One early attempt at creating local-correlation algorithms was by Schütz, Hetzer, and Werner, who used LMOs and PAOs to implement a local version of MP2. In their work, they gave each occupied molecular orbital pair its own set of PAOs, taking advantage of the limited spatial overlap between LMOs and PAOs. The concept of giving every MO pair its own virtual space is a precursor to PNO (pair natural orbital) based algorithms. Werner and coworkers later extended the same framework to CCSD and CCSD(T) 77 methods. In these methods, a set of redundant, linearly-dependent PAOs is assigned to each LMO based on the spatial overlap of the PAO with the LMO. In our work, following Pinski, Riplinger, Valeev, and Neese, 34 the overlap is computed through a measure called the "differential overlap integral" (DOI).