Global optimization: Structure determination of medium-sized structures from low-resolution powder X-ray diffraction data

 

The determination of the crystal structure from resolution-limited powder X-ray diffraction data is still a very demanding task, especially in the case of medium-sized inorganic compounds with a large number of independent variables; standard algorithms for optimizing structural models against measured diffraction data work only moderately effectively in the case of such high-dimensional problems or do not find the global optimum of the multimodal target function.

The aim of the research project was therefore to develop optimization algorithms that are adapted to the structure of the objective function to be optimized and thereby use inherent properties of this objective function to accelerate convergence.

In preliminary work, two approaches had proven to be particularly promising, which were intensively and systematically investigated in the project and are to be made available to the scientific community as an easy-to-use software package (as a free open-source solution):

Configuration optimization: By discretizing the problem - taking advantage of fundamental crystal-chemical considerations - the continuous, high-dimensional optimization task becomes a countable, combinatorial problem that appears to be solvable even for large structures in realistic times.

Successive line scans: The objective function has a characteristic trench structure, which makes it possible to find the global optimum with a high degree of probability with a series of successive one-dimensional cuts through the search space.

With both approaches, structures with 10 to 15 atoms in the asymmetric unit could regularly be determined from synthetic diffraction data. The systematic investigation and further development of these two approaches helps to significantly alleviate the problem of structure determination from low-resolution powder X-ray diffraction data and thus to a better understanding in particular of substances that are difficult or impossible to produce in the form of single crystals.

Team:

Prof. Dr. Georg Roth (Project manager)
Dipl.-Phys. Jan Simons (PhD student)

  Copyright: © DFG

Funding:

Deutsche Forschungsgemeinschaft
Grant Nr.: RO 2055/6-1
Project period: 01.11.2010 – 31.10.2013