Structural properties and quantum information measures of H, Li and Na atoms endohedrally captured in C36 and C60 cages

Ritz variational principle has been utilized to study the structural properties of the valence electron of the endohedrally captured H, Li and Na atom in fullerene C 36 and C 60 cages. The cage environment is incorporated by considering a spherical shell model potential. On the other hand, the interaction between the core and the valence electron corresponding to Li and Na atom has been mimicked by another model potential. The effect of the fullerene C 36 and C 60 cages on the total energy eigenvalue and different energy components contributing to the total energy (e.g. kinetic energy, Coulombic part of the potential energy, total cage potential etc.) has been studied for all H, Li and Na atoms. The position space as well as momentum space geometrical properties, variance, and Pearson correlation coefficient are also included in the present work. We have estimated the one-electron radial charge density in both position and momentum space which are clearly depicting the effect of the cage on the valence electron of H, Li and Na atom. Further, we have shown the effect of the fullerene cages on both position and momentum space Shannon, Fisher and disequilibrium entropies corresponding to all the above-mentioned atoms.