Complexity analysis of ionization processes and isoelectronic series

Information‐theoretic magnitudes measuring randomness (Shannon entropy, exponential entropy, power entropy), spread (variance), localization (disequilibrium or self‐similarity) and intrinsic accuracy (Fisher information) are used to compute several measures of complexity consisting, each one, of two localization–delocalization factors. These proposals have been tested on known, simple, but strongly organized and hierarchical systems (atoms) and processes (ionization). A complete numerical analysis at the Hartree–Fock level is done in position, momentum, and product spaces, where similar trends are followed by all studied complexities. It is also found that the complexity planes clearly reveal shell‐filling patterns across the periodic table. Characteristic features accompanying the ionization process are identified, and the physical reasons for the observed patterns are described. We conclude that (i) the studied complexity measures detect not only randomness or localization, but also pattern and organization, and (ii) their study is not only sufficient in the usual position space, but also in the complementary momentum space, to have a complete description of the information–theoretic behavior of these systems. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009