III - Data from GRINSP Back to the main page
Structure-types and isostructural compounds

These results and the PCOD were announced in the paper: "Inorganic structure prediction with GRINSP." A. Le Bail, J. Appl. Cryst. 38 (2005) 389-395. (open access at the IUCr journals).

Current number of entries from GRINSP in the PCOD and the P2D2 are corresponding to a total of 33705 unique models and more than 160.000 hypothetical phases, including the isostructural series. The hyperlink will provide more information on these series.
 
Entry numbers for
the archetypes		 Archetype formula or 
polyhedra involved		 Isostructural series added Total entry 
numbers
11695 (Al/P)O4 SiO2, (Si/P)O4, (Al/Si)O4, (Al/S)O4, BeF2 59675
4873 [VO5]/[BO3] 4873
4138 [AlO6]/[BO3] 4138
3603 [SiO4]/[BO3] [PO4]/[BO3], [SO4]/[BO3] 10272
2394 [VO5]/[PO4] [VO5]/[SiO4], [VO5]/[SO4], 
[TiO5]/[PO4], [TiO5]/[SiO4], [TiO5]/[SO4],
[MnO5]/[PO4], [MnO5]/[SiO4], [MnO5]/[SO4]		 21309
2803 [TiO6]/[SiO4] [ZrO6]/[SiO4], [ZrO6]/[SO4], [ZrO6]/[PO4], 
[NbO6]/[SiO4], [NbO6]/[SO4], [NbO6]/[PO4], 
[VO6]/[SiO4], [VO6]/[SO4], [VO6]/[PO4], 
[GaO6]/[SiO4], [GaO6]/[SO4], [GaO6]/[PO4], 
[TiO6]/[SO4], [TiO6]/[PO4], 
[FeF6]/[BeF4], [AlF6]/[BeF4], [CrF6]/[BeF4], [GaF6]/[BeF4]		 46028
2045 [TiO6]/[VO5] [VO6]/[VO5], [GaO6]/[VO5], [NbO6]/[VO5], 
[ZrO6]/[VO5], [MnO6]/[MnO5]		 11283
1318 V2O5 Mn2O5 2613
766 B2O3 766
33 AlF3 FeF3, GaF3, CrF3 131
24 [AlF6]/[CaF6] 24
13 [AlF6]/[NaF6] 13
sum = 33705 sum = 161125

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Criticism of the method

Are electrically neutral : B2O3, SiO2, V2O5, AlF3 series, as well as combinations such as [SiO4]/[BO3], [SiO4]/[VO5], [BO3]/[VO5] (...) whatever their formulations (polyhedra - triangles, tetrahedra, octahedra, etc - which form neutral networks by exclusive corner sharing will also form neutral networks if combined - mixed tetrahedra/octahedra, etc - by exclusive corner sharing). Other series like [TiO6]/[SiO4] (...) would need for the occupation of holes by appropriate ions in order to attain the neutrality.
 

The PCOD contains a lot of really existing crystal structures. With luck, it contains also lot of to-be-discovered new crystal structures with open frameworks (titano- or zircono-silicates, zeolites, etc.), which could be of interest to the microporous and metal organic framework (MOF) research communities. How is it possible to attain frequently an accuracy better than 1% on the cell parameters by using a naive cost function limited to the verification of ideal interatomic distances ? The compounds predicted by GRINSP [1] all respect most of Pauling’s rules, those stipulating vertex-connected polyhedral frameworks over edge- and face-sharing and the parsimony of different environments of a given ion in a crystal. Attempting inorganic crystal structure prediction in the larger land of edge- and face-sharing polyhedra, mixed together with corner-sharing, would require more precautions and more elaborate cost functions. Whether the PCOD contains many to-be-discovered phases, and how many are useless structure candidates are hard to say. The fact is that, in spite of the difficulties to check these more than 100,000 structures against known structures in the ICSD, a large number of the hypothetical titanosilicates were found to have real counterparts [2, 3] or to correspond to isostructural compounds. The aluminum fluoride series was more thoroughly investigated by DFT analysis and many virtual AlF3 were concluded to be viable polymorphs still undiscovered, whereas the known ones were in the list of the GRINSP productions [4]. It is thus expected that the PCOD may help sometimes, possibly through the P2D2 (Predicted Powder Diffraction Database) allowing for identification and structure solution even before indexing by a simple search-matching [5]. Regular updates will be performed so that the content should increase soon in quantity and hopefully in quality with required cell parameter accuracy better than 1% as a target.

Quality improvements are expected to come from, in a first step, the application of bond valence rules in GRINSP. The list of 'to do' things for that software is quite long :
- provide the final models in the correct SG, not in P1 (for that, the O atoms placed at the midpoints between the cations have to be checked against the special and general positions of the SG selected at the beginning of the model building).
- the refinement part (working on the atomic coordinates and cell parameters) has obviously to take account of these special positions if any.
- the electrical neutrality of the network has to be checked and finally ensured -if possible- by an automatic system of detection of holes, these holes being filled in by appropriate ions.
- a new cost function based on bond valence rules should ensure better results than the simple cost function based on ideal interatomic distances, but this remains to be tested...

All this could well reduce the number of structure candidates in the PCOD from 100,000 to 10,000 or less, excluding 90% or more of possibly not-viable hypothetical models...  Wait and see...

Anyway, GRINSP can only produce structure candidates in the quite limited category of the N- and N-N'-connected 3D nets, nothing else... Is it possible to imagine an algorithm similar but allowing to extend the exploration domain to other polyhedra connections than corner sharing ? Maybe...

Shall we realize energy minimization (using GULP for instance) for each of the candidate structure to its local minimum and compare energies ? Systematic studies of zeolites and aluminophosphates [6-7] by this way have led to cell parameters agreement better than 1% in most cases, the worst disagreement is less than 2%. By the use of the simple cost function based on ideal interatomic distances with GRINSP, the agreement is already generally close to that (less than 2%), this being due to the 3D network nature of these models, among other reasons.

Another imperfection in GRINSP is related to the way the models are recognized to be identical or different. This is done through the coordination sequence (CS) which is known to be not completely sure (examples are known of a few different zeolites presenting the same CS up to the 10th shell or more, and being still structurally different). But even if a few structures were excluded wrongly by this imperfect system, there are probably worse things occuring which allow for the selection of structure candidates that should not be kept in the lists...

The 2009 update leads to a doubling of the number of models based on corner-sharing tetrahedra and an increase by ~25% of the models based on octahedra/tetrahedra, simply by sampling them by more Monte Carlo searches. A total of ~10.000 zeolite models may look very small if compared to the ~3 millions from the Michael W. Deem team. The rejection criteria are not the same and no intercomparison is provided. Would some of the SLC and BKS data be rejected if the interatomic distance R factor of GRINSP was applied to them ? Would some of the GRINSP structure candidates be rejected if energy minimizations by GULP were applied to them ? No answer yet.

Rendez-vous in 2010 for a new GRINSP-3 version ? Who knows... it was already suggested that this could occur in 2009 and was obviously not the case...

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Details of the GRINSP series included into the PCOD

For each formulation is provided the number of unique models, the entry numbers, the lists of compounds sorted by the quality R factor based on the respect of the ideal interatomic distances, the framework density (FD), the connectivity sequences (CS) and finally the multiple CIF including all the models is available, zipped. The more frequent formulations occuring are also listed for the main examples in each series.

To be noted in this 2009 update is the appearing of microporous compounds predicted based on BeF4 tetrahedra with BeF2 formulation (like the SiO2 zeolites) or [MF6]/[BeF4] (M = Al, Fe, Cr, Ga) octahedra/tetrahedra series (all being electrically neutral without to have to add anything into their framework). In chemistry laboratories, no one wants to work with beryllium, that element being too poisoning (you loose your hairs, etc). However, many minerals are containing high proportions of Be, some being gems (esmeralda, beryl, etc), and women wear them without too much questioning... The lack of real knowledge about the relations between crystal structure and properties makes that we will not be able to tell if such (virtual) materials would have properties interesting enough for investing efforts in attempts of synthesizing them as real compounds. If you have developped a structure-properties new software, able to predict the properties of these virtual compounds, then get the crystal structures in the CIFs below. The compounds with the largest pores/channels are those with the smallest framework densities (FD) also given in ordered lists below.
 

1- Triangles series

Formulation : B2O3
766 models with R < 0.006
Entries : PCOD1500001 to PCOD1500766
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
 
 

2- Tetrahedra series

Formulation : SiO2
9349 models with R < 0.020
Entries : PCOD3100001 to PCOD3109349
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF

Formulation : known-SiO2
129 models corresponding to known zeotypes
Entries : PCOD3000201 to PCOD3000329
List sorted by FD

Formulation : BeF2
8731 models with R < 0.020
Entries : PCOD3400001 to PCOD3408731
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF

Mixte tetrahedra AlO4/SiO4
10720 models with R < 0.020
Entries : PCOD4400001 to PCOD4410720
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : Al and Si are ordered

Mixte tetrahedra AlO4/PO4
11695 models with R < 0.020
Entries : PCOD3300001 to PCOD3311695
Lists sorted by R, by FD - connectivity sequences - Multiple CIF
Note : Al and P are ordered

Mixte tetrahedra SiO4/PO4
9698 models with R < 0.020
Entries : PCOD3500001 to PCOD359698
Lists sorted by R, by FD - connectivity sequences - Multiple CIF
Note : Si and P are ordered

Mixte tetrahedra AlO4/SO4
9482 models with R < 0.020
Entries : PCOD4500001 to PCOD4509482
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : Al and S are ordered
 

3- Square-based pyramids

Formulation : V2O5
1318 models with R < 0.015
Entries : PCOD5000001 to PCOD5001318
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF

Formulation : Mn2O5
1295 models with R < 0.015
Entries : PCOD5010001 to PCOD5011295
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the V2O5 series
 

4- Octahedra series

Formulation : AlF3
33 models with R < 0.020
Entries : PCOD6000001 to PCOD6000033
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : these new entries are to be added to the previous ones described in  the paper
"Hypothetical AlF3 crystal structures."
A. Le Bail & F. Calvayrac, J. Solid State Chem., 179 (2006) 3159-3166.

Formulation : FeF3
33 models with R < 0.020
Entries : PCOD6001001 to PCOD6001033
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF

Formulation : GaF3
33 models with R < 0.020
Entries : PCOD6002001 to PCOD6002033
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF

Formulation : CrF3
32 models with R < 0.020
Entries : PCOD6003001 to PCOD6003032
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF

Mixte octahedra AlF6/CaF6
24 models with R < 0.020
Entries : PCOD6010001 to PCOD6010024
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF

Mixte octahedra AlF6/NaF6
13 models with R < 0.020
Entries : PCOD6011001 to PCOD6011013
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
 
 

5- Tetrahedra-triangles series

Mixte polyhedra : SiO4/BO3
3603 models with R < 0.010
Entries : PCOD7000001 to PCOD7003603
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF

Mixte polyhedra : PO4/BO3
3457 models with R < 0.010
Entries : PCOD7010001 to PCOD7013457
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
isostructral with the SiO4/BO3 series

Mixte polyhedra : SO4/BO3
3212 models with R < 0.010
Entries : PCOD7020001 to PCOD7023212
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
 
 

6- Square-based pyramid-triangles series

Mixte polyhedra : VO5/BO3
4873 models with R < 0.015
Entries : PCOD1530001 to PCOD1534873
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
 
 

7- Octahedra-triangles series

Mixte polyhedra : AlO6/BO3
4138 models with R < 0.012
Entries : PCOD6100001 to PCOD6104138
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
 
 

8- Octahedra-tetrahedra series

Mixte polyhedra : TiO6/SiO4
2803 models with R < 0.020
Entries : PCOD3201001 to PCOD3203803
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Notes : this is the complete list of titanosilicates (previous entries 3200000-etc).
Papers discussing these titanosilicates are :
Le Bail, A. (2007). “Predicted corner-sharing titanium silicates,” Z. Kristallogr. suppl. 26, 203–208.
    (supplementary material  - .doc file - for that publication above which was limited to 6 pages on the titanosilicates...)
Le Bail, A. (2007). “Inorganic structure prediction: Too much and not enough,” Solid State Phenom. 130, 1–6.
 

Mixte polyhedra : TiO6/PO4
2553 models with R < 0.020
Entries : PCOD3230001 to PCOD3232553
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : TiO6/SO4
2304 models with R < 0.020
Entries : PCOD3240001 to PCOD3242304
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : GaO6/SiO4
2502 models with R < 0.020
Entries : PCOD6490001 to PCOD6492502
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : GaO6/PO4
2456 models with R < 0.020
Entries : PCOD3210001 to PCOD3212456
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : GaO6/SO4
2280 models with R < 0.020
Entries : PCOD6480001 to PCOD6482280
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : NbO6/SiO4
2583 models with R < 0.020
Entries : PCOD3220001 to PCOD3222583
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra :NbO6/PO4
2392 models with R < 0.020
Entries : PCOD6470001 to PCOD6472392
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : NbO6/SO4
1982 models with R < 0.020
Entries : PCOD6460001 to PCOD6461982
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : VO6/SiO4
2621 models with R < 0.020
Entries : PCOD6400001 to PCOD6402621
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : VO6/PO4
2500 models with R < 0.020
Entries : PCOD6420001 to PCOD6422500
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : VO6/SO4
2228 models with R < 0.020
Entries : PCOD6410001 to PCOD6412228
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : ZrO6/SiO4
2524 models with R < 0.020
Entries : PCOD6450001 to PCOD6452524
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : ZrO6/PO4
2227 models with R < 0.020
Entries : PCOD6430001 to PCOD6432227
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : ZrO6/SO4
1862 models with R < 0.020
Entries : PCOD6440001 to PCOD6441862
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : FeF6/BeF4
2785 models with R < 0.020
Entries : PCOD3250001 to PCOD3252785
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : AlF6/BeF4
2239 models with R < 0.020
Entries : PCOD3260001 to PCOD3262239
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : CrF6/BeF4
2609 models with R < 0.020
Entries : PCOD3270001 to PCOD3272609
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates

Mixte polyhedra : GaF6/BeF4
2578 models with R < 0.020
Entries : PCOD3280001 to PCOD3282578
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the titanosilicates
 

9- Octahedra-square-based pyramids series

Mixte polyhedra : TiO6/VO5
2045 models with R < 0.020
Entries : PCOD4300001 to PCOD4302045
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
In that series can be found some oxygen-deficient perovskites.

Mixte polyhedra : VO6/VO5
1997 models with R < 0.020
Entries : PCOD5600001 to PCOD5601997
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the TiO6/VO5 series above

Mixte polyhedra : GaO6/VO5
1963 models with R < 0.020
Entries : PCOD5620001 to PCOD5621963
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the TiO6/VO5 series above

Mixte polyhedra : NbO6/VO5
1928 models with R < 0.020
Entries : PCOD5610001 to PCOD5611928
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the TiO6/VO5 series above

Mixte polyhedra : ZrO6/VO5
1843 models with R < 0.020
Entries : PCOD5630001 to PCOD5631843
Lists sorted by R, by FD
Connectivity sequences
Multiple CIF
Note : isotypical with the TiO6/VO5 series above

Mixte polyhedra : MnO6/MnO5
1507 models with R < 0.020
Entries : PCOD5640001 to PCOD5641507
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the TiO6/VO5 series above
 
 

10- Square-based pyramids - tetrahedra series

Mixte polyhedra : VO5/PO4
2394 models with R < 0.015
Entries : PCOD4000001 to PCOD4002394
Lists sorted by R, by FD - Multiple CIF - Connectivity sequences

Mixte polyhedra : VO5/SiO4
2424 models with R < 0.015
Entries : PCOD4010001 to PCOD4012424
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the VO5/PO4

Mixte polyhedra : VO5/SO4
2364 models with R < 0.015
Entries : PCOD4020001 to PCOD4022364
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the VO5/PO4

Mixte polyhedra : TiO5/SiO4
2541 models with R < 0.015
Entries : PCOD5400001 to PCOD5402541
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the VO5/PO4

Mixte polyhedra : TiO5/PO4
2446 models with R < 0.015
Entries : PCOD5410001 to PCOD5412446
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the VO5/PO4

Mixte polyhedra : TiO5/SO4
2083 models with R < 0.015
Entries : PCOD5420001 to PCOD5422083
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the VO5/PO4

Mixte polyhedra : MnO5/PO4
2449 models with R < 0.015
Entries : PCOD5430001 to PCOD5432449
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the VO5/PO4

Mixte polyhedra : MnO5/SO4
2067 models with R < 0.015
Entries : PCOD5440001 to PCOD5442067
Lists sorted by R, by FD - Connectivity sequences - Multiple CIF
Note : isotypical with the VO5/PO4

Mixte polyhedra : MnO5/SiO4
2541 models with R < 0.015
Entries : PCOD5450001 to PCOD5452541
Lists sorted by R, by FD  - Connectivity sequences  - Multiple CIF
Note : isotypical with the VO5/PO4

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References

[1] Le Bail, A. (2005). “Inorganic structure prediction with GRINSP,” J. Appl. Crystallogr. 38, 389–395.
[2] Le Bail, A. (2007). “Predicted corner-sharing titanium silicates,” Z. Kristallogr. suppl. 26, 203–208.
[3] Le Bail, A. (2007). “Inorganic structure prediction: Too much and not enough,” Solid State Phenom. 130, 1–6.
[4] Le Bail, A. and Calvayrac, F. (2006). “Hypothetical AlF3 crystal structures,” J. Solid State Chem. 179, 3159–3166.
[5] Le Bail, A. (2008). "Frontiers between crystal structure prediction and determination by powder diffractometry," Powder DiffractionS23, 5-12.
[6] Henson, N.J., Cheetham, A.K. and Gale, J.D. (1994). Chem. Mater. 6, 1647.
[7] Henson, N.J., Cheetham, A.K. and Gale, J.D. (1996). Chem. Mater. 8, 664.
 

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A. Le Bail - October 2009