whereby T ij ab = 2T ij ab T ij ba are the contravariant amplitudes, constructed from the T ij ab wave function amplitudes, which weight excitations from a pair of occupied orbitals ij to a pair of virtual orbitals ab. When using canonical orbitals (see Eq. ( )), it is di cult to reduce the computational e↵ort associated with the electron repulsion integrals (ERIs) K ij ab (Eq. ( )). However, if the occupied orbitals are unitarily transformed to localized molecular orbitals (LMOs), only a subset of pair energies are required. Those can be obtained from various localization procedures like Foster-Boys, Pipek-Mezey or as intrinsic bond orbitals (IBOs). In such a representation, only when an occupied electronic orbital i is in the vicinity of j does one need to (accurately) calculate its value, as electronic correlation rapidly decays with the interelectronic distance.