SYMMETRY AND THE GENERALIZED MAXIMUM DETERMINANT RULE
DE GELDER R, ELOUT MO, DEGRAAFF RAG, SCHENK H
ZEITSCHRIFT FUR KRISTALLOGRAPHIE
207: 237-243 Part 2 1993
Abstract:
In the general case of a Karle-Hauptman matrix containing no symmetry equivalent reflections, maximizing the determinant as a function of the phases does not necessarily lead to an unambiguous solution of the phase problem. Individual phases may be shifted from their correct values in a seemingly completely arbitrary way. This problem is discussed in simple mathematical terms and a method is proposed allowing the identification of those elements in a Karle-Hauptman matrix possibly suffering from the effects discussed, given the space-group symmetry and the composition of the matrix.The conclusion reached in this paper is that only the presence of a sufficiently large number of symmetry equivalent reflections and/or Friedel opposites in a Karle-Hauptman matrix causes the Generalized Maximum Determinant Rule to be an effective tool in ab initio phase determination.