X-ray crystal structure determination: numerical methods

The use of X-rays to determine the structure of molecules in the solid state expanded considerably with the advent of automated diffraction intensity meters and the emergence of inexpensive computers with high execution speed and large storage capacity. Physicists had solved the fundamental problems of diffraction. The relationships between diffraction directions and lattice parameters were well established, as were those between diffraction intensities and atomic coordinates. What remained was the problem of phase, since in optics, only intensity is accessible to experiment. This problem was solved in the 1950s and 1960s.

Nevertheless, the volume of calculations was considerable. The development of numerous programs by crystallographers encourages some chemists to use crystallographic methods as a black box. They are tempted to enter data into the programs without knowing either the principle or the limits, and without seeing that every crystal is a geometric entity whose symmetries and/or pseudo-symmetries play a considerable part in the calculations, generating correlations unsuspected by the untrained mind. The consequence is immediate: the operator, unaware of these problems, is overwhelmed by setbacks from which he does not know how to escape.

The aim of this article is to highlight the difficulties that can arise during crystal structure determination.