Inorganic structure prediction : too much and not enough Armel Le Bail Université du Maine,...

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 : [email protected]

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


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.


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 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/


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


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


HypotheticalCarbon

PolymorphSuggested

ByCASTEP


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 –

http://www.hypotheticalzeolites.net/





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/


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) 307-325; 361-383.





SPuDS

Dedicated especially to the prediction of perovskites.

M.W. Lufaso & P.M. Woodward, Acta Cryst. B57 (2001) 725-738.


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.





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).

Hypothetical zeolite PCOD1010026SG : P432, a = 14.623 Å, FD = 11.51

Other GRINSP predictions : > 3000 B2O3 polymorphs

Hypothetical B2O3 - PCOD1062004.

Triangles BO3 sharing corners. = 3-connected 3D nets

> 500 V2O5 polymorphs

square-based pyramids

= 5-connected 3D nets

12 AlF3 polymorphs

Corner-sharing octahedra.= 6-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.

Borosilicates

PCOD2050102, Si5B2O13, R = 0.0055.

> 3000 models

SiO4 tetrahedra

andBO3

triangles

Aluminoborates

> 2000 models

Example : [AlB4O9]-2, cubic, SG : Pn-3, a = 15.31 Å, R = 0.0051:

AlO6 octahedra and

BO3

triangles

Fluoroaluminates

Known Na4Ca4Al7F33 : PCOD1000015 - [Ca4Al7F33]4-.

Two-sizesoctahedra

AlF6 and CaF6

Unknown : PCOD1010005 - [Ca3Al4F21]3-

Results for titanosilicates

> 1000 models

TiO6 octahedra

andSiO4

tetrahedra

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.

Models with real counterparts

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)

Highest quality (?) models

Models with the largest porosity

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


PCOD3200081, P = 61.8%, FD = 13.0, DP = 3 [Si6TiO15]2- , cubic, SG = Pn-3


+10+6

PCOD3200026, P = 59.6%, FD = 13.0, DP = 3 [Si4TiO11]2- , tetragonal, SG = P42/mcm


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.

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Inorganic structure prediction : too much and not enough Armel Le Bail Université du Maine,...

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