Ab initiostructure solution by iterative phase-retrieval methods: performance tests on charge flipping and low-density elimination

Abstract

Comprehensive tests on the density‐modification methods charge flipping [Oszlányi & Sütő (2004). Acta Cryst. A60, 134–141] and low‐density elimination [Shiono & Woolfson (1992). Acta Cryst. A48, 451–456] for solving crystal structures are performed on simulated diffraction data of periodic structures and quasicrystals. A novel model‐independent figure of merit, which characterizes the reliability of the retrieved phase of each reflection, is introduced and tested. The results of the performance tests show that the quality of the phase retrieval highly depends on the presence or absence of an inversion center and on the algorithm used for solving the structure. Charge flipping has a higher success rate for solving structures, while low‐density elimination leads to a higher accuracy in phase retrieval. The best results can be obtained by combining the two methods, i.e. by solving a structure with charge flipping followed by a few cycles of low‐density elimination. It is shown that these additional cycles dramatically improve the phases not only of the weak reflections but also of the strong ones. The results can be improved further by averaging the results of several runs and by applying a correction term that compensates for a reduction of the structure‐factor amplitudes by averaging of inconsistently observed reflections. It is further shown that in most cases the retrieved phases converge to the best solution obtainable with a given method.

Unifying cluster-based structure models of decagonal Al–Co–Ni, Al–Co–Cu and Al–Fe–Ni

“…Additional low-density elimination iterations were performed to reduce the noise in the electron-density maps. 100 successful runs were averaged in order to generate high-quality electron-density maps (Fleischer et al, 2010).…”

“…we used a special averaging approach based on 100 successful charge-flipping structure solutions (Fleischer et al, 2010).…”

Ab initioreconstruction of difference densities by charge flipping

“…It is an established fact that charge flipping alone provides only a relatively inaccurate approximation of the true electron density, and that further iteration steps with different density modification are needed to improve the phases (Oszlá nyi & Sü to , 2008; Fleischer et al, 2010). Fleischer et al (2010) demonstrated quantitatively that the low-density elimination (LDE) method (Shiono & Woolfson, 1992) is a suitable iteration method to improve substantially the solution obtained by charge flipping.…”

Quasicrystals: What do we know? What do we want to know? What can we know?

“…Unfortunately, higher approximants are rare and not every QC is accompanied by one or more ACs. The best way to solve a QC structure at present is by a combination of nD charge flipping and the nD low-density elimination approach (see, e.g., Palatinus et al, 2011;Fleischer et al, 2010; and references therein), which are direct-space phasing methods. The resulting electron-density distribution function provides the necessary information for designing a starting model for subsequent structure refinements.…”