where R AB is the inter-distance between two fragments, A and B; êk is a unit number at k-th direction; µ A,x is the nuclear derivatives of the ground state dipole moment of A; and β β β B represents the electric hyperpolarizability tensor of B. It corresponds to the event that the incident and scattered photons of the Raman scattering are on the same fragment A, meanwhile one virtual photon is exchanged between the two fragments, i.e., excitation energy transfer (EET) occurs between two locally excited states of the two molecules. We note that to arrive at the hyperpolarizability-dipole interaction expression in Eq. ( ), two approximations are made for the coupling between the two locally excited states: the exchange integrals are ignored and a multipole expansion of the Coulomb interaction operator is adopted. (The third one is that charge-transfer excitations are not into consideration.) This expression, however, is incomplete because the distance could also be differentiable rather than taking the first-order term in dipole moment (shown in Eq. ( )).