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.