This work summarizes the author's activity in developing quantum crystallography. The approximations based on the intrinsic properties of the one-electron single-determinant density matrix, which allow its reconstructing from the experimentally measured coherent X-ray diffraction structure factors are discussed. The actual results obtained within such an approach are given. Article critically considers the early works in the field and places them to the present context. © 2017 Wiley Periodicals, Inc.
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