This is a recently published[1] (hypothetical) molecule which has such unusual properties that I cannot resist sharing it with you. It is an annulene with 144 all-cis CH groups, being a (very) much larger cousin of (also hypothetical) systems mooted in 2009[2],[3].
A 144-carbon annulene. Click for 3D.
One fascinating novel aspect of Berger’s work is that he identifies that such helical systems will exhibit a distinct anapolar ring current structure in a constant and homogeneous magnetic field, perpendicular to the main molecular plane. Such anapolar magnetism is distinctly different from the dipolar (diatropic) ring currents normally associated with aromatic molecules, and with the current interest in the magnetic properties of graphene-like objects (see also this blog post and also the helical metal wire) such molecules can only help to excite our imaginations.
I also show one of the more stable molecular orbitals for the [144]-annulene (ωB97XD/6-31G(d,p) calculation).‡ Molecular art indeed!
MO 461. Click for 3D.
If you go to the Knotplot site, there you will find a torus link of form (2,18), which displays as the below. Look familiar? Notice the chirality is opposite however!
‡Orbitals for smaller rings with such form can be found here.
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Unfortunatly, I missed some previous work on Henry's related systems when I published that... sad!
But there are some more fascinating aspects I discovered after publication. For instance imagine you expand from ((CH)8)18 - this one- to ((CH)8)n and approach infinity with n. given all of those are minma on the pes you end up with a straight helix. Now this helix has a periodicity of 8 CH units, which would be a structural isomer to the "normal helical polyacetylene" which shows seemingly unrational periodicities between 8 and 9. This is somehow a funny kind of isomerism, though its only a "Gedankenexperiment".
This may be entirely unconnected, but a few years back, I looked at helical carbon (i.e. no hydrogen atoms). A small unit of cyclic C22 can be made to loop back over itself over a distance of about 8-9 atoms. It thus adopts the shape of a Bernoulli lemniscate (in 3D).
The molecular orbitals of this system are also pretty wacky!
Also not in direct reply, but fascinating: When you lookup "magnetic field in toroidal solenoid" you find that the induced field increases going from the outer to the inner side of the torus-rod. And exactly according to that the chemical shieldings in (CH)144 for 1H and 13C behave like.
Molecular conjugated systems resemble current circuits, but you do not need a power supply, you simply put them into some even static magnetic fields!
There is (I have found out) an extensive literature on helical polyacetylene. One article that caught my eye (there are many) is this one: Two-Dimensional Surface Chirality Control by Solvent-Induced Helicity Inversion of a Helical Polyacetylene on Graphite; DOI: 10.1021/ja061238b. These polymers can be prepared as a single chiral enantiomer (which can be characterised by Electronic circular dichroism), and this article reports a helicity inversion induced by solvent. I find that pretty neat!
I would be interested in an ACID plot of the system. Its something I discovered also only recently, but I think for displaying conjugation its even better suited than the current plots, which are strongly dependent of the relative orientation of mag. field and molecule.
The [144] annulene is a 4n, n=36 electron closed shell system. If ρ( r) is in fact a torus link (even numbered linking number Lk in units of π) then it should not be what would conventionally described as aromatic. In fact, the bond lengths around the ring do not alternate much, which suggests that it is in fact delocalised (and hence by one criterion aromatic). But in truth, I do not suppose that the Hückel 4n+2/4n rules that are normally used in these circumstances have ever been tested for such large annulenes with so many electrons.
It might transpire that such anapolar systems are in a class of their own when it comes to describing their aromaticity! It is not every day that a truly new form of aromaticity is discovered.
So yes, the ACID plot would indeed be interesting. As would eg the properties of a dication or dianion of the [144] annulene.
When I remember correctly, upon adding or subtracting 2 electrons the scf does not converge anymore. The orbital energies are quite dense already (and/or the geometry is not stable anymore).
ps. The lemniscate is incredibly fascinating!
It seems as if Raphael and I are conducting an open science investigation here (something perhaps easier to do on a blog than in a conventional medium?). I gave the dication a go, and the result can be inspected at this digital repository link. It seems that the bond alternation increases, from ~1.39/1.42Å to 1.36/1.44 (ωB97XD/6-31G(d,p) level to allow for dispersion to develop) when two electrons are removed from helical [144]-annulene (in C18 symmetry). It returns to ~1.39/1.42 when four electrons are removed. So two electrons do seem to have a big effect (given that the system has 144 π-like electrons in total).
Would be a hint at a 4n-pi rule? The currents I integrated were quite large, both para and diatropic ones about double of what you have in benzene. But then HOMO and LUMO are a1 and a2, and for an "aromat" wouldnt you expect to have some degenerate HOMO and LUMO?
In Möbius systems, the degeneracies are only approximate, and do not arise from group theory (this arises because of the finite width of the band, and there are only degeneracies if the band is a wire of zero thickness).
There are many planar π-systems which sustain both para and diatropic ring currents, often in a concentric manner, and so it would be no surprise to find both types in a helical system (although the term concentric might have to be modified).
Perhaps a comparison of the ring currents for the neutral 144-electron system with the dicationic 142-electron system might be interesting?