Analysis of the electronic density using Riemannian geometry

Author: Pino R.  

Publisher: Edp Sciences

E-ISSN: 1286-4854|63|2|200-206

ISSN: 0295-5075

Source: EPL (EUROPHYSICS LETTERS), Vol.63, Iss.2, 2010-03, pp. : 200-206

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Abstract

Local-scaling transformations induce density-dependentdeformations of the geometry, i.e., new metrics. Wederived the Riemannian geometry tensors for the transformedmetrics. We evaluated numerically the curvature scalar for atoms,and it reveals the shell structure. The change of sign of thecurvature scalar from negative to positive corresponds to amaximum in the radial density, and the opposite change of sign toa minimum. We also explored some density-dependent conformallyflat metrics. In special cases, we obtained measures of thecurvature of the electronic density proportional to the Laplacianof the density and to the functional derivative of vonWeizsäcker's kinetic energy functional or Bohm's quantumpotential.