We, as chemists, do not use quaternions enough!

]]>Perhaps systems with half-helical turns (as required) can only be constructed if the restriction of all cis-alkenes is supplemented with some trans-motifs?

Some examples of (4n π-electron) molecules with odd linking numbers can be found in this article, but these contain trans as well as cis alkene bonds. This table also includes the NICS(0) value, which indicates that they are all diamagnetic (and hence what we refer to as aromatic). By the way, the systems of D5 and D7 symmetry were not stable minima; the latter for example was a transition state for bond shifting. But this might just be because it is so small, and a larger ring may behave differently.

]]>http://www.chem.helsinki.fi/~berger ]]>

Another thing: Dealing all the time with Hamitonians we forget about the other big discovery of the congenial Irish mathmatician, the quaternions!

There is something called “Quaternionenmaschine” in German. It shows nicely how to do the book keeping right about turns and twists.

We need odd powers of “k”. And k = ji =ji.

To generate a system with an odd (in units of 1π) linking number, it has become clear that we need to build a system with an half-integer number of helical turns (in units of 2π). Such a system would sustain a **torus knot** in the π-electron density, and this cannot be represented with just a single MO; one needs to add two MOs to do this.

Building such a model is the challenge for your coordinate building skills Raphael!

I have worked out the linking numbers for the two molecules we are considering here, namely SELQUW and HIYTAL. To show the associated 3D coordinate model, I need to put up another post, since I have not figured out how to make such models display in the window of a comment, such as this one.

]]>How is that possible?

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