Charge-transfer theory of surface enhanced Raman spectroscopy: Herzberg–Teller contributions

A comprehensive development of the charge-transfer theory of surface enhanced Raman scattering (SERS) is presented. We incorporate the Herzberg–Teller mixing of zero-order Born–Oppenheimer electronic states by means of vibronic interaction terms in the Hamiltonian. This is similar to the theory of Tang and Albrecht12 except that we include metal states as part of a molecule–metal system. When this is done we may no longer discard a term involving mixing of ground-state vibrations. The theory is comprehensive in that both molecule-to-metal and metal-to-molecule transfer is considered. Furthermore, both Franck–Condon and Herzberg–Teller contributions to the intensity are obtained. The former, however, contribute only to the intensity of totally symmetric vibrations, while the latter contribute to nontotally symmetric vibrations as well. Since overtones are observed in SERS only weakly if at all, the Herzberg–Teller terms are most consistent with experimental findings. The resulting formulas may be interpreted as a type of resonance Raman effect in which intensity for the charge transfer transitions is borrowed from an allowed molecular transition. We may also carry out the sum over metal states. This procedure predicts a logarithmic resonance at the Fermi level of the metal. We thus predict intensity vs voltage profiles such as I ∝ ‖ln(ωFI−ω+iΓ)‖2 which fits the experimental curves quite well.