The symmetry minimum function: high order image seeking functions in X-ray crystallography

Abstract

Methods for the solution of three-dimensional crystal structures from the three-dimensional Patterson function have been further developed by use of (a) the Symmetry Minimum Function which is based upon all symmetry interactions (e.g. :Harker lines and planes), (b) a simultaneous high order superposition function which makes use of all the symmetry of the space group, and (c) a combined high order superposition function in which the Symmetry Minimum Function is included to reduce the number of spurious peaks. These functions introduce a more direct method for the analysis of somewhat more complex structures than methods which have previously been described.

The molecular and crystal structure of N-(β-D-ribofuranosyl)imidazole

“…The other non-hydrogen atom positions were obtained in two ways: (i) from a symmetry-minimum function map (Simpson, Dobrott & Lipscomb, 1965) and ( A close examination of the data at this stage showed five reflections that were probably suffering from secondary extinction or counter paralysis. These reflexions, 020, 011,003, 110 and i02, were excluded from the data set and further least-squares cycles.…”

A neutron diffraction determination of the structure of beryllium sulphate tetrahydrate, BeSO4.4H2O

“…The statistical N(z 7 test of Howells, Phillips & Rogers (1950) seemed to favour the noncentric space group I4c2, so it was chosen to be the correct space group. The structure was solved by the procedure described by Simpson, Dobrott & Lipscomb (1965), in which the Patterson function P(uvw) is interpreted through the use of symmetry minimum and minimum functions.I" The computation of the sym-* This and all other calculations were carried out in the CDC 3600 computer at the Tata Institute of Fundamental Research, Bombay.…”

The Crystal and Molecular Structure of the Antihistaminic Drug Triprolidine Hydrochloride Monohydrate [trans-1-(p-Tolyl)-1-(2-pyridyl)-3-(1-pyrrolidino)-prop-1-ene]

“…(10). Refinement of the initial model by difference Fourier and block-diagonal least-squares methods has resulted in weighted (observational weights) and ilnweighted R factors of 0.077 and 0.051 respectively for the 2516 observed data of the con~plete set.…”