Residue-based charge flipping: A new variant of an emerging algorithm for structure solution from X-ray diffraction data

There is currently substantial interest and activity in the development and application of a new technique, called "charge flipping" (CF), that has emerged in the past few years for carrying out structure solution from X-ray diffraction data. We report here a new variant of this technique, termed "residue-based charge flipping" (RBCF), in which the residues of calculated and experimental structure factor amplitudes, together with the corresponding electron density residues, are introduced within the CF algorithm. An important feature of this approach is that it does not require a positive threshold electron density value (delta) to be specified to control the charge-flipping step within the algorithm (in contrast, it is well established that the success of standard CF calculations can depend critically on choosing a suitable value of delta for a given structural problem). Methodological details of the RBCF algorithm are described, and the results of the application of this technique for structure solution of three test structures are reported. The RBCF technique is shown to lead to the correct structure solution in all cases, with success rates of at least 90% (for independent calculations from different sets of initial random phases). Significantly, the convergence behavior of RBCF calculations is found to contrast markedly with that generally observed for standard CF calculations. In particular, convergence (assessed from the evolution of R-factor versus iteration number) typically progresses rapidly and immediately from the earliest iterations of RBCF calculations, rather than displaying an extended plateau region. This feature, and the fact that the RBCF technique does not use the delta parameter that is required in standard CF calculations, suggest that the RBCF algorithm may be a promising approach in future applications.