The information-theoretic measure of confined hydrogen atom has been investigated extensively in the literature. However, most of them were focused on the ground state and accurate values of information entropies, such as Shannon entropy, for confined hydrogen are still not determined. In this work, we establish the benchmark results of the Shannon entropy for confined hydrogen atom in a spherical impenetrable sphere, in both position and momentum spaces. This is done by examining the bound state energies, the normalization of wave functions, and the scaling property with respect to isoelectronic hydrogenic ions. The angular and radial parts of Shannon entropy in two conjugate spaces are provided in detail for both free and confined hydrogen atom in ground and several excited states. The entropies in position space decrease logarithmically with decreasing the size of confinement, while those in momentum space increase logarithmically. The Shannon entropy sum, however, approaches to finite values when the confinement radius closes to zero. It is also found that the Shannon entropy sum shares same trend for states with similar density distributions. Variations of entropy for nodeless bound states are significantly distinct form those owning nodes when changing the confinement radius. K E Y W O R D S confined hydrogen atom, momentum space, radial entropy, Shannon entropy Int J Quantum Chem. 2017;117:e25375. https://doi.org/10.1002/qua.25375.

Recent development of information theory provides researchers an alternative and useful tool to quantitatively investigate the variation of the electronic structure when atoms interact with the external environment. In this work, we make systematic studies on the information-theoretic measures for hydrogen-like ions immersed in weakly coupled plasmas modeled by Debye-Hückel potential. Shannon entropy, Fisher information, and Fisher-Shannon complexity in both position and momentum spaces are quantified in high accuracy for the hydrogen atom in a large number of stationary states. The plasma screening effect on embedded atoms can significantly affect the electronic density distributions, in both conjugate spaces, and it is quantified by the variation of information quantities. It is shown that the composite quantities (the Shannon entropy sum and the Fisher information product in combined spaces and Fisher-Shannon complexity in individual space) give a more comprehensive description of the atomic structure information than single ones. The nodes of wave functions play a significant role in the changes of composite information quantities caused by plasmas. With the continuously increasing screening strength, all composite quantities in circular states increase monotonously, while in higher-lying excited states where nodal structures exist, they first decrease to a minimum and then increase rapidly before the bound state approaches the continuum limit. The minimum represents the most reduction of uncertainty properties of the atom in plasmas. The lower bounds for the uncertainty product of the system based on composite information quantities are discussed. Our research presents a comprehensive survey in the investigation of information-theoretic measures for simple atoms embedded in Debye model plasmas.

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