A molecule with half-Möbius topology • Hacker News Board

Re: A molecule with half-Möbius topology

#11

Post by gus_massa » Sun, May 17, 2026, 6:09 PM UTC

stringfood wrote: post #5

klein bottle molecule?

No, imagine a licorine candy https://www.google.com/search?q=licorice+candy&tbm=isch but the cross section is a +.

(It's easier if you get one that is not twisted. Something like https://www.sugarrushlane.com/products/filled-red-licorice-s... but with 4 instead of 5 parts. Also imagine each of the 4 parts has a different color. )

Now make a circle with it.

If you don't twist it, you get an horizontal surface that looks like a thick border of a circle, and a vertical surface that looks like the round wall of a cylinder.

If you twist half a turn, when you connect the extremes the top of the + in one extreme is glued to the bottom of the + in the other extreme. Something similar withe the left and right parts of the +. Now you have two overlapped copies of a Möbious strip, each perpendicular to the other.

If you twist a quarter of a turn, when you connect the extremes the top of the + goes to the right, the right to the bottom, the bottom to the left an the left to the top. So you get only one "strip?"

Re: A molecule with half-Möbius topology

#12

Post by lupire » Sun, May 17, 2026, 11:29 PM UTC

gus_massa wrote: post #11

stringfood wrote: post #5

klein bottle molecule?

No, imagine a licorine candy https://www.google.com/search?q=licorice+candy&tbm=isch but the cross section is a +. (It's easier if you get one that is not twisted. Something like https://www.sugarrushlane.com/products/filled-red-licorice-s... but with 4 instead of 5 parts. Also imagine each of the 4 parts has a different color. ) Now make a circle with it. If you don't twist it, you get an horizontal surface that loo…

Note that the colors are important. You need a discrete structure with N rotational segments and a turn of 1/M. Otherwise any rational turn size will have have multiple Mobius strips.

Re: A molecule with half-Möbius topology

#13

Post by lupire » Sun, May 17, 2026, 11:49 PM UTC

vi_sextus_vi wrote: post #8

addaon wrote: post #4

From Wikipedia: > The Half-Möbius electronic topology is a form of quantum topology in molecular science in which the π-orbital basis of a cyclic molecule undergoes a 90-degree phase twist per revolution around the ring, requiring four complete circuits to return to its starting phase. This is distinct from both the topologically trivial (Hückel) case, in which no net twist occurs, and the classical Möbius case, in w…

https://research.ibm.com/blog/half-mobius-molecule describes the quantum-software-hardware co-design concept IBM is selling with that paper It took my pea brain a while.. is this a joke or meant to teach something.. & I still don't get it. Is the punch line "this is the first paper to name the concept Hueckel-orbitals", even planting their flag on Wikipedia to piss on a dead man? That's a deep dismissal of Leo Gross…

PP was just making a dumb joke. The Hückel topology is topologically trivial but chemically interesting. https://en.wikipedia.org/wiki/M%C3%B6bius%E2%80%93H%C3%BCcke...