Incorporation of Prior Phase Information Strengthens Maximum-Likelihood Structure Refinement

The application of a maximum-likelihood analysis to the problem of structure refinement has led to striking improvements over the traditional least-squares methods. Since the method of maximum likelihood allows for a rational incorporation of other sources of information, we have derived a likelihood function that incorporates experimentally determined phase information. In a number of different test cases, this target function performs better than either a least-squares target or a maximum-likelihood function lacking prior phases. Furthermore, this target gives significantly better results compared with other functions incorporating phase information. When combined with a procedure to mask `unexplained' density, the phased likelihood target also makes it possible to refine very incomplete models.