Rate expressions for excitation transfer. II. Electronic considerations of direct and through-configuration exciton resonance interactions

The electronic interactions which promote singlet-singlet and triplet-triplet electronic excitation (energy) transfer (EET) are investigated in detail. Donor and acceptor locally excited configurations, ψ(A*B) and ψ₄(AB*), respectively, are each allowed to mix with bridging ionic configurations, ψ₂(A⁺B^-) and ψ₃(A^-B⁺) to form the new donor and acceptor wave functions Ψ_R= ψ₁+λψ₂+μψ₃ and Ψ_P=ψ₄+μψ₂+λψ ₃. Use of the latter wave functions leads to the establishment of the matrix element T_RP=〈Ψ_R|H-E₁|Ψ _P〉≈=T₁₄-(T₁₂T₂₄+T ₁₃T₃₄)/A, with T_ij=〈ψ_i|H- E₁|ψ_j〉 and A = E₂ - E₁, as the exciton resonance interaction term for EET. Introduction of the Mulliken approximation shows that the "direct" exciton resonance interaction term (T₁₄) contributes primarily a Coulombic interaction, for singlet-singlet EET, while the "through-configuration" exciton resonance interaction term [-(T₁₂T₂₄+T₁₃T ₃₄)/A] replaces the Dexter exchange integral (which is a component of H₁₄) as the primary source of short-range orbital overlap-dependent EET. The origins of "Dexter-type" energy transfer are thus shown to be quite different from that originally outlined.