The Foster-Boys or Pipek-Mezey methods can be used to compute the unitary transformation matrix U . In this work, we use the Foster-Boys approach for all of our computations, following the work of Riplinger et al. and our previous work. We call the transformed set of active occupied molecular orbitals LMOs, or local molecular orbitals. In the DLPNO-CCSD algorithm, pairs of LMOs are classified as "dipole pairs," "semi-canonical MP2 pairs," "weak pairs," and "strong pairs"; these pairs are divided based on a series of pre-screening steps. The reader is referred to the work of Valeev, Neese, and coworkers and our previous work for a more comprehensive overview of the pair prescreening procedures. In the DLPNO-(T) algorithm, triplets (i, j, k) are determined from strong and weak pairs, so the number of relevant triplets also shows linear scaling. For more details on the triplet prescreening procedure performed in DLPNO-(T), the reader is referred to our previous work on DLPNO-CCSD(T). 2. Projected Atomic Orbitals (PAOs)