title: Volumic omit maps in ab initio dual-space phasing.
abstract: Alternating-projection-type dual-space algorithms have a clear construction, but are susceptible to stagnation and, thus, inefficient for solving the phase problem ab initio. To improve this behaviour new omit maps are introduced, which are real-space perturbations applied periodically during the iteration process. The omit maps are called volumic, because they delete some predetermined subvolume of the unit cell without searching for atomic regions or analysing the electron density in any other way. The basic algorithms of positivity, histogram matching and low-density elimination are tested by their solution statistics. It is concluded that, while all these algorithms based on weak constraints are practically useless in their pure forms, appropriate volumic omit maps can transform them to practically useful methods. In addition, the efficiency of the already useful reflector-type charge-flipping algorithm can be further improved. It is important that these results are obtained by using non-sharpened structure factors and without any weighting scheme or reciprocal-space perturbation. The mathematical background of volumic omit maps and their expected applications are also discussed.
authors.affiliation: Institute for Solid State Physics and Optics, Wigner Research Centre for Physics of the Hungarian Academy of Sciences, H-1525 Budapest, POB 49, Hungary.
authors.forename: Gábor
authors.initials: G
authors.lastname: Oszlányi
authors.affiliation: Institute for Solid State Physics and Optics, Wigner Research Centre for Physics of the Hungarian Academy of Sciences, H-1525 Budapest, POB 49, Hungary.
authors.forename: András
authors.initials: A
authors.lastname: Sütő
keywords: dual-space methods; iterative projection algorithms; omit maps; structure determination