for P = (ij, p s ). Here, i and j refer to doubly occupied molecular orbitals (MOs), a and b to virtual MOs, and p s (and q s for later use) to the spin coupling (p s = +1 for singlet and p s = -1 for triplet excitations in the usual sense). In Eq. ( ), t ab ij,ps is the excitation amplitude and is obtained by solving the canonical MP2 equation introduced later (Eq. ( )), and |ϕ ab ij,ps ⟩ is the doubly excited configuration. Note that Φ depends on the first-order wavefunciont parameter t, whereas small ϕ does not. T P Q is the topological factor and is defined by