Optimization Techniques for Phase Retrieval Based on Single-Crystal X-Ray Diffraction Data
Smith, Alexander Barton
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/82409
Description
Title
Optimization Techniques for Phase Retrieval Based on Single-Crystal X-Ray Diffraction Data
Author(s)
Smith, Alexander Barton
Issue Date
2008
Doctoral Committee Chair(s)
Sahinidis, Nikolaos V.
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Condensed Matter
Language
eng
Abstract
In this thesis we develop innovative optimization models for phasing crystal structures from X-ray diffraction data. First, an integer minimal principle for quartets and triplets is proposed for initially setting the phases of structure factors that compose a Karle-Hauptman matrix. Initialization in this manner is motivated by a proof of the relation between invariants and the Karle-Hauptman matrix determinant generated from a phase set. Phase initialization by the quartet and triplet model is shown to benefit CRUNCH for a variety of test structures. Next a reciprocal space integer minimal principle model and polynomial-time Sieve method are developed. The Sieve method is shown to phase one order-of-magnitude faster on average than SnB for a variety of test structures. A shift in emphasis to direct space algorithms is then precipitated by the applicability of the Sieve method to only centrosymmetric structures and reliance on invariant subsets completely free of odd triplets. Four direct space methods are introduced, a completely general density assignment MINLP, a NLP relaxation of the MINLP, a MILP for density assignment for restricted reflections, and finally, a MILP relaxation of the density assignment for restricted reflections. The potential for these models to provide accurate phasing is verified for a variety of test structures. Success of these models is limited by the ability to prepare a small grid from Patterson information, with greater than 25% of the atom positions present. This is prohibitive in the sense that the majority of structures must be solved utilizing periodic grid definition in the absence of a resolvable Patterson map. Finally, given the individual limitations of the reciprocal space and direct space methods, three direct-reciprocal space formulations are developed. Consideration of direct and reciprocal space simultaneously is demonstrated, for a variety of test structures, to enable detection of odd triplets and work in the context of periodic grids, which require no prior structural information.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
