  The Hubbard model provides an idealized description of electronic
correlations in solids. Despite its simplicity, the model features a
competition between several different phases that have made it one of the most
studied systems in theoretical physics. Real materials usually deviate from the
ideal 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 of
such a single-orbital Hubbard model. Here we show how this single orbital
Hubbard model can be indeed constructed within a "molecular" rather than atomic
basis set using ab initio constrained random phase approximation calculations.
This way, we provide the essential ingredients to connect experimental reality
with ab initio material descriptions and correlated electron theory, which
clarifies that monolayer Nb$_3$Cl$_8$ is a Mott insulator with a gap of about 1
to 1.2eV depending on its dielectric environment. By comparing with an
atomistic three-orbital model, we show that the single molecular orbital
description is indeed adequate. We furthermore comment on the expected
electronic and magnetic structure of the compound and show that the Mott
insulating state survives in the low-temperature and bulk phases of the
material.
