SYMMETRY AND THE GENERALIZED MAXIMUM DETERMINANT RULE

In the general case of a Karle-Hauptman matrix containing no symmetry equivalent reflections, maximizing the determinant as a function of th e phases does not necessarily lead to an unambiguous solution of the p hase problem. Individual phases may be shifted from their correct valu es in a seemingly completely arbitrary way. This problem is discussed in simple mathematical terms and a method is proposed allowing the ide ntification of those elements in a Karle-Hauptman matrix possibly suff ering from the effects discussed, given the space-group symmetry and t he composition of the matrix. The conclusion reached in this paper is that only the presence of a sufficiently large number of symmetry equi valent reflections and/or Friedel opposites in a Karle-Hauptman matrix causes the Generalized Maximum Determinant Rule to be an effective to ol in ab initio phase determination.