We used our data set to benchmark the quality of the mechanical embedding and the polarizable mechanical embedding schemes for estimating the the reference QM/MM coupling energy at the electrostatic embedding level, calculated using the LIO code. The data was analyzed by performing correlation plots and, to better visualize the results, the probability density was estimated through kernel density estimation (KDE), as implemented in the scipy 72 library. Equations ( ) and (5) were evaluated using all avail-able sets of charges obtained in vacuo for each structure. In a practical implementation, this atomic charges would be predicted by a ML method. In our case, such atomic atomic charges were obtained by actual QM methods (Hirshfeld, CM5 and MBIS charges were obtained from ANI-1x, and the other ones were calculated in this work). To highlight the aim of this work in assessing ML/MM embeddings we will denote the electrostatic coupling energies as E ME(or ME+P) ML/MM . In the case of the polarizable mechanical embedding (equation ( )), one faces a similar problem than in the case of atomic partial charges, that is the lack of a unique well-defined atomic polarizability. While the molecular polarizability is well defined as a tensor that refers to how the system responds to an externally applied electric field, atomic polarizabilities require the introduction of some partitioning scheme and are computationally very expensive to obtain. In this work, instead of using specific sets of atomic polarizabilities for each structure, we employed two sets of fixed atomic polarizabilities: The first one is based on the recommended values of static scalar dipole polarizabilities for neutral atoms, denoted as {α Z }. The second set is derived from atom type fitted isotropic polarizabilities, denoted as {α AT }. The atomic polarizabilities for each element and its atom types is summarized in Table .