TIL from article: (Dyson) orbitals can be seen with scanning tunneling microscope, that's how they didn't have to use their imagination (with regards to topology)
> 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 which the orbital undergoes a 180-degree half-twist per loop.
I choose to believe that Hückel was not the one who characterized or discovered the trivial case, but instead a disliked graduate student who was once insulted at a party as "emotionally, intellectually, and topologically trivial", and it just cascaded from there into naming things after him.
https://arxiv.org/abs/2507.03516
https://research.ibm.com/blog/half-mobius-molecule
TIL from article: (Dyson) orbitals can be seen with scanning tunneling microscope, that's how they didn't have to use their imagination (with regards to topology)
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 which the orbital undergoes a 180-degree half-twist per loop.
I choose to believe that Hückel was not the one who characterized or discovered the trivial case, but instead a disliked graduate student who was once insulted at a party as "emotionally, intellectually, and topologically trivial", and it just cascaded from there into naming things after him.
Don't try to convince me otherwise.
One of the smallest sculptures in the universe.
klein bottle molecule?