**>100.000 entries : >40.000 structures added to the ~60.000 entries
of the PCOD version 2**

These results 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**)

Three years of calculations were needed...

Note : Some two-dimensionnal models were not removed, many

of them are listed with the smallest framework densities (FD < 9
possibly)

(disconnected sheets, with one doubtful cell parameter).

**Structure-types and isostructural compounds**
**Problem with electrical neutrality**
**Criticism of the method**
**Details of the series included into the PCOD**

Current number of entries in the PCOD and the PPDF corresponding to a to tal of xxxxx unique models and more than 100.000 hypothetical phases, including the isostructural series. The hyperlink will provide more information on these series.

**Problem with electrical neutrality
:**

Are electrically neutral : B_{2}O_{3}, SiO_{2},
V_{2}O_{5}, AlF_{3} series, as well as combinations
such as [SiO_{4}]/[BO_{3}], [SiO_{4}]/[VO_{5}],
[BO_{3}]/[VO_{5}] (...) 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 [TiO_{6}]/[SiO_{4}] (...) 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 AlF

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...

Rendez-vous in 2009 for a new GRINSP-3 version ? Who knows...

**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 AlF_{3}
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 Diffraction, in the
press.

[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.

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.

**1- Triangles series**

**Formulation : B _{2}O_{3}**

766 models with R < 0.006

Entries : PCOD1500001 to PCOD1500766

Lists sorted by

Connectivity

Multiple

**2- Tetrahedra series**

**Formulation : SiO _{2}**

6022 models with R < 0.015

Entries : PCOD3100001 to PCOD3106022

Lists sorted by

Connectivity

Multiple

**Formulation : known-SiO _{2}**

129 models corresponding to known zeotypes

Entries : PCOD3000201 to PCOD3000329

List sorted by

**Mixte tetrahedra AlO _{4}/SiO_{4}**

6081 models with R < 0.015

Entries : PCOD4400001 to PCOD4406081

Lists sorted by

Connectivity

Multiple

Note : Al and Si are ordered

**Mixte tetrahedra AlO _{4}/PO_{4}**

6391 models with R < 0.015

Entries : PCOD3300001 to PCOD3306391

Lists sorted by

Connectivity

Multiple

Note : Al and P are ordered

**Mixte tetrahedra AlO _{4}/SO_{4}**

5600 models with R < 0.015

Entries : PCOD4500001 to PCOD4505600

Lists sorted by

Connectivity

Multiple

Note : Al and S are ordered

**3- Square-based pyramids**

**Formulation : V _{2}O_{5}**

1318 models with R < 0.015

Entries : PCOD5000001 to PCOD5001318

Lists sorted by

Connectivity

Multiple

**Formulation : Mn _{2}O_{5}**

1295 models with R < 0.015

Entries : PCOD5010001 to PCOD5011295

Lists sorted by

Connectivity

Multiple

Note : isotypical with the V

**4- Octahedra series**

**Formulation : AlF _{3}**

33 models with R < 0.020

Entries : PCOD6000001 to PCOD6000033

Lists sorted by

Connectivity

Multiple

Note : these new entries are to be added to the previous ones described in the paper

"Hypothetical AlF

A. Le Bail & F. Calvayrac, J. Solid State Chem., 179 (2006) 3159-3166.

**Formulation : FeF _{3}**

33 models with R < 0.020

Entries : PCOD6001001 to PCOD6001033

Lists sorted by

Connectivity

Multiple

**Formulation : GaF _{3}**

33 models with R < 0.020

Entries : PCOD6002001 to PCOD6002033

Lists sorted by

Connectivity

Multiple

**Formulation : CrF _{3}**

32 models with R < 0.020

Entries : PCOD6003001 to PCOD6003032

Lists sorted by

Connectivity

Multiple

**Mixte polyhedra AlF _{6}/CaF_{6}**

24 models with R < 0.020

Entries : PCOD6010001 to PCOD6010024

Lists sorted by

Connectivity

Multiple

**Mixte polyhedra AlF _{6}/NaF_{6}**

13 models with R < 0.020

Entries : PCOD6011001 to PCOD6011013

Lists sorted by

Connectivity

Multiple

**5- Tetrahedra-triangles series**

Mixte polyhedra : **SiO _{4}/BO_{3}**

3603 models with R < 0.010

Entries : PCOD7000001 to PCOD7003603

Lists sorted by

Connectivity

Multiple

Mixte polyhedra : **PO _{4}/BO_{3}**

3457 models with R < 0.010

Entries : PCOD7010001 to PCOD7013457

Lists sorted by

Connectivity

Multiple

isostructral with the SiO

Mixte polyhedra : **SO _{4}/BO_{3}**

3212 models with R < 0.010

Entries : PCOD7020001 to PCOD7023212

Lists sorted by

Connectivity

Multiple

**6- Square-based pyramid-triangles series**

**Mixte polyhedra : VO _{5}/BO_{3}**

4873 models with R < 0.015

Entries : PCOD1530001 to PCOD1534873

Lists sorted by

Connectivity

Multiple

**7- Octahedra-triangles series**

**Mixte polyhedra : AlO _{6}/BO_{3}**

4138 models with R < 0.012

Entries : PCOD6100001 to PCOD6104138

Lists sorted by

Connectivity

Multiple

**8- Octahedra-tetrahedra series**

**Mixte polyhedra : TiO _{6}/SiO_{4}**

2154 models with R < 0.020

Entries : PCOD3201001 to PCOD3203154

Lists sorted by

Connectivity

Multiple

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.

(

Le Bail, A. (2007). “Inorganic structure prediction: Too much and not enough,” Solid State Phenom. 130, 1–6.

**Mixte polyhedra : TiO _{6}/PO_{4}**

1975 models with R < 0.020

Entries : PCOD3230001 to PCOD3231975

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : TiO _{6}/SO_{4}**

1821 models with R < 0.020

Entries : PCOD3240001 to PCOD3241821

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : GaO _{6}/SiO_{4}**

1953 models with R < 0.020

Entries : PCOD6490001 to PCOD6491953

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : GaO _{6}/PO_{4}**

1913 models with R < 0.020

Entries : PCOD3210001 to PCOD3211913

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : GaO _{6}/SO_{4}**

1779 models with R < 0.020

Entries : PCOD6480001 to PCOD6481779

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : NbO _{6}/SiO_{4}**

2014 models with R < 0.020

Entries : PCOD3220001 to PCOD3222014

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : NbO _{6}/PO_{4}**

1859 models with R < 0.020

Entries : PCOD6470001 to PCOD6471859

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : NbO _{6}/SO_{4}**

1565 models with R < 0.020

Entries : PCOD6460001 to PCOD6461565

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : VO _{6}/SiO_{4}**

2038 models with R < 0.020

Entries : PCOD6400001 to PCOD6402038

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : VO _{6}/PO_{4}**

1938 models with R < 0.020

Entries : PCOD6420001 to PCOD6421938

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : VO _{6}/SO_{4}**

1743 models with R < 0.020

Entries : PCOD6410001 to PCOD6411743

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : ZrO _{6}/SiO_{4}**

1958 models with R < 0.020

Entries : PCOD6450001 to PCOD6451958

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : ZrO _{6}/PO_{4}**

1754 models with R < 0.020

Entries : PCOD6430001 to PCOD6431754

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**Mixte polyhedra : ZrO _{6}/SO_{4}**

1469 models with R < 0.020

Entries : PCOD6440001 to PCOD6441469

Lists sorted by

Connectivity

Multiple

Note : isotypical with the titanosilicates

**9- Octahedra-square-based pyramids series**

**Mixte polyhedra : TiO _{6}/VO_{5}**

2045 models with R < 0.020

Entries : PCOD4300001 to PCOD4302045

Lists sorted by

Connectivity

Multiple

In that series can be found some oxygen-deficient perovskites.

**Mixte polyhedra : VO _{6}/VO_{5}**

1997 models with R < 0.020

Entries : PCOD5600001 to PCOD5601997

Lists sorted by

Connectivity

Multiple

Note : isotypical with the TiO

**Mixte polyhedra : GaO _{6}/VO_{5}**

1963 models with R < 0.020

Entries : PCOD5620001 to PCOD5621963

Lists sorted by

Connectivity

Multiple

Note : isotypical with the TiO

**Mixte polyhedra : NbO _{6}/VO_{5}**

1928 models with R < 0.020

Entries : PCOD5610001 to PCOD5611928

Lists sorted by

Connectivity

Multiple

Note : isotypical with the TiO

**Mixte polyhedra : ZrO _{6}/VO_{5}**

1843 models with R < 0.020

Entries : PCOD5630001 to PCOD5631843

Lists sorted by

Connectivity

Multiple

Note : isotypical with the TiO

**Mixte polyhedra : MnO _{6}/MnO_{5}**

1507 models with R < 0.020

Entries : PCOD5640001 to PCOD5641507

Lists sorted by

Connectivity

Multiple

Note : isotypical with the TiO

**10- Square-based pyramids - tetrahedra series**

**Mixte polyhedra : VO _{5}/PO_{4}**

2394 models with R < 0.015

Entries : PCOD4000001 to PCOD4002394

Lists sorted by

Multiple

Connectivity

**Mixte polyhedra : VO _{5}/SiO_{4}**

2424 models with R < 0.015

Entries : PCOD4010001 to PCOD4012424

Lists sorted by

Connectivity

Multiple

Note : isotypical with the VO

**Mixte polyhedra : VO _{5}/SO_{4}**

2364 models with R < 0.015

Entries : PCOD4020001 to PCOD4022364

Lists sorted by

Connectivity

Multiple

Note : isotypical with the VO

**Mixte polyhedra : TiO _{5}/SiO_{4}**

2541 models with R < 0.015

Entries : PCOD5400001 to PCOD5402541

Lists sorted by

Connectivity

Multiple

Note : isotypical with the VO

**Mixte polyhedra : TiO _{5}/PO_{4}**

2446 models with R < 0.015

Entries : PCOD5410001 to PCOD5412446

Lists sorted by

Connectivity

Multiple

Note : isotypical with the VO

**Mixte polyhedra : TiO _{5}/SO_{4}**

2083 models with R < 0.015

Entries : PCOD5420001 to PCOD5422083

Lists sorted by

Connectivity

Multiple

Note : isotypical with the VO

**Mixte polyhedra : MnO _{5}/PO_{4}**

2449 models with R < 0.015

Entries : PCOD5430001 to PCOD5432449

Lists sorted by

Connectivity

Multiple

Note : isotypical with the VO

**Mixte polyhedra : MnO _{5}/SO_{4}**

2067 models with R < 0.015

Entries : PCOD5440001 to PCOD5442067

Lists sorted by

Connectivity

Multiple

Note : isotypical with the VO

**Mixte polyhedra : MnO _{5}/SiO_{4}**

2541 models with R < 0.015

Entries : PCOD5450001 to PCOD5452541

Lists sorted by

Connectivity

Multiple

Note : isotypical with the VO