Frontiers Between Crystal Structure Prediction and Determination by Powder Diffractometry Armel Le Bail Université du Maine, Laboratoire des Oxydes et Fluorures, CNRS UMR 6010, Avenue O. Messiaen, Le Mans, France

Outline - Introduction - Prediction software and examples - Fuzzy frontiers with SDPD - More examples from the GRINSP software - Opened doors, limitations, problems - « Immediate structure solution » by search-match - Conclusion - Live demo with EVA-Bruker + PPDF-1

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 actual compounds not yet characterized crystallographycally.

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?

But things are changing, maybe : Two databases of hypothetical compounds were built in One is exclusively devoted to zeolites : M.D. Foster & M.M.J. Treacy - Hypothetical Zeolites – The other includes zeolites as well as other predicted oxides (phosphates, sulfates, silicates, borosilicates, etc) and fluorides : the PCOD (Predicted Crystallography Open Database)

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) J.C. Schön & M. Jansen, Z. Krist. 216 (2001) ; Software : CASTEP, program for Zeolites, GULP, G42, Spuds, AASBU, GRINSP

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) Example : carbon polymorphs

Hypothetical Carbon Polymorph Suggested By CASTEP

Another CASTEP prediction

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 –

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 > 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.

GULP (at the Frontier ?) 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 full 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) GULP : J. D. Gale, J. Chem. Soc., Faraday Trans., 93 (1997)

Part of the command list of GULP :

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) ;

SPuDS Dedicated especially to the prediction of perovskites. M.W. Lufaso & P.M. Woodward, Acta Cryst. B57 (2001)

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) ; C. Mellot-Drazniek, S. Girard, G. Férey, C. Schön, Z. Cancarevic, M. Jansen, Chem. Eur. J. 8 (2002) 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.

Two (incredible ?) predictions « Giant structures solved by combined targeted chemistry and computational design." 2 cubic hybrid solids structures published : V ~ Å 3, a ~ 73Å, Fd-3m, 68 indpdt atoms (not-H) V ~ Å 3, a ~ 89Å, Fd-3m, 74 indpdt atoms (not-H) Presented more or less as being predicted, but with indexed powder patterns and guessed content. Are they SDPD or predictions ? The fuzzy frontier is there…

Angew. Chem. Int. Ed. 43 (2004) 2-7.

Super-tetrahedra sharing corners, building super- zeolites (MTN-analogue)

Science 309 (2005)

Same « prediction » process, building another MTN-analogue super-zeolite From different super-tetrahedra

Will you be able to equal or surpass these giant structure « predictions » ? YES If the molecule, the cell and the space group are known, then the direct space methods need only 50 or 100 reflections for solving the structure, whatever the cell volume (6 DoF per molecule rotated and translated). But this is not prediction. MAYBE By partial prediction (without cell but with known content). This is « molecular packing prediction ». NO Without cell and without content, full total prediction at such complexity level looks impossible. Anyway, you may try to impress some Nature or Science reviewer searching for « sensational » results, by your eloquence.

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

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, J. Solid State Chem. 179, 2006,

Observed and predicted cell parameters comparison Predicted by GRINSP (Å)Observed or idealized (Å) Dense SiO 2 abcRabc  (%) Quartz Tridymite Cristobalite Zeolites ABW EAB EDI GIS GME Aluminum fluorides  -AlF Na 4 Ca 4 Al 7 F AlF 3 -pyrochl Titanosilicates Batisite Pabstite Penkvilskite

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 4700 zeolites (not ) are proposed with cell parameters < 16 Å, placed into the PCOD database : 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).

Hypothetical zeolite PCOD SG : P432, a = Å, FD = 11.51

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

> 1300 V 2 O 5 polymorphs square-based pyramids = 5-connected 3D nets

>30 AlF 3 polymorphs Corner-sharing octahedra. = 6-connected 3D nets

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)

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.

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

Aluminoborates > 4000 models Example : [AlB 4 O 9 ] -2, cubic, SG : Pn-3, a = Å, R = : AlO 6 octahedra and BO 3 triangles

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

Unknown : PCOD [Ca 3 Al 4 F 21 ] 3-

Results for titanosilicates > 1700 models TiO 6 octahedra and SiO 4 tetrahedra

Numbers of compounds in ICSD version 1-4-1, (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 TiSiO 5 AB 2 X TiSi 2 O 7 AB 3 X TiSi 3 O 9 AB 4 X TiSi 4 O 11 AB 5 X TiSi 5 O 13 AB 6 X TiSi 6 O 15 Total 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.

Models with real counterparts

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 PCOD (Si 3 TiO 9 ) 2- : a = 7.22 Å; b = 9.97 Å; c =12.93 Å, SG P Known as K 2 TiSi 3 O 9.H 2 O (isostructural to mineral umbite): a = Å; b = Å; c = Å, SG P (Eur. J. Solid State Inorg. Chem. 34, 1997, )

Highest quality (?) models

Models with the largest porosity

PCOD : 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 = Å Ring apertures 9 x 9 x 9

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

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

PCOD , 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

Opened doors, Limitations, Problems GRINSP limitation : exclusively corner-sharing polyhedra. Opening the door potentially to > hypothetical compounds. More than silicates, phosphates, sulfates of Al, Ti, V, Ga, Nb, Zr, or zeolites, fluorides, etc. were included into PCOD in february Their powder patterns were calculated, building the PPDF-1 (Predicted Powder Diffraction File version 1) for search-match identification.

Predicted crystal structures provide predicted fingerprints

Calculated powder patterns in the PPDF-1 allow for identification by search-match (EVA - Bruker and Highscore - Panalytical) Providing a way for « immediate structure solution » We « simply » need for a complete database of predicted structures ;-)

Example 1 – The actual and virtual structures have the same chemical formula, PAD = 0.52% (percentage of absolute difference on cell parameters, averaged) :  -AlF 3, tetragonal, a = Å, c = Å. Predicted : Å, Å. A global search (no chemical restraint) is resulting in the actual compound (PDF-2) in first position and the virtual one (PPDF-1) in 2 nd (green mark in the toolbox).

Example 2 – Model showing uncomplete chemistry, PAD = Actual compound : K 2 TiSi 3 O 9  H 2 O, orthorhombic, a = Å, b = Å, c = Å. Predicted framework : TiSi 3 O 9, a = 7.22 Å, b = 9.97 Å, c =12.93 Å. Without chemical restraint, the correct PDF-2 entry is coming at the head of the list, but no virtual model. By using the chemical restraint (Ti + Si + O), the correct PPDF-1 entry comes in second position in spite of large intensity disagreements with the experimental powder pattern (K and H 2 O are lacking in the PCOD model) :

Example 3 – Model showing uncomplete chemistry, PAD = Predicted framework : Ca 4 Al 7 F 33, cubic, a = Å. Actual compound : Na 4 Ca 4 Al 7 F 33, a = Å. By a search with chemical restraints (Ca + Al + F) the virtual model comes in fifth position, after 4 PDF-2 correct entries, if the maximum angle is limited to 30°(2  ) :

Example 4 : heulandite

Example 5 : Mordenite

Two main problems in identification by search-match process from the PPDF-1 : - Inaccuracies in the predicted cell parameters, introducing discrepancies in the peak positions. - Uncomplete chemistry of the models, influencing the peak intensities. However, identification may succeed satisfyingly if the chemistry is restrained adequately during the search and if the averaged difference in cell parameters is smaller than 1%.

« New similarity index for crystal structure determination from X-ray powder diagrams, » D.W.M. Hofmann and L. Kuleshova, J. Appl. Cryst. 38 (2005) A similarity index less sensitive to cell parameter discrepancies

δ-Zn 2 P 2 O 7 Bataille et al., J. Solid State Chem. 140 (1998) Typical case to be solved by prediction α β γ δ Uncertain indexing, line profiles broadened by size/microstrain effects (Powder pattern not better from synchrotron radiation than from conventional X-rays) But the fingerprint is there…

Expected GRINSP 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… Nothing planned about hybrids…

Current PCOD Content 4786SiO 2 + the isostructural (Al/P)O 4, (Al/Si)O 4 and (Al/S)O AlO 6 /BO VO 5 /PO 4 + the isostructural VO 5 /SiO 4, VO 5 /SO 4, TiO 5 /SiO TiO 6 /SiO 4 + the isostructural phosphates and sulfates and also replacing Ti by Ga, Nb, V, Zr 1328TiO 6 /VO 5 + the isostructural VO 6 /VO V 2 O 5 33AlF 3 + the isostructural FeF 3, GaF 3 and CrF 3 24AlF 6 /CaF 6 13AlF 6 /NaF different structure-types,> hypothetical phases You may ask for other isostructural series or build them… Expected > at the next update in September 2007…

Two things that don’t work well enough up to now… Validation of the Predictions - Ab initio calculations (WIEN2K, etc) : not fast enough for the validation of > structure candidates (was 2 months for 12 AlF 3 models) Identification (is this predicted structure already known?) - There is no efficient tool for the fast comparison of these thousands of inorganic predicted structures to the known structures (inside of ICSD)

One advice, if you become a structure predictor Send your data (CIFs) to the PCOD, thanks…

CONCLUSIONS Structure and properties full 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