# What is a topological isomer?

I'm working on a project where I have to understand the concept of topological isomer. I found a review or two containing the idea but I couldn't find a book or a detailed description of what a topological isomer is. I would like a suggestion for a book, article or other resource that gives me a clear definition (Wikipedia doesn't do a good job either). Or I would like someone to give me a clear description of what a topological isomer is.

• Wikipedia has a page on topoisomers May 18 '17 at 9:43

"Isomers" are compounds that are equivalent but for a certain change in structural property. There's different types of isomers depending on which sort of structural property you need to change in order to inter-convert the two molecules.

• Structural isomers are equivalent in their atomic makeup but differ based on their chemical connectivity. For example, 1-propanol and 2-propanol are structural isomers - they share the same formula ($\ce{C3H8O}$) but differ in how those atoms are connected. You can change one to the other by rearranging how the atoms are connected to each other.

• Stereoisomers are identical in chemical makeup and connectivity, but differ in the spatial orientation of their atoms. There's several different subtypes, which vary based on what sort of change to the molecules can interconvert them.

• E-Z isomers can be interconverted by a theoretical rotation around a double bond - something that normally doesn't happen.
• Optical isomers can be interconverted by mirroring the molecule (again, something that doesn't happen)
• Diastereomers can be interconverted by mirroring the arrangement around a certain subset of atoms.
• Conformational isomers are like stereoisomers, but with the distinction that they differ based on changes which do happen under normal conditions. For example, by a rotation around a single bond, or by the umbrella-like inversion of a nitrogen. Different conformational isomers are normally not isolatable from each other, as they rapidly interconvert.

• There's a subset of these isomers called atropisomers which would otherwise be interconvertable, but local conditions (e.g. steric hinderance) means that the interconversion is slow under standard conditions, such that the different isomeric forms can be isolated from each other.

Okay, that brings us to your question on topological isomers. These are conceptually very closely related to conformational isomers and atropisomers. Like conformational isomers, topological isomers are equivalent in chemical formula, connectivity, and even the normal stereochemical properties like E-Z and R-S designations. However, like atopisomers - and unlike most standard conformational isomers - two different topological isomers cannot interconvert on an appreciable timescale, and thus each isomer can be isolated from the other. But unlike atropisomers, the difference between two topoisomers is not due to rotation around a single bond.

Instead, the difference between two different topoisomer is due to the different topology of the molecules. Topology is a somewhat complex mathematical topic, but for our purposes here, you can think of topology as a description about the invariant way something structured on a global scale, that can't be changed by bending, twisting, folding, etc.

For example, take a rubber band. No matter how you bend, twist, fold or tie the rubber band, it's still topologically the same. (That's part of the definition of "topology".) However, if you cut the rubber band, pass it through itself and reattach it, you can get something that's called a trefoil knot. If you look locally at the rubber band, all the connectivity is the same. There isn't any twists in the trefoil that couldn't also be present in the original circular band form. But on a global scale the trefoil and the band are very different. There's no way you can bend, fold, twist, tie, etc. the two to interconvert them without cutting. Because of this, we say the trefoil and the circular band are topologically distinct, in a way the circular band and a twisted form of a circular band aren't.

This is the difference that's being expressed in the case of topological chemical isomers. All of the local structure between the two is the same, but the large-scale global structure of the molecule is such that you cannot interconvert the two isomers without breaking bonds. You can't make one into the other simply by rotating a bond -- not even by rotating a bond that is energetically disfavorable to rotate.

• Do the optical isomers of something like hexahelicene count as topological isomers? Would make a good example if they do. May 19 '17 at 10:22