The charge-flipping algorithm in crystallography

Acta Cryst. (2013). B69, 1-16 (http://doi.org/ksg)

Iteration paths of several dual-space algorithms for a convex consistent problem (upper panel) and non-convex inconsistent problem (lower panel). ER = error reduction, CF = charge flipping, DM = difference map, AAR = averaged alternating reflections, RAAR = relaxed averaged alternating reflections.

Dual-space iterative algorithms are conceptually simple, yet very efficient phasing algorithms applicable for solution of the crystallographic phase problem. Among the broad family of these algorithms the charge flipping algorithm (CFA) is the most widely used algorithm in crystallography. The article reviews the history of the dual-space algorithms in crystallography, the relationship of CFA to other dual-space algorithms, the variants of CFA, and the applications of CFA to routine structure solution, solution of aperiodic structures, powder diffraction data, macromolecular crystallography and single-particle imaging.