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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
Armel Le Bail
Université du Maine, Laboratoire des Oxydes et Fluorures, CNRS UMR 6010, Avenue O. Messiaen, 72085 Le Mans, FranceEmail : [email protected]
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.
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/
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
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
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 –
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.
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/
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.
Dedicated especially to the prediction of perovskites.
M.W. Lufaso & P.M. Woodward, Acta Cryst. B57 (2001) 725-738.
(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.
From different super-tetrahedra
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.
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.
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.
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
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 B2O3 - PCOD1062004.Triangles BO3 sharing corners.= 3-connected 3D nets
= 5-connected 3D nets
Corner-sharing octahedra.= 6-connected 3D nets
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.
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.
PCOD2050102, Si5B2O13, R = 0.0055.
> 3000 models
Example : [AlB4O9]-2, cubic, SG : Pn-3, a = 15.31 Å, R = 0.0051:
> 4000 models
Known Na4Ca4Al7F33 : PCOD1000015 - [Ca4Al7F33]4-.
> 1700 models
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.
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...
Ring apertures9 x 9 x 9
[Si6TiO15]2- , cubic, SG = P4132, a = 13.83 Å
Ring apertures10 x 8 x 8
Ring apertures12 x 12 x 12+10+6
Ring apertures12 x 10 x 10
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.
Providing a way for « immediate structure solution »
We « simply » need for a complete database of predicted structures ;-)
- 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) 861-866.
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…
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…
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…
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)
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