Prsentation PowerPoint

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Global Optimisation Techniques Applied to the
Prediction of Structures Gordon Conference
style  Workshop, 5-7 July 2006, University
College London
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_at_cristal.orgWeb
http//cristal.org/
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• CONTENT
• I- IntroductionII- GRINSP algorithm and
  resultsIII- Results for titanosilicates Predicti
  on conditions Models with real
  counterparts Highest quality (?) models Models
  with the largest porosityIV- Opened doors,
  limitations, problemsV- Conclusions

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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.
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If we had a really powerful materials theory
It would allow complete prediction. These
predictions would be made available in huge
databases(currently the case for gt 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
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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
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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 4.912 5.404 0.9Tridymite 5.073 5.07
3 8.400 0.0045 5.052 5.052 8.270  0.8Crist
obalite 5.024 5.024 6.796 0.0018 4.969 4.96
9 6.926 1.4 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
10.2 0.3GME 13.609 13.609 9.931 0.0031
13.7 13.7 9.9 0.6 Aluminum
fluorides?-AlF3 10.216 10.216 7.241 0.0159 1
0.184 10.184 7.174  0.5Na4Ca4Al7F33 10.876 10.87
6 10.876 0.0122 10.781 10.781 10.781 0.9AlF3-py
rochl. 9.668 9.668 9.668 0.0047 9.749 9.749
9.749 0.8 TitanosilicatesBatisite 10.633 14.0
05 7.730 0.0076 10.4 13.85 8.1 2.6Pabsti
te 6.724 6.724 9.783 0.0052 6.7037 6.7037 9
.824 0.9Penkvilskite 8.890 8.426 7.469 0.007
6 8.956 8.727 7.387 1.3
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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.
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Step 2 - Optimization The X atoms are placed at
the (M/M')-(M/M') midpoints (corner-sharing). Inte
ratomic 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 ? (R1R2R3)/
(R01R02R03), where Rn and R0n for n 1, 2, 3
are defined by Rn ? wn(d0n-dn)2, R0n
? wnd0n2, Where the d0n are the ideal distances
M-X (n1), X-X (n2) and M-M (n3), the dn being
the observed distances in the model. Weighting
is applied through the wn .
No powder data.
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Comments
Minimizing distance differences is a very basic
approach.
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.
Intuitively, is it clear that this simple
approach will give good results only for regular
polyhedra.
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More details on step 2
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).
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Running GRINSP
1- The user has first to build a file according
to his/her desires
Example
TiO6/VO5 - all space groups ! Title line 55 55
! Space groups range (you may test the range
1 230) 2 0 2 192 ! Npol, connectivity, min
max number of M/M atoms 6 5 ! Polyhedra
coordinations Ti O ! Elements for the
first polyhedra V O ! Elements for the
second polyhedra 3. 30. 3. 30. 3. 30. !
Min max a, b, c 5. 35. !
Min max framework density 20000 300000 0.02
0.12 ! Ncells, MCmax, Rmax, Rmax to optimize 5000
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.
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2 Verify that the atom pairs are defined
See into the file distgrinsp.txt distributed with
the package
V O 5 3.050 4.050 3.550 1.526 2.126
1.826 2.282 2.882 2.582 4.20 7.00 Ti O
6 3.300 4.300 3.800 1.650 2.250 1.950 2.458 3.057
2.758 4.45 6.95
Distances minimum, maximum and 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-O in
octahedral coordination TiO6. Trigonal prisms may
well be produced, but with larger R values.
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3- Start GRINSP
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4- Wait(hours, days, weeks, months) and see
the summary at the end of the output file with
extension .imp
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5 See the results (here by applying Diamond
to a CIF)
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GRINSP is  Open Source , GNU Public Licence
Downloadable from the Internet at
http//www.cristal.org/grinsp/
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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 lt
0.01 and cell parameters lt 16 Å, placed into the
PCOD database http//www.crystallography.net/pco
d/ 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).
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Hypothetical zeolite PCOD1010026SG P432, a
14.623 Å, FD 11.51
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Example of CIF produced by GRINSP and inserted
into the PCOD The coordination sequence is
added at the end as a comment
..
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Does GRINSP can also predict gt 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.
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Other GRINSP predictions gt 3000 B2O3
polymorphs
Hypothetical B2O3 - PCOD1062004.Triangles BO3
sharing corners.
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gt 500 V2O5 polymorphs
square-based pyramids
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gt 30 AlF3 polymorphs
Corner-sharing octahedra.
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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
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Ternary compounds MaMbXc 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.
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Borosilicates PCOD2050102, Si5B2O13, R 0.0055.
SiO4 tetrahedraandBO3 triangles
gt 3000 models
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Aluminoborates
Example AlB4O9-2, cubic, SG Pn-3, a 15.31
Å, R 0.0051
AlO6 octahedra andBO3triangles
gt 2000 models
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Fluoroaluminates Known Na4Ca4Al7F33 PCOD1000015
- Ca4Al7F334-.
Two-sizesoctahedra AlF6 and CaF6
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Unknown PCOD1010005 - Ca3Al4F213-
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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.
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III Results for titanosilicates
TiO6 octahedra andSiO4 tetrahedra
gt 1000 models
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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
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More than 70 of the predicted titanosilicates
have the general formula TiSinO(32n)2-
Numbers of compounds in ICSD version 1-4-1,
2005-2 (89369 entries) potentially fitting
structurally with the TiSinO(32n)2- series of
GRINSP predictions, addingeither C, C2 or CD
cations for electrical neutrality.
n C C2 CD Total GRINSP ABX5
1 300 495 464 35 1294 93AB2X7
2 215 308 236 11 770 179AB3X9
3 119 60 199 5 383 174AB4X11
4 30 1 40 1 72 205AB5X13 5 9 1 1 0 11 36AB6
X15 6 27 1 13 1 42 158Total 2581 845
Not all these ICSD structures are built up from
corner sharing octahedra and tetrahedra.
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Models with real counterparts
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Example in PCOD
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)
Not too bad if one considers that K et H2O are
not taken into account in the model prediction...
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PCOD2200042 TiSi2O72- identified as
corresponding toNenadkevichite ? NaTiSi2O7?2H2O

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The CS(Coordination Sequence)is not sufficient
for a perfectidentification
Narsarsukite Na2TiSi4O11
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
PCOD2200033 TiSi4O112-
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A few other identified models
PCOD entry Mineral name/formula 2200093 Vlasov
ite3200122 VP2O7-I3200543 VP2O7-II2200170
Gittinsite2200178 KTiPO52200040 ZrP2O72200
030 Armstrongite2200032 Bazirite2200095 Ko
mkovite/Hilairite3200659 Zekzerite etc, etc
(overview not completed)
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Highest quality (?) models
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Models with the largest porosity
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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.
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PCOD3200086 P 70.2, FD 10.6, DP 3
(dimensionality of the pore/channels system)
Ring apertures9 x 9 x 9
Si6TiO152- , cubic, SG P4132, a 13.83 Å
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PCOD3200867, P 61.7, FD 12.0, DP 3
Si2TiO72- , orthorhombic, SG Imma
Ring apertures10 x 8 x 8
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PCOD3200081, P 61.8, FD 13.0, DP 3
Si6TiO152- , cubic, SG Pn-3
Ring apertures12 x 12 x 12106
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PCOD3200026, P 59.6, FD 13.0, DP 3
Si4TiO112- , tetragonal, SG P42/mcm
Ring apertures12 x 10 x 10
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PCOD3200037, P 50.8, FD 13.3, DP 3 (for a
2.5 Å diameter guest) to DP 2 (at 3 Å)
Si2Ti3O136- , trigonal, SG P-3
Ring apertures8 x 8 x 6
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PCOD3200837, P 59.4, FD 13.3, DP 3
Si4TiO112- , orthorhombic, SG Cccm
Ring apertures12 x 10 x 106
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PCOD3200518, P 47.3, FD 14.2, DP 1 with 2
tunnels of 358 and 104 Å3 (for V 983 Å3)
Si4Ti3O176- , orthorhombic, SG Pmc21
Ring apertures168
Trigonal prisms
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PCOD2200205, P 52.3, FD 14.9, DP 3
Si6TiO152- , orthorhombic, SG Pmma
Ring apertures10 x 8 x 6
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PCOD2200199, P 52.3, FD 14.9, DP 3
Si6TiO152- , monoclinic, SG P2/m
Ring apertures10 x 8 x 6
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PCOD3200052, P 53.7, FD 15.2, DP 3 to DP
1 and 0 Si12TiO272- , trigonal, SG P-31c
Ring apertures8 x 6 x (86)
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IV Opened doors, Limitations, Problems GRINSP
limitation exclusively corner-sharing
polyhedra. Opening the door potentially to gt
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.
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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.
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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 crystallographers eye.
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).
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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.
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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.
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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
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Two things that dont work well enough up to now
- Ab initio calculations (WIEN2K, etc) not fast
enough for classifying gt 10000 structure
candidates (was 2
months for 12 AlF3 models)
- Identification of the known structures (ICSD)
among gt10000 hypothetical compounds
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One advice
Send your data (CIFs) to the PCOD, thanks(no
proteins, no nucleic acid, not 1.000.000 zeolites)
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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.