in which S is the overlap matrix of the non-orthogonal AO basis, as they are sufficiently close to the original AO basis. Other localization procedures can be explored as well, as long as they fulfill the condition of orthonormality. MI indices between AOs will provide a measure for locality of quantum correlations, however, it is overly fine-grained from a molecular perspective, for which full atoms are better suited as building blocks. Therefore, it is important to extend the MI index I ij from the orbital to the atomic picture. For this, one can define the full set of AOs associated with one particular atom as the subsystem, or block, of interest. Obviously, this is strongly dependent on the choice of basis set and can become prohibitively expensive for a large basis set, as the RDM of the 2-atom subsystem requires a computation that scales as a diatomic full Configuration Interaction for each individual charge-or particle number sector. To overcome this limitation we employed an intuitively effective approximation, which involves approximating the existing MI between atoms I AB by summing over all MI that exists between the constituent orbitals of those atoms. This can be expressed as