Partitioning of the molecular density matrix over atoms and bonds
  A double-index atomic partitioning of the molecular first-order density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas off-diagonal contributions carry information about the bonds. The resulting matrices have good localization properties, in contrast to single-index atomic partitioning schemes of the molecular density matrix. It is shown that the electron density assigned to individual atoms, when derived from the density matrix partitioning, can be made con- sistent with well-known partitions of the electron density over AIM basins, either with sharp or with fuzzy boundaries. The method is applied to a test set of about 50 molecules, representative for various types of chemical binding. A close correlation is observed between the trace of the bond matrices and the SEDI (shared electron density index) bond index. 
Diederik Vanfleteren, Dimitri Van Neck, Patrick Bultinck, Paul W.   Ayers and Michel Waroquier
physics.chem-ph physics.comp-ph quant-ph