  Strong/static electronic correlation mediates the emergence of remarkable
phases of matter, and underlies the exceptional reactivity properties in
transition metal-based catalysts. Modeling strongly correlated molecules and
solids calls for multi-reference Ans\"atze, which explicitly capture the
competition of energy scales characteristic of such systems. With the efficient
computational screening of correlated solids in mind, the ghost Gutzwiller
(gGut) Ansatz has been recently developed. This is a variational Ansatz which
can be formulated as a self-consistent embedding approach, describing the
system within a non-interacting, quasiparticle model, yet providing with
accurate spectra in both low and high energy regimes. Crucially, small
fragments of the system are identified as responsible for the strong
correlation, and are therefore enhanced by adding a set of auxiliary orbitals,
the ghosts. These capture many-body correlations through one-body fluctuations
and subsequent out-projection when computing physical observables. gGut has
been shown to accurately describe multi-orbital lattice models at modest
computational cost. In this work, we extend the gGut framework to strongly
correlated molecules. To adapt the gGut Ansatz for molecular calculations, we
address the fact that, unlike in the lattice model previously considered,
electronic interactions in molecules are not local. Hence, we explore a
hierarchy of approximations of increasing accuracy capturing interactions
between fragments and environment, and within the environment, and discuss how
these affect the embedding description of correlations in the whole molecule.
We will compare the accuracy of the gGut model with established methods to
capture strong correlation within active space formulations, and assess the
realistic use of this novel approximation to the theoretical description of
correlated molecular clusters.
