state properties where the larger increase is for the Shannon entropy and Fisher information of the He atom in the ground-state. Our findings show that the GM potential leads to the largest change in electronic properties due to the overlap with the wave-functions. In the absence of the C-60 cavity, our findings are in excellent agreement with other theoretical results. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

In this study, the Shannon entropy and Fisher information of H, He, Li+, and Be2+ atoms confined by a C-60 cavity were investigated using numerical methods. The presence of the C-60 cavity was found to modify the electronic properties of the atoms, with significant effects on the ground- and excited-states of hydrogen and slight changes on the properties of two-electron atoms. The Gaussian model potential showed the largest impact on electronic properties due to the overlap with wave-functions.