A robust tangent procedure

Third-generation direct methods programs are based on a phasing algorithm (e.g. the tangent or the parameter shift method) and on dual space refinement techniques. The two spaces may be alternated during the phasing procedure or used in a sequential way: for example, first phase and after extend and refine. The tangent approach in SIR2011 belongs to the second category: phases are first estimated by the tangent formula, then their extension and refinement is performed in direct space via electron density modification techniques. In this article a number of new algorithms are described, with the aim of improving the SIR2011 tangent step and allowing more efficient phase extension and refinement. New criteria were chosen for defining the number of reflections to phase, for modifying the tangent weighting scheme, and for fixing the active use of the psi-0 triplets and of the quartet invariants. Each tangent trial may now be submitted to the RELAX procedure, a tool for moving to the correct position a well oriented but misplaced structural model. The resulting procedure shows surprising efficiency, testified by a wide set of applications. The experimental results have been compared with the tangent and VLD (vive la difference) approaches implemented in SIR2011.