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Updated: Mar 18, 2026

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Volumic omit maps in ab initio dual-space phasing.

Gábor Oszlányi1, András Sütő1

  • 1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics of the Hungarian Academy of Sciences, H-1525 Budapest, POB 49, Hungary.

Acta Crystallographica. Section A, Foundations and Advances
|July 1, 2016
PubMed
Summary

New volumic omit maps improve crystal structure solution by preventing stagnation in dual-space algorithms. These real-space perturbations enhance weak constraint methods and charge-flipping for ab initio phase problem solving.

Keywords:
dual-space methodsiterative projection algorithmsomit mapsstructure determination

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Area of Science:

  • Crystallography
  • Materials Science
  • Computational Chemistry

Background:

  • Alternating-projection algorithms struggle with stagnation for ab initio phase problem solving.
  • Existing weak constraint methods (positivity, histogram matching, low-density elimination) are often ineffective in pure forms.

Purpose of the Study:

  • To introduce and evaluate volumic omit maps as a novel perturbation method.
  • To enhance the efficiency of dual-space algorithms and charge-flipping for solving the crystallographic phase problem.
  • To assess the performance of weak constraint algorithms when augmented with volumic omit maps.

Main Methods:

  • Development of volumic omit maps: periodic real-space perturbations deleting subvolumes.
  • Application of omit maps to basic algorithms: positivity, histogram matching, low-density elimination.
  • Testing and statistical analysis of solution quality with and without omit maps.
  • Improvement of the reflector-type charge-flipping algorithm using volumic omit maps.

Main Results:

  • Volumic omit maps effectively transform weak constraint algorithms into practically useful methods.
  • The efficiency of the charge-flipping algorithm is further improved by volumic omit maps.
  • Successful phase determination was achieved using non-sharpened structure factors, without weighting schemes or reciprocal-space perturbations.

Conclusions:

  • Volumic omit maps are a powerful tool for overcoming stagnation in dual-space algorithms.
  • Augmenting weak constraint methods with volumic omit maps significantly improves their utility for ab initio structure solution.
  • The proposed method offers a robust and efficient approach to solving the crystallographic phase problem.