This article presents a unified expression for surface-enhanced Raman spectroscopy (SERS).
The expression contains a product of three resonance denominators, representing the surface plasmon resonance, the metal−molecule charge-transfer resonance at the Fermi energy, and an allowed molecular resonance. This latter resonance is that from which intensity is borrowed for charge transfer; and when the molecular resonance is active, it is responsible for surface-enhanced resonance Raman spectroscopy. The authors examined this expression in various limits to explore the relative contribution of each resonance. First, the authors examined the situation in which only the surface plasmon resonance is active and analyzed the various contributions to the Raman signal, including the surface selection rules. The authors then examined additional contributions from charge-transfer or molecular resonances. They determined that the three resonances are not totally independent, since they are linked by a product of four matrix elements in the numerator. These linked matrix elements provide comprehensive selection rules for SERS. One involves a harmonic oscillator in the observed normal mode. This is the same mode that appears in the vibronic coupling operator linking one of the states of the allowed molecular resonance to the charge-transfer state. The charge-transfer transition moment is linked to the surface plasmon resonance by the requirement that the transition dipole moment be polarized along the direction of maximum amplitude of the field produced by the plasmon (i.e., perpendicular to the metal surface). It was determined that these selection rules governed the observed SERS spectral intensities and applied these to the observed spectra of several molecules. The authors also suggest a quantitative measure of the degree to which charge transfer contributes to the overall SERS enhancement. (publisher abstract modified)