Improved treatment of severely or exactly overlapping Bragg reflections for the application of direct methods to powder data

A new method has been developed for the improved intensity assignment of severely or exactly overlapping Bragg reflections in a powder diffraction pattern. This fast iterative Patterson squaring (FIPS) method addresses, in particular, the systematic lack of small and large normalized intensities (|E| values) in severely overlapping powder data, which causes (a) the intensity statistics to be strongly acentric (even when the structure itself is centrosymmetric) and (b) the under-estimation of strong structure-invariant relationships. Direct methods for structure determination are more likely to succeed with FIPS-improved data than with conventionally used equipartitioned data (ratio of |E| values for overlapping reflections set to 1.0). In the case of the molecular sieve AFR (in which 65% of the reflections severely overlap), the ab initio structure solution was only possible after a redistribution of the intensities by the FIPS method.