Extending the charge-flipping method towards structure solution from incomplete data sets

The charge-flipping method tends to fail if applied to an incomplete diffraction data set. The reason is artifacts induced in the density maps by Fourier transforming the data. It is shown that the missing data can be sufficiently well approximated on the basis of the Patterson map of the unknown structure optimized by the maximum entropy method (MEM). Structures that could not be solved by the original charge-flipping algorithm can be solved by the proposed method. The method has been tested on experimental data of one inorganic and two organic structures and on several types of missing data. In many cases, up to 50% of missing reflections, or even more, can be tolerated and the structure can still be reconstructed by charge flipping.