Microporous Titanium SilicatesPredicted by GRINSP

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.orgWeb : http://cristal.org/

Global Optimisation Techniques Applied to the Prediction of Structures« Gordon Conference style » Workshop, 5-7 July 2006, University College London

CONTENT

I- IntroductionII- GRINSP algorithm and resultsIII- Results for titanosilicates

Prediction conditionsModels with real counterpartsHighest quality (?) modelsModels with the largest porosity

IV- Opened doors, limitations, problemsV- Conclusions

I- 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.

It would allow complete prediction.

These predictions would be made available in huge databases(currently the case for > 1.000.000 zeolites).

We would have predicted the physical properties as well.

We would try to synthesize the most interesting compounds.

This is pure fiction up to now...But clearly is THE XXIth century challenge.

Trying to make a very tiny step on that long way : GRINSP

If we had a really powerful materials theory…

II- GRINSP algorithm

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., 2006, in the press

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

More details about the GRINSP algorithm

Two steps :

 Step 1 - Generation of raw models

Haphazard (by Monte Carlo) is used todetermine the cell dimensions;

select Wyckoff positions; place M/M’ atoms.

The cell is progessively filled up to the respect of geometrical restraints and constraints fixed by the user (exact coordination, but large tolerance

on distances), if possible. The number of M/M' atoms placed is not predetermined. Atoms do not move.

It is recommended to survey all the 230 space groups.

Step 2 - OptimizationThe X atoms are placed at the (M/M')-(M/M') midpoints (corner-sharing).

Interatomic distances and cell parameters are optimized (by Monte Carlo) : it is verified that regular polyhedra (M/M’)Xn can really be built starting from the

raw initial models with M/M’ atoms only.

Cost function :

R = [(R1+R2+R3)/ (R01+R02+R03)],

where Rn and R0n for n = 1, 2, 3 are defined by :

Rn = [wn(d0n-dn)]2, R0n = [wnd0n]

2,

Where the d0n are the ideal distances M-X (n=1), X-X (n=2) and M-M (n=3),

the dn being the observed distances in the model.

Weighting is applied through the wn .No powder data.

The cost function would be better defined by applying the bond valence rules or by making energy calculations (in projet for the next GRINSP

version) both would be more time consuming, especially for energy calculations.

Minimizing distance differences is a very basic approach.

Intuitively, is it clear that this simple approach will give good results only for regular polyhedra.

Comments

Atoms move that time, no jump is allowed which would break coordinations. The cell parameters established at step 1 can change

considerably during the optimization (up to 30%).

The original space group of which the Wychoff positions were used to place the M/M' atoms at step 1 may not be convenient after placing the X atoms and optimization, this is why the final model is proposed in the P1

space group (coordinates placed into a CIF).

The final choice of the symmetry has to be done by applying a checking software like PLATON (A.L. Spek).

More details on step 2

Running GRINSP :

1- The user has first to build a file according to his/her desires

Example :

TiO6/VO5 - all space groups ! Title line55 55 ! Space groups range (you may test the range 1 230) 2 0 2 192 ! Npol, connectivity, min & max number of M/M’ atoms6 5 ! Polyhedra coordinationsTi O ! Elements for the first polyhedra V O ! Elements for the second polyhedra 3. 30. 3. 30. 3. 30. ! Min & max a, b, c5. 35. ! Min & max framework density20000 300000 0.02 0.12 ! Ncells, MCmax, Rmax, Rmax to optimize5000 1 ! Number of MC steps/atom at optimization, code for cell 1 ! Code for output files

Note : that calculation would need 1 day with a single processor running at 3GHz.

2 – Verify that the atom pairs are defined :

See into the file distgrinsp.txt distributed with the package :

V O 53.050 4.050 3.5501.526 2.126 1.8262.282 2.882 2.5824.20 7.00

Ti O 63.300 4.300 3.8001.650 2.250 1.9502.458 3.057 2.7584.45 6.95

Distances minimum, maximumand ideals for pairs V-V,

V-O et O-O in fivefold coordination,plus a range for second V-V neighbours

(square pyramids favoured).

The same for Ti-Ti, Ti-O et O-Oin octahedral coordination TiO6.

Trigonal prisms may well be produced, but with larger R values.

3-

Start GRINSP

4-

Wait…(hours, days,

weeks, months…) and see the summary at

the end of the output file

with extension .imp :

5 –

See the results

(here by applying Diamond

to a CIF) :

GRINSP is « Open Source », GNU Public Licence

Downloadable from the Internet at : http://www.cristal.org/grinsp/

Predictions produced by GRINSP

Binary compounds

Formulations M2X3, MX2, M2X5 et MX3 were examined.

Zeolites MX2

More than 1000 zeolites (not 1.000.000) are proposed with R < 0.01 and 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

…..

Example of CIF produced by GRINSP and inserted into the

PCOD

The coordination sequence is added at

the end as a comment

Does GRINSP can also predict > 1.000.000 zeolites ?

Yes if Rmax was fixed at 0.03 instead of 0.01, if the cell parameters limit (16Å) was enlarged,

and if all models describing a same zeotype in various cells and space groups were saved.

Is it useful ?

In a specialized database, yes,in a general database, no.

Other GRINSP predictions : > 3000 B2O3 polymorphs

Hypothetical B2O3 - PCOD1062004.

Triangles BO3 sharing corners.

> 500 V2O5 polymorphs

square-based pyramids

> 30 AlF3 polymorphs

Corner-sharing octahedra.

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. In press

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

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-

Satellite programs distributed with the GRINSP package

GRINS : allows to build quickly isostructural compounds by substitution of elements from previous models.- FeF3, CrF3, GaF3, etc, from AlF3

- gallophosphates, zirconosicilates, or sulfates, etc, from titanosilicates.

CUTCIFP, CIF2CON, CONNECT, FRAMDENS programs for - cutting multiple CIFs into series of single CIFs, - extraction of coordination sequences from CIFs, - analysis of series of CIFs, recognition of identical/

different models and sorting them according to R, - extraction of framework densities, sorting.

III – Results for titanosilicates

> 1000 models

TiO6 octahedra

andSiO4

tetrahedra

Prediction conditions : Si4+ and Ti4+

Si O 42.570 3.570 3.070 1.310 1.910 1.610 2.229 3.029 2.629 4.40 6.00

Ti O 63.300 4.300 3.8001.650 2.250 1.9502.458 3.058 2.7584.45 6.95

Cell parameters : max 16 Å

230 space groups, one day calculation per space group, processor Intel Pentium IV 2.8 GHz

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 ICSD structures are built up from corner sharing octahedra and tetrahedra.

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)

PCOD2200042 [TiSi2O7]2- identified as corresponding to

Nenadkevichite NaTiSi2O72H2O

The CS(Coordination Sequence)

is not sufficient for a perfectidentification…

Narsarsukite :Na2TiSi4O11

PCOD2200033 :[TiSi4O11]2-

Both have same CS, but the model is a subcell with

subtle differences.# PCOD2200033# 2# 2 8# 6 18 34 54 86 126 166 214 # 4 12 28 52 82 118 164 216

A few other identified models

PCOD entry Mineral name/formula

2200093 Vlasovite3200122 VP2O7-I3200543 VP2O7-II2200170 Gittinsite2200178 KTiPO5

2200040 ZrP2O7

2200030 Armstrongite2200032 Bazirite2200095 Komkovite/Hilairite3200659 Zekzerite

etc, etc (overview not completed…)

Highest quality (?) models

Models with the largest porosity

Porosity examined with PLATON (option SOLV or VOID)

Küppers, Liebau & Spek, J. Appl. Cryst. 39 (2006) 338-346.

Calculation with PLATON commands :

SET VDWR O 1.35 Si 0.5 Ti 0.6

CALC VOID PROBE 1.25 (and 1.50) GRID 0.12 LIST

The titanosilicate model with largest channels attains 70% porosity, FD = 10.6 (Framework Density : number of cations for 1000 Å3)

This is close to the best zeolites.

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

PCOD3200037, P = 50.8%, FD = 13.3, DP = 3 (for a 2.5 Å diameter guest) to DP = 2 (at 3 Å)

[Si2Ti3O13]6- , trigonal, SG = P-3

Ring apertures8 x 8 x 6

PCOD3200837, P = 59.4%, FD = 13.3, DP = 3 [Si4TiO11]2- , orthorhombic, SG = Cccm

Ring apertures12 x 10 x 10

+6

PCOD3200518, P = 47.3%, FD = 14.2, DP = 1 with 2 tunnels of 358 and 104 Å3 (for V = 983 Å3)

[Si4Ti3O17]6- , orthorhombic, SG = Pmc21

Ring apertures16+8

Trigonal prisms :

PCOD2200205, P = 52.3%, FD = 14.9, DP = 3 [Si6TiO15]2- , orthorhombic, SG = Pmma

Ring apertures10 x 8 x 6

PCOD2200199, P = 52.3%, FD = 14.9, DP = 3 [Si6TiO15]2- , monoclinic, SG = P2/m

Ring apertures10 x 8 x 6

PCOD3200052, P = 53.7%, FD = 15.2, DP = 3 to DP = 1 and 0

[Si12TiO27]2- , trigonal, SG = P-31c

Ring apertures8 x 6 x (8+6)

IV – Opened doors, Limitations, Problems

GRINSP limitation : exclusively corner-sharing polyhedra.

Opening the door potentially to > 50.000 hypothetical compounds.

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.

For zeolites, identification to one of the 150 known structure-types is fast, this is not the case for most other

structures (lack of efficient and reliable descriptors independent of the cell parameters and symmetry which

would have to be included into the ICSD, and user friendly).

Improving the PCOD(Predicted Crystallography Open Database)

Need for automatization for fast growing, but this is incompatible with some details :

It is better if all these hypothetical structures are examined by a crystallographer’s eye.

Problem with identification

due to cell parameters inaccuracy

« 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.

Problem with identification due to errors on the powder patterns intensities

These titanosilicates, niobiosilicates, zirconosilicates, vanadophosphates, gallophosphates, etc, etc, hypothetical

compounds have to be filled with appropriate cations and re-optimized so as to obtain better cell parameters and more precise

predicted powder pattern intensities.

What GRINSP may also do :

Predict ice structures (if modified for distorted OH4 tetrahedra)

Study oxygen vacancies in perovskites (already done)

Predict of tetrahedral, octahedral (etc) (inter)metallic structures

(GRINSPM version working already)

Etc

Two things that don’t work well enough up to now…

- Ab initio calculations (WIEN2K, etc) : not fast enough for classifying > 10000 structure candidates

(was 2 months for 12 AlF3 models)

- Identification of the known structures (ICSD) among >10000 hypothetical compounds

One advice

Send your data (CIFs) to the PCOD, thanks…(no proteins, no nucleic acid, not 1.000.000 zeolites)

V - 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.

If we are unable to do that, we have to stop pretending to understand and master the crystallography laws.