The fitting of an idempotent density matrix to x-ray structure factors
is discussed. If the density matrix is identified with a single, Slat
er determinant of orbitals, then a model wave function can be recovere
d, enabling the computation of two-electron properties as well as the
usual one-electron properties derived from the electron density. Hence
this approach is potentially superior to the usual multipole expansio
n used in charge-density analysis, although the current are formalisms
are only useful for molecular crystals of very small molecules. A pro
cedure is described, and applications to one theoretical example (meth
ylamine) and one experimental example (formamide) are presented.