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Z. Kristallogr. 216 (2001) 5 9 # by Oldenbourg Wissenschaftsverlag, Munchen Å

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Application of simulated annealing approach for structure solution of molecular crystals from X-ray laboratory powder data
S. G. Zhukov*,I, V. V. ChernyshevI, E. V. BabaevI, E. J. SonneveldII and H. SchenkII
I II

Moscow State University, Department of Chemistry, 119899, Moscow, Russia University of Amsterdam, Laboratory of Crystallography, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands

Received March 17, 2000; accepted July 7, 2000

Abstract. Simulated annealing approach was successfully applied to solve three unknown molecular structures from X-ray laboratory powder data using a priory known structural fragments. Some possible developments of the method are discussed.

Introduction
For crystal structure determination from powder diffraction data one can use a number of methods that have been discussed in details in recent reviews (Giacovazzo, 1996; Harris & Tremayne, 1996; Le Bail, 1998; Louer, 1999). Å The most known of them, implemented in available programs, are the direct methods (Jansen, Peschar, Schenk, 1992a;1992b; Altomare, Cascarano, Giacovazzo, Guagliardi, Burla, Polidori, Camalli, 1994), the maximum entropy and likelihood-ranking method (Bricogne & Gilmore, 1990), the direct grid search (Masciocchi, Bianchi, Cairati, Mezza, Pulati, Sironi, 1994; Chernyshev & Schenk, 1998) and the global optimization procedures: genetic algorithm (Kariuki, Serrano-Gonzalez, Johnston, Harris, 1997) and Monte Carlo based methods (Harris, Tremayne, Lightfoot, Bruce, 1994; Andreev, Lightfoot, Bruce, 1997). In recent years the Monte Carlo simulated annealing approach has been applied in a large variety of structural studies (Deem, Newsam, 1992; Tremayne, Kariuki, Harris, 1997; Andreev & Bruce, 1998; David, Shankland, Shankland, 1998) and the software package has been developed (Engel, Wilke, Konig, Harris, Leusen, 1999). Recently the new optimizaÅ tion method, based on the combined cost function including the potential energy and the difference between the calculated and measured diffraction patterns has been suggested and successfully tested on a number of ionic and intermetallic compounds (Putz, Schon, Jansen, 1999). Å However, the structure solution from powder data is not a straightforward and routine task yet. Therefore, till now there is still a strong need for elaboration of efficient solving procedures. The aim of this work was the development of the simulated annealing approach. It was successfully applied to

the study of crystal structures from laboratory Guinier data using a priory known molecule fragments. Three unknown molecular structures of 2-chloro-1-(p-nitrophenacyl)-pyridinium bromide (C13H10N2O3Cl)þ Br (compound I); 2-(p-nitrophenyl)-thiazolo[3,2-a]-pyridinium perchlorate (C13H9N2O2S)þ ClO4 (compound II) and 3-(p-nitrobenzoyl)2-oxo-oxazolo[3,2-a]pyridine C14H8N2O5 (compound III) have been solved.

Method and structure solution
The simulated annealing (SA) procedure was based on the standard Metropolis Monte Carlo method (Metropolis, Rosenbluth, Rosenbluth, Teller, Teller, 1953). For structure solution one can use the figure-of-merit (FOM) function, such as R-factors, calculated over the whole powder pattern (Harris et al., 1994): P P Rwp ? ? wi jYobs; i À Ycalc; j j2 = wi jYobs; j j2 1=2 RB ? P jY
obs; i

ÀY

calc; j

j=

P

jYobs; j j

where Yobs,i - the experimental intensity of i-th point; Ycalc,i - the calculated intensity; wi = 1/Yobs. However, this method is time consuming and, instead of it, in (David et al., 1998) the FOM function was suggested, which is based on the extracted integrated intensities from the profile refinement using the Pawley method (Pawley, 1981): PP ðIh À cjFh j2 ÞðV 1 Þhk ðIk À cjFk j2 Þ c2 ?
h k

* Correspondence author (e mail : zhukov@struct.chem.msu.ru)

where Ih, Ik - the Lorentz-polarization corrected extracted intensities; Vhk - the covariance matrix from the profile refinement; c - the scale factor; jFh j; jFk j - the calculated structure factors of the trial structure. The using of the covariance matrix permits to handle the correlation between the extracted intensities of the overlapping reflections. However, in the case of the moderate overlapping it is possible to simplify the FOM function for faster computation. Following (Chernyshev & Schenk, 1998) we used the FOM function R(X): P P RðX Þ ? jXobs; j À c Á Xcalc; j j= Xobs; j


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Compound Formula Sp.gr. a, A b, A c, A b, deg. A V, 3 Z Absorption coef. m (cmÀ1) Calculated density dx (g cm 1) F(000) I (C13H10N2O3Cl)þ Á Br Fdd2 30.77(1) 35.04(1) 5.130(3) 5531 16 59.2 1.72 2848 II (C13H9N2O2S)þ Á ClO Pbca 16.65(1) 24.09(1) 7.518(3) 3016 8 38.6 1.57 1456 III C14H8N2O5 P21 =n 13.64(1) 22.28(1) 3.917(3) 90.63(2) 1190 4 10.8 1.65 608

S. G. Zhukov, V. V. Chernyshev, E. V. Babaev et al. Table 1. Crystal data of 2 chloro 1 (p nitro phenacyl) pyridinium bromide (I); 2 (p nitro phenyl) thiazolo[3,2 a] pyridinium perchlorate (II); 3 (p nitrobenzoyl)2 oxo oxazolo[3,2 a]pyridine (III).

À

4

where j-summation is over the number of the extracted intensities, including the single and overlapping reflecP P miF 2obs,i ; Xcalc ? yi mi F 2calc,i with itions; Xobs ? summation over the overlapping reflections; mi - the multiplicity of the i-th reflection; yi - the texture correction coefficient; c - the scale factor. The values of Xobs could be easily obtained using the Pawley or Le Bail profile refinement (Pawley, 1981; Le Bail, Duroy, Fourquet, 1988). Thus, the problem of the extracting of the intensity of each overlapping reflection is avoided and the peak overlapping is intrinsically taken care of. This approach permits a large reduction of computing time in comparison with the use of the whole pattern profile. During the SA run several rigid molecular fragments were displaced independently with the random translational and rotational shifts {Xi Yi Zi wi ji ci} ! {Xi Yi Zi wi ji ci} þ aR; F xi, where xi - a random number between - 1 and 1; aR; F - the maximum possible shift of the translation or rotation. For each random configuration the FOM function was calculated after a rapid scale factor minimization. Following (Metropolis, et al., 1953) the trial structure was accepted with the probability P ? exp fÀðRtrial À Rprev Þ=T g and rejected with the probability (1 À P), where Rtrial, Rprev - the values of the FOM function of the trial and previously accepted configurations, T - the analogy of the slowly decreasing temperature. The choice of the appropriate value of a is important for the uniform exploring of the phase space. In (Serra, Stanton, Kais, Bleil, 1997) it was shown that the different types of the random shift distribution leads to a different exploration of the phase space. Therefore we used a(T) with normal distribution N(a, s), where the standard de-

viation s decreases with decreasing temperature. As a result large shifts were permitted at high temperatures and at low temperatures the variation of a was negligible. The studied powders were synthesised following the standard methods (Babaev, 2000). The X-ray powder patterns were measured using an evacuated Guinier-Johanson camera (Enraf-Nonius FR552) with quartz monochromatized CuKa1 radiation. Digitised intensities were collected with a LS18 microdensitometer from 4.0 to 83.0 degrees 2q in steps of 0.01 . Cell parameters of the three compounds were determined by indexing of the powder patterns with the use of the ITO program (Visser, 1969) and space groups were derived from systematic extinctions (see Table 1). The Pawley profile refinement, SA procedure and Rietveld refinement were performed with the updated MRIA program (Zlokazov & Chernyshev, 1992). The split-type pseudo-Voight peak profile function (Toraya, 1986) and March-Dollase texture formalism (Dollase, 1986) were used for powder pattern processing. For the SA minimization we constructed the initial molecular models from the chemically stable and rigid fragments. Preliminary information about the possible molecular structure was obtained using the IR and NMR spectroscopy measurements. In the case of the compound I the p-nitro-benzoyl and the (2-Cl-pyridine-1)methyl groups with the Br atom have been taken to generate the random configurations; for the compound II we used the p-nitro-phenyl and the thiazolo[3,2-a]pyridyl groups and the ClO4 anion, and for compound III two independent units: the 2-oxo-oxazolo[3,2-a]pyridine and the p-nitrobenzoyl groups have been used. The molecular fragments are shown in Fig. 1.

a

b

c
2 (p nitrophenyl) thiazolo[3,2 a] pyridinium perchlorate (compound II); c) 3 (p nitrobenzoyl)2 oxo oxazolo[3,2 a]pyridine (compound III).

Fig. 1. Molecular fragments used for simulated annealing minimization. a) 2 chloro 1 (p nitrophenacyl) pyridinium bromide (compound I); b)


Simulated annealing approach for structure solution

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a

b

Fig. 2. Rietveld plots of a) 2 chloro 1 (p nitro phenacyl) pyridinium bromide (compound I); b) 2 (p nitrophenyl) thiazolo[3,2 a] pyridinium perchlorate (compound II); c) 3 (p nitroben zoyl)2 oxo oxazolo[3,2 a]pyridine (compound III).

c


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Table 2. Simulated annealing (SA) data of structure solution of: 2 chloro 1 (p nitrophenacyl) pyridinium bromide (I); 2 (p nitrophenyl) thiazolo[3,2 a] pyridinium perchlorate (II); 3 (p nitrobenzoyl)2 oxo oxazolo[3,2 a]pyridine (III). Com pound I II III N of Xobs 70 100 100 120 70 100 N of non hydrogen atoms 20 23 21 N of N of SA runs degrees of freedom 15 18 12 11 16 7 R(X) (%) of solution 48 39 52

S. G. Zhukov, V. V. Chernyshev, E. V. Babaev et al.

Table 3. The results of full pattern decomposition and Rietveld re finements of: 2 chloro 1 (p nitrophenacyl) pyridinium bromide (I); 2 (p nitrophenyl) thiazolo[3,2 a] pyridinium perchlorate (II); 3 (p nitro benzoyl)2 oxo oxazolo[3,2 a]pyridine (III). Compound I Compound II Compound III Full pattern decompositiona 7.6 Rwp, % 3.2 Rexp, % 5.6 c2 Rietveld refinement Rwp, % Rexp, % c2 Texture correction, direction parameter r a: Rwp, R
exp

7.3 2.6 7.9 8.1 2.6 9.9 010 0.91

5.6 2.5 4.8 5.7 2.5 5.3 001 0.83

8.0 3.2 6.1 001 0.78

are defined in (Young, Wiles, 1982)

lowed to be partly flexible including a certain degree of flexibility in bond length, bond angles and torsion angles (see Andreev, et al., 1997; Andreev & Bruce, 1998). However, the increasing of the number of degrees of freedom may lead to good values of the FOM function but not to the correct structure, hence, the number of simulated annealing steps and runs should be increased to find the structure. It seems to be worthwhile to accompany the simulated annealing run with an intermediate Rietveld refinement to exclude false minima at low "temperatures" (see Engel et al., 1999). One of the crucial points is the choice of the simulated annealing scheme, i.e. the random shift distribution and the type of the acceptance probability. It was shown (Serra, et al., 1997) that the exploring of phase space essentially depends on the distribution type of the random shift vector. The use of the suggested Tsallis distribution may improve the exploration of the phase space during the random walk. Another point is the acceptance criterion, which is usually taken from the Metropolis algorithm, but could also be based on another probability type for speeding up the minimization process. This will be studied in our future work. The systematic errors, for instance the noticeable texture, may lead to the failure of the structure determination. If texture free measurements are impossible then the experimental data could be corrected using a trial and error method or by applying the special procedures (Peschar, Schenk, Capkova, 1995).
Acknowledgment. This work has been supported by the Netherlands Organisation for Scientific Research (NWO).

The number of SA runs to find the actual structure solution varied from 7 to 16 depending on the degrees of freedom. At each temperature the total number of possible random steps was equal Ntot ? 20000 Á Nunits. However, the temperature was decreased compulsorily if the number of successful trials has exceeded 0.3 Á Ntot. Usually 70 - 120 Xobs extracted intensities in total were used for the SA calculation. Each SA run took one or several hours on a Pentium-III computer depending on the number of Xobs and the degrees of freedom. The details of SA procedures for the studied compounds are summarised in Table 2. Special attention was paid to the preferred orientation effect. Because it is difficult to avoid it completely during the experiments we used several data sets for structure solution with March-Dollase texture correction applied along several probable directions and different texture coefficients. The results of the final Rietveld refinements of the crystal structures are given in Table 3. The details of the crystal structures are to be published in a separate papers. In Fig. 2a, b, c the Rietveld plots for the compounds 1, 2 and 3 are shown.

References
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Concluding remarks
The simulated annealing method is efficient for the crystal structure determination from X-ray powder data using a priory known structural fragments. Even without the precise knowledge of the possible molecular structure it gives the correct positions of the molecular groups. A useful addition could be made if the structural fragments are al-


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