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A double-atom partitioning of the molecular one-electron density matrix isused to describe atoms and bonds. All calculations are performed in Hilbertspace. The concept of atomic weight functions (familiar from Hirshfeld analysisof the electron density) is extended to atomic weight matrices. These areconstructed to be orthogonal projection operators on atomic subspaces, whichhas significant advantages in the interpretation of the bond contributions. Inclose analogy to the iterative Hirshfeld procedure, self-consistency is builtin at the level of atomic charges and occupancies. The method is applied to atest set of about 67 molecules, representing various types of chemical binding.A close correlation is observed between the atomic charges and the Hirshfeld-Iatomic charges.

Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors