A Bayesian approach to phase extension Original Research Article

A Bayesian approach to the heavy-atom method for solving crystal structures is presented. It is shown that, in contrast to conventional procedures, probability theory makes full use of the information inherent in a known fragment since both the related phase and amplitude play a central role. This property is particularly important for powder data, where peak overlap makes it difficult to infer the intensities of individual reflections reliably. A covariance matrix is also shown to be essential, in the latter case, for capturing the constraints imposed by the diffraction measurements in the space of the structure factors. Prior knowledge about the positivity of the underlying electron density, at least for X-ray diffraction, can be encoded through the use of an entropic prior, which further enhances the quality of the results. The use of the theory is illustrated with synchrotron data from a powdered sample of the pharmaceutical molecule chlorothiazide.