On relations between correlation, fluctuation and localization

The ground states of many-electron systems (atoms, molecules, solids) are c onsidered under the aspect of mutual relations among the phenomena of corre lation, fluctuation, and localization. Known measures of the correlation st rength are summarized (Collins' information entropy, Kutzelnigg's statistic al correlation coefficients, Fulde's correlation strength, Cioslowski's str ength of short-range correlation) and new indices are proposed (normalizati on of the correlation tail of the natural occupation numbers, 'occupation g ap', on-top properties of the intracule pair densities for parallel- and an tiparallel spin electron pairs). In addition to these quantum-kinematical q uantities, new reference-free ratios of kinetic and potential energies are proposed. Also the concept of local (spatially distributed) correlation mea sures is presented. It is shown how correlation suppresses fluctuation (e.g . in Wigner-Seitz cells, Bader's basins, Daudel's leges, etc.) and drives l ocalization. The uniform electron gas and the isoelectronic He series serve as illustrating examples. (C) 2000 Elsevier Science B.V. All rights reserv ed.