where h and V are the standard one-and two-electron integrals between the N orbitals, and c † µ c µ creates (annihilates) an electron in a local orbital (LO), ϕ µ . The LOs can be obtained from Foster-Boys localization method or using Intrinsic Atomic Orbitals (IAO), etc, and form an orthonormal basis. Suppose the HF solution of the Hamiltonian Ĥ is |Φ 0 ⟩. We define a fragment