Volume 63, Number 2, July 2003
|Page(s)||200 - 206|
|Section||Atomic and molecular Physics|
|Published online||01 November 2003|
Analysis of the electronic density using Riemannian geometry
Department of Chemistry, Rice University - Houston, TX
Corresponding author: firstname.lastname@example.org
Accepted: 15 May 2003
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.
PACS: 31.10.+z – Theory of electronic structure, electronic transitions, and chemical binding / 31.15.Ew – Density-functional theory / 02.40.Ky – Riemannian geometries
© EDP Sciences, 2003
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.