  A double-atom partitioning of the molecular one-electron density matrix is
used to describe atoms and bonds. All calculations are performed in Hilbert
space. The concept of atomic weight functions (familiar from Hirshfeld analysis
of the electron density) is extended to atomic weight matrices. These are
constructed to be orthogonal projection operators on atomic subspaces, which
has significant advantages in the interpretation of the bond contributions. In
close analogy to the iterative Hirshfeld procedure, self-consistency is built
in at the level of atomic charges and occupancies. The method is applied to a
test set of about 67 molecules, representing various types of chemical binding.
A close correlation is observed between the atomic charges and the Hirshfeld-I
atomic charges.
