Solving Structures from Powder Data in Direct Space - State of the Art - Armel Le Bail Université du Maine, Laboratoire des oxydes et Fluorures, CNRS UMR 6010, Avenue O. Messiaen, Le Mans Cedex 9, France.

CONTENT Introduction Computer Programs DASH EAGER ENDEAVOUR ESPOIR FOX OCTOPUS POWDERSOLVE PSSP SAFE SA (Simulated Annealing) TOPAS Conclusions / Advertisements / Tests with ESPOIR

Introduction The final SDPD step is always the Rietveld method application. Going to this last step needs at least an approximate model to be improved by the Rietveld refinement and eventually completed by further Fourier difference synthesis. How can be obtained this starting approximate (or sometimes complete) model by a direct space approach is the only question considered here. Not to mention that before that structure solution step, you must have yet recorded a powder pattern (so you must have a sample), established that the structure is unknown, indexed the powder pattern, proposed a space group, and you must possess some chemical knowledge of the sample.

The SDPD maze… From the book: Structure Determination from Powder Diffraction Data IUCr Monographs on Crystallography 13 Oxford Science Publications (2002)

Chemical Information Chemical knowledge is indispensable to the application of the direct space methods since they consist in placing atoms, either independent or as a whole molecule, at some positions in the cell, generally wrong positions at the beginning of the process, and moving them by translations (as well as rotations for a molecule or polyhedron) up to obtain a satisfying fit to the powder pattern or to a mathematical representation of that pattern. Going from wrong atomic positions to the final roughly correct ones is made by a process called global optimization which can be realized by different but finally similar procedures: Monte Carlo (MC), Monte Carlo with simulated annealing (SA) or/and with parallel tempering (PT), genetic algorithm (GA). These processes present a similarity in the use of random number sequences: atoms and molecules realize a random walk.

Some Definitions Sometimes the "direct space methods" (not to be confused with the direct methods) are called "global optimization methods" or "model building methods", and even sometimes "real space methods". "Direct space" was the definition retained in the pioneering papers. "Direct space" as opposed to "reciprocal space" has an adequate crystallographic structural sense, and should be preferred to "real space", which, opposed to "imaginary" would call to mind both parts of the diffusion factors. "Global optimization" has a large sense and designates the task of finding the absolutely best set of parameters in order to optimize an objective function, a task not at all limited to crystallography.

Direct Space Pioneering Papers Already an old story M. W. Deem and J. M. Newsam, Nature 342 (1989) M. W. Deem and J. M. Newsam, J. Am. Chem. Soc. 114 (1992) J.W. Newsam, M.W. Deem & C.M. Freeman, Accuracy in Powder Diffraction II, NIST Special Publication 846 (1992) L.A. Solovyov & S.D. Kirik, Mat. Sci. Forum (1993) K.D.M. Harris, M. Tremayne, P. Lightfoot & P.G. Bruce, J. Am. Chem. Soc. 116 (1994) D. Ramprasad, G.P. Pez, B.H. Toby, T.J. Markley & R.M. Pearlstein, J. Amer. Chem. Soc. 117 (1995)

For instance : J.W. Newsam, M.W. Deem & C.M. Freeman, Accuracy in Powder Diffraction II, NIST Special Publication 846 (1992)

Computer Programs - Nowadays Selection of programs applying direct space methods for the structure solution from powder diffraction data (CH 2 CH 2 O) 6 :LiAsF 6 ProgramAccessGO DataExample DoF DASHCSAPCapsaicin 16 EAGER AGAWPPh 2 P(O)(CH 2 ) 7 P(O)Ph 2 18 ENDEAVOURCSA IAg 2 PdO 2 45 ESPOIROMC LGormanite54 FOXOSAWPAl 2 (CH 3 PO 3 ) 3 24 OCTOPUSAMCWPRed Fluorescein7 POWDERSOLVECMCWPDocetaxel29 PSSPOSALMalaria Pigment Beta Haematin 14 SAFEASAWPC 32 N 3 O 6 H SAASAWP(CH 2 CH 2 O) 6 :LiAsF 6 79 TOPASCSAWPCaffeine Anhydrous93 Access : C = Commercial with academic prices, O = Open access, A = contact the authors GO = Global Optimization : MC = Monte Carlo, SA = MC+Simulated Annealing, GA = Genetic Algorithm Data : P = Pawley, L = Le Bail, I = Integrated intensities, WP = Whole Pattern DoF = degrees of freedom corresponding to the example

Degrees of Freedom (DoF) Irrespectively to the number of atoms, a molecule can be located easily in a cell, as a rigid body, corresponding to 3 positional and 3 orientational degrees of freedom (DoF), by checking the fit quality on, say, the first 50 peaks of the diffraction pattern. But the number of DoFs will increase by one for every added free torsion angle, and more complications arise if several independent molecules have to be located altogether or/and if water molecules or chlorine/sulphur/etc atoms are involved. For inorganic compounds, in principle an atom in general position corresponds to 3 DoFs (the three xyz atomic coordinates), however, chemistry may say if some polyhedra are to be expected, then an octahedron for instance, instead of corresponding to 7x3=21 DoFs when described by the atomic coordinates, can be translated and rotated as a whole polyhedron, corresponding to only 6 DoFs.

Flexibility Most of these computer programs are also able to start from a complete set of independent atoms, at random at the beginning, and then will try to find their positions, moving them while matching to the data. Combinations of (several) molecules (or polyhedra) together with independent atoms are of course possible. Limitation The main difficulty may come finally at the Rietveld refinement stage, if the powder pattern quality becomes too low compared to the number of parameters, then it will be necessary to apply some constraints and/or restraints. And it may be difficult to complete the structure…

These computer programs are obtaining more and more success, surpassing in number the solutions by traditional approaches (Patterson or Direct methods as applied in computer programs like SHELXS - etc - or adapted to powder data in EXPO). Nevertheless, the number of SDPD per year remains quite small (close to 100, to be compare to from single crystal data). Cumulated histogram of the total number of published SDPD. Picture from the SDPD Database: iniref.html

The following details about the direct space computer programs were gathered and presented by Yuri G. Andreev at the EPDIC-8 congress (Uppsala, Suède, 2002), obtained from the authors themselves. Things have not changed a lot after two years. Note that EXPO2004/5 adds also now the direct space approach to its traditional way to solve structures (direct methods especially adapted to powder data), and even can mix the two approaches. To this list of programs may be added a few others which have special abilities for zeolites (ZEFSA-II, FOCUS, GRINSP). Comments

SA Correlated integrated intensities Chem. Commun. 931 (1998) Capsaicin - most complex structure in terms of number of variables Chem. Commun. 931 (1998) 10 torsions and 6 external DoF. Academics receive a 95% discount DASH W.I.F. David and K. Shankland Rutherford Appleton Laboratory, further developed by J. Cole and J. van de Streek CCDC, UK Telmisartan forms A and B - fairly typical structure J. Pharm. Sci. 89, 1465 (2000) 7 torsions and 6 external DoF.

EAGER K.D.M. Harris, R.L. Johnston, D. Albesa Jové, M.H. Chao, E.Y. Cheung, S. Habershon, B.M. Kariuki, O.J. Lanning, E. Tedesco, G.W. Turner University of Birmingham, UK Genetic Algorithm Full profile Acta Cryst. A, 54, 632 (1998) Heptamethylene-1,7-bis(diphenylphosphane oxide) Ph 2 P(O)(CH 2 ) 7 P(O)Ph 2 - typical structure. B.M. Kariuki, P. Calcagno, K.D.M. Harris, D. Philp, R.L. Johnston. Angew. Chem. Int. Ed. 38, 831 (1999). 35 non-H atoms in the a.u. 18 DoF including 12 torsion angles. Under active development

ENDEAVOUR K. Brandenburg and H. Putz, Crystal Impact, Bonn, Germany Combined global optimization of R-factor and potential energy using SA Integrated intensities J.Appl.Cryst. 32, 864 (1999) Ag 2 NiO 2 - typical structure Schreyer and Jansen, Sol. State Sci. 3(1-2), 25, (2001). 15 atoms in the a.u. of P1. 45 DoF. Available from Crystal Impact at reduced price for academic users.

ESPOIR A. Le Bail, Universite du Maine, France Reverse Monte Carlo and pseudo SA Integrated intensities or full profile on a pseudo powder pattern regenerated from extracted |F obs | Mat. Sci. Forum , 65 (2001). Souzalite/Gormanite Le Bail, Stephens and Hubert, European J. Mineralogy 15 (2003) atoms in the a.u. of P-1. Fe at 0,0,0 54 DoF. Free and Open - all available : executable as well as Fortran and Visual C++ source code (GPL - GNU Public Licence). Web site:

FOX V. Favre-Nicolin and R. Cerny, University of Geneva, Switzerland (Free Objects for Xtallography) Parallel Tempering or SA. Automatic correction of special positions and of sharing of atoms between polyhedra, without any a priori knowledge; multi-pattern Full profile, integrated intensities, partial integrated intensities J.Appl.Cryst. 35 (2002) 734. Aluminum methylphosphonate Al 2 (CH 3 PO 3 ) 3 - most complex structure Edgar et al. Chem. Commun. 808, (2002). 3 molecules and 2 Al atoms in the a.u. 24 DoF including bond lengths and bond angles. Free, open-source published under the GPL license

OCTOPUS K.D.M. Harris, M. Tremayne and B.M. Kariuki University of Birmingham, UK Monte Carlo Full profile J. Am. Chem. Soc. 116, 3543 (1994). Red fluorescein - typical structure. Tremayne, Kariuki and Harris. Angew. Chem. Int. Ed. 36, 770 (1997). 25 non-H atoms in the a.u. 7 DoF including 1 torsion angle. Under active development

POWDERSOLVE (part of Reflex Plus integrated package) G. Engel, S. Wilke, D. Brown, F. Leusen, O. Koenig, M. Neumann, C. Conesa- Morarilla Accelrys Ltd., Cambridge, UK Monte Carlo SA and Monte Carlo parallel tempering (Falcioni and Deem. J. Chem. Phys. 110 (1999)1754.) Full profile J. Appl.Cryst. 32, 1169 (1999) Docetaxel (C 43 H 53 NO 14 ·3H 2 O) - most complex structure L. Zaske, M.-A. Perrin and F. Leveiller, J. Phys. IV, Pr10, 221 (2001) 29 DoF including 3 rotations, 12 translations and 14 torsion angles. Can be purchased from Accelrys Inc., generous discounts given to academic researchers

SA Free, including open source. Available at PSSP P. Stephens and S. Pagola State University of New York, Stony Brook, (Powder Structure Solution Program) USA Integrated intensities (Le Bail) with novel handling of peak overlap Submitted to J.Appl.Cryst. Preprint available on Malaria Pigment Beta Haematin - most complex structure. Pagola, Stephens, Bohle, Kosar, and Madsen. Nature (2000) 43 non-H atoms in the a.u. 14 DoF.

SA + option of using a structure envelope. Not ready for general distribution but will be in public domain (still not by the end of 2004). Verify at: SAFE S. Brenner, L.B. McCusker and Ch. Baerlocher ETH Zentrum, Zurich, Switzerland (Simulated Annealing and Fragment search within an Envelope) Full-profile J. Appl. Cryst. 35, 243 (2002) Tri-  -peptide C 32 N 3 O 6 H 53 - the most complex structure. Brenner, McCusker and Baerlocher J.Appl.Cryst. 35, 243 (2002) 17 torsion angles and 6 positional and orientational DoF.

SA Simulated Annealing Y. G. Andreev and P. G. Bruce, University of St. Andrews Full-profile J. Appl. Cryst. 30, 294 (1997) (CH 2 CH 2 O) 6 :LiAsF 6 (CH 2 CH 2 O) 6 :LiAsF 6 - most complex structure. MacGlashan, Andreev, and Bruce Nature (1999) 26 non-H atoms in the a.u. 79 DoF including 15 torsion angles. Free, very user unfriendly. Requires changing of the code for each new structure determination. Customised molecular description without Z- matrix input.

TOPAS A.A. Coelho, R.W.Cheary, A. Kern, T. Taut. Bruker AXS GmbH, Karlsruhe, Germany SA (together with user definable penalty functions, rigid bodies, various bond length restraints and lattice energy minimization techniques including user definable force fields) Full-profile or integrated intensities J. Appl. Cryst. 33, 899 (2000) Caffeine Anhydrous C 8 H 10 N 4 O 2 Stowasser and Lehmann, Abstract submitted to the XIX IUCr Congress 5 molecules in the a.u. 93 DoF. Discounted price (500 €) for academic users. See :

Which software could solve the problems proposed during two previous SDPD Round Robin ? 1998 SDPDRR : DASH SDPDRR : FOX and TOPAS

CONCLUSIONS The capacities for solving structures from powder diffraction data have never been so efficient than during the past 5-12 years evolutions. One has to find his way in the SDPD maze and to select the appropriate methods and computer programs at each step of the problem (identification - which should fail to establish any relation with a known structure-, indexing, whole pattern fitting with cell constraints, structure solution, Rietveld refinement).

Advice When a SDPD is decided, you know already the complexity level. Then select the appropriate radiation, a 3rd generation synchrotron pattern being the best choice for complex cases. It is better to wait a bit for a good pattern and to solve the problem than to waste large time and not to solve the problem. Applying direct space methods requires generally much less data (3 to 5 intensities per degree of freedom may be sufficient) than direct methods. However, big organic or organometallic problems can be completely solved only if one disposes of a maximum of knowledge about the molecular formula together with the most excellent data.

Use your common sense Very complex molecules will present more serious difficulties at the Rietveld structure refinement stage : the ratio of the effective number of structure factors with the number of atomic coordinates to refine may be as small as 3 or less (because there is soon no accurate intensity on the powder pattern at resolution d <1.5 Å), so that the model needs to be constrained/restrained. This may lead to difficulties to locate some additional water molecule, or to be absolutely sure that there is not any misunderstanding somewhere which could explain why the Bragg R factor R B is going to be sometimes as large as 10 or 15%. No need to say that some proposed H atom positions will have sometimes a low credibility. You will have to know « how much is too much », or your manuscript will be rejected (by a good reviewer).

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