TY - JOUR
T1 - Analysis of the electronic density using Riemannian geometry
AU - Pino, R.
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2003/7
Y1 - 2003/7
N2 - Local-scaling transformations induce density-dependent deformations of the geometry, i.e., new metrics. We derived the Riemannian geometry tensors for the transformed metrics. We evaluated numerically the curvature scalar for atoms, and it reveals the shell structure. The change of sign of the curvature scalar from negative to positive corresponds to a maximum in the radial density, and the opposite change of sign to a minimum. We also explored some density-dependent conformally flat metrics. In special cases, we obtained measures of the curvature of the electronic density proportional to the Laplacian of the density and to the functional derivative of von Weizsäcker's kinetic energy functional or Bohm's quantum potential.
AB - Local-scaling transformations induce density-dependent deformations of the geometry, i.e., new metrics. We derived the Riemannian geometry tensors for the transformed metrics. We evaluated numerically the curvature scalar for atoms, and it reveals the shell structure. The change of sign of the curvature scalar from negative to positive corresponds to a maximum in the radial density, and the opposite change of sign to a minimum. We also explored some density-dependent conformally flat metrics. In special cases, we obtained measures of the curvature of the electronic density proportional to the Laplacian of the density and to the functional derivative of von Weizsäcker's kinetic energy functional or Bohm's quantum potential.
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U2 - 10.1209/epl/i2003-00515-8
DO - 10.1209/epl/i2003-00515-8
M3 - Article
AN - SCOPUS:0038379840
SN - 0295-5075
VL - 63
SP - 200
EP - 206
JO - Europhysics Letters
JF - Europhysics Letters
IS - 2
ER -