A Bayesian approach to phase extension

A Bayesian approach to the heavy-atom method for solving crystal structures is presented. It is shown that, in contrast to conventional procedures, pr obability theory makes full use of the information inherent in a known frag ment since both the related phase and amplitude play a central role. This p roperty 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 sp ace of the structure factors. Prior knowledge about the positivity of the u nderlying 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 fr om a powdered sample of the pharmaceutical molecule chlorothiazide. (C) 200 1 Elsevier Science Ltd. All rights reserved.