A reciprocal space approach for locating symmetry elements in Patterson superposition maps
Thomas L. Hendrixson · 1989
A method for determining the location and possible existence of symmetry elements in Patterson superposition maps has been developed. A comparison of the original superposition map and a superposition map operated on by the symmetry element gives possible translations to the location of the symmetry element. A reciprocal space approach using structure factor-like quantities obtained from the Fourier transform of the superposition function is then used to determine the "best" location of the symmetry element. Constraints based upon the space group requirements are also used as a check on the locations. The locations of the symmetry elements are used to modify the Fourier transform coefficients of the superposition function to give an approximation of the structure factors, which are then refined using the EG relation. The analysis of several compounds using this method is presented. Reciprocal space techniques for locating multiple images in the superposition function are also presented, along with methods to remove the effect of multiple images in the Fourier transform coefficients of the superposition map;In addition, crystallographic studies of the extended chain structure of (NHC[subscript]5H[subscript]5) SbI[subscript]4 and of the twinning method of the orthorhombic form of the high-T[subscript] c superconductor YBa[subscript]2Cu[subscript]3O[subscript] 7-x are presented.