The Foster-Boys or Pipek-Mezey localization approaches can be used to effectively localize the MOs. For all computations presented here, we use the Foster-Boys approach, following the work of Riplinger et al. Localizing molecular orbitals reduces the number of "strongly correlated pairs" of molecular orbitals ij from O(N 2 ) to O(N ). In this context, we define "significantly correlated pairs" to be pairs that need to be treated with MP2 or a higher level of correlation. Otherwise, a dipole estimate vant triplets is also linear scaling. For clarity, "semi-canonical MP2" is obtained by using the standard (canonical) MP2 energy expression, and the effect of off-diagonal LMO Fock matrix elements that would contribute in the case of non-canonical Hartree-Fock orbitals are neglected. In the case of canonical molecular orbitals, "semi-canonical MP2" is the exact MP2 energy. However, when localized molecular orbitals are used, the full MP2 energy requires an iterative solution.