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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btw there is also a "Gaussian" type b3lyp in Turbomole, the Gaussian version apparently uses the VWN(III) while Turbomole uses VWN(V). Seems that there are some different versions of the Vosko-Wilk-Nussair correlation functional around.
Here the b97-d with dispersion on:
dist 3 c -- 11 c = 2.6530 au = 140.39 pm
dist 5 c -- 6 c = 2.6530 au = 140.39 pm
dist 16 c -- 18 c = 2.6530 au = 140.39 pm
dist 22 c -- 23 c = 2.6530 au = 140.39 pm
dist 1 c -- 2 c = 2.6535 au = 140.41 pm
dist 1 c -- 4 c = 2.6535 au = 140.41 pm
dist 8 c -- 9 c = 2.6534 au = 140.41 pm
dist 10 c -- 12 c = 2.6534 au = 140.41 pm
dist 15 c -- 17 c = 2.6534 au = 140.41 pm
dist 19 c -- 20 c = 2.6535 au = 140.41 pm
dist 20 c -- 21 c = 2.6535 au = 140.41 pm
dist 25 c -- 26 c = 2.6534 au = 140.41 pm
dist 7 c -- 8 c = 2.6554 au = 140.52 pm
dist 12 c -- 13 c = 2.6554 au = 140.52 pm
dist 14 c -- 15 c = 2.6554 au = 140.52 pm
dist 24 c -- 25 c = 2.6554 au = 140.52 pm
dist 6 c -- 7 c = 2.6558 au = 140.54 pm
dist 11 c -- 14 c = 2.6558 au = 140.54 pm
dist 13 c -- 16 c = 2.6558 au = 140.54 pm
dist 23 c -- 24 c = 2.6558 au = 140.54 pm
dist 9 c -- 10 c = 2.6759 au = 141.60 pm
dist 17 c -- 26 c = 2.6759 au = 141.60 pm
dist 2 c -- 3 c = 2.6765 au = 141.63 pm
dist 4 c -- 5 c = 2.6765 au = 141.63 pm
dist 18 c -- 19 c = 2.6765 au = 141.63 pm
dist 21 c -- 22 c = 2.6765 au = 141.63 pm
I mentioned earlier try another calibration for a [38] nonaphyrin, for which an X-ray is known. The experimental difference in the meso bond lengths was measured as Δ0.014Å. RHF gets Δ0.115, and B3LYP is Δ0.012Å.
To this I can now add a B97D/6-311G(d,p) calculation (doi: m9.figshare.156033) giving 0.007 as the bond alternation (averaged over 6 meso-positions). This is about half the experimental (x-ray) value. So up to about 38 electrons, I think this method (and B86?) are under-estimating the degree of bond alternation. Molecule HIYTAL, a [46] electron system, is rather bigger, and at the limit of what might be calculated, but its worth a go I think. After that, we might tentatively be in a position to extrapolate to 144 electrons! (?).
Molecule SELQUW I have noticed is a [56] dodecaphyrin which is actually smaller than the [46] decaphyrin HIYTAL. Both have helical winds related to the [144] annulene that started this discussion, and both are viable calculation candidates (but it will take a few days to optimise their geometries at the levels discussed here). So watch this space.