Chapter

Patterson syntheses for structure determination

William Clegg

in Crystal Structure Analysis

Second edition

Published in print June 2009 | ISBN: 9780199219469
Published online September 2009 | e-ISBN: 9780191722516 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199219469.003.0009

Series: International Union of Crystallography Texts on Crystallography

Patterson syntheses for structure determination

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The Patterson synthesis is a reverse Fourier transform in which the amplitudes are replaced by their squares and the phases are omitted. Peaks in a Patterson map represent vectors between pairs of atoms; the Patterson function is the convolution of the electron density with itself. Patterson space groups are the combinations of Laue classes with unit cell centring arrangements. The large number of broad Patterson peaks leads to much overlap, with peaks due to pairs of heavy atoms (many electrons) dominating. Heavy atoms may thus often be found by Patterson map analysis, especially when they are related by symmetry, giving peaks in special positions (Harker sections and lines). Examples are shown in several space groups. Care is needed in some cases, when ambiguous solutions may be found. Geometrically rigid groups of atoms may also be located from a Patterson map by combined rotational and translational search methods.

Keywords: Patterson synthesis; interatomic vectors; convolution; heavy atom method; Harker sections and lines; Patterson search methods

Chapter.  6939 words.  Illustrated.

Subjects: Crystallography

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