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Inorganic Structure

Prediction with GRINSP

Armel Le Bail

Universit du Maine, Laboratoire des oxydes et

Fluorures, CNRS UMR 6010, Avenue O. Messiaen,

72085 Le Mans Cedex 9, France.

Email : alb@cristal.org

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CONTENT

Introduction

GRINSP algorithmGRINSP predictions

Opened doors, and limitations

Prediction confirmation

Conclusion

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I- INTRODUCTION

To predict a crystal structure is to be able to announce itbefore any confirmation by chemical synthesis or discovery

in nature.

A predicted structure should be sufficiently accurate forthe calculation of a predicted powder pattern that would

further be used with success in the identification of a realcompound not yet characterized.

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If the state of the art had dramatically evolved, we should have hugedatabases of predicted compounds.

Not any new crystal structure would surprise us since it would

correspond already to an entry in that database.

Moreover,we would have obtained in advance the physical propertiesand we would have preferably synthesized those interesting compounds.

Of course, this is absolutely not the case.

Where are we

with inorganic structure prediction?

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Things are changing, maybe :

Two databases of hypothetical compounds were built in 2004.

>100000 hypothetical zeolites at :http://www.hypotheticalzeolites.net/

>2000 inorganic compounds in PCOD(zeolites as well as otheroxides and fluorides) at :

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

However, inorganic prediction software and methods remain scarce:

CASTEP, GULP, G42, SPuDS, AASBU, CERIUS2

Hence the development of a newone : GRINSP

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II- GRINSP Algorithm

Geometrically Restrained INorganic Structure Prediction

Applies the knowledge of the common geometrical characteristics of awell defined group of crystal structures (N-connected 3D nets with N =

3, 4, 5, 6 and combinations of two N values), in a Monte Carlo

algorithm,

In GRINSP, the quality of a model is established by a cost functiondepending on the weighted differences between calculated and idealinteratomic first neighbour distances M-X, X-X and M-M in binary

MaXb or ternary MaM'bXc compounds.

J. Appl. Cryst. 38, 2005, 389-395.

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Comparison of a few GRINSP-predicted

cell parameters with observed ones

Predicted () Obser ved or idealized ()

Dense SiO2 a b c R a b cQuartz 4.965 4.965 5.375 0.0009 4.912 4.912 5.404Tridymite 5.073 5.073 8.400 0.0045 5.052 5.052 8.270Cristobalite 5.024 5.024 6.796 0.0018 4.969 4.969 6.926

Zeolites

ABW 9.872 5.229 8.733 0.0056 9.9 5.3 8.8EAB 13.158 13.158 15.034 0.0037 13.2 13.2 15.0EDI 6.919 6.919 6.407 0.0047 6.926 6.926 6.410GIS 9.772 9.772 10.174 0.0027 9.8 9.8 10.2GME 13.609 13.609 9.931 0.0031 13.7 13.7 9.9JBW 5.209 7.983 7.543 0.0066 5.3 8.2 7.5LTA 11.936 11.936 11.936 0.0035 11.9 11.9 11.9RHO 14.926 14.926 14.926 0.0022 14.9 14.9 14.9

Aluminum fluoridesX-AlF3 10.216 10.216 7.241 0.0162 10.184 10.184 7.174

Na4Ca4Al7F33 10.860 10.860 10.860 0.0333 10.781 10.781 10.781AlF3-pyrochl. 9.668 9.668 9.668 0.0047 9.749 9.749 9.749

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More details on the GRINSP algorithm

Two steps :

1- Generation of structure candidates

First the M/M atoms are placed in a boxwhose dimensions are selectedat random, and the model should exactly correspond to the geometricalspecifications (exact coordinations, but some tolerance on distances).

The cell is progressively filled with M/M atoms, up to completelyrespect the geometrical restraints, if possible. The numberof M/M' atoms

placed is not predetermined.

In this first step, atoms do not move, their possible positions are testedand checked, then they are retained or not.

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2- Local optimization

The X atoms are added at the midpoints of the (M/M')-(M/M') first neighbours.It is verified by distance and cell improvements (Monte Carlo moves) that

regular (M/M)Xnpolyhedra can really be built.

The cost function is based on the verification of the provided ideal distances M-

M, M-X and X-X first neighbours. A total Rfactor is defined as :R= [(R1+R2+R3)/ (R01+R02+R03)],

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

Rn = 7 [wn(d0n-dn)]2, R0n = 7 [wnd0n]

2,

where d0n are the ideal first interatomic distances M-X (n=1), X-X (n=2) andM-M (n=3), whereas dn are the observed distances in the structural model. The

weights retained (wn) are those used in the DLS software for calculatingidealized zeolite framework data (w1= 2.0, w2 = 0.61 and w3 = 0.23).

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The ideal distances are to be provided by the user for pairs of atomssupposed to form polyhedra (for instance in the case of SiO4 tetrahedra,

one expects to have d1 = 1.61 , d2 = 2.629 and d3 = 3.07 ).

For ternary compounds, the M-M' ideal distances are calculated byGRINSP as being the average of the M-M and M'-M' distances. It is clearthat this Rfactor considers only the X-X intra-polyhedra distances,

neglecting any X-X inter-polyhedra distances This cost function Rcouldpossibly be better defined differently, for instance by using the bond

valence sum rules (this is in project for the next GRINSP version).

Minimizing the Difference ofDistances with Ideal distances

is a very basic approach

This basic approach can work only for regular polyhedra

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During this second step, the atoms are moving, but nojump is allowedbecause a jump would break the coordinations established at the firststep. This is a simple routine for local optimization. The change in thecell parameters from the structure candidate to the final model may be

quite considerable (up to 30%),

During the optimization, the original space group used for placing theM/M' atoms may change after adding the X atoms, so that the final

structure is always proposed in the P1 space group, and presented in aCIF.

The final choice of the real symmetry has to be done by using a programlike PLATON.

More on the optimization second step

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How GRINSP works :

1- Create a small datafile corresponding to your desire

Example for such a datafile:

TiO6/VO5 Pbam - 55 ! Title

P B A M ! Space group4 2 0 2 ! Nsym (symmetry code), Npol, etc

6 5 ! Coordinations of these npol polyhedron-type

Ti O ! Definition of the elements for the first polyhedron

V O ! Definition of the elements for the second polyhedron

3. 16. 3. 16. 3. 16. ! Min and max a, b, c

90. 90. 90. 90. 90. 90.! Min and max angles5. 35. ! Min and max framework density

200000 300000 0.02 0.25 ! Nruns, MCmax, Rmax saving, optimizing

20000 1 ! number of MC optimization cycles, refinement code

9550000 ! first filename (will be 9550000.cif, .xtl, .dat, etc)

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2 Verify if your atom-pairs are already defined :

See into the distgrinsp.txt file :V O 5

3.050 4.050 3.550

1.5262.126 1.826

2.2822.8822.5824.20 7.00

Ti O 6

3.300 4.300 3.800

1.650 2.250 1.950

2.4583.057 2.758

4.45 6.95

These are minimal, maximal

and ideal distances for V-V,

V-O and O-O in VO5 squarepyramids,

and for Ti-Ti, Ti-O and O-O

in TiO6 octahedra.

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3-

Run GRINSP

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4-

Wait a bit

(one day)

and, when

finished, seethe summary

file :

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5

See the

results

(here

usingDiamond

from a

CIF) :

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GRINSP is Open Source, GNU Public Licence

Download it at : http://www.cristal.org/grinsp/

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III- GRINSP Predictions

Binary compounds

Formulations M2X3, MX2, M2X5 and MX3 were examined

Zeolites

More than a thousand models (not >100000) were built withR< 0.01 and cell parameters < 16 and placed into the PCOD database.

The way GRINSP recognizes a zeotype is by comparing the coordinationsequence (CS) of any model with a list of previously established ones (as

well as with the other CS already stored during the current run).

The CIFs can be obtained by consulting the PCOD database, giving theentry number provided with the figure caption

(for instance PCOD1010026, etc).

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Hypothetical zeolite PCOD1010026

SG : P432, a = 14.623 , FD = 11.51

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Hypothetical zeolite PCOD1030081

SG : P6/m, a = 15.60 , c = 7.13, FD = 16.0.

Estimated number of zeolite models proposed by GRINSP : > 2000

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Hypothetical aluminosilicate PCOD1010038

SG : P432, a = 14.70 - FD = 11.32formulation : [Si2AlO6]

-1

Estimated number of aluminosilicates proposed by GRINSP : > 2000

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Hypothetical aluminophosphate

SG : Pma2, a = 15.81 , b = 8.06 , c = 5.64 - FD = 13.9formulation : [Al4PO10]

-3

Estimated number of aluminophosphates proposed by GRINSP : > 2000

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Can GRINSP predict > 100000 zeolites as well ?

Yes, if Rmax fixed at 0.02 instead of 0.01,

if the cell parameters maximum limits (16) are enlarged,

and if multi-redundant solutions in various space groups

are all kept.

I prefer not.

Is there any sense to predict > 100000 zeolites

when less than 200 are known ?

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B2O

3polymorphs predicted by GRINSP

Not a lot of crystalline varieties are known for this B2O3

composition. Too many are proposed by GRINSP.

Hypothetical B2O3 PCOD1062004.

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Hypothetical B2O3 PCOD1051002

Estimated number of B2O3 models proposed by GRINSP : > 3000

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M2X5 compounds

Example : unknown V2O5, SG: Pbam, a = 13.78, b = 14.55 ,

c = 7.25 , FD = 16.5, R = 0.0056, VO5

square pyramids :

Estimated number of V2O5 models proposed by GRINSP : > 200

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AlF3

polymorphs yet to be synthesized,

predicted by GRINSP

All the known structure-types (5) were retrieved,

Two other structure types existing with stuffed MX3 formulations

were proposed.

Five unknown, yet to be synthesized" AlF3

polymorphs were

predicted

That time, the total number is small :

12 models only with R < 0.02.

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Classification of the 12AlF3

polymorphs proposed by GRINSP

(identified as known or unknown) according to increasing values of

the distance quality factor R < 0.02

Structure-type FD a b c E F K SG Z N R HTB 19.68 6.99 6.99 7.21 90.0 90. 120.0 P63/mmc 6 1 0.0035TlCa2Ta5O15 20.67 7.00 7.23 9.56 90.0 90.0 90.0 Pmmm 10 2 0.0040U-1 (AlF3) 21.27 6.99 7.22 13.5 90.0 105. 90.0 P21/m 14 3 0.0042Pyrochlore 17.71 9.67 9.67 9.67 90.0 90.0 90.0 Fd-3m 16 1 0.0046U-2 (AlF3) 20.43 6.88 6.89 8.25 90.0 90.0 90.0 P-4m2 8 2 0.0057Perovskite 21.16 3.62 3.62 3.62 90.0 90.0 90.0 Pm-3m 1 1 0.0063Ba4CoTa10O30 21.15 9.45 13.8 7.22 90.0 90.0 90.0 Iba2 20 2 0.0095TTB 20.78 11.5 11.5 7.22 90.0 90.0 90.0 P42/mbc 20 2 0.0099U-3 (AlF3) 22.37 6.96 7.40 5.21 90.0 90.0 90.0 Pnc2 6 2 0.0160X-AlF3 21.17 10.2 10.2 7.24 90.0 90.0 90.0 P4/nmm 16 3 0.0162U-4 (AlF3) 21.71 10.5 10.5 6.68 90.0 90.0 90.0 I41/a 16 1 0.0181U-5 (AlF3) 19.74 7.12 7.12 11.98 90.0 90.0 90.0 P42/mmc 12 2 0.0191

FD = framework density (number of Al atoms for a volume of 10003).

SG = higher symmetry spage group in which the initial model of Al-only atoms was obtained (not being

necessarily the true final space group obtained after including the F atoms).

Z = number of AlF3

formula per cell.

N = number of Al atoms with different coordination sequences.

R = quality factor regarding the ideal Al-F, F-F and Al-Al first neighbour interatomic distances.

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Yet to be synthesized U-3 (AlF3).

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Known : X-AlF3

- tetrahedra and chains of octahedra

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Unknown : U-4 (AlF3),

dense packing of tetrahedra of octahedra, exclusively

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Model 13 : U-6 (AlF3), R > 0.02, not viable due to a too high level

of octahedra distortion and short F-F distances

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By-products of the search with GRINSP

Irregular polyhedra can be produced

For instance, sixfold polyhedra other than octahedra can beproduced: trigonal prisms or pentagonal based pyramids.

Since they do not correspond to one unique ideal X-M distance or

M-X distance, they are ranked with high R-values.

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Octahedra + pentagonal based pyramids :

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Octahedra + trigonal prisms :

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Chimeric compound mixing trigonal prisms

with distorted trigonal bipyramids

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Ternary MaMbXc compounds with corner-

sharing 3D nets

M/Mwith same coordination but different ionic radii

ordifferent coordination

The built ternary compound will not always be electricallyneutral.

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Borosilicates

PCOD2050102, Si5B2O13, R= 0.0055.

Estimated number of models built by GRINSP : >3000

SiO4

tetrahedraand

BO3

triangles

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Aluminoborates

Estimated number of models built by GRINSP : >2

000

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

AlO6

octahedraand

BO3

triangles

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Titanosilicates

[Si2TiO7]2-, R= 0.0044, SG : P42/mmc, a = 7.73 , c = 10.50 , FD = 19.1.

Estimated number of models built by GRINSP : > 500

TiO6

octahedraand

SiO4tetrahedra

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Fluoroaluminates

Known asNa4Ca4Al7F33 : PCOD1000015 - [Ca4Al7F33]4-.

AlF6

andCaF6

octahedra

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Unknown : PCOD1010005 - [Ca3Al4F21]3-.

Estimated number of fluoroaluminates models built by GRINSP : ???

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A satellite software (GRINS) can build isostructural compounds

faster than running again GRINSP

However, changing the atomic radius may lead to different

structures

Automatization is essential for the fast feeding of the PCOD,

unfortunately, human eyes looking at the predictedstructure is still essential : 5 minutes at least are needed for

an evaluation before adding the CIF into the database.

With zeolites, identification is easy because the coordination

sequences of the known phases helps to recognize if theprediction leads to a new model or is already known

But this is less easy with non-zeolites because there is no

general extension of structure-types descriptors

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IV - Opened doors and limitations

Limitation : corner-sharing polyhedra

Potentially already > 50 or 100.000 hypothetical compounds in PCOD(only 2000 added yet)

Scheduled improvementsMake appear corner-, edge-, and face-sharing polyhedra, altogether.

Propose an automatic way toobtain an electrical neutrality by thedetection of holes and the filling of these holes by large cations.

Use of bond valence rules at the optimization step, or/and energycalculations.

Extension to quaternary compounds.

Etc.

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With a few modifications, GRINSP couldPredict structures for ice H2O (on the basis of distorted OH4 tetrahedra):

or predict alloys MxMy characterized by MM4 and MM4 tetrahedra,

or predict fullerene structures,

or predict structures for series of organic compounds provided

they can be described by common geometrical features, etc.

You are limited only by your own imagination

GRINSP l d di d i i

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GRINSP can already predict structures deriving

from perovskite by oxygen vacancies :

Octahedra and square pyramids : > 500 predictions

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Brownmillerite

A problem with ICSD is the difficulty to identify if

a predicted structure-type is already described in the database.

Generalized topology descriptors are lacking

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V- Prediction confirmation

More difficult even is the prediction of the synthesis conditions for

making to appear these predicted crystal structures. However, if the

chemical composition involves at least 3 elements or more, one may

try the battery of classical synthesis methods.

If an interesting model is predicted having the [Ca3Al4F21]3-

formulation, may be it could be really synthesized as Na3Ca

3Al4F21

or Li3Ca

3Al4F21, or may be not.

We can already be sure that most predictions will be vain, never

confirmed, because the synthesis route may depend on a precursor(organometallic, hydrate, amorphous compound) which itself is yet

unknown, or because the prediction is simply false.

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The [Ca4Al7F33]4- network proposed by GRINSP really exists with the

Na4Ca4Al7F33 formulation.

The more the predicted inorganic formula is complex,the more easy classical and direct synthesis routes can be tested,

but metastable compounds will mostly occur from indirect routes.

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For the confirmation of the predictions, we will have to

wait for decades or centuries, who knows.

Anyway, structure (and properties) prediction is an

unavoidable part of our future in crystallography and

chemistry. Advantages are obvious.

We need for searchable databases of predicted

compounds, preferably open data on the Web.

If we are not able to do that, we cannot pretend having

understood and mastered the crystallography rules.

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Citation from FrankC. Hawthorne (1994) :

"The goals of theoretical crystallography may be summarized as follow:

(1) predict the stoichiometry of the stable compounds;(2) predict the bond topology (i.e. the approximate atomic arrangement)of the stable compounds;(3) given the bond topology, calculate accurate bond lengths and angles

(i.e. accurate atomic coordinates and cell dimensions);(4) given accurate atomic coordinates, calculate accurate static anddynamic properties of a crystal.

Foroxides and oxysalts, we are now quite successful at (3) and (4), butfail miserably at (1) and (2)"

F. C. Hawthorne,Acta Cryst. B50 (1994) 481-510.

As a conclusion : generalizing GRINSP would be an

empirical answer at goals (1) and (2).

We have to stop to fail miserably !

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We need for a database pointing at the

future materials.

I suggest you to explore your usual crystallographydomain, and to help me to feed PCOD with high

quality hypothetical compounds either with

GRINSP or using any other prediction software.

VI - Conclusion

This is the future of chemistry and crystallography.

Thanks !