# Let’s Talk about MOFs—Topology and Terminology of Metal-Organic Frameworks and Why We Need Them

## Abstract

**:**

## 1. Introduction

## 2. Terminology—General Classification

#### 2.1. Controversy of Metal-Organic Framework versus Coordination Polymer

#### 2.2. Definitions in the IUPAC 2013 Recommendations

## 3. The IUPAC 2013 Recommendations Concerning Nets and Network Topologies

#### 3.1. Topology

**dia**), quartz (

**qtz**) or any other topology, see Figure 1.

**Figure 1.**Network topologies with four-connected branching points or vertices: (

**a**) The

**dia**-net based on the diamond structure; (

**b**) The chiral

**qtz**-net based on the quartz structure; (

**c**) The 2D

**sql**-net.

**dia**-net or the six-connected net based on primitive cubic packing, the

**pcu**-net in for example MOF-5, it is recommended to use freely available software. Two of these systems are continually updated, SYSTRE [14] that will give you the topology once you have decided about vertices and connectivity from your structure, and TOPOS [15,16] that have the possibility of a custom or a fully automated determination of the network topology as well as a complete structure analysis module.

- (1)
- Understand the structure of the materials you have prepared;
- (2)
- Compare your results to materials others have made;
- (3)
- Make your scientific communication more efficient;
- (4)
- Truly make something new by design.

#### 3.2. Topology Descriptors: The Point Symbol

**dia**and the

**qtz**net in Figure 1, they both have six-rings as the shortest ring. So then we can make the concept a bit more detailed and instead count all the shortest rings emanating from a vertex via the different links that it has, giving us three numbers for a three-connected vertex, six for a four-connected vertex and so on. This is a more useful code called the point symbol [19], and is written with the ring sizes in ascending order with the number of rings in superscript.

**dia**- and the

**qtz**-net as the former has point symbol 6

^{6}and the latter point symbol 6

^{4}8

^{2}.

#### 3.3. Topology Descriptors: The Vertex Symbol

**srs**-net, and the non-chiral

**ths**-net both have the point symbol 10

^{3}. We can then extend the concept and for each pair of links sticking out from a vertex calculate how many different ways we can construct these shortest rings. For a diamond net there are for example two different six-rings connecting each pair of links. This we call the vertex symbol [19], and we write this with subscripts for the number of possibilities and with multiplication dots in between each symbol. For

**srs**we get 10

_{5}·10

_{5}·10

_{5}and for

**ths**10

_{2}·10

_{4}·10

_{4}.

#### 3.4. Topology Descriptors: The Coordination Sequence

**lon**-net is very real and has identical point and vertex symbols as the

**dia**-net, 6

^{6}and 6

_{2}·6

_{2}·6

_{2}6

_{2}6

_{2}6

_{2}respectively, so how can we differentiate between them? The structural difference is that some of the six-rings are in boat rather than chair conformation, so that for clear cut cases, where the network of your structure is close to the ideal (most symmetric) form of one of the two nets they are quite easy to distinguish. But we need something we can compute and so turn to the coordination sequence which simply means that we grow the network from one point to its nearest neighbors and count how many these are. For the first point in a four-connected net these are obviously four, but for subsequent growth generations it gets complicated. Usually one computes these up to the 10th generation, sum up including generation 0, and report this as the td10 value. For the

**dia**- and

**lon**-nets this gives:

**dia:**1 + 4 + 12 + 24 + 42 + 64 + 92 + 124 + 162 + 204 + 252 = 981

**lon:**1 + 4 + 12 + 25 + 44 + 67 + 96 + 130 + 170 + 214 + 264 = 1027

**edq**and

**cdj**being one such exception [21].

## 4. A Measure of Complexity: Transitivity and Genus

#### The pqrs Numbers, the Transitivity Symbol

**dia**-net g = 3).

**Figure 2.**(

**a**) Fragment of the diamond net (

**dia**). Different tiles marked in red, purple and blue. (

**b**) Framework of two tiles; (

**c**) Framework of two tiles separated; (

**d**) Two tiles separated. This net has only one type of vertex (p), one type of edge (q) one type of face (r) and one type of tile (s), so it has the transitivity 1111.

**srs**-net, the 4-connected

**nbo**- and

**dia**-nets, the 6-connected

**pcu**-net, and the 8-connected

**bcu**-net. These five are in some sense the extended network analogues of the platonic bodies, the five polyhedra built from one kind of face and one kind of vertex.

## 5. The Space within, Dual Nets and Interpenetration

#### 5.1. Dual Nets

**Figure 3.**(

**a**) The

**pcu**net transitivity 1111 with its dual net that is an identical

**pcu**net (self-dual); (

**b**) The

**nbo**net in white, transitivity 1111, with its dual the

**bcu**net, also with transitivity 1111. Thus an identical net can easily interpenetrate the

**pcu**net, while this possibility is not obvious for

**nbo**or

**bcu**.

#### 5.2. Interpenetration

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix

_{4}O

_{4}-cubane based MOF forming a

**dia**-net [35].

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**MDPI and ACS Style**

Öhrström, L. Let’s Talk about MOFs—Topology and Terminology of Metal-Organic Frameworks and Why We Need Them. *Crystals* **2015**, *5*, 154-162.
https://doi.org/10.3390/cryst5010154

**AMA Style**

Öhrström L. Let’s Talk about MOFs—Topology and Terminology of Metal-Organic Frameworks and Why We Need Them. *Crystals*. 2015; 5(1):154-162.
https://doi.org/10.3390/cryst5010154

**Chicago/Turabian Style**

Öhrström, Lars. 2015. "Let’s Talk about MOFs—Topology and Terminology of Metal-Organic Frameworks and Why We Need Them" *Crystals* 5, no. 1: 154-162.
https://doi.org/10.3390/cryst5010154