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 : alb@cristal.org

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 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

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 (at the Frontier ?)

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 :

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.

Two (incredible ?) predictions

« Giant structures solved by

combined targeted chemistry and computational design."

2 cubic hybrid solids structures published :

- 2004 - V ~380.000 Å3, a ~ 73Å, Fd-3m, 68 indpdt atoms (not-H)

- 2005 - V ~702.000 Å3, 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) 2040-2042.

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 » ?

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

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

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 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 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

> 1300 V2O5 polymorphs

square-based pyramids

= 5-connected 3D nets

>30 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

> 4000 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

> 1700 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 130 TiSiO5

AB2X7 2 215 308 236 11 770 207 TiSi2O7

AB3X9 3 119 60 199 5 383 215 TiSi3O9

AB4X11 4 30 1 40 1 72 257 TiSi4O11

AB5X13 5 9 1 1 0 11 75 TiSi5O13

AB6X15 6 27 1 13 1 42 207 TiSi6O15

Total 2581 1091

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

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 > 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.

Predictedcrystal 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) : -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 – 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 – 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

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) 861-866.

A similarity index less sensitive to cell parameter discrepancies

δ-Zn2P2O7 Bataille et al., J. Solid State Chem. 140 (1998) 62-70.

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 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

4786 SiO2 + the isostructural (Al/P)O4, (Al/Si)O4 and (Al/S)O4

4138 AlO6/BO3

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

1318 V2O5

33 AlF3 + the isostructural FeF3, GaF3 and CrF3

24 AlF6/CaF6

13 AlF6/NaF6

15.781 different structure-types, > 60.000 hypothetical phasesYou 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 well 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 predictorSend your data (CIFs) to the PCOD, thanks…

http://www.crystallography.net/pcod/

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