Computer crystallochemical analysis: an...

Computer crystallochemical analysis: an overview

Vladislav A. Blatov Samara State University, Samara, Russia

1000 km

Samara

Moscow

http://upload.wikimedia.org/wikipedia/commons/f/f2/Raketa_Samara.jpg

Main ideas

• We are at a new stage of crystal chemistry development• Computers can do much more in crystal chemistry than you suppose• Crystallographic data contain much more information than you think

Crystal chemistry => chemical composition vs. crystal structure

Content

1. Why listen to this lecture? 2. Why crystallochemical analysis?

3. Why computer crystallochemical analysis? 4. History of crystallochemical analysis

5. General principles of computer crystallochemical analysis 6. Models

7. Data 8. Algorithms

9. Results 10. Outlook

Why listen to this lecture?Diamond

Platon CrystalMaker

…

Do you know any general crystallochemical

law?

What should crystallochemical analysis do?

crystallochemical = stereochemical

=> local parameters

crystallochemical => global parameters

(i)

analysis of chemical interactions in crystals crystallochemical analysis

(ii)analysis of the crystal architecture built by

chemical interactions

crystallochemical

analysis

Crystal chemistry => chemical composition vs. crystal structure

Why computer crystallochemical analysis?

CSD 500000 entries

ICSD 100000 entries

CrystMet 100000 entries

PCD 180000 entries

Crystallochemical laws / regularities


Subjectivity Objectivity

Content






History of crystallochemical analysis

Observational phenomenological

stage

Kepler's

tract “The six-cornered snowflake", 1611

Steno’s law of constancy of dihedral angles, 1669

Haüy’s

law of rational relations, 1784

http://en.wikipedia.org/wiki/File:Niels_stensen.jpg

http://en.wikipedia.org/wiki/File:Johannes_Kepler_1610.jpg

http://en.wikipedia.org/wiki/File:Ambroise_Tardieu42.jpg


Observational phenomenological

stage

E. Mitscherlich

–

isomorphism, 1819

E. Mitscherlich

–

polymorphism, 1822

Crystallochemical

phenomena!

http://upload.wikimedia.org/wikipedia/commons/3/30/Eilhard_Mitscherlich.jpg


Mathematical fundamentals

J. Hessel, 1830 –

32 geometric crystal classes

A. Bravais, 1848 –

14 three-periodic lattices

E. Fedorov

& A. Schönflies, 1890 –

230 space groups

http://en.wikipedia.org/wiki/File:Bravais2.gif

http://upload.wikimedia.org/wikipedia/commons/9/9a/Jewgraf_Stepanowitsch_Fjodorow.jpg


Microscopic observations

M. Laue, 1912 –

diffraction of X-rays in crystals

W.G. Bragg and W.L. Bragg, 1913 –

first structure

determinations

http://upload.wikimedia.org/wikipedia/commons/6/6f/Bundesarchiv_Bild_183-U0205-502%2C_Max_von_Laue.jpg


Experimental technique and methods of X-ray analysis

1920s –

1960sPhotomethods

and technique

First printed manuals on crystal structuresFirst really crystallochemical laws –(L. Pauling, V. Goldschmidt, A. Kitaigorodskii)A.F. Wells, 1954 –

graph representation

http://en.wikipedia.org/wiki/File:Pauling.jpg

http://en.wikipedia.org/wiki/File:Victorgoldschmidt0006MA8633570-0001.jpg


Time of automated diffractometers

1960s –

present time

Rapid accumulation of experimental data

Now the number of determined crystal structures exceeds 600,000 and grows faster and faster

http://algol.fis.uc.pt:8080/CEMDRX/equipment/pictures-of-equipment/kappa_apex_2.jpg/image_view_fullscreen


Time of electronic crystal structure databases

1970s –

present time

Death of printed handbooks (Structurbericht,

Structure Reports)

Appearance of CSD, ICSD, CrystMet, PDB

http://www.google.ru/imgres?imgurl=http://lib-rar.com/images/knigi.jpg&imgrefurl=http://lib-rar.com/newlibrary.html&usg=__yOpohIuANkfEbyvLSnFYL_JNhXw=&h=395&w=537&sz=48&hl=ru&start=1&um=1&itbs=1&tbnid=lmvQcnqhHVgg4M:&tbnh=97&tbnw=132&prev=/images%3Fq%3D%25D0%259A%25D0%25BD%25D0%25B8%25D0%25B3%25D0%25B0%26um%3D1%26hl%3Dru%26newwindow%3D1%26tbs%3Disch:1


Creating mathematical methods, computer algorithms and programs for automated crystallochemical

analysis of the electronic crystal structure databases

1990s –

present timeApplications:

crystal design, crystal engineering, nanochemistry, supramolecular

chemistry and other modern trends in materials science


General crystallochemical laws "composition –

structure –

property"

2010s (?) –

future time

Applications: creating new crystals and materials

The discoverers are sitting here (?)

Content






General principles of computer crystallochemical analysis

1.

Use only reliable structure data (cell dimensions, space group, atomic coordinates). Be careful with modeling data!

2.

Only structure data are the basis for mathematical models. The models should be quite simple and universal to process structures of different composition and complexity.

General principles of computer crystallochemical analysis

3.

All basic concepts of the models must be strictly defined. The concepts have to be clear to computer that has much more formal logic than a man!

4.

The data analysis must be formalized as well.

5.

The crystallochemical computer programs have to be able to analyze the whole available experimental information.

6.

No information should be ignored!

Content






Models: Lattice

Hexagonal lattice Atom coordinates C1 0.00000 0.00000 0.00000 Space Group: P6/mmm Cell Dimensions a=1.0000 b=1.0000 c=10.0000 =90.00 =90.00 =120.00

Crystallographic, not crystallochemical model

Models: Net

Inherently crystallochemical, but no geometrical properties are analyzed

Models: Labeled quotient graph

Chung, S.J., Hahn, Th. & Klee, W.E. (1984). Acta Cryst. A40, 42-50.

h.c.p. 3D graphVertices & edges of the labeled quotient graph

Labeled quotient graph

Models: Embedded net

Diamond (dia) net in the most symmetrical embedding

Models: Polyhedral subdivision

Voronoi-Dirichlet polyhedron and partition: bcu

net

Kd

=0.5


Physical meaning of Voronoi-Dirichlet polyhedra

Parameter Meaning

Volume, Å3 Relative size of atom or molecule in the crystal field

Rsd , ÅGeneralized crystallochemical atomic/molecular radius

i Strength of atomic/molecular interaction

Nf Number of atoms/molecules in contact


Tilings: dia

and bcu

nets

dia bcu

‘Normal’

crystal chemistry ‘dual’

crystal chemistry

Content






Data: Electronic crystallographic databases

CSD 500000 entries

ICSD 100000 entries

CrystMet 100000 entries

Pearson’s Crystal Data

180000 entries

Data: Electronic crystallochemical databases

RCSR 1764

entries; http://rcsr.anu.edu.au

TTD Collection 71067 entries; http://www.topos.ssu.samara.ru

TTO Collection 9006

entries; http://www.topos.ssu.samara.ru

Atlas of Zeolite Frameworks, 194

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

Data: Electronic databases of hypothetical nets

EPINET 14532 entries; http://epinet.anu.edu.au/

Atlas of Prospective Zeolite Frameworks 5,389,407

entries;

http://www.hypotheticalzeolites.net/

Content






Algorithms: requirements

universality rigour

automation

Algorithms: Searching for errors in crystal data

Parameters to be checked:

-

interatomic distances, bond or dihedral angles - VDP volume

-

VDP second moment of inertia -

atomic coordination number

-

dimensionality of complex groups

Algorithms: building adjacency matrix

Method of intersecting spheres

For inorganic compounds

Method of spherical sectors

For organic, inorganic and metal-organic compounds

Distances For all types of compounds, using atomic radii and Voronoi polyhedra

Solid Angles For artificial nets, intermetallides, noble gases, using Voronoi polyhedra

Van der

Waals Specific Valence Valence Valence

Algorithms: building adjacency matrix

Solid angle of a VDP face is proportional to the bond strength

Algorithms: building Voronoi polyhedra

Very fast 'gift wrapping' algorithm (Preparata

& Shamos, 1985) of computing a convex hull for a set of image points with coordinates (2xi

/Ri2, 2yi

/Ri2, 2zi

/Ri2),

where (xi

, yi

, zi

) are the Cartesian coordinates of the surrounding atoms, and Ri

is the distance from the VDP atom to the ith

neighboring atom.

Initial structure Image points Convex hull Structure & VDP

Algorithms: structure representations

Complete representation

(all bonds, all atoms)

Partial representations(not all bonds)

Partial representations(not all atoms)

Partial representations(not all bonds, not all atoms)


complete representation partial representation

benzene


complete representation partial representations

Ice VIII


Diaqua-bis(glycolato)-Mn(II) Complete representation

Standard partial representation

Standard simplified representation (vcn; 7/3/o11)


2-Butyne-1,4-diol Complete representation

Standard partial representation

Standard simplified representation (dia)

Valence bonds

Van der Waals bonds

Hydrogen bonds

Weights


Weighted colored labeled quotient graph


Clustering bonds in -CaSO4

> 10.5% sma

> 14.0% qtz

> 24.5%

I II

Atom roles: origin (OA), removed (RA), contracted (CA), target (TA)

Contracted atom Target atoms Origin: U, Cu, P; Removed: water molecules Contracted: phosphate oxygens

Target: P

Cu[UO2

PO4

]2

12H2

O



(i) {All atoms}={Atoms}+{Pseudo-atoms} (ii) {OA}{RA}=; {OA}{CA}=, {RA}{CA}=

(iii) {TA}{OA} (iv) {OA}{RA}{CA}={All atoms}

(v) {OA} (vi) {TA}

{CA}

{OA}+{RA}+{CA}+{TA} = collection = structure representation


{A, B}={All atoms} Collections ({OA},{RA},{CA},{TA}):

(i) ({A}, {B}, , ), the subnet of A atoms; (ii) ({A}, , {B}, {A}), the net of A atoms with the A–B–A

bridges (B atoms are spacers); (iii) ({B}, {A}, , ); (iv) ({B}, , {A}, {B}) are the same

nets of B atoms. There are four representations of this structure at a

given level of bond strength.

Example: a binary compound An

Bm

1. Coordination sequence (CS)

2. Extended point

symbol (ES)

3. Vertex symbol (VS)

Determining net topology

Ni: 6 20 42 74 114 164 222 290 366 452As: 6 18 42 74 114 162 222 290 366 450Ni: 4.4.4.4.4.4.4.4.4.4.4.4.64

.64

.64

As: 4.4.4.4.4.4.42

.42

.42

.68

.68

.68

.68

.68

.68

Ni: 4.4.4.4.4.4.4.4.4.4.4.4.*.*.*As: 4.4.4.4.4.4.42

.42

.42

.64

.64

.64

.64

.64

.64

NiAs

Topological type: nia

RCSR 1764 entries http://rcsr.anu.edu.au/

EPINET 14532 entrieshttp://epinet.anu.edu.au/

TTD Collection 71067 entrieshttp://www.topos.ssu.samara.ru

TOPOS

ADS program

Shell graph SGn (N); n shells, N atoms + origin, N=Ni ; i=1-n

SG1 (4) SG2 (16) SG3 (40)

SG4 (82) SG5 (146)

Diamond, dia

Degree of similarity D=n:N

Algorithms: determining net topology

Algorithms: ambient isotopic nets

Polythreading, 1D+1D1D Polycatenation, 2D+2D3D

Interpenetration, 3D+3D3D Self-catenation

Algorithms: link types

Hopf non-Hopf Multiknot Threading

Algorithms: tilings

Weak ring

Catenated

rings Crossing rings

Essential rings

Algorithms: tilings

Zeolite IMF, 19 kinds of tiles, 16 topological types

Shell graph SGn (N); n shells, N atoms + origin, N=Ni ; i=1-n

SG1 (4) SG2 (16) SG3 (40)

SG4 (82) SG5 (146)

Diamond, dia

Algorithms: nanoclusters 1. Primary nanoclusters

Algorithms: nanoclusters 2. Highest symmetry and homogeneity

Zn4, 96gZn3, 48fZn1, 16c Zn2, 16d

Zr, 8b

ZrZn22

Samson S. (1961) Acta Cryst. 14,

1229

Ilyushin G.D., Blatov V.A. (2009)

Acta Cryst. B65, 300

Algorithms: nanoclusters 3. Highest coordination number

Zn4, 12Zn3, 12Zn1, 12 Zn2, 14

Zr, 16

ZrZn22

Samson S. (1961) Acta Cryst. 14,

1229

Ilyushin G.D., Blatov V.A. (2009)

Acta Cryst. B65, 300

Algorithms: nanoclusters 4. Nanoclusters do not interpenetrate

β-Mg2

Al3

: five fused 61-atom 2-shell nanoclusters

centers 1st

shell 2nd

shell

β-Mg2

Al3

: complete constructing with two kinds of 2-shell nanoclusters

Algorithms: nanoclusters 5. Nanoclusters include all atoms of the structure

centers 1st

shell 2nd

shell

Algorithms: nanoclusters 6. Parsimony (Ockham’s Razor) principle

β-Mg2

Al3

: 44 possible nanocluster models

Mg9(2) Al14(2)Mg9(1) Al14(2) Mg3(1) ZA1(8a)(3) Mg9(1) ZA2(16d)(2)ZA1(8a)(3) Mg9(1) ZA2(16d)(1)Mg9(2) ZA2(16d)(1) Al14(2)ZA1(8a)(1) Mg9(2) Al14(2)…

Algorithms: nanoclusters 7. Primary nanoclusters and supraclusters

β-Mg2

Al3

: supracluster AB2

consisting of three primary nanoclusters

61-atom nanocluster A

63-atom nanocluster B

Algorithms: nanoclusters 8. Underlying net

β-Mg2

Al3

: underlying net AB2

of the topology of the Laves phase MgCu2

Algorithms: nanoclusters 9. Self-assembly

Assembling supraclusters

to the Laves phase MgCu2

network

β-Mg2

Al3

Content






dia 41.9%

srs 7.6%

pcu 17.3%others

33.2%

Blatov, V. A., Carlucci, L., Ciani, G. &

Proserpio, D. M. (2004).

CrystEngComm, 6, 377-395.

301 Interpenetrating MOFs

Baburin, I. A., Blatov, V. A., Carlucci, L.,

Ciani, G. & Proserpio, D. M. (2005).

J. Solid State Chem. 178, 2452-2474.

144 Interpenetrating inorganic frameworks

dia 44.4%

srs 6.3%

pcu 18.8%

others 30.5%

Results: topological classification of nets

dia 20.7%

srs 6.4%

pcu 12.9%

others 60.0%

Ockwig, N. W., Delgado-Friedrichs, O., O'Keeffe, M. & Yaghi, O. M. (2005). Acc. Chem. Res. 38, 176-182.

1127 metal-organic frameworks

Uninodal Edge-transitive


Baburin, I. A., Blatov, V. A. (2007). Acta Cryst. B63, 791-802.

1551 organic frameworks

Uninodal Edge-transitive

dia 22.6%

sxd 6.3%

pcu 9.8%

others 61.3%



Valence-bonded metal-organic frameworks

dia

–

pcu

–

srs

Hydrogen-bonded single organic networks

dia –

pcu –

sxd –

hex

Hydrogen-bonded single metal- organic networks

pcu

–

bcu

–

hex –

dia

Hydrogen-bonded interpenetrated organic networks

dia –

cds –

lvt

Hydrogen-bonded interpenetrated metal-organic networks

pcu

–

dia –

cds

All the nets are uninodal, and all but cds, hex and sxd

are edge-transitive, all are high-symmetric

Results: relations between structures

284 My

(TO4

)z

(T=Si, Ge, P, As, S, Se, Cl, Br, I)

quasi-binary representation My

[T]z

({M,T}, , {O}, {T})

50% My

(TO4

)z

correspond to binary compounds (NaCl, NiAs, FeB, -Al2

O3

, etc.)

Ilyushin

G.D., Blatov, V. A., Zakutkin

Yu.A.

(2004). Z. Krislallogr. 219, 468-478.

Results: tilings

Results: Topological types of intermetallics

ICSD~ 125000 entries

CRYSTMET~ 30000 entries

Pearson’s Crystal Data~ 105000 entries

TOPOS database on intermetallics ~ 22545 entries

Topological types of intermetallics ~ 3000 entries

Type Number %f.c.c. 3008 13.3b.c.c. 2480 11.0MgCu2 1678 7.4h.c.p. 875 3.9CuZn3 781 3.5

Results: finite fragments in crystals

49-atom cluster

in Ag17

Mg44

Cambridge Cluster Database

Results: finite fragments in crystals

R4

M42

606 structures

R6

M44

84 structures

R8

M78

16 structures

Cu4 Cd3 , Fe11 Zn40 , Ir4 Mg29 , Na6 Tl

Results: constancy of atomic volume in crystals

‘…the volume of the domain of an atom of a definite chemical type at a fixed oxidation state, electronic configuration, and type of neighbouring atoms is

almost constant in different structures.’ Blatov, V.A. and Serezhkin, V.N. (2000)

Voronoi polyhedra in tens of thousands structures

Summary and outlook

Local properties Stereochemistry

Global properties Crystal chemistry

Summary and outlook

Crystal chemistry

Crystal chemistry

Thanks for your attention!

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