Molecules Structure as Planar Graphs?

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Discussion Overview

The discussion revolves around the representation of organic molecules as planar graphs, exploring the reasons behind this phenomenon from a physical chemistry perspective. Participants examine the implications of molecular structure on graph representation, considering both theoretical and practical aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that almost all organic molecules can be represented as planar graphs, questioning the underlying reasons for this characteristic.
  • Others point out that while many organic molecules can be simplified to 2D representations, their actual structures are three-dimensional, as illustrated by examples like ethane.
  • A participant references Kuratowski's theorem, suggesting that non-planarity in organic molecules requires a high degree of interconnectedness, which is uncommon in most organic structures.
  • There is mention of specific molecules, such as adamantane, which challenge the notion of planar representation, with some arguing that it can be drawn flat while others disagree.
  • Participants discuss the criteria for defining which organic molecules are considered, raising questions about the scope of the discussion, such as whether it includes all organic molecules with a CAS number or only those with a limited number of carbon atoms.
  • Some express uncertainty about the chemical explanations for planar representations, suggesting that the issue may not be strictly chemical in nature.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the planar representation of organic molecules, with no consensus reached on the conditions under which non-planarity occurs or the implications of specific examples like adamantane.

Contextual Notes

Participants highlight the complexity of defining the scope of organic molecules and the potential for exceptions to the generalization of planar representation. The discussion also touches on the distinction between topological and geometric representations of molecular structures.

LarryS
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I have read that the structure of almost all organic molecules can be represented visually as Planar Graphs, i.e. 2-dimensional lattice-like structures consisting of nodes (points) connected by lines in which no lines cross. From the perspective of Physical Chemistry, does anybody know why this is so? Some graphs are of such complexity that they required 3 dimensions to guarantee that no lines cross - reference "3 Utilities Puzzle".
 
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mathman said:
https://www.google.com/search?q=eth...PLNdKwsAT85oDYCg&ved=0CC8QsAQ&biw=943&bih=672

It is a simplification for showing on a sheet of paper. The above shows that something as simple as ethane has a three dimensional structure.

Yes, actually, I was referring to the "simplification for showing on a sheet of paper" rather than to the structure in real 3D space. For most organic molecules, it is possible to represent the topological relationship of the atoms and their connections via covalent bonds on a 2D "surface" - on a plane or on a sphere. From what I have read, organic chemists do not know why this is so.
 
Because most organic molecules do not have the degree of interconnectedness required to be non-planar.

Kuratowski's theorem says that every nonplanar graph contains either a topological K5 or a topological K3,3. In other words, for an organic molecule to be non-planar, you have to either have:

1. Five carbon atoms such that there is a chain (of bonds and atoms) from each one to each of the others, with none of these 10 chains sharing any bonds or atoms with any of the others; or:

2. Two sets of atoms of valence 3 or more, such that there is a chain from each atom in the first set to each atom in the second set, with none of these 9 chains sharing any bonds or atoms with any of the others.

To satisfy either of these conditions, you need a lot of high-order carbons and a lot of different paths between them. That would require a large and highly interconnected molecule. But it's by no means beyond the realm of possibility, and I have to imagine that some proteins, with their abundant disulfide interconnections, are non-planar (containing K3,3). It also seems like some people have synthesized non-planar molecules intentionally: see this article, for example.

EDIT: After posting I found this article which discusses the issue further. The author seems to have a bit of confusion between nonplanarity and knottedness (you can have a knotted molecule that has a planar graph), but apart from that the analysis seems good.
 
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Adamantane comes to mind as a molecule for which this does not appear to be true.
 
Of course there are molecules where this is not true, e.g. adamantane.
The problem with this kind of question is which metric to use:
All organic molecules with a CAS number? All possible organic molecules with, say, up to 100 C atoms?
 
referframe said:
I have read that the structure of almost all organic molecules can be represented visually as Planar Graphs, i.e. 2-dimensional lattice-like structures consisting of nodes (points) connected by lines in which no lines cross. Does anybody know why this is so? Is it due to the properties of covalent bonds?

There is a grain of truth in that, while I think I can imagine some examples of molecules that we won't be able to reproduce this way, most molecules I can think of are "topologically flat" (with all possible disclaimers about them being in fact 3d).

No idea about explanations. And I am not convinced they are strictly chemical.

Ygggdrasil said:
Adamantane comes to mind as a molecule for which this does not appear to be true.

DrDu said:
Of course there are molecules where this is not true, e.g. adamantane.

Sorry guys, that's incorrect. Adamantan can be drawn flat - hint.
 
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Borek said:
Sorry guys, that's incorrect. Adamantan can be drawn flat - hint.

Gotcha! It is K4, not K5.
 

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