GTECS3D: A new Program for Graphtheoretical Evaluation of extended Network Structures

by Kevin Lamberts

Institute of Inorganic Chemistry, RWTH Aachen University, Landoltweg 1, Aachen 52074, Germany.
E-mail: kevin.lamberts@ac.rwth-aachen.de

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1. Introduction

Periodic network-structures were of high interest over the last decades [1] but are often difficult to characterize. Programs and databases like TOPOS [2] and RCSR [3] support a precise description and comparison of complex frameworks. The presented software GTECS3D is a new, straight-forward program which draws on graphtheoretical algorithms for automated structure simplification and features high-end graphical visualization output. Some of its powerful functions are shown on new bimetallic coordination networks based on Al(acacCN)3 [4] and its transmetalation product [5].

2. Startup and Initialization

Upon opening a cif-file with GTECS3D the structure is initialized, an adjacency matrix is calculated and some basic properties of the resulting graph are calculated and shown in the log-window:

> component 1 periodic: (-1,1,0),(1,1,0),(0,0,-1)
> 3-dimensional, determinant: 2
> 1 component found, extent: 3 x 3 x 2
> n=146 ; m=160 ; d=1 ; D=6

The above output is for the structure obtained by partial degradation of Al(acacCN)3 [4] and directly shows some properties of the network: One adjacent component was found, expanding infinitely in 3 dimensions (given by the three vectors). Its determinant is 2, which indicates a 2-fold interpenetration of the network. Additionally a minimum number of unit cells needed for comprehension of the topology is suggested, followed by some graph-theoretical properties which are namely:

n number of nodes
m number of edges
d minimal connectivity
D maximum connectivity

As the suggested number of visualized unit cells is 18 the first picture looks confusing.

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At this point the automated simplification algorithms are very useful. Removal of 1-connected nodes removes all dead ends of the net.

3. Simplification of the Network

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The result of the removal of 1-connected nodes is shown above. Highlighted in green is a 4-ring which is built by two Ag-centers bridged by two oxygen atoms. This ring can be contracted automatically to its center with another algorithm of GTECS3D. All 4-rings are found and their atoms are reduced to one node by retaining the connectivity to all other nodes. This results in the following network:

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The next step is often the reduction of 2-connected nodes, which in principle reduces linear bridging ligands to edges, connecting the metal centers. An additional colorization of the network shows the interpenetration of the two nets.

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As the network is now reduced to its underlying net with only 2 different nodes a calculation of topological indices is possible.

4. Topology Determination

For calculation of vertex- and point-symbol one has to distinguish between smallest rings and smallest cycles [6]. Whereas the latter can be used for the determination of the point-symbol and is calculated easily, the determination of rings can be time-consuming. Nevertheless, these functions are implemented in GTECS3D together with a calculation of the coordination sequence for all nodes. However, in the discussed network all smallest cycles are also smallest rings so that both algorithms yield the following, identical result:

> Ag1: 4(1) 4(1) 8(7) 8(7) 8(7) 8(7), CoordinationSequence: (1,4,10,24,42,64,90,124, 162,204,250, cum10=975)
> Mark1: 4(1) 4(1) 8(2) 8(2) 8(8) 8(8), CoordinationSequence: (1,4,10,24,42,64,92,124, 162,204,252, cum10=979)

Searching for these properties in the RCSR [3] shows that the network is known as ”pts-c” as shown in the picture below: A twofold interpenetrated PtS-network.

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Taken from: http://rcsr.anu.edu.au/nets/pts-c

5. Conclusions

Using the new program GTECS3D, network structures obtained from reactions of the building block Al(acacCN)3 with Ag-salts could be simplified and investigated concerning their topology. One network is known as ”pts-c”, other occuring nets are the uninodal 3-dimensional network from the transmetalation reaction shown at the top (vertex-symbol 4.6.6.6.6.62), a cubic structure with ”srs”-topology (105.105.105) and 2-dimensional nets with 63 and 4.82 topology. All networks can be simplified easily with GTECS3D which can be downloaded for free from:

www.gtecs.rwth-aachen.de

References

[1] Issue: The pervasive chemistry of metal-organic frameworks. Chem. Soc. Rev. 5, 2009.
[2] V. A. Blatov. IUCr Comp. Comm. Newsletter 7, 2006, 4.
[3] M. O’Keeffe, M. A. Peskov, S. J. Ramsden and O. M. Yaghi. Accts. Chem. Res. 41, 2008, 1782.
[4] C. Merkens, N. Becker, K. Lamberts and U. Englert. Dalton Trans. 41, 2012, 8594.
[5] A. D. Burrows, K. Cassar, M. F. Mahon and J. E. Warren. Dalton Trans. 24, 2007, 2499.
[6] V. A. Blatov, M. O’Keeffe and D. M. Proserpio. Cryst. Eng. Comm. 12, 2010, 44.

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