An integer minimal principle and triplet sieve method for phasing centrosymmetric structures

Alexander B. Smith, Hongliang Xu, Nikolaos V. Sahinidis

Research output: Contribution to journalArticlepeer-review


In this paper, a new integer minimal principle model for centrosymmetric structures is presented; one which fully accounts for reciprocal-space phase shifts present in non-symmorphic space groups. Additionally, characterization of false minima of the model is done in terms of even and odd triplets. Based on this characterization, a triplet sieve method is proposed. First, Gaussian elimination using only a subset of reliable triplets is employed for phasing. Triplet subsets are generated using a progressively smaller set of the strongest reflections. Several phase solution sets are generated by enumerating the degrees of freedom present. To facilitate computational evaluation of the quality of these phase solutions, these phase sets are passed into the crystallographic software SnB, which expands the reflection set in two cycles. The final solution is identified via statistics of two crystallographic figures of merit. Computational results are presented for a variety of structures.

Original languageEnglish (US)
Article numberdr5014
Pages (from-to)164-171
Number of pages8
JournalActa Crystallographica Section A: Foundations of Crystallography
Issue number2
StatePublished - Mar 1 2007


  • Centrosymmetric structures
  • Integer minimal principle
  • Phasing
  • Triplet sieve method

ASJC Scopus subject areas

  • Structural Biology


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