Charge flipping is a recently discovered algorithm of ab initio structure determination that is easy to implement and adapt to various tasks. It is essentially an iterative Fourier cycle that modifies the calculated electron density and structure factors in the appropriate half-cycles. The modifications have two different roles: they either act as constraints or as (weak) perturbations. Constraints are needed to limit the size of the search space, while perturbations are needed to avoid stagnation. The name-giving step of charge flipping is a good example of a fine balance, changing the sign of electron density below a small positive threshold simultaneously forces the constraint of positivity and introduces high-frequency, orthogonal perturbations. The basic algorithm has several attractive properties: it solves the structure without utilizing atom types, chemical composition or any information on the space group symmetry.

The crystallographic community has already found that charge flipping works well in practice:  structure solution examples of small molecules, modulated crystals, quasicrystals, and of powder diffraction data have all been reported (see [1] for references). Many variants of the basic algorithm exist, which usually add more constraints and add/remove some perturbations. Any improvement developed for single crystal data is likely to work for powder data, although the limit of structure size/complexity that can be solved is naturally smaller. The only extension required by powder charge flipping is the need to repartition the calculated intensity of overlapping reflections. At least three different approaches have been tested, the one that worked most efficiently does repartitioning in an auxiliary cycle where histogram matching is also performed. Our experience confirms that such an auxiliary cycle is useful and can easily be extended to contain a variety of other actions. The efficiency strongly depends on small details. As a general rule, structure solution of powder data requires more constraints and less perturbation, and between subsequent interventions one must allow a reasonable period of pure charge flipping.

There are two remaining problems that require further investigation. While missing data at high resolution is a general problem of any ab initio method, problems with the utilization of symmetry is specific to charge flipping. Most space groups fix the origin and the structure can emerge only at a single position. Charge flipping that works in P1 allows continuous phase changes and therefore, the structure can emerge at the continuum of shifted positions. This is such a big an advantage that it prevented us from the efficient use of symmetry information. At present we are trying to combine the best of both approaches, and prescribe only partial symmetry.

[1]  G. Oszlányi & A. Sütő,  Acta Cryst. A 64, 123-134 (2008)

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