# FOX, Current State and Possibilities

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. New Features in FOX

#### 2.1. Preparation of Powder Diffraction Data

_{20}figure of merit [11]. The indexing of powder patterns measured on multiphase samples is possible using the “decomposition-aided indexing” [12]: the in-situ powder diffraction data are recorded while the sample is heated up to the disappearing of the peaks of one unknown phase (decomposition, melting, reaction). This allows the identification of the peaks corresponding to the disappearing phase in the initial powder pattern.

^{2}[14] as well as the number of systematic extinctions is recorded for each space group. The results (see Figure 1) are finally listed by increasing values of χ

^{2}, and the most likely choice usually corresponds to one that has a low χ

^{2}with a high number of extinctions. This systematic approach is akin (though less sophisticated) to the one proposed by [15], but does not provide a single figure-of-merit (the likelihood in [15]) that includes information on both the quality of the fit and the number of extinctions.

#### 2.2. Global Optimization Features

^{4}to 5 × 10

^{4}trials/s for 20 independent atoms and 100 reflections, depending on the space group (numbers given using a single 2.5 GHz Intel i7 processor core), i.e., typically a million trial configurations per minute for simple structures.

^{2}hypersurface in order to find the solution, such as hybrid Monte-Carlo [21,22] or a Lamarckian approach combined to genetic algorithms [23]. In FOX, it is now possible to perform automatic least-squares refinements, either at the end of a parallel tempering run, or every 150 × 10

^{3}trials. This allows the speed of convergence to be greatly increased; e.g., for cimetidine [24], the average number of trials for solving the structure diminishes from 1.6 × 10

^{6}to 6 × 10

^{5}, while the number of least-squares steps only marginally increases the average number of trials per second. This was measured by performing 100 runs of 5 million trials with and without automatic least-squares every 150 × 10

^{5}trials, by stopping the optimization when the log-likelihood falls below a cut-off value, guaranteeing that the proximity to the global minimum was certain. Finally, it was also suggested [25] that it would be possible to solve structures by a performing a large number of downhill minimizations from random starting structures—this experimental approach is also possible in FOX by enabling automatic least-squares with a small number of trials per run.

#### 2.3. Distributed Computing

#### 2.4. Import and Export, CIF and Crystallography Open Database

## 3. Examples

#### 3.1. Inorganic Structure—Rigid Body and Orientation Disorder

_{3}BH

_{4}B

_{12}H

_{12}is an inorganic crystal structure containing rigid complex anions BH

_{4}

^{−}and B

_{12}H

_{12}

^{2−}[32]. It was solved from synchrotron powder diffraction data in the space group Pc using three independent potassium atoms, one borohydride (BH

_{4}

^{−}) and one closo-borane (B

_{12}H

_{12}

^{2−}) complex anion (Figure 4). While the tetrahedron of the borohydride is available in FOX as a pre-programmed object, the closo-borane was imported from the Z-matrix. The structural model was then verified by DFT calculations and its symmetry corrected to P2/c. The overlooked 2-fold axis is due to the weak contribution of hydrogen atoms of the borohydride to the X-ray powder diffraction pattern, as it was broken only by the borohydride orientation.

#### 3.2. Organic Structure—Molecule with Flexible Cycle

^{3}), and the fact that the systematic extinctions satisfying P2

_{1}2

_{1}2

_{1}space group, the asymmetric part of the unit cell contains only one molecule of the Schiff base (Z = 4) with 21 DoF. The solution should be easily found in a couple of minutes or a few hours. However, the determination of the crystal structure by using the default setting of the global optimization algorithm was not giving any satisfactory results after 10 tested runs, each with 5 × 10

^{6}trials (approximately 24 min per run). On the other hand, all 10 runs of the MD approach (move’s frequency was set to 0.05 and amplitude of the move’s energy was set to 60—small distortion of the molecule), where each run tested 5 × 10

^{6}trials (approximately 50 min per run), resulted in all 10 giving promising results with low values for cost functions, and with reasonable and similar conformations of the Schiff base.

^{6}trials.

## 4. Availability of FOX

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**FOX 2017.2 indexing and profile fitting interface.

**Top left**: profile fitting widget, allowing to select groups of parameters to optimize using Le Bail and full-profile least squares.

**Bottom left**: result of the space group explorer, where all space groups compatible with the unit cell are tested and listed with increasing Goodness-of-Fit. The correct choice in this case is the first one, with the highest number of systematic extinctions.

**Top right**: zoomed portion of the observed and calculated powder pattern in profile fitting (Le Bail) mode, with the list of peaks found and predicted indexing.

**Bottom right**: results from a ‘quick’ indexing, with solutions listed by decreasing M

_{20}score.

**Figure 2.**FOXGrid server interface, giving access to distributed computing options. In this example, a single job has been loaded, with 4 runs done out of 8. Each run starts from a randomized structure, for one million trials. In this case, only the local computer is used, with 4 computing units to exploit the 4 cores of the computer. The results already obtained are listed at the bottom right (and, in this case, are all correct solutions), and can be individually displayed. The inset widget on the right shows the simple interface for creating a new job.

**Figure 3.**Main FOX interface. Left: main window with the beginning of the description of a crystal structure. Top right: 3D view of the structure, with the help text, showing only the asymmetric unit. Several shortcuts are available to easily toggle between different views (full unit cell, toggle hydrogens, fade atoms outside display volume…). Bottom right: result of querying the Crystallography Open Database [30], after searching for structures with elements C, N, O, F, Fe and 6 different elements. A simple double-click allows to load the CIF in FOX, where the molecules are automatically built by analysing the atomic distances.

**Figure 4.**Monoclinic K

_{3}BH

_{4}B

_{12}H

_{12}, an example of an inorganic structure (P2/c, a = 7.0497(2), b = 6.9917(2), c = 13.4192(3) Å, β = 94.508(1)° at RT) with rigid complex anions BH

_{4}

^{−}and B

_{12}H

_{12}

^{2−}[32]. Synchrotron powder diffraction data (SNBL at the ESRF Grenoble, λ = 0.81984 Å), K

_{3}BH

_{4}B

_{12}H

_{12}(peaks labelled in green), unreacted K

_{2}B

_{12}H

_{12}(peaks labelled in blue), potassium (green), boron (red), hydrogen (white).

**Figure 5.**Evolution of the CF (Cost Function) during the 10 runs

**a**) when the default setting of the optimization algorithm was used and

**b**) when the MD approach was used. Evolution of CF of each run is drawn with different shade of grey, starting from light grey for the first run, and ending with black for the final, 10th, run. Both graphs are zoomed to see more detail, and the red line shows the value of the CF at 4.26 × 10

^{6}, which corresponds to the highest resulting CF value in the MD result list, and illustrates the “scale” between left and right graphs.

**Figure 6.**(

**a**) Overlay of results found by the default setting of the parallel tempering algorithm without MD approach. Evolution of the conformation towards the correct one is clearly visible from the changing colour of the first (light blue) to the last (purple) result. (

**b**) Overlay of results found by the MD approach. One-coloured stick styles represent results suggested by the described optimization process combined with MD moves. The picture shows that atomic positions suggested by the optimization method are distributed around the correct atomic positions. Ball style with different atomic colours represents the published solution in both parts of the picture.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Černý, R.; Favre-Nicolin, V.; Rohlíček, J.; Hušák, M.
FOX, Current State and Possibilities. *Crystals* **2017**, *7*, 322.
https://doi.org/10.3390/cryst7100322

**AMA Style**

Černý R, Favre-Nicolin V, Rohlíček J, Hušák M.
FOX, Current State and Possibilities. *Crystals*. 2017; 7(10):322.
https://doi.org/10.3390/cryst7100322

**Chicago/Turabian Style**

Černý, Radovan, Vincent Favre-Nicolin, Jan Rohlíček, and Michal Hušák.
2017. "FOX, Current State and Possibilities" *Crystals* 7, no. 10: 322.
https://doi.org/10.3390/cryst7100322