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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As a helical system, the [144] annulene would be expected to have an optical rotation. Using the modern version of the theory introduced by Kirkwood (see here), and using ωB97XD/6-31G(d,p), [α]589 and [α]880 can be obtained as -209088° and +73952° respectively (for the P-helical form). In other words the ORD (optical rotatory dispersion) is enormously varying with wavelength.
I suspect there are many sources of error for this calculation, but nevertheless, these numbers are startlingly large!
I have (re)optimized the [((CH)8)18]2+ (how to get the indices here?) at B-P/SV(P) level in D18, without dispersion correction (for consistency with my previous calculations). I find bond lengths almost equal in size between 1.399 and 1.401 Angströms (LES frequency analysis is running). Then I found a spectacularly large magnetically induced ring current: in toal 49 nA/T (57 diatropic and -8 nA/T paratropic, thereof). I dare say that is world record for a pure hydrocarbon. For comparison in ((CH)8)18 its 15 nA/T in total (30 diatropic and -15 nA paratropic). My results hint at an extremely strong aromaticity for 4n+2. At the moment I have no explanation for the disagreement with Henry's results from the ωB97XD/6-31G(d,p) calculation. Can it be only dispersion? I continue checking my results.
The only other explanation is a different electron occupancy? Or that one or the other is not a stable minimum in D18 symmetry. I too am doing a frequency calculation for the 2+ system, and we can compare results. It might also be that single-ζ basis sets over-symmetrize? Thus hydrogen bonds in such a basis are often placed in a single-well rather than a double-well potential?
Normally, if one changes an electron count by 2 in such a system, the diatropic/paratropic ring currents invert (see for example 10.1021/ol703129z) so this system is unusual no matter how it emerges!
If the bond length result of 1.399/1.401 for the bonds in the di-cation is the true answer, then that also would be intriguing. Shaik has argued that the distortivity of π-electrons means that in planar annulenes, the bonds should start to become unequal/alternate at about 26 electrons or greater. Here we would be seeing no such effect at 142 electrons! Perhaps the helical twist has attenuated the distortivity?
Orbital occ. is ok. 1006 electrons. The 14 highest occ. orbitals are of e type, lumo is a1. total energy is -5567.87560 in (CH)8)18 it is 5568.230915. For the ((CH)8)18 most results from SV(P) were very close to TZVP ones, I cannot remember principal differences. freq still running ...
btw. isn't sv(p) double zeta?
The neutral system is actually _very_ paramagnetic with 15 nA/T paratropic current (something I probably could not gauge in the original work, because the 30 nA diatropic currents are also huge). In total it is of course diamangnetic since its closed shell, like rectangular cyclobutadiene, which is in total also diamagnetic but shows large paratropic currents and is an anti-aromat like ((CH)8)18).
It seems the 4n+2 and 4n rules are fullfilled, however the current in the dication is huge and the shieldings in ((CH8)18)2+ are also extreme. I will report these values soon.
On this last point then, if we could keep the 144 electrons (=4n) but switch the topology of the electron density from a torus link to a torus knot (by adding one extra C(+) atom say) then we should get a huge diatropic rather an paratropic current!
Yes, I would expect that. Btw. Rob is interested! I am awaiting exteremly excited coordinates for [(((CH)9)17)]-, or would you expect any troubles from an anion? I would go for 9-fold periodicity since the "normal polyacetylenes" as I mentioned above are between 8 and 9, and 7 might be too much strain.
Sorry, I have missunderstoos your last question. At the moment I do not fully understand the influence of the topology on the direction of the currents. All I see is that 4n+2 is aromatic and 4n is anti-aromatic. So I simply would go for the odd-twist-Möbius system and give it 4n+2 electrons.
I think 4n is anti-aromatic for even (zero) twists, and aromatic for odd twists. Conversely, 4n+2 is aromatic for even (zero) twists and anti-aromatic for odd twists. So I think the interesting one would be a 4n electron system with odd twists.
I agree, 9 is better than 7, but I think the difference may mostly impact upon the dispersion interactions. Also, anions need better basis sets than cations!