On the relation between the diffraction ratio, the doublet values and the reliability of the triplet estimates

A diffraction ratio is proposed that predicts the differences to be expected between the intensities of two-isomorphous data sets. This ratio is important for the ab initio structure determination of isomorphously related structures by means of direct methods. The diffraction ratio is shown to be linearly related to the average doublet phase sum of the isomorphous data. It is argued that the doublets are essential for correct triplet-phase-sum estimates. The diffraction ratio and the idealized average triplet-phase-sum error, as calculated from a recent probabilistic theory, turn out to be related. A minimum diffraction ratio is required to obtain a triplet-phase-sum-error level comparable with that of small structures that are solved routinely by conventional direct methods. The diffraction ratio can be used to maximize the triplet-phase-sum reliability before collecting the data by choosing the optimal wavelength in a single anomalous-scattering experiment, selecting the most suitable heavy-atom derivative in a single-isomorphous-replacement experiment or selecting the optimal wavelengths in a multiwavelength experiment.