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Crystal Structure AnalysisPrinciples and Practice$
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William Clegg, Alexander J Blake, Jacqueline M Cole, John S O Evans, Peter Main, Simon Parsons, and David J Watkin

Print publication date: 2009

Print ISBN-13: 9780199219469

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780199219469.001.0001

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Patterson syntheses for structure determination

Patterson syntheses for structure determination

(p.117) 9 Patterson syntheses for structure determination
Crystal Structure Analysis

William Clegg

Oxford University Press

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

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