I guess some theoretical chemistry basics omitted in the short article wouldn't hurt:
In order to describe chemical reactions or atomic arrangements in terms of wave equations one normally treats the motion of the nuclei (slow/heavy) and the motion of the electrons (fast/light) separately simplifying the Schrödinger equation to the Born-Oppenheimer approximation.
In introductory chemistry textbooks [0] a diatomic example is mostly used as an illustration, for >2 atoms usually only the ground state is considered. This is because (1) in a diatomic setting the vibrational degree of freedom in the nucleus reduces to 1 and (2) the ground state can be well distinguished from other electronic states.
However when studying (advanced theoretical) chemistry or material sciences, polyatomic arrangement with tightly packed electronic states and a lot of nuclear degrees of freedom are the norm and the theory of so-called conical intersection of electronic energies essential in that regard.
Early on this was taken into account as the Jahn-Teller distortion[1]: a kind of spontaneous symmetry-breaking which seemed exotic when it was first described in the 1930s; in that same vein Teller later proposed an ultrarare occurrence within a few vibrational periods (sub-femtoseconds) by which a loss of electronic excitation was not followed by a photon being emitted: radiationless decay. Now, in refined orbital models [2] this seems to be a normal state of affairs e.g. in organic chemistry.[3]
Because of the tiny time scales involved theoretically predicted phenomena like a Geometrical phase/Berry phase (which itself has the Foucault pendulum in relation to Earth's latitude as its mechanical analogue [4]) have not been observed, yet. So borrowing from a topological analogue (Dirac points) [5] a quantum simulation seemed feasible.
To be honest the actual paper [6] linked in the article was hard to follow through so I found a similar paper [7] where the presentation of the general idea is more clear and concise.
[0]https://chem.libretexts.org/Courses/Pacific_Union_College/Qu...
[1]https://en.m.wikipedia.org/wiki/Jahn%E2%80%93Teller_effect
[2]https://core.ac.uk/download/pdf/9426023.pdf
[3]https://en.m.wikipedia.org/wiki/Quenching_(fluorescence)
[4]https://en.m.wikipedia.org/wiki/Geometric_phase#Foucault_pen...
[5]https://condensedconcepts.blogspot.com/2015/08/conical-inter...
[6]https://arxiv.org/pdf/2211.07320.pdf
[7]https://arxiv.org/pdf/2211.07319.pdf