Hubbard dimer physics and the magnetostructural transition in the correlated cluster material Nb$_3$Cl$_8$

We present a combined computational and experimental study of Nb$_3$Cl$_8$, a correlated layered material containing Nb trimers, through the lens of competing intra- and intercluster interactions. Different proposed explanations for its magnetostructural transition such as charge disproportionation, antiferromagnetic quenching, and interlayer singlet formation are investigated in light of the various reported low-temperature structures. Our findings rule out the previously proposed charge-disproportionation, suggest an intricate interplay between Mott physics and the formation of interlayer singlets, and also hint at a possible explanation of the observed intratrimer scissoring distortion. We suggest that the physics of Nb$_3$Cl$_8$ should be understood in the context of weakly coupled Hubbard dimers.