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, 72085 Le Mans, France Email : [email protected] Outline
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, 72085 Le Mans, FranceEmail : [email protected]
INTRODUCTION Determination by Powder Diffractometry
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.
Where are we with Determination by Powder Diffractometryinorganic 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.
But things are changing, maybe : Determination by Powder Diffractometry
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, sulfates, silicates, borosilicates, etc) and fluorides :the PCOD (Predicted Crystallography Open Database)http://www.crystallography.net/pcod/
Prediction software Determination by Powder Diffractometry
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.
CASTEP, program for Zeolites, GULP, G42, Spuds, AASBU, GRINSP
CASTEP Determination by Powder Diffractometry
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
Hypothetical Determination by Powder DiffractometryCarbonPolymorphSuggestedByCASTEP
Another CASTEP prediction Determination by Powder Diffractometry
ZEOLITES Determination by Powder Diffractometry
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… Determination by Powder Diffractometry
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.
GULP (at the Frontier ?) Determination by Powder Diffractometry
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 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) 95-132.
GULP : J. D. Gale, J. Chem. Soc., Faraday Trans.,93 (1997) 629-637. http://gulp.curtin.edu.au/
Part of the command list of GULP : Determination by Powder Diffractometry
G42 Determination by Powder Diffractometry
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.
SPuDS Determination by Powder Diffractometry
Dedicated especially to the prediction of perovskites.
M.W. Lufaso & P.M. Woodward, Acta Cryst. B57 (2001) 725-738.
AASBU method Determination by Powder Diffractometry
(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.
Angew. Chem. Int. Ed. 43 (2004) 2-7. Determination by Powder Diffractometry
Super-tetrahedra sharing corners, building super-zeolites (MTN-analogue)
Science 309 (2005) 2040-2042. (MTN-analogue)
Same « prediction » process, building another MTN-analogue super-zeolite
From different super-tetrahedra
Will you be able to equal or surpass these MTN-analogue super-zeolitegiant structure « predictions » ?
YESIf 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.
MAYBEBy partial prediction (without cell but with known content).This is « molecular packing prediction ».
NOWithout 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 MTN-analogue super-zeolite
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 extendthe investigations to larger series of inorganic compounds characterized by corner-sharing polyhedra.
GRINSP MTN-analogue super-zeolite
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.
Observed and predicted cell parameters comparison MTN-analogue super-zeolite
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
Predictions produced by GRINSP MTN-analogue super-zeolite
Formulations M2X3, MX2, M2X5 et MX3 were examined.
Zeolites MX2 (= 4-connected 3D nets)
More than 4700 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).
Hypothetical zeolite PCOD1010026 MTN-analogue super-zeoliteSG : P432, a = 14.623 Å, FD = 11.51
Other GRINSP predictions : MTN-analogue super-zeolite> 3000 B2O3 polymorphs
Hypothetical B2O3 - PCOD1062004.Triangles BO3 sharing corners.= 3-connected 3D nets
> 1300 V MTN-analogue super-zeolite2O5 polymorphs
= 5-connected 3D nets
>30 AlF MTN-analogue super-zeolite3 polymorphs
Corner-sharing octahedra.= 6-connected 3D nets
Do these AlF MTN-analogue super-zeolite3 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.
Ternary compounds M MTN-analogue super-zeoliteaM’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.
Borosilicates MTN-analogue super-zeolite
PCOD2050102, Si5B2O13, R = 0.0055.
> 3000 models
Aluminoborates MTN-analogue super-zeolite
Example : [AlB4O9]-2, cubic, SG : Pn-3, a = 15.31 Å, R = 0.0051:
> 4000 models
Fluoroaluminates MTN-analogue super-zeolite
Known Na4Ca4Al7F33 : PCOD1000015 - [Ca4Al7F33]4-.
Unknown MTN-analogue super-zeolite : PCOD1010005 - [Ca3Al4F21]3-
Results for titanosilicates MTN-analogue super-zeolite
> 1700 models
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, adding either C, C2 or CD cations for electrical neutrality.
n +C +C2 +CD Total GRINSP
ABX5 1 300 495 464 35 1294 130 TiSiO5AB2X7 2 215 308 236 11 770 207 TiSi2O7AB3X9 3 119 60 199 5 383 215 TiSi3O9AB4X11 4 30 1 40 1 72 257 TiSi4O11AB5X13 5 9 1 1 0 11 75 TiSi5O13AB6X15 6 27 1 13 1 42 207 TiSi6O15Total 2581 1091
Not all these 2581 ICSD structures are built up from corner sharing octahedra and tetrahedra. Many isostructural compounds inside.
Models with real counterparts general formula [TiSi
Example in PCOD general formula [TiSi
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...
Highest quality (?) models general formula [TiSi
Models with the largest porosity general formula [TiSi
PCOD3200086 : P = 70.2%, FD = 10.6, general formula [TiSiDP = 3 (dimensionality of the pore/channels system)
Ring apertures9 x 9 x 9
[Si6TiO15]2- , cubic, SG = P4132, a = 13.83 Å
PCOD3200867, P = 61.7%, FD = 12.0, D general formula [TiSiP = 3 [Si2TiO7]2- , orthorhombic, SG = Imma
Ring apertures10 x 8 x 8
PCOD3200081, P = 61.8%, FD = 13.0, D general formula [TiSiP = 3 [Si6TiO15]2- , cubic, SG = Pn-3
Ring apertures12 x 12 x 12+10+6
PCOD3200026, P = 59.6%, FD = 13.0, D general formula [TiSiP = 3 [Si4TiO11]2- , tetragonal, SG = P42/mcm
Ring apertures12 x 10 x 10
Opened doors, Limitations, Problems general formula [TiSi
GRINSP limitation : exclusively corner-sharing polyhedra.
Opening the door potentially to > 1.000.000 hypothetical compounds.
More than 60.000 silicates, phosphates, sulfates of Al, Ti, V, Ga, Nb, Zr, or zeolites, fluorides, etc. were included into PCOD in february 2007.
Their powder patterns were calculated, building the PPDF-1(Predicted Powder Diffraction File version 1) for search-match identification.
Predicted general formula [TiSicrystal 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 identification by search-match – The actual and virtual structures have the same chemical formula, PAD = 0.52% (percentage of absolute difference on cell parameters, averaged) : -AlF3, tetragonal, a = 10.184 Å, c = 7.174 Å. Predicted : 10.216 Å, 7.241 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 2nd (green mark in the toolbox).
Example 2 identification by search-match – Model showing uncomplete chemistry, PAD = 0.63. Actual compound : K2TiSi3O9H2O, orthorhombic, a = 7.136 Å, b = 9.908 Å, c =12.941 Å. Predicted framework : TiSi3O9, 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 H2O are lacking in the PCOD model) :
Example 3 identification by search-match – Model showing uncomplete chemistry, PAD = 0.88. Predicted framework : Ca4Al7F33, cubic, a = 10.876 Å. Actual compound : Na4Ca4Al7F33, a = 10.781 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 identification by search-match
Example 5 : Mordenite identification by search-match
Two main problems in identification identification by search-match 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%.
A similarity index less sensitive to cell parameter discrepancies
« 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.
Typical case to be solved by prediction discrepancies
δ-Zn2P2O7 Bataille et al., J. Solid State Chem. 140 (1998) 62-70.
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 : discrepancies
Edge, face, corner-sharing, mixed.
Hole detection, filling them automatically, appropriately, for electrical neutrality.
Using bond valence rules or/and energy calculationsto 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 discrepancies
4786 SiO2 + the isostructural (Al/P)O4, (Al/Si)O4 and (Al/S)O4
2394 VO5/PO4 + the isostructural VO5/SiO4, VO5/SO4, TiO5/SiO4
1747 TiO6/SiO4 + the isostructural phosphates and sulfates and also replacing Ti by Ga, Nb, V, Zr
1328 TiO6/VO5 + the isostructural VO6/VO5
33 AlF3 + the isostructural FeF3, GaF3 and CrF3
15.781 different structure-types, > 60.000 hypothetical phases You may ask for other isostructural series or build them… Expected > 120.000 at the next update in September 2007…
Two things that don’t work discrepancieswell enough up to now…
Validation of the Predictions
- Ab initio calculations (WIEN2K, etc) : not fast enough for the validation of > 60000 structure candidates (was 2 months for 12 AlF3 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 discrepancies
Send your data (CIFs) to the PCOD, thanks…http://www.crystallography.net/pcod/
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