Parameter Space Concept as structure solution methodology for single crystal diffractometry

• Applicant: Professor Dr. Matthias Zschornak, since 7/2023
• Subject Area: Experimental Condensed Matter Physics ; Mineralogy, Petrology and Geochemistry
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 442646446

The applied project aims to raise the Parameter Space Concept (PSC) for atomically resolved structure determination of crystalline materials from diffractometry data, which has been worked out to a large extent theoretically, to the level of user-friendly use. Since 2005, the solution algorithms of the PSC have been continuously refined to be applicable to general, non-centrosymmetric three-dimensional structures. Gradually more and more complex challenges of structure determination could be successfully solved. In addition, we also want to try to apply "self-learning" IT techniques (AI) to suitable parts of the PSC. The general aim of the project is not to establish competition with concepts based mainly on Fourier techniques (e.g. SHEL-X). Rather, the principle superiorities of the PSC are to be used where, for example, a "problem structure" exists. This concerns, among other things, material-scientific problems, for example with ferroic substances or those with atomic mismatches or mixtures, and thus cases of pseudosymmetric structures, which are often difficult or impossible to solve conventionally. Last but not least, a precise and unambiguous positioning of heavy atoms can be achieved within macromolecular structures as a solid basis for the subsequent routine determination of the light atom parameters.The main strengths of the PSC are that only "sufficient" reflex amplitudes are required and the phase problem is eliminated. Ideally, for m atoms, 3m independent, error-free and absolutely scaled amplitudes are sufficient to find the structure with "infinite" spatial resolution. The main weakness of the PSC is the large computational effort (increases more than exponentially with m - curse of dimensions - but only linearly with the number n of reflex amplitudes used). This limitation is gradually removed by the rapid increase in generally accessible computing power, so that, according to current estimates, the methodology can probably already cope with structures with approx. one hundred degrees of freedom. The project focuses on the implementation of the algorithms into a program in the form of a package for routine users of single crystal diffractometry that is as close as possible to the black box principle. Partial goals are the standardization of the algorithm structures, the calculation of corresponding data fields based on reduction of experimental diffractometry data or according to the strategies of grid computing, as well as the application of this basis to further more complex structure solution problems, and the subsequent elaboration of the program with detailed tests for diffractometry data of arbitrary crystal structures. So far, the PSC methodology has not been implemented in standard programs as an alternative to the already established methods of direct or Fourier-based methods, despite the advantages mentioned above.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Karl F. Fischer
• Ehemaliger Antragsteller: Professor Dr. Dirk Carl Meyer, until 7/2023