in which E rep is the repulsion plus DFT double counting term, N orb and N at is respectively the number of molecular orbitals and the number of atoms, f i is the occupation number of orbital i, Ĥ0 is the reference Hamiltonian, ρ 0 = Nat A ρ 0 A , in which ρ 0 A are the spherically symmetric spin-unpolarized neutral atoms. The ∆q A are the atomic Mulliken charges calculated as ∆q A = q A -q 0 A (difference between the actual atomic population and the number of valence electron in the corresponding free atom). The γ AB are the charge-transfer term, which depend on the distance between two atoms A and B. The long-range correction term is defined as