Topological Crystal Chemistry : nets and entanglements in periodic structures

Topological Crystal Chemistry : nets and entanglements in periodic structures L. Carlucci, G. Ciani and D. M. Proserpio DCSSI, Università degli studi di Milano Milano - Italy V.A. Blatov Samara State University Samara - Russia

early 90 Crystal Engineering Crystal Design Infinite Polymeric Frameworks Coordination Polymers Organic/Inorganic Hybrid Materials Metal Organic Frameworks Inorganic Chemistry (solid state) Supramolecular Architectures

Coordination Polymers/Networks - Metal-Organic Frameworks MOF and Supramolecular networks node Ligand or H-bond... or weaker interactions... Different frameworks could be obtained on changing the coordination/h-bond geometry of the nodes...

Metal ions: Ag, Cu, Ni, Co, Zn, Cd coordination number and geometry M M M M M Ligands donors: N, O, P, S bi/polidentate neutral/anionic Lenght rigidity/flexibility

Simplifications: Keep only atoms with cooordination > 2 Nodes/Vertex of the Net N Simplification of polydentate groups with centres of the same coordination N N O N

Three ways of drawing a feldspars the most abundant minerals in the earth s crust M[(Si/Al) 4 O 8 ], e.g. albite, Na(Si 3 AlO 8 ), orthoclase, K(Si 3 AlO 8 ), anorthite, Ca(Si 2 Al 2 O 8 ). ball and stick polyhedra net From the framework of alumino-silicates removing -T-O-T-, we get a net (here 4-coordinated graph), and so for minerals, zeolites, all classic solid-state chemistry

A Net, as used in solid state chemistry, is a n-periodic connected simple graph n-periodic (n=1,2,3) = has translational symmetry in n-independent directions connected = there is a continuous path between every pair of vertices simple = contains only simple edges 2-p 2D 3-p 3D 2-p 3D

Periodic Structures and Crystal Chemistry n-periodic Structures Structures (as nets) that have translational symmetry in exactly n independent directions. Any crystalline material is a 3D ordered arrangement of atoms (any crystal is a 3D supramolecular entity) depending on the interactions considered we may see chains 1-periodic, layers 2-periodic or 3-periodic netwoks

Interactions Covalent Ionic Coordination H-bond van der Waals CH... O CH... π π... π theoretical

MOF structures reported in the CSD (Cambridge Structural Database) Doubling time 3.6 yrs compared with 9.3 yrs for all CSD! # of structures in CSD nov 2010 531715

...end of the nineties 1998 IF 4.0 2000 IF 4.3 Crystal Engineering / Crystal Design Infinite Polymeric Frameworks Coordination Polymers Organic/Inorganic Hybrid Materials Metal Organic Frameworks Supramolecular Architectures

Topological Crystal Chemistry : nets and entanglements in periodic structures

simplification and rationalization... Topology is the theory of shapes which are allowed to stretch, compress, flex and bend, but without tearing or gluing 2-p p 2D honeycomb layer 6 3 -hexagonal brick wall parquet

DIAMOND and diamondoid net

SbCl 3 (p-diacetylbenzene)

Topological Crystal Chemistry : nets and entanglements in periodic structures

Cuprite Cu 2 O Niggli 1922

interpenetration of diamondoid nets

Crystallographic observation: all interpenetrated nets are generated from one independent atom What are the symmetry relations among the interpenetrated sub-nets? Can we find a systematic way to classify all the possible 3D interpenetration phenomena? YES using TOPOS.

Structure consists of 3D framework with C There are 2 interpenetrating nets FIV: Full interpenetration vectors ---------------------------------- [0,1,0] (1.15A) [0,0,1] (1.15A) [1,0,0] (1.15A) ---------------------------------- (...) Class I Z=2

Class I Nets related by translation only

Class I Nets related only by translation Class III Nets related only by non-translational symmetry elements Class III I Nets related by translational and non-translational symmetry elements

diamondoid nets BF 4 - ClO 4 - PF 6 - - AsF 6 - SbF 6 - CF 3 SO 3 NC-(CH 2 ) 2 -CN 1,4-butanedinitrile succinonitrile diam 5f diam 5f diam 5f diam 5f diam 5f diam 4f

[Ag(1,4-butanedinitrile) 2 ](X) X= BF 4-, ClO 4-, PF 6-, AsF 6-, SbF - 6 Diamondoid-5f 26-29 x 21-23 21-23

[Ag(1,4-butanedinitrile) 2 ](X) X= BF 4-, ClO 4-, PF 6-, AsF 6-, SbF - 6 Diamondoid-5f 26-29 x 21-23 21-23 related by Translations Class I

Class III Nets related only by non-translational symmetry elements

4 1 dia 4-fold 4 related by screw axis 4 1 Class II

Class IIII Nets related by translational AND non-translational symmetry elements

[ZnL 2 ](ClO 4 ) 2 (1996/2002) dia 6-fold6 related by translation AND non-translational sym. op. Class III

306 cit. 114 cit.

world records of Interpenetration Approx. 1000 structures are interpenetrated 2000 11-fold dia H-bond 2002 10-fold dia CP (Ia) 2005 18-fold srs H-bond (IIIb) 2008 12-fold dia/ths CP (IIIa) 2009 18-fold dia H-bond (IIIb) 2011 54-fold srs CP (IIIb)

and now what? Can we show that, within the same number and kind of interpenetrated sub-nets, are they topologically equivalent? all dia 2-fold are equivalent (isomorphous)? dia 2fold class I can be transformed to class II??

Ring links ------------------------------------------------------ Cycle 1 Cycle 2 Chain Cross Link Hopf Mult ------------------------------------------------------ 6a 6a inf. 1 1 * 6 ------------------------------------------------------

The resulting single net (green dotted lines) represent the netof-catenated-links and is independent of the symmetry/space group. Q: dia 2fold class Ia can be transformed to class IIa?? A: YES, for 52 known cases! only one example is different (6-c hxg net)

and the difference for is due to extra crossings : 3 vs. 1 Ring links ------------------------------------------------------ Cycle 1 Cycle 2 Chain Cross Link Hopf Mult ------------------------------------------------------ 6a 6a inf. 1 1 * 2 6a 6b inf. 1 1 * 4 6b 6a inf. 1 1 * 4 6b 6b inf. 1 1 * 6 ------------------------------------------------------

and the difference is detected also by Knotplot

Dia 4 fold From 38 cases in 5 classes Only 2 distinct topological types

Coordination polymers Supramolecular networks Metal-organic frameworks Polycatenation Topological self-catenation Interpenetration Borromean entanglements Euclidean Polythreading A new complexity of the solid state

quoted more than 900 times

Geometrical requirement for Inextricable Entanglement Topological Entanglement Euclidean Entanglement

[Cd 2 (bpethy) 3 ](NO 3 ) 4 2D // 2D 2D-3f N C C N Interpenetration 6 3

[Cd 2 (bpethy) 3 ](NO 3 ) 4 2D // 2D 2D-3f DEKQOZ, DEKQUZ Interpenetration Interpenetration

Can we entangle 1D or 2D nets in a different way (topological)? Interpenetration vs. Polycatenation

1D Ladders + Hopf Links 1D 1D 2fold 2007 1D 1D 2D 2004 1D // 1D 2D 1997

1D Ladders + Hopf Links dimensionality unchanged dimensionality changed 1D 1D 2fold 2007 1D 1D 2D 2004 1D // 1D 2D 1997

1D Ladders + Hopf Links Double ladders 1D // 1D 3D (2006)

dimensionality unchanged Inextricable Entanglement via Hopf links 1D + 1D 2D/3D 2D parallel 2D 2D inclined 3D 3D 3D increase of dimensionality Interpenetration Polycatenation Topological Entanglement

inclined polycatenation 3D [Cu 2 (pyz) 3 ](SiF 6 ) Zaworotko group, 1994 [Ag 2 (H 2 L) 3 (cucurbituril) 3 ](NO 3 ) 8 K. Kim group, 1997 hexagonal (6 3 ) layers, hcb

2D parallel polycatenation 3D [Cu(bpethe) 1.5 (PPh 3 )](PF 6 ) S.W. Keller group, 2001 undulated hexagonal (6 3 ) layers

Inextricable Entanglement via Hopf links dimensionality unchanged: INTERPENETRATION 1D+1D 1D 2D+2D (parallel) 2D 3D+3D 3D components 1D, 2D or 3D the whole is an infinite periodic architecture kd+ kd kd md+nd kd m k; n < k increase of dimensionality: POLYCATENATION 0D+0D 1D, 2D or 3D 0D+1D 1D, 2D or 3D 0D+2D 2D or 3D 0D+3D 3D 1D+1D 2D or 3D 1D+2D 2D or 3D 1D+3D 3D 2D+2D (inclined) 3D 2D+2D (parallel) 3D 2D+3D 3D components 0D, 1D, 2D or 3D the whole has the SAME dimensionality of the components the number of entangled components is finite (n-fold) each component is interlaced with ALL the others the whole has HIGHER dimensionality of at least one component the number of entangled components is infinite at least one component is not interlaced with all the others

Topological Entanglement Interpenetration Polycatenation

Borromean links

2D // 2D 2D Borromean layers? (6 3 ) [Cu 2 (tmeda) 2 {Au(CN) 2 } 3 ](ClO 4 ) D.B. Leznoff et al., IC 2001 [{Ni(cyclam)} 3 (TCPEB)] 2 M. P. Suh et al., IC 2003 [K(K.2.2.2)]I(1,8-diiodoperfluorooctane) 1.5 I... I - P. Metrangolo et al., CG&D 2003

3-Borromean layers 2D // 2D 2D

2D // 2D 2D NOT interpenetrated nor catenated Borromean Entanglements

n-borromean networks? [Ag 2 (H 2 L) 3 ](NO 3 ) 2 M.L. Tong et al., Angew 1999 [Ag 2 L 3 (OH)](ClO 4 ) S. Muthu et al., Dalton 2002

2D // 2D... Borromean (6 3 ) undulated layers...

2D // 2D 3D n-borromean 3D 1D network chain...

2010 16 Borromean entanglement 7 3D 9 2D

Topological Entanglement Interpenetration Polycatenation self-catenation Borromean entanglements

smallest threfoil square knot of 24 nodes on pcu net self-catenation (Links): "shortest rings" catenated by other "shortest rings" of the same net

Self-catenation (Polyknotting or Self-penetration) some of the rings are linked as in a chain (Hopf links) 3-coordinated 12 3 -twt (12 4. 12 7. 12 7 )

[Ag(2-ethylpyrazine) 2 ] SbF 6 catenated 8-rings Coesite SiO 2 Binodal (4 2. 6 3. 8) (4 2. 6. 8 2. 9) VS: (4. 6. 4. 6. 8. 9. 7 2 )(4. 8. 4. 9 7. 6. 8) N N 4. 8 2

6 10 -fnu (4 8.6 7 )-msw (4 8.6 6.8)- rob (4 2.6.8 2.9)(4 2.6 3.8)- coe 12 3 -twt

Graph isomorphic but non-ambient isotopic nets 3D 2-periodic

3D 3-periodic

Stephen Hyde group

The 3-chain gives a new 1D polymer?...

TOPOS Polycatenation Topological self-catenation Interpenetration Borromean entanglements Euclidean Polythreading A new complexity of the solid state