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The Hubbard model provides an idealized description of electroniccorrelations in solids. Despite its simplicity, the model features acompetition between several different phases that have made it one of the moststudied systems in theoretical physics. Real materials usually deviate from theideal of the Hubbard model in several ways, but the monolayer of Nb$_3$Cl$_8$has recently appeared as a potentially optimal candidate for the realization ofsuch a single-orbital Hubbard model. Here we show how this single orbitalHubbard model can be indeed constructed within a "molecular" rather than atomicbasis set using ab initio constrained random phase approximation calculations.This way, we provide the essential ingredients to connect experimental realitywith ab initio material descriptions and correlated electron theory, whichclarifies that monolayer Nb$_3$Cl$_8$ is a Mott insulator with a gap of about 1to 1.2eV depending on its dielectric environment. By comparing with anatomistic three-orbital model, we show that the single molecular orbitaldescription is indeed adequate. We furthermore comment on the expectedelectronic and magnetic structure of the compound and show that the Mottinsulating state survives in the low-temperature and bulk phases of thematerial.

Nb$_3$Cl$_8$: A Prototypical Layered Mott-Hubbard Insulator