The accuracy of electron-density maps in X-ray analysis with special reference to dibenzyl

Abstract

Methods of correcting the systematic errors in electron-density maps due to using finite series of structure factors are discussed. Random errors in the maps are caused by experimental and computational rounding-off errors and by errors in the correction for finite series. Expressions are derived for the standard deviations of these random errors, which have a Gaussian probability distribution. It is shown how statistical significance tests can be used in the comparison of different bond-lengths, etc. These methods are illustrated by a detailed examination of the accuracy of the dibenzyl structure, which confirms Jeffrey's conclusions on shortened central bonds. Other topics include discussions of the shape of the atomic peaks in maps and the variation of errors with limiting reciprocal radii.