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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
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
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
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?
XX Conference on Applied Crystallography, Wisla, Poland, September 2006
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
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
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
HypotheticalCarbon
PolymorphSuggested
ByCASTEP
XX Conference on Applied Crystallography, Wisla, Poland, September 2006
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
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.
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
Part of the command list of GULP :
XX Conference on Applied Crystallography, Wisla, Poland, September 2006
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
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
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
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.
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.
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 4.9125.404 0.9
Tridymite 5.073 5.073 8.400 0.0045 5.052 5.052 8.270 0.8
Cristobalite 5.024 5.024 6.796 0.0018 4.969 4.969 6.9261.4
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 15.0 0.3EDI 6.919 6.919 6.407 0.0047 6.926 6.926 6.410
0.1GIS 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 9.90.6
Aluminum 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 10.781 0.9
AlF3-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 9.8240.9Penkvilskite 8.890 8.426 7.469 0.0076 8.956 8.727 7.387
1.3
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).
Other GRINSP predictions : > 3000 B2O3 polymorphs
Hypothetical B2O3 - PCOD1062004.
Triangles BO3 sharing corners. = 3-connected 3D nets
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.
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.
Aluminoborates
> 2000 models
Example : [AlB4O9]-2, cubic, SG : Pn-3, a = 15.31 Å, R = 0.0051:
AlO6 octahedra and
BO3
triangles
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 93
AB2X7 2 215 308 236 11 770 179
AB3X9 3 119 60 199 5 383 174
AB4X11 4 30 1 40 1 72 205
AB5X13 5 9 1 1 0 11 36
AB6X15 6 27 1 13 1 42 158
Total 2581 845
More than 70% of the predicted titanosilicates have the general formula [TiSinO(3+2n)]
2-
Not all these 2581 ICSD structures are built up from corner sharing octahedra and tetrahedra. Many isostructural compounds inside.
Example in PCOD
Not too bad if one considers that K et H2O are not taken into account in the model prediction...
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)
PCOD3200086 : P = 70.2%, FD = 10.6, DP = 3 (dimensionality of the pore/channels system)
[Si6TiO15]2- , cubic, SG = P4132, a = 13.83 Å
Ring apertures9 x 9 x 9
PCOD3200867, P = 61.7%, FD = 12.0, DP = 3 [Si2TiO7]2- , orthorhombic, SG = Imma
Ring apertures10 x 8 x 8
PCOD3200081, P = 61.8%, FD = 13.0, DP = 3 [Si6TiO15]2- , cubic, SG = Pn-3
Ring apertures12 x 12 x 12
+10+6
PCOD3200026, P = 59.6%, FD = 13.0, DP = 3 [Si4TiO11]2- , tetragonal, SG = P42/mcm
Ring apertures12 x 10 x 10
Opened doors, Limitations, Problems
GRINSP limitation : exclusively corner-sharing polyhedra.
Opening the door potentially to > 50.000 hypothetical compounds.The predicted titanosilicates can be extrapolated to phosphates,
sulfates, and/or replacing Ti by Nb, V, Zr, Ga, etc.
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.
Expected improvements :
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…
Two things that don’t work well enough up to now…
Validation
- Ab initio calculations (WIEN2K, etc) : not fast enough for the validation of > 10000 structure candidates
(was 2 months for 12 AlF3 models)
Identification
- There is no efficient tool for the identification of the known structures (from the ICSD) among >10000
hypothetical compounds
One advice, if you become a structure predictor
Send your data (CIFs) to the PCOD, thanks…(no proteins, no nucleic acid, not 1.000.000 zeolites)
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,
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.