where t ab ij represents the doubles amplitudes, and u ab ij is defined as 2t ab ij -t ba ij . The amplitudes used in the pair density can computed using canonical virtual orbitals, PAOs, or an initially larger PNO space. Neese et al. initially used MP2 10 amplitudes computed in the canonical virtual orbital space when computing the pair density to form PNOs. This, however, adds the O(N 5 ) scaling of canonical MP2 to the method to LPNO-CEPA and LPNO-CCSD methods, and ERI transformations remain expensive from this approach. This issue was solved when Neese et al. introduced the "cascaded" approach to their LPNO methodology, that allows the formation of the pair density in the sparse PAO basis, allowing the computation of PNOs and corresponding ERI transformations at linear-scaling cost. This union of PAO and PNO forms the basis of the DLPNO family of algorithms. In DLPNO-CCSD, semicanonical MP2 amplitudes (so-called since off-diagonal LMO Fock matrix contributions are neglected), are used to form the PAO pair density, which is diagonalized to form the PNOs of pair ij.