A charge-flipping algorithm to handle incomplete data

Missing data are a general hindrance for all iterative, dual-space methods of structure determination. Charge flipping is no exception; its real-space perturbation may turn out to be too strong if the amount of diffraction data is not sufficient. To handle this situation, we introduce a variant of the basic algorithm which combines the original charge-flipping density modification in real space, the reflector of the Fourier-modulus projection in reciprocal space and the parameterless iteration scheme of averaged alternating reflections (AAR). This simple algorithm is a balance of increased perturbations and full negative feedback, with the extra freedom that it can be fine-tuned by a different treatment of different unobserved reflections. The efficiency of the method was tested using several single-crystal data sets and varying the amount of missing data at both high and low resolution. The results prove that many small-molecule structures can be solved by utilizing significantly less data than is standard in current crystallographic practice.