Evaluation of reflection intensities for the components of multiple Laue diffraction spots by direct methods

In a Laue diffraction pattern, 10–20% of the spots result from the exact superposition of two or more reflections that are 'harmonics', e.g. hkl, 2h, 2k, 21. .... For the solution of large or difficult structures, the intensities of the remaining 80–90% of the reflections, measurable as singles, may not be sufficient and thus evaluation of the intensities of the components of the multiple spots is important. A procedure for this deconvolution is given, based on the assumption of non-negativity and nonoverlapping peaks in the Patterson function. It has been tested with Laue diffraction data from an organic crystal, C₂₅H₂₀N₂O₂, where it allowed 275 reflection intensities to be evaluated from multiple spots, 140 of them with |F|² > 3σ(|F|²). For these 140 reflections, agreement with F_calc is reasonable (R = 0.14) and their addition to the 1129 singles made structure solution (by direct methods) significantly easier.