Ab initio determination of a crystal structure by means of the Schrödinger equation

It is shown that the use of the Schrödinger equation may lead to the ab initio determination of the positions of the nuclei in a crystal, given a limited number of diffracted-beam intensities. In particular, it is shown that an extremely simplified Schrödinger equation in physical momentum space provides a sufficiently sound theoretical basis to develop an algorithm using diffraction data alone. This algorithm has been tested with a known 41 atom crystalline structure (not including hydrogen atoms) in space group P1. The extracted information is sufficient to determine the positions of all atoms. In addition, theoretical developments relevant to the connection between momentum space in quantum mechanics and diffraction theory have been formulated.