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Inorganic structure prediction : too much and not enough Armel Le Bail

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.

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Inorganic structure prediction : too much and not enough Armel Le Bail

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  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 AlF3 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. Where are we with inorganic crystal structure prediction? 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. 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. HypotheticalCarbonPolymorphSuggestedByCASTEP XX Conference on Applied Crystallography, Wisla, Poland, September 2006

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

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  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

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  16. 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.

  17. GULP Appears to be able to predict crystal structures (one can find in the manual the data for the prediction of TiO2 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

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

  19. 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

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  23. 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

  24. 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

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  28. 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 extendthe investigations to larger series of inorganic compounds characterized by corner-sharing polyhedra.

  29. 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 MaXb or ternary MaM'bXc compounds. J. Appl. Cryst. 38, 2005, 389-395. J. Solid State Chem. 179, 2006, 3159-3166.

  30. Observed and predicted cell parameters comparison Predicted by GRINSP (Å) Observed or idealized (Å) Dense SiO2 a b c R a b c  (%) Quartz 4.965 4.965 5.375 0.0009 4.912 4.912 5.404 0.9Tridymite 5.073 5.073 8.400 0.0045 5.052 5.052 8.270  0.8Cristobalite 5.024 5.024 6.796 0.0018 4.969 4.969 6.926 1.4 Zeolites ABW 9.872 5.229 8.733 0.0056 9.9 5.3 8.8 0.8EAB 13.158 13.158 15.034 0.0037 13.2 13.2 15.00.3EDI 6.919 6.919 6.407 0.0047 6.926 6.926 6.4100.1GIS 9.772 9.772 10.174 0.0027 9.8 9.8 10.20.3GME 13.609 13.609 9.931 0.0031 13.7 13.7 9.9 0.6Aluminum fluorides-AlF3 10.216 10.216 7.241 0.0159 10.184 10.184 7.174  0.5Na4Ca4Al7F33 10.876 10.876 10.876 0.0122 10.781 10.781 10.7810.9AlF3-pyrochl. 9.668 9.668 9.668 0.0047 9.749 9.749 9.749 0.8 TitanosilicatesBatisite 10.633 14.005 7.730 0.0076 10.4 13.85 8.1 2.6Pabstite 6.724 6.724 9.783 0.0052 6.7037 6.7037 9.824 0.9Penkvilskite 8.890 8.426 7.469 0.0076 8.956 8.727 7.387 1.3

  31. Predictions produced by GRINSP Binary compounds Formulations M2X3, MX2, M2X5 et MX3 were examined. Zeolites MX2 (= 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).

  32. Hypothetical zeolite PCOD1010026SG : P432, a = 14.623 Å, FD = 11.51

  33. Other GRINSP predictions : > 3000 B2O3 polymorphs Hypothetical B2O3 - PCOD1062004.Triangles BO3 sharing corners.= 3-connected 3D nets

  34. > 500 V2O5 polymorphs square-based pyramids = 5-connected 3D nets

  35. 12 AlF3 polymorphs Corner-sharing octahedra.= 6-connected 3D nets

  36. Do these AlF3 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.

  37. Ternary compounds MaM’bXc 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.

  38. Borosilicates PCOD2050102, Si5B2O13, R = 0.0055. SiO4tetrahedraandBO3triangles > 3000 models

  39. Aluminoborates Example : [AlB4O9]-2, cubic, SG : Pn-3, a = 15.31 Å, R = 0.0051: AlO6octahedra andBO3triangles > 2000 models

  40. Fluoroaluminates Known Na4Ca4Al7F33 : PCOD1000015 - [Ca4Al7F33]4-. Two-sizesoctahedra AlF6and CaF6

  41. Unknown : PCOD1010005 - [Ca3Al4F21]3-

  42. Results for titanosilicates TiO6octahedra andSiO4 tetrahedra > 1000 models

  43. More than 70% of the predicted titanosilicates have the general formula [TiSinO(3+2n)]2- Numbers of compounds in ICSD version 1-4-1, 2005-2 (89369 entries) potentially fitting structurally with the [TiSinO(3+2n)]2- series of GRINSP predictions, addingeither C, C2 or CD cations for electrical neutrality. n +C +C2 +CD Total GRINSP ABX5 1 300 495 464 35 1294 93AB2X7 2 215 308 236 11 770 179AB3X9 3 119 60 199 5 383 174AB4X11 4 30 1 40 1 72 205AB5X13 5 9 1 1 0 11 36AB6X15 6 27 1 13 1 42 158Total 2581 845 Not all these 2581 ICSD structures are built up from corner sharing octahedra and tetrahedra. Many isostructural compounds inside.

  44. Models with real counterparts

  45. Example in PCOD Model PCOD2200207 (Si3TiO9)2- :a = 7.22 Å; b = 9.97 Å; c =12.93 Å, SG P212121 Known as K2TiSi3O9.H2O (isostructural to mineral umbite):a = 7.1362 Å; b = 9.9084 Å; c =12.9414 Å, SG P212121(Eur. J. Solid State Inorg. Chem. 34, 1997, 381-390) Not too bad if one considers that K et H2O are not taken into account in the model prediction...

  46. Highest quality (?) models

  47. Models with the largest porosity

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