| Abstract
| - A comparison of the measure of the delocalization of a particle based on the two-particle distribution functionand that based on the single-particle density matrix is made using a simple set of wave functions which spanstates ranging from single determinant ground and doubly excited states through states mimicking correlatedstates and which include the singly excited state for electrons and for bosons replacing electrons in H2. Thecomparison further includes an analysis of the application of the measures to a classical ideal gas and acompressible fluid. It is found that the values of the integrated atom−atom measures agree for a range ofwave functions involving combinations of the two single determinant (and equivalent Bose) wave functionsbut disagree for a different range of these wave functions and for the singly excited wave functions. Asidefrom the single determinant (and equivalent Bose) wave functions, the two sets of point−point measures thatunderlie the integrated measures all differ. For the sets of wave functions considered, the values of the measuresare identical for electrons and bosons. When applied to a closed classical ideal gas and to a closed compressiblefluid, the delocalization measure based on the two-particle distribution has a residual long range term, whereasthe sharing index in the classical limit gives a completely localized particle. In general, the two measuresdescribe different aspects of the behavior of the particles. The measures based on the two-particle distributionfunction give only two-particle properties and the single-particle density, and the sharing quantities give onlysingle-particle properties. The latter includes, however, the quantitative measures of the delocalization of asingle particle, the point−point sharing index and the sharing amplitude.
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