Characteristic features of Shannon information entropy of confined atoms

Abstract

The Shannon information entropy of 1-normalized electron density in position and momentum space S_r and S_p, and the sum S_T, respectively, are reported for the ground-state H, He⁺, Li²⁺, H⁻, He, Li⁺, Li, and B atoms confined inside an impenetrable spherical boundary defined by radius R. We find new characteristic features in S_T denoted by well-defined minimum and maximum as a function of confinement. The results are analyzed in the background of the irreducible lower bound stipulated by the entropy uncertainty principle [ I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975) ]. The spherical confinement model leads to the S_T values which satisfy the lower bound up to the limits of extreme confinements with the interesting new result displaying regions over which a set of upper and lower bounds to the information entropy sum can be locally prescribed. Similar calculations on the H atom in 2s excited states are presented and their novel characteristics are discussed.