Eugeny V. Alexandrov

Underlying nets in three-periodic coordination polymers: topology, taxonomy and prediction from a computer-aided analysis of the Cambridge Structural Database

We discuss a recently developed approach to formalize the analysis of extended architectures by successive simplifications of a crystal structure perceived as a periodic net. The approach has been implemented into the program package TOPOS that allows one to simplify and classify coordination polymers of any complexity in an automated mode. Using TOPOS, we retrieved 6620 3-periodic coordination polymers from the Cambridge Structural Database and represented them in a standard way as underlying nets. The topological classification of both 975 interpenetrating and 5645 single 3-periodic underlying nets has been performed and compared. The up-to-date methods for prediction of the topology of underlying nets are discussed and the ways to develop reticular chemistry are outlined.

A topological method for the classification of entanglements in crystal networks

A rigorous method is proposed to describe and classify the topology of entanglements between periodic networks if the links are of the Hopf type. The catenation pattern is unambiguously identified by a net of barycentres of catenating rings with edges corresponding to the Hopf links; this net is called the Hopf ring net. The Hopf ring net approach is compared with other methods of characterizing entanglements; a number of applications of this approach to various kinds of entanglement (interpenetration, polycatenation and self-catenation) both in modelled network arrays and in coordination networks are considered.

Topological Motifs in Cyanometallates: From Building Units to Three-Periodic Frameworks

This review focuses on topological features of three-periodic (framework) p, d, and f metal cyano complexes or cyanometallates, i.e. coordination compounds, where CN(-) ligands play the main structure-forming role. In addition, molecular, one-periodic (chain), and two-periodic (layer) cyanometallates are considered as possible building blocks of the three-periodic cyanometallates. All cyanometallates are treated as systems of nodes (mononuclear, polynuclear, or transitional metal cluster complexes) joined together via CN-containing spacers. The most typical nodes and spacers as well as methods of their connection are described and systematized. Particular attention is paid to the overall structural motifs in the three-periodic cyanometallates, especially to the relations between the local coordination (coordination figure) of structural units and the entire framework topology. The chemical factors are discussed that influence the cyanometallate topological properties due to modification of nodes, spacers, or coordination figures.

New knowledge and tools for crystal design: local coordination versus overall network topology and much more

The problem of predicting crystal structures is discussed in the context of artificial intelligence systems. The steps of creation of an expert system are considered as applied to crystal design, where the crucial step is the invention of new structure descriptors. A number of such descriptors proposed quite recently are listed; most of them characterize local coordination or overall topology of the structure network. An important part of the expert system is the knowledge database that contains correlations between the descriptors; it is used by a computer analyzer, the inference machine, to make a conclusion about the possibility of obtaining a particular structural motif. All the steps for developing the expert system are illustrated with the analysis of 811 cyanide complexes and examples of the structure prediction are given.

How 2-periodic coordination networks are interweaved: entanglement isomerism and polymorphism

The entanglements of 1319 2-periodic coordination polymers are examined and fully classified using the extended ring nets (ERNs) approach. The ERNs characterize the entanglement to the greatest detail ever achieved: all possible classes/types/modes of entanglements observed and reported in the literature so far result in 216 ERN topologically distinct modes of entanglements with 74% of all the structures falling into only 21 of them. We also introduce the notion of entanglement isomerism to designate the coordination polymers that have the same chemical composition, local and overall topology, but differ by their catenation patterns as mapped into their ERNs.

Topologically guided tuning of Zr-MOF pore structures for highly selective separation of C6 alkane isomers

As an alternative technology to energy intensive distillations, adsorptive separation by porous solids offers lower energy cost and higher efficiency. Herein we report a topology-directed design and synthesis of a series of Zr-based metal-organic frameworks with optimized pore structure for efficient separation of C6 alkane isomers, a critical step in the petroleum refining process to produce gasoline with high octane rating. Zr6O4(OH)4(bptc)3 adsorbs a large amount of n-hexane but excluding branched isomers. The n-hexane uptake is ~70% higher than that of a benchmark adsorbent, zeolite-5A. A derivative structure, Zr6O4(OH)8(H2O)4(abtc)2, is capable of discriminating all three C6 isomers and yielding a high separation factor for 3-methylpentane over 2,3-dimethylbutane. This property is critical for producing gasoline with further improved quality. Multicomponent breakthrough experiments provide a quantitative measure of the capability of these materials for separation of C6 alkane isomers. A detailed structural analysis reveals the unique topology, connectivity and relationship of these compounds.The separation of C6 alkane isomers is crucial to the petroleum refining industry, but the distillation methods in place are energy intensive. Here, the authors design a series of topologically-guided zirconium-based metal-organic frameworks with optimized pore structures for efficient C6 alkane isomer separations.

Distinguishing Metal-Organic Frameworks

We consider two metal–organic frameworks as identical if they share the same bond network respecting the atom types. An algorithm is presented that decides whether two metal–organic frameworks are the same. It is based on distinguishing structures by comparing a set of descriptors that is obtained from the bond network. We demonstrate our algorithm by analyzing the CoRe MOF database of DFT optimized structures with DDEC partial atomic charges using the program package ToposPro.

Interpenetration of three-periodic networks in crystal structures: Description and classification methods, geometrical-topological conditions of implementation

This review describes the current state of studies on the phenomenon of interpenetration of framework groups in crystal structures. The generally accepted terminology used in the description of topology of interpenetrating motifs, symmetric and topological properties of interpenetrating systems is given. The main advances of crystal chemistry in the systematization of interpenetrating structures are elucidated. It is noted that the major trend in the crystal chemistry of interpenetration is the development of methods for the topological classification of the entanglements of interpenetrating groups and the search for the regularities of their implementation in crystalline substances. The main ways of the formation of interpenetrating structures, the appearing here geometrical-topological restrictions, and also the effect of stereochemical factors and synthesis conditions on the possibility of interpenetration are considered.

Multilevel topological analysis in application to design of coordination networks

Topological methods of analysis of coordination networks have become an integral part of design of coordination polymers, MOFs, and zeolites. It helps to chemists to understand the novelty of findings, to reveal relations between different structures, to propose new design concepts, and to communicate effectively with each other. However, this is not the limit of the methods. Description of coordination environment of structural units (metal atoms, ligands, SBUs), network topology (topological type), and topology of entanglement (entanglement pattern) intrinsically leads to finding relations between the topological parameters. Further, the correlations can be grouped (systematized) in a hierarchical manner to produce a knowledge database for design and prediction of new materials (their structure and properties) [1, 2]. Thus, new structural characteristics, the so-called descriptors, have to be invented for prediction of particular structural features. For example, we have proposed to use topological type of Hopf ring net for analysis of topology entanglements in coordination networks. Now we put forward Extended ring net (ERN), which incorporates information about topology of entangled nets and topology of entanglements. ERN is able to distinguish patterns of entanglements up to isomorphism and polymorphism, that allowed us to describe new type of isomerism of coordination polymers, entanglement isomerism. MOF structures are usually considered as a result of assembly of secondary building units in an isoreticular manner. Usually SBU is considered as a topologically dense 0D polynuclear complex group, which coordination figure is predetermined by orientation of points of extension (functional groups of ligands connected by linkers). However, many practically important MOFs contain infinite SBUs; e.g. rod-shaped 1D {AlOH(CO2)2} groups are connected by benzene linkers in parallel fashion into framework MIL-53. We have produced a comprehensive systematics of infinite SBUs and ways for their connection with new algorithms of rod-MOFs description as 2D net of rods connections. Selection of correct structural groups is also important for design of self-catenated networks. We proposed a universal algorithm for selection of all reasonable subnets and determining the structure driving ones. To describe the geometry and topology of voids and channels in porous structures we combined topological methods and Voronoi partitioning. The improved Voronoi partitioning provides much more characteristics of porous structures, e.g. periodicity, topology and crystallographic orientation of channels, minimal cages of framework, open sights of metal atoms etc. These descriptors give us an opportunity to define metal-organic nanotube as a 1-periodic tiling of face-shared 3D tiles. To enhance the usability of the results of topological analysis we collected values of descriptors into a knowledge database [2]. The database was applied in finding relations between topological parameters for heterometallic coordination polymers based on {Cu(Me2mal)2} SBU (H2Me2mal = dimethylmalonic acid) [3]. The authors thank the Russian government (grant No. 14.B25.31.0005), Russian Science Foundation (grant No. 16-1310158), and Russian Ministry of Science for finantinal support. E.V.A. is gratefull to Russian Foundation for Basic Research (grant No. 16-37-00147). [1] Alexandrov, E.V. et al. (2015) Chem. Rev. 115, 12286-12319. rn[2] Alexandrov, E.V. et al. (2015) CrystEngComm., 17, 2913-2924. rn[3] Gogoleva, N. V. et al. (2016) Eur. J. Inorg. Chem., doi: 10.1002/ejic.201601047.