Fisher–Shannon (FS) and López-Ruiz, Mancini, and Calbet (LMC) complexity measures, detecting not only randomness but also structure, are computed by using near Hartree–Fock wave functions for neutral atoms with nuclear charge $Z=1–103$ in position, momentum, and product spaces. It is shown that FS and LMC complexities are qualitatively and numerically equivalent for these systems. New complexity candidates are defined, computed, and compared by using the following information-theoretic magnitudes: Shannon entropy, Fisher information, disequilibrium, and variance. Localization-delocalization planes are constructed for each complexity measure, where the subshell pattern of the periodic table is clearly shown. The complementary use of $r$ and $p$ spaces provides a compact and more complete understanding of the information content of these planes.

The Fisher-Shannon plane which embodies the Fisher information measure in conjunction with the Shannon entropy is tested in its ability to quantify and compare the informational behavior of the process of atomic ionization. We report the variation of such an information measure and its constituents for a comprehensive set of neutral atoms, and their isoelectronic series including the mononegative ions, using the numerical data generated on 320 atomic systems in position, momentum, and product spaces at the Hartree-Fock level. It is found that the Fisher-Shannon plane clearly reveals shell-filling patterns across the periodic table. Compared to position space, a significantly higher resolution is exhibited in momentum space. Characteristic features in the Fisher-Shannon plane accompanying the ionization process are identified, and the physical reasons for the observed patterns are described.

The Fisher–Shannon and LMC shape complexities and the Shannon–disequilibrium, Fisher–Shannon and Fisher–disequilibrium information planes, which consist of two localization–delocalization factors, are computed in both position and momentum spaces for the one-particle densities of 90 selected molecules of various chemical types, at the CISD/6-311++G(3df,2p) level of theory. We found that while the two measures of complexity show general trends only, the localization–delocalization planes clearly exhibit chemically significant patterns. Several molecular properties (energy, ionization potential, total dipole moment, hardness, electrophilicity) are analyzed and used to interpret and understand the chemical nature of the composite information–theoretic measures above mentioned. Our results show that these measures detect not only randomness or localization but also pattern and organization.