  Model Hamiltonians are regularly derived from first-principles data to
describe correlated matter. However, the standard methods for this contain a
number of largely unexplored approximations. For a strongly correlated impurity
model system, here we carefully compare a standard downfolding technique with
the best possible ground-truth estimates for charge-neutral excited state
energies and wavefunctions using state-of-the-art first-principles many-body
wave function approaches. To this end, we use the vanadocene molecule and
analyze all downfolding aspects, including the Hamiltonian form, target basis,
double counting correction, and Coulomb interaction screening models. We find
that the choice of target-space basis functions emerges as a key factor for the
quality of the downfolded results, while orbital-dependent double counting
correction diminishes the quality. Background screening to the Coulomb
interaction matrix elements primarily affects crystal-field excitations. Our
benchmark uncovers the relative importance of each downfolding step and offers
insights into the potential accuracy of minimal downfolded model Hamiltonians
