On relations between correlation, fluctuation and localization

The ground states of many-electron systems (atoms, molecules, solids) are considered under the aspect of mutual relations among the phenomena of correlation, fluctuation, and localization. Known measures of the correlation strength are summarized (Collins' information entropy, Kutzelnigg's statistical correlation coefficients, Fulde's correlation strength, Cioslowski's strength of short-range correlation) and new indices are proposed (normalization of the correlation tail of the natural occupation numbers, 'occupation gap', on-top properties of the intracule pair densities for parallel- and antiparallel spin electron pairs). In addition to these quantum-kinematical quantities, new reference-free ratios of kinetic and potential energies are proposed. Also the concept of local (spatially distributed) correlation measures is presented. It is shown how correlation suppresses fluctuation (e.g. in Wigner-Seitz cells, Bader's basins, Daudel's leges, etc.) and drives localization. The uniform electron gas and the isoelectronic He series serve as illustrating examples. (C) 2000 Elsevier Science B.V. All rights reserved.