# Presentation: 882426

## Data Mining on the Crystallographic Data of Zeolites

**Shujiang Yang**, Mohammed Lach-hab,
- Iosif I. Vaisman, and Estela Blaisten-Barojas
*Computational Materials Science Center*
*George Mason University*
*Fairfax, VA 22030*

**Supported by NSF grant CHE-0626111**
- ICSD data -- courtesy of the Ceramics Division of NIST.

**CIDU Poster on DASHlink**

## Outline

** ****Zeolite structure: framework types**
** ****Zeolites in the Inorganic Crystal Structure Database**
**(ICSD, maintained jointly by FIZ Karlsruhe and NIST )**
** ****Features for machine learning**
** ****Tessellation based topological descriptors**
** ****Physical and chemical descriptors**
** ****Machine learning classification of zeolites**
**Zeolite structure predictor (ZSP)**

## Applications of zeolites

**Adsorption**
- Purification, drying, separation, etc.
**Ion exchange**
- Water softening, waste treatment, fertilizers, etc.
**Heterogeneous catalysis**
- Multiple organic and inorganic chemical reactions.
- Petrochemical industry: **nearly all gasoline is produced with the use of zeolites!**
**Emerging applications**
- health, sensors, solar energy conversion ...

## General information of zeolites

**General chemical formula of zeolites**

**Primary building units**
**T****O****4**** ,**** *****T****** is ******Si, Al, P****** ******...***

**General information of zeolites**

**cation**

**framework**

**adsorbent phase**

**Some natural zeolites**
- http://museumvictoria.com.au/mineralogy/zeolite.html

##     A heulandite zeolite 3D structure

## Framework types of zeolites

-  **Distinguish zeolites by framework types**
-  A framework type describes the connectivity of the tetrahedrally connected T atoms within a network.
-  Does not include cations, adsorbed phase, framework composition, crystallographic symmetry and unit cell dimensions.
-  **Framework type codes**
-  Rules set up by an IUPAC Commission on Zeolite Nomenclature in 1978 define frameworks designated by **three capital letters**.
-  The framework type codes are assigned and curated by the International Zeolite Association Structure Commission (IZA-SC).

##   IZA-SC approved framework types 

**There are 179 zeolite framework types**

- http://www.iza-structure.org/databases/

## Zeolite framework types in ICSD

**Framework types (FT) ordered by number of zeolites per type**

**Total number of FT : 96**
***14 FT: more than 20 zeolite structures each***
*7 FT:   each between 10 and 20*
*19 FT: each between 5 and 10 (not labeled)*
*56 FT: each below 5 (not labeled)*

**Number of crystals / class**

**Framework type**

## A sample ICSD record

- CopyRight   ©2005 by Fachinformationszentrum Karlsruhe, and the U.S. Secretary of Commerce on behalf of the United States.  All rights reserved.
- Coll Code   XXXX
- Rec  Date   1980/01/01
- Mod  Date   2000/12/16
- Chem Name   Cobalt Sodium Tecto-alumosilicate *
- Structured  Co4 Na4 (Si12 Al12 O48)
- Sum         Al12 Co4 Na4 O48 Si12
- ANX         ABC6X12
- Min Name    Zeolite A
- Min Origin  Zeolite A (Co-exchanged, dehydrated) - synthetic
- Min Group   Zeolite
- D(calc)     1.65
- Formula Wt  1756.424
- Title  Crystal structures of dehydrated partially cobalt(II)exchanged zeolite ...
- Author(s)   Riley, P.E.;Seff, K.
- Reference   Inorganic Chemistry (1974), 13, 1355-1360
- Unit Cell   12.087(5) 12.087(5) 12.087(5) 90. 90. 90.
- Vol         1765.86
- Z           1
- Space Group P m -3 m
- SG          PM3-M
- SG Number   221
- Cryst Sys   cubic

**A sample ICSD record**

- Laue Class  m3-m
- Pearson     cP80
- Wyckoff     m k i h g2
- R Value     0.072
- Symmetry
-       1      0    0    0    1    0    0    1    0    0   -1    0    0
-       2      0    0    1    0    0    1    0    0    0    0    0   -1
-       3      0    1    0    0    0    0    0    1    0    0   -1    0
-       4      0    0    0    1    0    1    0    0    0    0   -1    0
-       5      0    0    1    0    0    0    0    1    0   -1    0    0
-       6      0    1    0    0    0    0    1    0    0    0    0   -1
-       ••••••
- Red Cell    P  12.087 12.087 12.087 90 90 90 1765.857
- Trans Red   1.000 0.000 0.000 / 0.000 1.000 0.000 / 0.000 0.000
-                    1.000
- Comments    R(isotropic)=0.086
-             Total SOF on at least one site differs from unity (SOF <
-             0.997 resp. SOF > 1.003)
-             Compound with mineral name: Zeolite A
-             Structure type : Zeolite-A
- Atom  #   OX   SITE      x           y           z           SOF      H
-  Si   1  +4    24 k  0           0.183(1)    0.367(1)       0.5        0
-  Al   1  +3    24 k  0           0.183(1)    0.367(1)       0.5        0
-  O    1  -2    12 h  0           0.201(3)    0.5            1.         0
-  O    2  -2    12 i  0           0.298(2)    0.298(2)       1.         0
-  O    3  -2    24 m  0.115(1)    0.115(1)    0.323(1)       1.         0
-  Co   1  +2    8 g   0.200(2)    0.200(2)    0.200(2)       0.5        0
-  Na   1  +1    8 g   0.158(2)    0.158(2)    0.158(2)       0.5        0
- *end for    ICSD #XXXX

##     Computational geometry treatment

- T-atom
- selection

- Delaunay
- tessellation

## Why Delaunay tessellation?

**Objective **definition of** nearest neighbors **in space.

- Singh, R. K.; Tropsha, A.; Vaisman, I. I. *J. Comput. Bio. ***1996***, 3*, 213.

**In 2-D:**** Voronoi****/****Delaunay**** tessellation**

**Each ****T-atom**** **is represented as a** ****point**** **in space.
**Voronoi polyhedra****: **any position inside is closer to its **point** than to any other **point**.
**Delaunay simplex****: **formed by connecting **points** whose **Voronoi polyhedra** share a common vertex. It is a **triangle in 2D** or **tetrahedron in 3D** space.

## Topological descriptors: Delaunay simplex

| Geometric Properties of a Tetrahedron | Geometrical
Descriptors |
| --- | --- |
| average edge length | d_mean |
|  | σ_d |
| tetrahedrality | T_mean |
|  | σ_T |
| in-sphere volume (iV) | iV_mean |
|  | σ_iV |

**Geometrical descriptors are based on the *****mean***** and *****standard deviation (******σ******)***** properties of all simplices in the carved sphere.**

## More Topological descriptors

**Secondary simplex**
**corresponding to the second coordination shell of points.**
**Six additional topological descriptors**** **
***d2_av, ******σ******_******d2,***
***T2_av, ******σ******_******T2,***
***iV2_av, ******σ******_******iV2***

**The ****central Delaunay simplex (1-2-3-4)**** and its **secondary simplex (5-6-7-8)

## Physical and chemical descriptors

**Framework density ***(fd)*
*number of T-atoms per 1000 Å**3**.*
**Unit cell volume ****(***vol***)**
**Space group ****(***sg; as a nominal attribute***)**
**Chemical composition of T-atoms**
*comp_Si*
*comp_Al*
*comp_P*

##   Zeolite Structure Predictor: Machine learning 

**Model: **Zeolite Structure Predictor (ZSP)1; framework based zeolite classification
**Procedure: **learn by training using known class types; then test on unknown class types
**Algorithms: **Random Forest as implemented in WEKA
**Feature vector: **18 attributes
**Delaunay**: *d_mean, **σ**_**d, T_mean, **σ**_**T, iV_av, **σ**_* *iV,*
**Secondary**:*  **d2_mean, **σ**_* *d2, T2_mean, **σ**_* *T2, iV2_mean, **σ**_* *iV2,*
**Physical & chemical:***  **comp_Si, comp_Al, comp_P, fd, vol, sg.*

- 1Carr, D. A.; Lach-hab, M.; Yang, S.; Vaisman, I. I.; Blaisten-Barojas, E. *Micropor. Mesopor. Mater. ***2008**, *in press*.

## ZSP: Binary classification

- Data: 40 framework types, each having at least 5 crystals; 1334 instances total.
- Datasets with 2 frameworks: 780 pairs.
- Perfect classification for most pairs of classes.
- Non-perfect classification involve classes populated with fewer instances.

## The ZSP learning curve 

-  Data set consists of **14** framework type classes, each possesses at least 20 instances
-  Data set is balanced: 20 zeolites per class.
-  Each point is an average of 100 runs.

## The ZSP learning curve 

-  Data set consists of **6** framework type classes, each possesses at least 65 instances
-  Data set is balanced: 65 zeolites per class.
-  Each point is an average of 100 runs.

##     Effect of dataset size on the ZSP 

**    ****Effect of dataset size on the ZSP **

| subset | subset-1 | subset-2 | subset-3 |
| --- | --- | --- | --- |
| x=instances/class | 5≤ x <10 | 10≤ x <20 | x ≥20 |
| classes | 19 | 7 | 14 |
| total instances | 119 | 101 | 1114 |
| OOB | 0.093±0.013 | 0.020±0.005 | 0.019±0.001 |
| accuracy (%) | 92.3±1.0 | 98.1±0.3 | 98.5±0.1 |

## Normalized confusion matrix

**Subset: ****14**** framework types, 1114 instances**
**A ****diagonal**** value of 100 refers to perfect prediction. **
**Stratified 10-fold cross-validation**

**   ****a   b   c   d   e   f    g   h   i    j   k   l   m   n   <-- classified**
** ****100**** ****0   0   0   0   0   0   0   0   0   0   0   0   0****  |   a = CHA**
**  **** ****0****  ****85****  ****5****   ****0****   ****5****   ****0   0   0   0   0   0   0****  **** 5****   0****  |   b = EDI**
**   ****0   0**** ****100**** ****0   0   0   0   0   0   0   0   0   0   0****  |   c = FAU**
**   ****0   ****3 ****  0****  ****91 **** ****0   0   0   0   0   0   ****3****   0   0   0****  |   d = FER**
**   ****0   0   ****7****   0****  ****70****  ****0   ****7   4****   0   0   ****4****   0   ****7  **** 0****  |   e = GIS**
**   ****0   0   0   0   0**** ****100**** ****0   0   0   0   0   0   0   0****  |   f = HEU**
**   ****0   0   0   0   ****5 ****  0****  ****90****  ****0   ****5****   0   0   0   0   0****  |   g = KFI**
**   ****0   0   0   0   ****3****   0   0**** **** 97****  ****0   0   0   0   0   0****  |   h = LAU**
**   ****0   0   0   0   0   0   0   0**** ****100**** ****0   0   0   0   0****  |   i = LTA**
**   ****0   0   0   0   0   0   0   0   0**** ****100**** ****0   0   0   0****  |   j = LTL**
**   ****0   0   0   0   0   0   0   0   0   0**** ****100**** ****0   0   0****  |   k = MFI**
**   ****0   0   0   0   0   0   0   0   0   0   0**** ****100**** ****0   0****  |   l = MOR**
**   ****0   0   0   0   0   0   0   0   0   0   0   0**** ****100**** ****0****  |   m = NAT**
**   ****0   0   0   0   0   0   0   0   0   0   0   0   0**** ****100****|   n = RHO**

## Performance of the ZSP model

**Performance of the ZSP model**

| dataset | dataset-1 | dataset-2 | dataset-3 | dataset-4 |
| --- | --- | --- | --- | --- |
| instances/class, x | x ≥5 | x ≥10 | x ≥20 | x ≥65 |
| classes | 40 | 21 | 14 | 6 |
| total instances | 1334 | 1215 | 1114 | 900 |
| OOB | 0.032±0.002 | 0.021±0.001 | 0.019±0.001 | 0.003±0.001 |
| accuracy (%) | 97.0±0.1 | 98.6±0.1 | 98.5±0.1 | 100.0±0.1 |

## Conclusions

**New implementation of the Zeolite-Structure-Predictor is designed based on framework types and novel topological descriptors.**
**The Zeolite-Structure-Predictor** **can be used to classify zeolites with high accuracy. The performance depends on the data set size.**
**The machine learning classification can be used as an alternative to the conventional framework classification, but it is more robust to errors than the latter.**
**This methodology can be applied for classifying other inorganic crystals.**