The decay, and consequently the sparsity, in the one-electron reduced density matrix (1-RDM) can also be exploited. As the distance between the centroids of atomic orbitals (AOs) increases, the magnitude of the 1-RDM decreases, allowing us to re-express ∆P µν in terms of ∆P µν,µ∈ν . However, it is important to note that since the decay of the AO 1-RDM is much slower than that of the transformation matrix due to the highly localized nature of the fragments, the benefit gained from this approximation will be minimal unless the system size is very large.