  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.
