1. Inorganic structure prediction : too much and not enough Armel Le Bail Université du Maine, Laboratoire des oxydes et Fluorures, CNRS UMR 6010, Avenue O. Messiaen, 72085 Le Mans Cedex 9, France. Email : alb@cristal.org XX Conference on Applied Crystallography, Wisla, Poland, September 2006

2. CONTENTS - Introduction - Prediction software and examples - More examples from the GRINSP software (especially AlF 3 polymorphs and titanosilicates) - Opened doors, limitations, problems - Conclusion XX Conference on Applied Crystallography, Wisla, Poland, September 2006

3. INTRODUCTION Personnal views about crystal structure prediction : “Exact” description before synthesis or discovery in nature. These “exact” descriptions should be used for the calculation of powder patterns included in a database for automatic identification of real compounds not yet characterized crystallographycally. XX Conference on Applied Crystallography, Wisla, Poland, September 2006

4. If the state of the art had dramatically evolved in the past ten years, we should have huge databases of predicted compounds, and not any new crystal structure would surprise us since it would corespond already to an entry in that database. Moreover, we would have obtained in advance the physical properties and we would have preferably synthesized those interesting compounds. Of course, this is absolutely not the case. Where are we with inorganic crystal structure prediction? XX Conference on Applied Crystallography, Wisla, Poland, September 2006

5. But things are changing, maybe : Two databases of hypothetical compounds were built in 2004. One is exclusively devoted to zeolites : M.D. Foster & M.M.J. Treacy - Hypothetical Zeolites – http://www.hypotheticalzeolites.net/ The other includes zeolites as well as other predicted oxides (phosphates, borosilicates, etc) and fluorides : the PCOD (Predicted Crystallography Open Database) http://www.crystallography.net/pcod/ XX Conference on Applied Crystallography, Wisla, Poland, September 2006

6. Prediction software Especially recommended lectures (review papers) : 1- S.M. Woodley, in: Application of Evolutionary Computation in Chemistry, R. L. Johnston (ed), Structure and bonding series, Springer- Verlag 110 (2004) 95-132. 2- J.C. Schön & M. Jansen, Z. Krist. 216 (2001) 307-325; 361-383. Software : CASTEP, program for Zeolites, GULP, G42, Spuds, AASBU, GRINSP XX Conference on Applied Crystallography, Wisla, Poland, September 2006

7. CASTEP Uses the density functional theory (DFT) for ab initio modeling, applying a pseudopotential plane-wave code. M.C Payne et al., Rev. Mod. Phys. 64 (1992) 1045. Example : carbon polymorphs XX Conference on Applied Crystallography, Wisla, Poland, September 2006

8. Hypothetical Carbon Polymorph Suggested By CASTEP XX Conference on Applied Crystallography, Wisla, Poland, September 2006

9. Another CASTEP prediction XX Conference on Applied Crystallography, Wisla, Poland, September 2006

12. ZEOLITES The structures gathered in the database of hypothetical zeolites are produced from a 64-processor computer cluster grinding away non-stop, generating graphs and annealing them, the selected frameworks being then re-optimized using the General Utility Lattice Program (GULP, written by Julian Gale) using atomic potentials. M.D. Foster & M.M.J. Treacy - Hypothetical Zeolites – http://www.hypotheticalzeolites.net/ XX Conference on Applied Crystallography, Wisla, Poland, September 2006

17. Zeolite predictions are probably too much… Less than 200 zeotypes are known Less than 10 new zeotypes are discovered every year Less than half of them are listed in that >1.000.000 database So that zeolite predictions will continue up to attain several millions more… Quantum chemistry validation of these prediction is required, not only empirical energy calculations, for elimination of a large number of models that will certainly never be confirmed.

18. GULP Appears to be able to predict crystal structures (one can find in the manual the data for the prediction of TiO 2 polymorphs). Recently, a genetic algorithm was implemented in GULP in order to generate crystal framework structures from the knowledge of only the unit cell dimensions and constituent atoms (so, this is not prediction...), the structures of the better candidates produced are relaxed by minimizing the lattice energy, which is based on the Born model of a solid. S.M. Woodley, in: Application of Evolutionary Computation in Chemistry, R. L. Johnston (ed), Structure and bonding series, Springer-Verlag 110 (2004) 95-132. GULP : J. D. Gale, J. Chem. Soc., Faraday Trans., 93 (1997) 629-637. http://gulp.curtin.edu.au/ XX Conference on Applied Crystallography, Wisla, Poland, September 2006

19. Part of the command list of GULP : XX Conference on Applied Crystallography, Wisla, Poland, September 2006

20. G42 A concept of 'energy landscape' of chemical systems is used by Schön and Jansen for structure prediction with their program named G42. J.C. Schön & M. Jansen, Z. Krist. 216 (2001) 307-325; 361-383. XX Conference on Applied Crystallography, Wisla, Poland, September 2006

24. SPuDS Dedicated especially to the prediction of perovskites. M.W. Lufaso & P.M. Woodward, Acta Cryst. B57 (2001) 725-738. XX Conference on Applied Crystallography, Wisla, Poland, September 2006

25. AASBU method (Automated Assembly of Secondary Building Units) Developed by Mellot-Draznieks et al., C. Mellot-Drazniek, J.M. Newsam, A.M. Gorman, C.M. Freeman & G. Férey, Angew. Chem. Int. Ed. 39 (2000) 2270-2275; C. Mellot-Drazniek, S. Girard, G. Férey, C. Schön, Z. Cancarevic, M. Jansen, Chem. Eur. J. 8 (2002) 4103-4113. Using Cerius2 and GULP in a sequence of simulated annealing plus minimization steps for the aggregation of large structural motifs. Cerius2, Version 4.2, Molecular Simulations Inc., Cambridge, UK, 2000. XX Conference on Applied Crystallography, Wisla, Poland, September 2006

29. Not enough If zeolites are excluded, the productions of these prediction software are a few dozen… not enough, not available in any database. A recent (2005) prediction program is able to extend the investigations to larger series of inorganic compounds characterized by corner-sharing polyhedra.

30. GRINSP Geometrically Restrained INorganic Structure Prediction Applies the knowledge about the geometrical characteristics of a particular group of inorganic crystal structures (N-connected 3D networks with N = 3, 4, 5, 6, for one or two N values). Explores that limited and special space (exclusive corner-sharing polyhedra) by a Monte Carlo approach. The cost function is very basic, depending on weighted differences between ideal and calculated interatomic distances for first neighbours M-X, X-X and M-M for binary M a X b or ternary M a M' b X c compounds. J. Appl. Cryst. 38, 2005, 389-395. J. Solid State Chem. 179, 2006, 3159-3166.

31. Observed and predicted cell parameters comparison Predicted by GRINSP (Å)Observed or idealized (Å) Dense SiO 2 abcRabc  (%) Quartz4.9654.9655.3750.00094.9124.9125.4040.9 Tridymite5.0735.0738.4000.00455.0525.0528.270 0.8 Cristobalite5.0245.0246.7960.00184.9694.9696.9261.4 Zeolites ABW9.8725.2298.7330.00569.95.38.80.8 EAB13.15813.15815.0340.003713.213.215.00.3 EDI6.9196.9196.4070.00476.9266.9266.4100.1 GIS9.7729.77210.1740.00279.89.810.20.3 GME13.60913.6099.9310.003113.713.79.90.6 Aluminum fluorides  -AlF 3 10.21610.2167.2410.015910.18410.1847.174 0.5 Na 4 Ca 4 Al 7 F 33 10.87610.87610.8760.012210.78110.78110.7810.9 AlF 3 -pyrochl.9.6689.6689.6680.00479.7499.7499.7490.8 Titanosilicates Batisite10.63314.0057.7300.0076 10.413.858.12.6 Pabstite6.7246.7249.7830.00526.70376.70379.8240.9 Penkvilskite 8.8908.4267.4690.0076 8.9568.7277.3871.3

32. Predictions produced by GRINSP Binary compounds Formulations M 2 X 3, MX 2, M 2 X 5 et MX 3 were examined. Zeolites MX 2 (= 4-connected 3D nets) More than 1000 zeolites (not 1.000.000) are proposed with cell parameters < 16 Å, placed into the PCOD database : http://www.crystallography.net/pcod/ GRINSP recognizes a zeotype by comparing the coordination sequences (CS) of a model with a previously established list of CS and with the CS of the models already proposed during the current calculation).

33. Hypothetical zeolite PCOD1010026 SG : P432, a = 14.623 Å, FD = 11.51

34. Other GRINSP predictions : > 3000 B 2 O 3 polymorphs Hypothetical B 2 O 3 - PCOD1062004. Triangles BO 3 sharing corners. = 3-connected 3D nets

35. > 500 V 2 O 5 polymorphs square-based pyramids = 5-connected 3D nets

36. 12 AlF 3 polymorphs Corner-sharing octahedra. = 6-connected 3D nets

37. Do these AlF 3 polymorphs can really exist ? Ab initio energy calculations by WIEN2K « Full Potential (Linearized) Augmented Plane Wave code » A. Le Bail & F. Calvayrac, J. Solid State Chem. 179 (2006) 3159-3166.

38. Ternary compounds M a M’ b X c in 3D networks of polyhedra connected by corners Either M/M’ with same coordination but different ionic radii or with different coordinations (mixed N-N’-connected 3D frameworks) These ternary compounds are not always electrically neutral.

39. Borosilicates PCOD2050102, Si 5 B 2 O 13, R = 0.0055. > 3000 models SiO 4 tetrahedra and BO 3 triangles

40. Aluminoborates > 2000 models Example : [AlB 4 O 9 ] -2, cubic, SG : Pn-3, a = 15.31 Å, R = 0.0051: AlO 6 octahedra and BO 3 triangles

41. Fluoroaluminates Known Na 4 Ca 4 Al 7 F 33 : PCOD1000015 - [Ca 4 Al 7 F 33 ] 4-. Two-sizes octahedra AlF 6 and CaF 6

42. Unknown : PCOD1010005 - [Ca 3 Al 4 F 21 ] 3-

43. Results for titanosilicates > 1000 models TiO 6 octahedra and SiO 4 tetrahedra

44. Numbers of compounds in ICSD version 1-4-1, 2005-2 (89369 entries) potentially fitting structurally with the [TiSi n O (3+2n) ] 2- series of GRINSP predictions, adding either C, C 2 or CD cations for electrical neutrality. n+C+C 2 +CDTotalGRINSP ABX 5 130049546435129493 AB 2 X 7 221530823611770179 AB 3 X 9 3119601995383174 AB 4 X 11 430140172205 AB 5 X 13 591101136 AB 6 X 15 627113142158 Total2581845 More than 70% of the predicted titanosilicates have the general formula [TiSi n O (3+2n) ] 2- Not all these 2581 ICSD structures are built up from corner sharing octahedra and tetrahedra. Many isostructural compounds inside.

45. Models with real counterparts

46. Example in PCOD Not too bad if one considers that K et H 2 O are not taken into account in the model prediction... Model PCOD2200207 (Si 3 TiO 9 ) 2- : a = 7.22 Å; b = 9.97 Å; c =12.93 Å, SG P2 1 2 1 2 1 Known as K 2 TiSi 3 O 9.H 2 O (isostructural to mineral umbite): a = 7.1362 Å; b = 9.9084 Å; c =12.9414 Å, SG P2 1 2 1 2 1 (Eur. J. Solid State Inorg. Chem. 34, 1997, 381-390)

47. Highest quality (?) models

50. Models with the largest porosity

51. PCOD3200086 : P = 70.2%, FD = 10.6, D P = 3 (dimensionality of the pore/channels system) [Si 6 TiO 15 ] 2-, cubic, SG = P4 1 32, a = 13.83 Å Ring apertures 9 x 9 x 9

52. PCOD3200867, P = 61.7%, FD = 12.0, D P = 3 [Si 2 TiO 7 ] 2-, orthorhombic, SG = Imma Ring apertures 10 x 8 x 8

53. PCOD3200081, P = 61.8%, FD = 13.0, D P = 3 [Si 6 TiO 15 ] 2-, cubic, SG = Pn-3 Ring apertures 12 x 12 x 12 +10+6

54. PCOD3200026, P = 59.6%, FD = 13.0, D P = 3 [Si 4 TiO 11 ] 2-, tetragonal, SG = P4 2 /mcm Ring apertures 12 x 10 x 10

55. Opened doors, Limitations, Problems GRINSP limitation : exclusively corner-sharing polyhedra. Opening the door potentially to > 50.000 hypothetical compounds. The predicted titanosilicates can be extrapolated to phosphates, sulfates, and/or replacing Ti by Nb, V, Zr, Ga, etc. More than 10.000 should be included into PCOD before the end of 2006. Then, their powder patterns will be calculated and possibly used for search-match identification.

56. Expected improvements : Edge, face, corner-sharing, mixed. Hole detection, filling them automatically, appropriately, for electrical neutrality. Using bond valence rules or/and energy calculations to define a new cost function. Extension to quaternary compounds, combining more than two different polyhedra. Etc, etc. Do it yourself, the GRINSP software is open source…

57. Two things that don’t work well enough up to now… Validation - Ab initio calculations (WIEN2K, etc) : not fast enough for the validation of > 10000 structure candidates (was 2 months for 12 AlF 3 models) Identification - There is no efficient tool for the identification of the known structures (from the ICSD) among >10000 hypothetical compounds

58. One advice, if you become a structure predictor Send your data (CIFs) to the PCOD, thanks… (no proteins, no nucleic acid, not 1.000.000 zeolites)

59. CONCLUSIONS Structure and properties prediction is THE challenge of this XXIth century in crystallography. Advantages are obvious (less serendipity and fishing-type syntheses). We have to establish databases of predicted compounds, preferably open access on the Internet, finding some equilibrium between too much and not enough. If we are unable to do that, we have to stop pretending to understand and master the crystallography laws.