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

Abstract

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.

Structural diversity of six metal–organic frameworks from a rigid bisimidazole ligand and their adsorption of organic dyes

“…3d). 13 For the mean planes of these three layers are parallel and coincident, we can see that along the a axis there still exist 1D open channels, which are occupied by the uncoordinated DMF molecules (Fig. 3e).…”

A Theoretical Schema for Building Weavings of Nets via Colored Tilings of Two‐Dimensional Spaces and Some Simple Polyhedral, Planar and Three‐Periodic Examples

“…The weaving in Figure (f) is more commonly reported in MOFs . However both weavings have been observed in MOFs . As an aside, we comment on a recent preprint, in which the author suggests that the simplest weavings of a pair of (6,3) nets is a more twisted version than those deduced here.…”

“…Escher's weaving emerges as the lowest transitivity pattern. The weaving in Figure (f) is more commonly reported in MOFs . However both weavings have been observed in MOFs .…”

Isotopy classes for 3-periodic net embeddings

“…(ii) A more sophisticated operation which has been used for the classification of coordination polymers replaces each minimal ring of edges by a node (barycentrically placed) and adds an edge between a pair of such nodes if their minimal rings are entangled. In this way one arrives at the Hopf ring net (HRN) of an embedded net N (Alexandrov et al, 2012(Alexandrov et al, , 2017. This is usually well defined as a (possibly improper) linear 3-periodic net and it has proven to be an effective discriminator in the taxonomic analysis of crystals and coordination polymer databases.…”

“…We note here some natural entanglement invariants of Borromean type. In fact the embedded nets of dimension type {3; 2} have been rather thoroughly identified by Carlucci et al (2014), Alexandrov et al (2017) where it is shown that subdimensional 2-periodic components can be catenated or woven in diverse ways.…”