Strengthened translation functions. An automated method for the positioning of a correctly oriented fragment by translation functions in DIRDIF Fourier space

Translation functions are used to determine the position of a correctly oriented molecular fragment. Usually, translation functions are defined for the Patterson space. A new translation function is presented, which is defined as a convolution in electron-density space, and expressed as a Fourier synthesis. After expansion of the reflection data to space group P1, coefficients for the synthesis are obtained by direct methods on difference structure factors (the DIRDIF procedures). From the position of the maximum in the translation function, the position of the known fragment relative to symmetry elements can be obtained. The new translation function provides a fast and reliable method for the positioning of a correctly oriented fragment, if the fragment constitutes at least about 10% of the total scattering power of the primitive unit cell. The procedure has been automated in the computer program TRADIR. Examples of applications on known and unknown structures are given.