Automatic determination of crystal structures using Karle–Hauptman matrices

This paper describes a method for automatic structure determination by the application of Karle–Hauptman matrices to the phase problem. A new method, the common-minor strategy, is used to combine the information contained in several Karle–Hauptman matrices. Sets of phases large enough to define the structure are obtained. If the matrices are linked properly, phases contained in a larger array of matrices can be adequately restricted to a common origin. The partial solutions obtained on Fourier transformation are extended to the complete structure in a fully automatic manner. A new algorithm is presented for the maximization of the determinant of a Karle–Hauptman matrix as a function of the phases.