1. Microporous Titanium Silicates Predicted by GRINSP 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 Web : http://cristal.org/ Global Optimisation Techniques Applied to the Prediction of Structures « Gordon Conference style » Workshop, 5-7 July 2006, University College London

2. CONTENT I- Introduction II- GRINSP algorithm and results III- Results for titanosilicates Prediction conditions Models with real counterparts Highest quality (?) models Models with the largest porosity IV- Opened doors, limitations, problems V- Conclusions

3. I- 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.

4. It would allow complete prediction. These predictions would be made available in huge databases (currently the case for > 1.000.000 zeolites). We would have predicted the physical properties as well. We would try to synthesize the most interesting compounds. This is pure fiction up to now... But clearly is THE XXIth century challenge. Trying to make a very tiny step on that long way : GRINSP If we had a really powerful materials theory…

5. II- GRINSP algorithm 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., 2006, in the press

6. 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

7. More details about the GRINSP algorithm Two steps : Step 1 - Generation of raw models Haphazard (by Monte Carlo) is used to determine the cell dimensions; select Wyckoff positions; place M/M’ atoms. The cell is progessively filled up to the respect of geometrical restraints and constraints fixed by the user (exact coordination, but large tolerance on distances), if possible. The number of M/M' atoms placed is not predetermined. Atoms do not move. It is recommended to survey all the 230 space groups.

8. Step 2 - Optimization The X atoms are placed at the (M/M')-(M/M') midpoints (corner-sharing). Interatomic distances and cell parameters are optimized (by Monte Carlo) : it is verified that regular polyhedra (M/M’)X n can really be built starting from the raw initial models with M/M’ atoms only. Cost function : R =  [(R 1 +R 2 +R 3 )/ (R 01 +R 02 +R 03 )], where R n and R 0n for n = 1, 2, 3 are defined by : R n =  [w n (d 0n -d n )] 2, R 0n =  [w n d 0n ] 2, Where the d 0n are the ideal distances M-X (n=1), X-X (n=2) and M-M (n=3), the d n being the observed distances in the model. Weighting is applied through the w n. No powder data.

9. The cost function would be better defined by applying the bond valence rules or by making energy calculations (in projet for the next GRINSP version) both would be more time consuming, especially for energy calculations. Minimizing distance differences is a very basic approach. Intuitively, is it clear that this simple approach will give good results only for regular polyhedra. Comments

10. Atoms move that time, no jump is allowed which would break coordinations. The cell parameters established at step 1 can change considerably during the optimization (up to 30%). The original space group of which the Wychoff positions were used to place the M/M' atoms at step 1 may not be convenient after placing the X atoms and optimization, this is why the final model is proposed in the P1 space group (coordinates placed into a CIF). The final choice of the symmetry has to be done by applying a checking software like PLATON (A.L. Spek). More details on step 2

11. Running GRINSP : 1- The user has first to build a file according to his/her desires Example : TiO6/VO5 - all space groups ! Title line 55 55 ! Space groups range (you may test the range 1 230) 2 0 2 192 ! Npol, connectivity, min & max number of M/M’ atoms 6 5 ! Polyhedra coordinations Ti O ! Elements for the first polyhedra V O ! Elements for the second polyhedra 3. 30. 3. 30. 3. 30. ! Min & max a, b, c 5. 35. ! Min & max framework density 20000 300000 0.02 0.12 ! Ncells, MCmax, Rmax, Rmax to optimize 5000 1 ! Number of MC steps/atom at optimization, code for cell 1 ! Code for output files Note : that calculation would need 1 day with a single processor running at 3GHz.

12. 2 – Verify that the atom pairs are defined : See into the file distgrinsp.txt distributed with the package : V O 5 3.050 4.050 3.550 1.526 2.126 1.826 2.282 2.882 2.582 4.20 7.00 Ti O 6 3.300 4.300 3.800 1.650 2.250 1.950 2.458 3.057 2.758 4.45 6.95 Distances minimum, maximum and ideals for pairs V-V, V-O et O-O in fivefold coordination, plus a range for second V-V neighbours (square pyramids favoured). The same for Ti-Ti, Ti-O et O-O in octahedral coordination TiO 6. Trigonal prisms may well be produced, but with larger R values.

13. 3- Start GRINSP

14. 4- Wait… (hours, days, weeks, months…) and see the summary at the end of the output file with extension.imp :

15. 5 – See the results (here by applying Diamond to a CIF) :

16. GRINSP is « Open Source », GNU Public Licence Downloadable from the Internet at : http://www.cristal.org/grinsp/

17. 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 More than 1000 zeolites (not 1.000.000) are proposed with R < 0.01 and 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).

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

22. ….. Example of CIF produced by GRINSP and inserted into the PCOD The coordination sequence is added at the end as a comment

23. Does GRINSP can also predict > 1.000.000 zeolites ? Yes if R max was fixed at 0.03 instead of 0.01, if the cell parameters limit (16Å) was enlarged, and if all models describing a same zeotype in various cells and space groups were saved. Is it useful ? In a specialized database, yes, in a general database, no.

24. Other GRINSP predictions : > 3000 B 2 O 3 polymorphs Hypothetical B 2 O 3 - PCOD1062004. Triangles BO 3 sharing corners.

25. > 500 V 2 O 5 polymorphs square-based pyramids

26. > 30 AlF 3 polymorphs Corner-sharing octahedra.

27. 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. In press

28. 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 These ternary compounds are not always electrically neutral.

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

30. 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

31. 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

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

33. Satellite programs distributed with the GRINSP package GRINS : allows to build quickly isostructural compounds by substitution of elements from previous models. - FeF 3, CrF 3, GaF 3, etc, from AlF 3 - gallophosphates, zirconosicilates, or sulfates, etc, from titanosilicates. CUTCIFP, CIF2CON, CONNECT, FRAMDENS programs for - cutting multiple CIFs into series of single CIFs, - extraction of coordination sequences from CIFs, - analysis of series of CIFs, recognition of identical/ different models and sorting them according to R, - extraction of framework densities, sorting.

34. III – Results for titanosilicates > 1000 models TiO 6 octahedra and SiO 4 tetrahedra

35. Prediction conditions : Si 4+ and Ti 4+ Si O 4 2.570 3.570 3.070 1.310 1.910 1.610 2.229 3.029 2.629 4.40 6.00 Ti O 6 3.300 4.300 3.800 1.650 2.250 1.950 2.458 3.058 2.758 4.45 6.95 Cell parameters : max 16 Å 230 space groups, one day calculation per space group, processor Intel Pentium IV 2.8 GHz

36. 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 ICSD structures are built up from corner sharing octahedra and tetrahedra.

37. Models with real counterparts

38. 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)

39. PCOD2200042 [TiSi 2 O 7 ] 2- identified as corresponding to Nenadkevichite  NaTiSi 2 O 7  2H 2 O

40. The CS (Coordination Sequence) is not sufficient for a perfect identification… Narsarsukite : Na 2 TiSi 4 O 11 PCOD2200033 : [TiSi 4 O 11 ] 2- Both have same CS, but the model is a subcell with subtle differences. # PCOD2200033 # 2 # 2 8 # 6 18 34 54 86 126 166 214 # 4 12 28 52 82 118 164 216

41. A few other identified models PCOD entryMineral name/formula 2200093Vlasovite 3200122VP 2 O 7 -I 3200543VP 2 O 7 -II 2200170Gittinsite 2200178KTiPO 5 2200040ZrP 2 O 7 2200030Armstrongite 2200032Bazirite 2200095Komkovite/Hilairite 3200659Zekzerite etc, etc (overview not completed…)

42. Highest quality (?) models

45. Models with the largest porosity

46. Porosity examined with PLATON (option SOLV or VOID) Küppers, Liebau & Spek, J. Appl. Cryst. 39 (2006) 338-346. Calculation with PLATON commands : SET VDWR O 1.35 Si 0.5 Ti 0.6 CALC VOID PROBE 1.25 (and 1.50) GRID 0.12 LIST The titanosilicate model with largest channels attains 70% porosity, FD = 10.6 (Framework Density : number of cations for 1000 Å 3 ) This is close to the best zeolites.

47. 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

48. 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

49. 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

50. 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

51. PCOD3200037, P = 50.8%, FD = 13.3, D P = 3 (for a 2.5 Å diameter guest) to D P = 2 (at 3 Å) [Si 2 Ti 3 O 13 ] 6-, trigonal, SG = P-3 Ring apertures 8 x 8 x 6

52. PCOD3200837, P = 59.4%, FD = 13.3, D P = 3 [Si 4 TiO 11 ] 2-, orthorhombic, SG = Cccm Ring apertures 12 x 10 x 10 +6

53. PCOD3200518, P = 47.3%, FD = 14.2, D P = 1 with 2 tunnels of 358 and 104 Å 3 (for V = 983 Å 3 ) [Si 4 Ti 3 O 17 ] 6-, orthorhombic, SG = Pmc2 1 Ring apertures 16+8 Trigonal prisms :

54. PCOD2200205, P = 52.3%, FD = 14.9, D P = 3 [Si 6 TiO 15 ] 2-, orthorhombic, SG = Pmma Ring apertures 10 x 8 x 6

55. PCOD2200199, P = 52.3%, FD = 14.9, D P = 3 [Si 6 TiO 15 ] 2-, monoclinic, SG = P2/m Ring apertures 10 x 8 x 6

56. PCOD3200052, P = 53.7%, FD = 15.2, D P = 3 to D P = 1 and 0 [Si 12 TiO 27 ] 2-, trigonal, SG = P-31c Ring apertures 8 x 6 x (8+6)

57. IV – Opened doors, Limitations, Problems GRINSP limitation : exclusively corner-sharing polyhedra. Opening the door potentially to > 50.000 hypothetical compounds. 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.

58. 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.

59. For zeolites, identification to one of the 150 known structure-types is fast, this is not the case for most other structures (lack of efficient and reliable descriptors independent of the cell parameters and symmetry which would have to be included into the ICSD, and user friendly). Improving the PCOD (Predicted Crystallography Open Database) Need for automatization for fast growing, but this is incompatible with some details : It is better if all these hypothetical structures are examined by a crystallographer’s eye.

60. Problem with identification due to cell parameters inaccuracy « New similarity index for crystal structure determination from X-ray powder diagrams, » D.W.M. Hofmann and L. Kuleshova, J. Appl. Cryst. 38 (2005) 861-866.

61. Problem with identification due to errors on the powder patterns intensities These titanosilicates, niobiosilicates, zirconosilicates, vanadophosphates, gallophosphates, etc, etc, hypothetical compounds have to be filled with appropriate cations and re- optimized so as to obtain better cell parameters and more precise predicted powder pattern intensities.

62. What GRINSP may also do : Predict ice structures (if modified for distorted OH 4 tetrahedra) Study oxygen vacancies in perovskites (already done) Predict of tetrahedral, octahedral (etc) (inter)metallic structures (GRINSPM version working already) Etc

63. Two things that don’t work well enough up to now… - Ab initio calculations (WIEN2K, etc) : not fast enough for classifying > 10000 structure candidates (was 2 months for 12 AlF 3 models) - Identification of the known structures (ICSD) among >10000 hypothetical compounds

64. One advice Send your data (CIFs) to the PCOD, thanks… (no proteins, no nucleic acid, not 1.000.000 zeolites)

65. V - 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. If we are unable to do that, we have to stop pretending to understand and master the crystallography laws.